{"id":100747,"date":"2026-09-05T08:17:03","date_gmt":"2026-09-05T00:17:03","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/100747.html"},"modified":"2026-09-05T08:17:03","modified_gmt":"2026-09-05T00:17:03","slug":"%e8%87%aa%e5%8a%a8%e9%a9%be%e9%a9%b6slam%e5%9f%ba%e7%a1%80%ef%bc%9a%e5%87%a0%e4%bd%95%e5%ad%a6%e4%b8%8e%e8%bf%90%e5%8a%a8%e5%ad%a6%e5%85%a8%e8%a7%a3%e6%9e%90","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/100747.html","title":{"rendered":"\u81ea\u52a8\u9a7e\u9a76SLAM\u57fa\u7840\uff1a\u51e0\u4f55\u5b66\u4e0e\u8fd0\u52a8\u5b66\u5168\u89e3\u6790"},"content":{"rendered":"<p>\u8fd9\u4efd\u7b14\u8bb0\u4e3a\u4f60\u8be6\u7ec6\u68b3\u7406\u81ea\u52a8\u9a7e\u9a76\u4e0e\u673a\u5668\u4ebaSLAM\u6280\u672f\u4e2d\u81f3\u5173\u91cd\u8981\u7684\u201c\u51e0\u4f55\u5b66\u201d\u4e0e\u201c\u8fd0\u52a8\u5b66\u201d\u57fa\u7840\u3002\u8fd9\u90e8\u5206\u5185\u5bb9\u662f\u6574\u4e2a\u81ea\u52a8\u9a7e\u9a76\u5b66\u79d1\u7684\u5730\u57fa&#xff0c;\u540e\u9762\u7684IMU\u9884\u79ef\u5206\u3001\u6fc0\u5149\u91cc\u7a0b\u8ba1\u3001\u72b6\u6001\u4f30\u8ba1&#xff08;\u6ee4\u6ce2\u4e0e\u4f18\u5316&#xff09;\u5168\u90fd\u6784\u5efa\u4e8e\u6b64\u3002\u6211\u4eec\u629b\u5f00\u67af\u71e5\u7684\u8bfe\u672c\u53e3\u543b&#xff0c;\u7528\u5de5\u7a0b\u5e08\u7684\u89c6\u89d2&#xff0c;\u628a\u8fd9\u4e9b\u6982\u5ff5\u3001\u5b9a\u7406\u548c\u5e94\u7528\u573a\u666f\u63b0\u5f00\u63c9\u788e\u3002<\/p>\n<hr \/>\n<h2><\/h2>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260905001701-6a9b5f7db18ed.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>\u7b2c\u4e00\u90e8\u5206&#xff1a;\u51e0\u4f55\u5b66 \u2014\u2014 \u6211\u4eec\u5982\u4f55\u63cf\u8ff0\u7a7a\u95f4\u4e0e\u59ff\u6001&#xff1f;<\/h3>\n<p>\u5728\u8ba9\u8f66\u52a8\u8d77\u6765\u4e4b\u524d&#xff0c;\u6211\u4eec\u5f97\u5148\u5b9a\u4e49\u6e05\u695a\u201c\u8f66\u5728\u54ea\u513f\u201d\u4ee5\u53ca\u201c\u8f66\u4e0a\u7684\u4f20\u611f\u5668\u600e\u4e48\u6446\u201d\u3002\u8fd9\u5c31\u662f\u51e0\u4f55\u5b66\u7684\u4efb\u52a1\u3002<\/p>\n<h4>1. \u5750\u6807\u7cfb\u4e0e\u5411\u91cf\u8fd0\u7b97<\/h4>\n<p>\u5728\u4e00\u4e2a\u4e09\u7ef4\u6b27\u51e0\u91cc\u5f97\u7a7a\u95f4\u91cc&#xff0c;\u6211\u4eec\u901a\u5e38\u7528\u4e09\u4e2a\u76f8\u4e92\u5782\u76f4\u7684\u5355\u4f4d\u5411\u91cf&#xff08;\u6bd4\u5982 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">e1,e2,e3e_1, e_2, e_3<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff09;\u6765\u642d\u4e00\u4e2a\u53c2\u8003\u7cfb\u3002\u81ea\u52a8\u9a7e\u9a76\u7cfb\u7edf\u91cc&#xff0c;\u6211\u4eec\u901a\u5e38\u4f1a\u5b9a\u4e49\u597d\u8fd9\u51e0\u4e2a\u5750\u6807\u7cfb&#xff1a;<\/p>\n<ul>\n<li>\u4e16\u754c\u5750\u6807\u7cfb&#xff08;\u60ef\u6027\u7cfb&#xff09;&#xff1a;\u4e00\u5f20\u56fa\u5b9a\u7684\u201c\u5730\u56fe\u201d&#xff0c;\u7528\u6765\u63cf\u8ff0\u8f66\u8f86\u7684\u5168\u5c40\u4f4d\u59ff\u3002<\/li>\n<li>\u8f66\u4f53\u5750\u6807\u7cfb&#xff1a;\u56fa\u8fde\u5728\u8f66\u8eab\u4e0a\u7684\u53c2\u8003\u7cfb\u3002\u901a\u5e38\u6211\u4eec\u89c4\u5b9aX\u8f74\u5411\u524d\u3001Y\u8f74\u5411\u5de6\u3001Z\u8f74\u5411\u4e0a&#xff08;\u524d\u5de6\u4e0a&#xff09;&#xff0c;\u5e76\u6ee1\u8db3\u53f3\u624b\u5b9a\u5219\u3002<\/li>\n<li>\u4f20\u611f\u5668\u5750\u6807\u7cfb&#xff1a;\u50cf\u76f8\u673a\u3001\u6fc0\u5149\u96f7\u8fbe\u90fd\u6709\u81ea\u5df1\u7684\u4e60\u60ef\u3002\u6bd4\u5982\u76f8\u673a\u5e38\u7528\u201c\u53f3\u4e0b\u524d\u201d\u3002<\/li>\n<\/ul>\n<p>\u5750\u6807\u53d8\u6362\u662f\u51e0\u4f55\u5b66\u7684\u6838\u5fc3\u3002\u5047\u8bbe\u540c\u4e00\u4e2a\u70b9&#xff0c;\u5728\u4e16\u754c\u7cfb\u4e0b\u5750\u6807\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">pwp_w<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5728\u8f66\u4f53\u7cfb\u4e0b\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">pbp_b<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">b<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5b83\u4eec\u7684\u5173\u7cfb\u7531\u4e00\u4e2a\u65cb\u8f6c\u77e9\u9635 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RwbR_{wb}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0077em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mord mathnormal mtight\">b<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c\u5e73\u79fb\u5411\u91cf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">twbt_{wb}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7651em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mord mathnormal mtight\">b<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u786e\u5b9a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">pw&#061;Rwbpb&#043;twb p_w &#061; R_{wb} p_b &#043; t_{wb} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0077em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mord mathnormal mtight\">b<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">b<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7651em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mord mathnormal mtight\">b<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u8fd9\u91cc\u6211\u4eec\u5fc5\u987b\u517b\u6210\u4e00\u4e2a\u597d\u4e60\u60ef&#xff1a;\u4e0b\u6807\u4ece\u53f3\u5f80\u5de6\u8bfb\u3002 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RwbR_{wb}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0077em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mord mathnormal mtight\">b<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u610f\u601d\u662f&#xff0c;\u628a\u8f66\u4f53\u7cfb&#xff08;b&#xff09;\u91cc\u7684\u5750\u6807&#xff0c;\u5de6\u4e58\u5b83&#xff0c;\u5c31\u53d8\u6210\u4e86\u4e16\u754c\u7cfb&#xff08;w&#xff09;\u91cc\u7684\u5750\u6807\u3002\u8fd9\u6837\u5199\u4ee3\u7801\u548c\u63a8\u516c\u5f0f\u65f6\u601d\u8def\u6700\u987a\u7545\u3002\u5982\u679c\u5199\u6210\u9f50\u6b21\u5f62\u5f0f&#xff08;\u53d8\u6362\u77e9\u9635 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">TT<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;\u5c31\u662f&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">pw&#061;[Rwbtwb01]pb p_w &#061; \\\\begin{bmatrix} R_{wb} &amp; t_{wb} \\\\\\\\ 0 &amp; 1 \\\\end{bmatrix} p_b <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4em;vertical-align: -0.95em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0077em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mord mathnormal mtight\">b<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mord mathnormal mtight\">b<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">b<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u53cd\u5bf9\u79f0\u77e9\u9635\u7b97\u5b50&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u2227^\\\\wedge<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7519em\"><\/span><span class=\"mord\"><span class=\"\"><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff1a;<br \/>\n\u5728\u63a8\u5bfc\u4e2d&#xff0c;\u5411\u91cf\u5916\u79ef <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">a\u00d7ba \\\\times b<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span> \u7ecf\u5e38\u88ab\u5199\u6210\u77e9\u9635\u4e58\u6cd5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">a\u2227ba^\\\\wedge b<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7519em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span>\u3002\u8fd9\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">a\u2227a^\\\\wedge<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7519em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5c31\u662f\u628a\u5411\u91cf\u53d8\u6210\u53cd\u5bf9\u79f0\u77e9\u9635&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">a\u2227&#061;[0\u2212a3a2a30\u2212a1\u2212a2a10] a^\\\\wedge &#061; \\\\begin{bmatrix} 0 &amp; -a_3 &amp; a_2 \\\\\\\\ a_3 &amp; 0 &amp; -a_1 \\\\\\\\ -a_2 &amp; a_1 &amp; 0 \\\\end{bmatrix} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8019em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.6em;vertical-align: -1.55em\"><\/span><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05em\"><span class=\"\" style=\"top: -4.05em\"><span class=\"pstrut\" style=\"height: 5.6em\"><\/span><span class=\"\" style=\"width: 0.667em;height: 3.6em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05em\"><span class=\"\" style=\"top: -4.21em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -1.81em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2212<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05em\"><span class=\"\" style=\"top: -4.21em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2212<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -1.81em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05em\"><span class=\"\" style=\"top: -4.21em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2212<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -1.81em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05em\"><span class=\"\" style=\"top: -4.05em\"><span class=\"pstrut\" style=\"height: 5.6em\"><\/span><span class=\"\" style=\"width: 0.667em;height: 3.6em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u8fd9\u4e2a\u7b26\u53f7\u5728\u540e\u9762\u63a8\u5bfc\u89d2\u901f\u5ea6\u3001\u674e\u4ee3\u6570\u65f6\u4f1a\u50cf\u80f6\u6c34\u4e00\u6837&#xff0c;\u628a\u5404\u79cd\u53c9\u4e58\u8fd0\u7b97\u7c98\u6210\u7b80\u6d01\u7684\u77e9\u9635\u5f62\u5f0f\u3002<\/p>\n<h4>2. \u63cf\u8ff0\u65cb\u8f6c\u7684\u4e09\u628a\u201c\u6b66\u5668\u201d<\/h4>\n<p>\u5728\u7a0b\u5e8f\u4e2d\u8868\u793a\u4e00\u4e2a\u65cb\u8f6c&#xff0c;\u6211\u4eec\u4e3b\u8981\u7528\u4e09\u79cd\u65b9\u5f0f&#xff0c;\u5b83\u4eec\u5404\u6709\u6240\u957f&#xff1a;<\/p>\n<p>\u7b2c\u4e00\u628a\u6b66\u5668&#xff1a;\u65cb\u8f6c\u77e9\u9635&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SO(3)SO(3)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">3<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff09;<br \/>\n\u65cb\u8f6c\u77e9\u9635\u662f\u4e00\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">3\u00d733\\\\times3<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">3<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span> \u7684\u6b63\u4ea4\u77e9\u9635&#xff0c;\u884c\u5217\u5f0f\u4e3a1\u3002\u5b83\u76f4\u89c2&#xff0c;\u4f46\u5360\u4e869\u4e2a\u6570\u503c&#xff0c;\u6709\u5197\u4f59\u7ea6\u675f\u3002\u5b83\u5c5e\u4e8e\u201c\u7279\u6b8a\u6b63\u4ea4\u7fa4 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SO(3)SO(3)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">3<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u201d\u3002<\/p>\n<p>\u7b2c\u4e8c\u628a\u6b66\u5668&#xff1a;\u65cb\u8f6c\u77e2\u91cf&#xff08;\u89d2\u8f74 \/ \u674e\u4ee3\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">so(3)\\\\mathfrak{so}(3)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathfrak\">so<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">3<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff09;<br \/>\n\u60f3\u8c61\u62e7\u87ba\u4e1d&#xff1a;\u62e7\u52a8\u7684\u89d2\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8\\\\theta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><\/span><\/span><\/span><\/span> \u548c\u87ba\u4e1d\u5200\u7684\u65b9\u5411 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">nn<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5408\u8d77\u6765\u5c31\u662f\u65cb\u8f6c\u77e2\u91cf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">w&#061;\u03b8nw &#061; \\\\theta n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span>\u3002\u5b83\u53ea\u67093\u4e2a\u6570\u503c&#xff0c;\u6ca1\u6709\u7ea6\u675f\u3002<br \/>\n\u5b83\u901a\u8fc7\u7f57\u5fb7\u91cc\u683c\u65af\u516c\u5f0f&#xff08;\u6307\u6570\u6620\u5c04&#xff09;\u548c\u65cb\u8f6c\u77e9\u9635\u4e92\u8f6c&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">R&#061;exp\u2061(w\u2227)&#061;cos\u2061\u03b8I&#043;(1\u2212cos\u2061\u03b8)nn\u22a4&#043;sin\u2061\u03b8n\u2227 R &#061; \\\\exp(w^\\\\wedge) &#061; \\\\cos\\\\theta I &#043; (1-\\\\cos\\\\theta)nn^\\\\top &#043; \\\\sin\\\\theta n^\\\\wedge <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0519em;vertical-align: -0.25em\"><\/span><span class=\"mop\">exp<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7778em;vertical-align: -0.0833em\"><\/span><span class=\"mop\">cos<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">I<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1491em;vertical-align: -0.25em\"><\/span><span class=\"mop\">cos<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8019em\"><\/span><span class=\"mop\">sin<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u53cd\u8fc7\u6765&#xff0c;\u4ece\u65cb\u8f6c\u77e9\u9635\u6c42\u65cb\u8f6c\u77e2\u91cf&#xff08;\u5bf9\u6570\u6620\u5c04&#xff09;&#xff0c;\u89d2\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8\\\\theta<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><\/span><\/span><\/span><\/span> \u662f&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8&#061;arccos\u2061(tr\u2061(R)\u221212) \\\\theta &#061; \\\\arccos\\\\left( \\\\frac{\\\\operatorname{tr}(R)-1}{2} \\\\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4em;vertical-align: -0.95em\"><\/span><span class=\"mop\">arccos<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">(<\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mop\"><span class=\"mord mathrm\">tr<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u65cb\u8f6c\u8f74 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">nn<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span> \u5c31\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RR<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span> \u5bf9\u5e94\u7279\u5f81\u503c1\u7684\u90a3\u4e2a\u5355\u4f4d\u7279\u5f81\u5411\u91cf\u3002<br \/>\n\u5e94\u7528\u573a\u666f&#xff1a;\u5728\u56fe\u4f18\u5316\u540e\u7aef&#xff0c;\u6211\u4eec\u559c\u6b22\u628a\u5b83\u4f5c\u4e3a\u4f18\u5316\u53d8\u91cf&#xff0c;\u56e0\u4e3a\u5b83\u65e0\u7ea6\u675f&#xff0c;\u968f\u4fbf\u52a0\u51cf&#xff0c;\u6c42\u5bfc\u65b9\u4fbf\u3002<\/p>\n<p>\u7b2c\u4e09\u628a\u6b66\u5668&#xff1a;\u56db\u5143\u6570<br \/>\n\u4e00\u4e2a\u5b9e\u90e8\u52a0\u4e09\u4e2a\u865a\u90e8&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">q&#061;q0&#043;q1i&#043;q2j&#043;q3k&#061;[s,v]\u22a4q &#061; q_0 &#043; q_1 i &#043; q_2 j &#043; q_3 k &#061; [s, v]^\\\\top<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7778em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.854em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.854em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0991em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mclose\"><span class=\"mclose\">]<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u5b83\u53ea\u9700\u89814\u4e2a\u6570&#xff0c;\u8ba1\u7b97\u6548\u7387\u9ad8&#xff0c;\u4e14\u4e0d\u4f1a\u50cf\u6b27\u62c9\u89d2\u90a3\u6837\u9047\u5230\u201c\u4e07\u5411\u9501\u201d\u3002<br \/>\n\u7528\u56db\u5143\u6570\u6765\u65cb\u8f6c\u4e00\u4e2a\u7a7a\u95f4\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/span>&#xff08;\u628a\u5b83\u5f53\u6210\u865a\u56db\u5143\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">[0,v]\u22a4[0, v]^\\\\top<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0991em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mclose\"><span class=\"mclose\">]<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;\u516c\u5f0f\u662f\u4e58\u4e24\u904d&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">p\u2032&#061;qpq\u22121 p&#039; &#061; q p q^{-1} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9963em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0585em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u56db\u5143\u6570\u548c\u65cb\u8f6c\u77e9\u9635\/\u65cb\u8f6c\u77e2\u91cf\u7684\u8f6c\u6362\u5173\u7cfb\u5982\u4e0b\u3002\u56db\u5143\u6570\u5230\u65cb\u8f6c\u77e9\u9635&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">R&#061;vv\u22a4&#043;s2I&#043;2sv\u2227&#043;(v\u2227)2 R &#061; vv^\\\\top &#043; s^2 I &#043; 2sv^\\\\wedge &#043; (v^\\\\wedge)^2 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9824em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9474em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">I<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8852em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1141em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u56db\u5143\u6570\u5230\u65cb\u8f6c\u77e2\u91cf&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8&#061;2arccos\u2061s,n&#061;vsin\u2061(\u03b8\/2) \\\\theta &#061; 2\\\\arccos s, \\\\quad n &#061; \\\\frac{v}{\\\\sin(\\\\theta\/2)} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8389em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">2<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\">arccos<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0436em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.1076em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mop\">sin<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"mord\">\/2<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5e94\u7528\u573a\u666f&#xff1a;\u5de5\u7a0b\u843d\u5730\u7684\u9996\u9009\u3002\u4f60\u8f66\u4e0a\u7684\u7ec4\u5408\u5bfc\u822a\u3001\u5f00\u6e90SLAM\u6846\u67b6&#xff08;\u5982LOAM\u3001VINS&#xff09;\u5e95\u5c42\u5b58\u50a8\u59ff\u6001\u51e0\u4e4e\u90fd\u7528\u56db\u5143\u6570\u3002<\/p>\n<h4>3. \u674e\u7fa4\u3001\u674e\u4ee3\u6570\u4e0eBCH\u516c\u5f0f<\/h4>\n<p>\u6211\u4eec\u53ef\u4ee5\u628a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SO(3)SO(3)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">3<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u770b\u4f5c\u4e00\u4e2a\u5f2f\u66f2\u7684\u201c\u65cb\u8f6c\u5c0f\u533a\u201d&#xff08;\u674e\u7fa4&#xff09;&#xff0c;\u800c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">so(3)\\\\mathfrak{so}(3)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathfrak\">so<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">3<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u662f\u8fd9\u4e2a\u5c0f\u533a\u6bcf\u4e2a\u70b9\u4e0a\u7684\u201c\u5e73\u5766\u5207\u5e73\u9762\u201d&#xff08;\u674e\u4ee3\u6570&#xff09;\u3002\u6307\u6570\u6620\u5c04\u548c\u5bf9\u6570\u6620\u5c04\u5c31\u662f\u8fde\u63a5\u4e24\u8005\u7684\u6865\u6881\u3002<\/p>\n<p>BCH\u516c\u5f0f&#xff08;Baker-Campbell-Hausdorff&#xff09; \u662f\u8fd9\u91cc\u7684\u91cd\u5934\u620f\u3002\u5b83\u89e3\u51b3\u7684\u662f&#xff1a;\u5728\u65cb\u8f6c\u77e9\u9635\u4e0a\u4e58\u4e00\u4e2a\u5fae\u5c0f\u589e\u91cf&#xff0c;\u5bf9\u5e94\u5230\u674e\u4ee3\u6570\u4e0a\u52a0\u4e00\u4e2a\u589e\u91cf&#xff0c;\u8fd9\u4e24\u8005\u600e\u4e48\u6362\u7b97&#xff1f;<br \/>\n\u4e00\u9636\u7ebf\u6027\u8fd1\u4f3c\u4e0b&#xff0c;\u5b83\u4eec\u901a\u8fc7\u4e00\u4e2a\u96c5\u53ef\u6bd4\u77e9\u9635 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">JrJ_r<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0962em\">J<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0962em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">r<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u6216 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">JlJ_l<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0962em\">J<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0962em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8054\u7cfb&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">exp\u2061(\u0394\u03d5\u2227)exp\u2061(\u03d5\u2227)&#061;exp\u2061((\u03d5&#043;Jl\u22121(\u03d5)\u0394\u03d5)\u2227) \\\\exp(\\\\Delta\\\\phi^\\\\wedge)\\\\exp(\\\\phi^\\\\wedge) &#061; \\\\exp((\\\\phi &#043; J_l^{-1}(\\\\phi)\\\\Delta\\\\phi)^\\\\wedge) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0519em;vertical-align: -0.25em\"><\/span><span class=\"mop\">exp<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\">exp<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mop\">exp<\/span><span class=\"mopen\">((<\/span><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1555em;vertical-align: -0.2914em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0962em\">J<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -2.4086em;margin-left: -0.0962em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0197em\">l<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2914em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">\u0394<\/span><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5e94\u7528\u573a\u666f&#xff1a;\u8fd9\u662fIMU\u9884\u79ef\u5206\u7684\u7075\u9b42\u3002\u5f53\u6211\u4eec\u5728\u4f18\u5316\u7b97\u6cd5\u91cc\u5fae\u8c03\u67d0\u4e00\u5e27\u7684\u4f4d\u59ff\u65f6&#xff0c;\u9700\u8981\u5feb\u901f\u77e5\u9053\u8fd9\u4e2a\u5fae\u8c03\u4f1a\u600e\u4e48\u5f71\u54cd\u524d\u540e\u5e27\u7684IMU\u6d4b\u91cf\u6b8b\u5dee&#xff0c;\u8fd9\u4e2a\u201c\u5f71\u54cd\u5173\u7cfb\u201d\u5c31\u662f\u901a\u8fc7BCH\u7684\u96c5\u53ef\u6bd4\u4f20\u9012\u7684\u3002<\/p>\n<hr \/>\n<h3>\u7b2c\u4e8c\u90e8\u5206&#xff1a;\u8fd0\u52a8\u5b66 \u2014\u2014 \u8f66\u52a8\u8d77\u6765\u4e4b\u540e&#xff0c;\u6570\u5b66\u600e\u4e48\u8ffd&#xff1f;<\/h3>\n<p>\u6709\u4e86\u9759\u6001\u7684\u51e0\u4f55\u63cf\u8ff0&#xff0c;\u6211\u4eec\u6765\u770b\u770b\u8fd9\u4e9b\u91cf\u968f\u65f6\u95f4\u53d8\u5316\u65f6&#xff0c;\u4f1a\u4ea7\u751f\u4ec0\u4e48\u7269\u7406\u89c4\u5f8b\u3002\u8fd9\u662f\u8fde\u63a5\u4f20\u611f\u5668\u6570\u636e\u548c\u8f66\u8f86\u72b6\u6001\u7684\u6865\u6881\u3002<\/p>\n<h4>1. \u6cca\u677e\u65b9\u7a0b&#xff1a;\u89d2\u901f\u5ea6\u7684\u6e90\u5934<\/h4>\n<p>\u6211\u4eec\u77e5\u9053\u65cb\u8f6c\u77e9\u9635\u6ee1\u8db3 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">R\u22a4R&#061;IR^\\\\top R &#061; I<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8491em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">I<\/span><\/span><\/span><\/span><\/span>\u3002\u4e24\u8fb9\u5bf9\u65f6\u95f4\u6c42\u5bfc&#xff0c;\u4f1a\u5f97\u5230\u4e00\u4e2a\u975e\u5e38\u4f18\u7f8e\u7684\u65b9\u7a0b&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">R\u02d9\u22a4R&#043;R\u22a4R\u02d9&#061;0\u21d2R\u22a4R\u02d9&#061;\u2212(R\u22a4R\u02d9)\u22a4 \\\\dot{R}^\\\\top R &#043; R^\\\\top \\\\dot{R} &#061; 0 \\\\quad \\\\Rightarrow \\\\quad R^\\\\top \\\\dot{R} &#061; -(R^\\\\top \\\\dot{R})^\\\\top <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0035em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9202em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><span class=\"\" style=\"top: -3.2523em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.0556em\"><span class=\"mord\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9202em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9202em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><span class=\"\" style=\"top: -3.2523em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.0556em\"><span class=\"mord\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u21d2<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9202em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9202em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><span class=\"\" style=\"top: -3.2523em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.0556em\"><span class=\"mord\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1702em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2212<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9202em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><span class=\"\" style=\"top: -3.2523em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.0556em\"><span class=\"mord\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u8fd9\u8bf4\u660e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">R\u22a4R\u02d9R^\\\\top \\\\dot{R}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9202em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9202em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><span class=\"\" style=\"top: -3.2523em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.0556em\"><span class=\"mord\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u4e00\u4e2a\u53cd\u5bf9\u79f0\u77e9\u9635\u3002\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u77ac\u65f6\u89d2\u901f\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c9\\\\omega<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c9<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4ee4 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c9\u2227&#061;R\u22a4R\u02d9\\\\omega^\\\\wedge &#061; R^\\\\top \\\\dot{R}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7519em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c9<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9202em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9202em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><span class=\"\" style=\"top: -3.2523em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.0556em\"><span class=\"mord\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u8fd9\u5c31\u5f15\u51fa\u4e86\u6cca\u677e\u65b9\u7a0b&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">R\u02d9&#061;R\u03c9\u2227 \\\\dot{R} &#061; R \\\\omega^\\\\wedge <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9202em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9202em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><span class=\"\" style=\"top: -3.2523em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.0556em\"><span class=\"mord\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8019em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c9<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c9\\\\omega<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c9<\/span><\/span><\/span><\/span><\/span> \u5c31\u662f\u9640\u87ba\u4eea\u76f4\u63a5\u6d4b\u91cf\u7684\u7269\u7406\u91cf\u3002\u8fd9\u4e2a\u65b9\u7a0b\u7684\u89e3\u975e\u5e38\u6f02\u4eae&#xff0c;\u5b83\u76f4\u63a5\u662f\u6307\u6570\u6620\u5c04\u7684\u5f62\u5f0f&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">R(t)&#061;R(t0)exp\u2061(\u03c9\u2227\u0394t) R(t) &#061; R(t_0) \\\\exp(\\\\omega^\\\\wedge \\\\Delta t) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0519em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\">exp<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c9<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u79bb\u6563\u5316\u540e&#xff0c;\u5c31\u662f\u5f53\u524d\u65cb\u8f6c\u4e58\u4e0a\u4e00\u4e2a\u7531\u89d2\u901f\u5ea6\u7b97\u51fa\u6765\u7684\u5c0f\u589e\u91cf\u3002\u8fd9\u662fIMU\u8fdb\u884c\u59ff\u6001\u79ef\u5206\u7684\u6838\u5fc3\u4ee3\u7801\u903b\u8f91\u3002<\/p>\n<h4>2. \u56db\u5143\u6570\u8fd0\u52a8\u5b66&#xff1a;\u90a3\u4e2a\u5173\u952e\u7684\u201c1\/2\u201d\u7cfb\u6570<\/h4>\n<p>\u5982\u679c\u6211\u4eec\u7528\u56db\u5143\u6570\u6765\u8868\u793a\u65cb\u8f6c&#xff0c;\u5bf9\u5355\u4f4d\u6027\u7ea6\u675f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">q\u2217q&#061;1q^* q &#061; 1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8831em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6887em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u6c42\u5bfc&#xff0c;\u53ef\u4ee5\u5f97\u5230\u56db\u5143\u6570\u7684\u8fd0\u52a8\u5b66\u65b9\u7a0b&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">q\u02d9&#061;q\u03d6 \\\\dot{q} &#061; q \\\\varpi <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8623em;vertical-align: -0.1944em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6679em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.0556em\"><span class=\"mord\">\u02d9<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03d6<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03d6\\\\varpi<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03d6<\/span><\/span><\/span><\/span><\/span> \u662f\u7eaf\u865a\u56db\u5143\u6570\u3002\u4e3a\u4e86\u8ba9\u56db\u5143\u6570\u7684\u89d2\u901f\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c9\\\\omega<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c9<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SO(3)SO(3)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">3<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u91cc\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c9\\\\omega<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c9<\/span><\/span><\/span><\/span><\/span> \u7edf\u4e00\u7269\u7406\u610f\u4e49&#xff0c;\u6211\u4eec\u628a\u5b83\u6539\u5199\u4e3a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">q\u02d9&#061;12q[0,\u03c9]\u22a4 \\\\dot{q} &#061; \\\\frac{1}{2} q [0, \\\\omega]^\\\\top <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8623em;vertical-align: -0.1944em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6679em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.0556em\"><span class=\"mord\">\u02d9<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0074em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mopen\">[<\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c9<\/span><span class=\"mclose\"><span class=\"mclose\">]<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u4e3a\u4ec0\u4e48\u4f1a\u6709\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">1\/21\/2<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">1\/2<\/span><\/span><\/span><\/span><\/span> &#xff1f;<br \/>\n\u56e0\u4e3a\u56db\u5143\u6570\u65cb\u8f6c\u4e00\u4e2a\u70b9\u8981\u4e58\u4e24\u904d&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">qpq\u22121q p q^{-1}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0085em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;\u6240\u4ee5\u5b83\u7684\u201c\u65cb\u8f6c\u901f\u5ea6\u201d\u5929\u7136\u5c31\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SO(3)SO(3)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">3<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u91cc\u7684\u4e00\u534a\u3002\u8fd9\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">1\/21\/2<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">1\/2<\/span><\/span><\/span><\/span><\/span> \u662f\u8fde\u63a5\u4e24\u79cd\u6570\u5b66\u8bed\u8a00\u7684\u6865\u6881\u3002<br \/>\n\u5728\u4ee3\u7801\u91cc&#xff0c;\u5982\u679c\u7528\u56db\u5143\u6570\u66f4\u65b0\u59ff\u6001&#xff0c;\u79bb\u6563\u516c\u5f0f\u5c31\u662f&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">qnew\u2248qold\u2297[1,12\u03c9\u0394t] q_{\\\\text{new}} \\\\approx q_{\\\\text{old}} \\\\otimes \\\\left[ 1, \\\\frac{1}{2} \\\\omega \\\\Delta t \\\\right] <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6776em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">new<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7778em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">old<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2297<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4em;vertical-align: -0.95em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c9<\/span><span class=\"mord\">\u0394<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u6ce8\u610f&#xff1a;\u957f\u65f6\u95f4\u66f4\u65b0\u540e\u4e00\u5b9a\u8981\u5bf9\u56db\u5143\u6570\u91cd\u65b0\u5f52\u4e00\u5316&#xff0c;\u5426\u5219\u6570\u503c\u8bef\u5dee\u4f1a\u7d2f\u79ef\u5bfc\u81f4\u5b83\u4e0d\u662f\u5355\u4f4d\u56db\u5143\u6570\u3002\u800c\u65cb\u8f6c\u77e9\u9635\u5c31\u4e0d\u5b58\u5728\u8fd9\u4e2a\u95ee\u9898&#xff0c;\u56e0\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">exp\u2061(\u03c9\u2227)\\\\exp(\\\\omega^\\\\wedge)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0019em;vertical-align: -0.25em\"><\/span><span class=\"mop\">exp<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c9<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5929\u751f\u5c31\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SO(3)SO(3)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">3<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u4e0a\u3002<\/p>\n<h4>3. \u7ebf\u901f\u5ea6\u4e0e\u52a0\u901f\u5ea6&#xff1a;\u6ca1\u4f60\u60f3\u7684\u90a3\u4e48\u7b80\u5355<\/h4>\n<p>\u8fd9\u662f\u533a\u5206\u201c\u7406\u8bba\u6d3e\u201d\u548c\u201c\u5b9e\u6218\u6d3e\u201d\u7684\u5173\u952e\u3002\u540c\u4e00\u4e2a\u7a7a\u95f4\u70b9&#xff0c;\u5728\u4e24\u4e2a\u6709\u76f8\u5bf9\u65cb\u8f6c\u7684\u5750\u6807\u7cfb\u4e0b&#xff0c;\u901f\u5ea6\u662f\u4e0d\u4e00\u6837\u7684\u3002<br \/>\n\u5047\u8bbe\u5750\u6807\u7cfb1\u548c2&#xff0c;\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/span> \u57282\u7cfb\u4e0b\u7684\u5750\u6807\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">p2p_2<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;2\u7cfb\u76f8\u5bf9\u4e8e1\u7cfb\u6709\u89d2\u901f\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c9\\\\omega<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c9<\/span><\/span><\/span><\/span><\/span>\u3002\u90a3\u4e48 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/span> \u57281\u7cfb\u4e0b\u7684\u901f\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">v1v_1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">v1&#061;R12(\u03c9\u2227p2&#043;v2) v_1 &#061; R_{12} (\\\\omega^\\\\wedge p_2 &#043; v_2) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0519em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0077em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">12<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c9<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u591a\u51fa\u6765\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c9\u2227p2\\\\omega^\\\\wedge p_2<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9463em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c9<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5c31\u662f\u65cb\u8f6c\u5e26\u6765\u7684\u9644\u52a0\u901f\u5ea6\u3002<\/p>\n<p>\u52a0\u901f\u5ea6\u5c31\u66f4\u590d\u6742\u4e86&#xff0c;\u4f1a\u591a\u51fa\u4e09\u9879\u79d1\u6c0f\u3001\u5411\u5fc3\u7b49\u52a0\u901f\u5ea6&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">a1&#061;R12(a2&#043;2\u03c9\u2227v2\u23df\u79d1\u6c0f\u52a0\u901f\u5ea6&#043;\u03c9\u02d9\u2227p2\u23df\u89d2\u52a0\u901f\u5ea6\u9879&#043;\u03c9\u2227\u03c9\u2227p2\u23df\u5411\u5fc3\u52a0\u901f\u5ea6) a_1 &#061; R_{12} (a_2 &#043; \\\\underbrace{2\\\\omega^\\\\wedge v_2}_{\\\\text{\u79d1\u6c0f\u52a0\u901f\u5ea6}} &#043; \\\\underbrace{\\\\dot{\\\\omega}^\\\\wedge p_2}_{\\\\text{\u89d2\u52a0\u901f\u5ea6\u9879}} &#043; \\\\underbrace{\\\\omega^\\\\wedge \\\\omega^\\\\wedge p_2}_{\\\\text{\u5411\u5fc3\u52a0\u901f\u5ea6}}) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0077em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">12<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.2782em;vertical-align: -1.4763em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -1.5237em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord cjk_fallback mtight\">\u79d1\u6c0f\u52a0\u901f\u5ea6<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"svg-align\" style=\"top: -2.202em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"stretchy\" style=\"height: 0.548em;min-width: 1.6em\"><span class=\"brace-left\" style=\"height: 0.548em\"><\/span><span class=\"brace-center\" style=\"height: 0.548em\"><\/span><span class=\"brace-right\" style=\"height: 0.548em\"><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c9<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.798em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.4763em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.3227em;vertical-align: -1.5208em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -1.4792em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord cjk_fallback mtight\">\u89d2\u52a0\u901f\u5ea6\u9879<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"svg-align\" style=\"top: -2.1576em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"stretchy\" style=\"height: 0.548em;min-width: 1.6em\"><span class=\"brace-left\" style=\"height: 0.548em\"><\/span><span class=\"brace-center\" style=\"height: 0.548em\"><\/span><span class=\"brace-right\" style=\"height: 0.548em\"><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6679em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c9<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1389em\"><span class=\"mord\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8424em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.5208em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.3227em;vertical-align: -1.5208em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -1.4792em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord cjk_fallback mtight\">\u5411\u5fc3\u52a0\u901f\u5ea6<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"svg-align\" style=\"top: -2.1576em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"stretchy\" style=\"height: 0.548em;min-width: 1.6em\"><span class=\"brace-left\" style=\"height: 0.548em\"><\/span><span class=\"brace-center\" style=\"height: 0.548em\"><\/span><span class=\"brace-right\" style=\"height: 0.548em\"><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c9<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c9<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8424em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.5208em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5e94\u7528\u573a\u666f&#xff1a;\u4f60\u8f66\u4e0a\u7684IMU&#xff08;\u52a0\u901f\u5ea6\u8ba1&#xff09;\u6d4b\u5230\u7684\u6839\u672c\u4e0d\u662f\u5355\u7eaf\u7684\u8f66\u5728\u4e16\u754c\u4e0a\u8dd1\u7684\u52a0\u901f\u5ea6\u3002\u5b83\u6d4b\u7684\u662f\u201c\u6bd4\u529b\u201d&#xff0c;\u91cc\u9762\u5305\u542b\u4e86\u91cd\u529b\u3001\u8f66\u81ea\u8eab\u7684\u7ebf\u52a0\u901f\u5ea6&#xff0c;\u4ee5\u53ca\u4e0a\u9762\u8fd9\u4e00\u5806\u4e71\u4e03\u516b\u7cdf\u7684\u79d1\u6c0f\u529b\u3001\u5411\u5fc3\u529b\u3002\u5728\u505aGNSS\/IMU\u7ec4\u5408\u5bfc\u822a\u65f6&#xff0c;\u8fd9\u4e9b\u9879\u4e00\u4e2a\u90fd\u4e0d\u80fd\u5c11&#xff0c;\u5426\u5219\u8f66\u4e00\u8f6c\u5f2f\u5b9a\u4f4d\u5c31\u4f1a\u5f80\u5916\u98d8\u3002<\/p>\n<h4>4. \u6270\u52a8\u6a21\u578b&#xff1a;\u6c42\u5bfc\u7684\u201c\u61d2\u4eba\u795e\u5668\u201d<\/h4>\n<p>\u5f53\u6211\u4eec\u5728SLAM\u540e\u7aef\u5199\u4f18\u5316\u4ee3\u7801\u65f6&#xff0c;\u7ecf\u5e38\u8981\u5bf9\u65cb\u8f6c\u77e9\u9635 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RR<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span> \u6c42\u5bfc\u3002\u5982\u679c\u76f4\u63a5\u5bf99\u4e2a\u77e9\u9635\u5143\u7d20\u6c42\u5bfc&#xff0c;\u96c5\u53ef\u6bd4\u77e9\u9635\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">9\u00d799\\\\times9<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">9<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">9<\/span><\/span><\/span><\/span><\/span> \u7684&#xff0c;\u7b97\u8d77\u6765\u60f3\u6b7b\u3002<br \/>\n\u6270\u52a8\u6a21\u578b\u8bf4&#xff1a;\u522b\u76f4\u63a5\u52a8 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RR<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6211\u4eec\u5728\u5b83\u53f3\u8fb9&#xff08;\u6216\u5de6\u8fb9&#xff09;\u4e58\u4e00\u4e2a\u5fae\u5c0f\u7684\u6270\u52a8 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03d5\\\\phi<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">\u03d5<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u7136\u540e\u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03d5\\\\phi<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">\u03d5<\/span><\/span><\/span><\/span><\/span> \u6c42\u5bfc\u3002\u8fd9\u6837\u96c5\u53ef\u6bd4\u5c31\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">3\u00d733\\\\times3<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">3<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span> \u7684&#xff0c;\u975e\u5e38\u7b80\u6d01\u3002<br \/>\n\u6bd4\u5982&#xff0c;\u5bf9\u65cb\u8f6c\u540e\u7684\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RaRa<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u5173\u4e8e\u65cb\u8f6c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RR<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span> \u6c42\u53f3\u6270\u52a8\u7684\u96c5\u53ef\u6bd4&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u2202Ra\u2202\u03d5&#061;lim\u2061\u03d5\u21920R(I&#043;\u03d5\u2227)a\u2212Ra\u03d5&#061;\u2212Ra\u2227 \\\\frac{\\\\partial R a}{\\\\partial \\\\phi} &#061; \\\\lim_{\\\\phi \\\\to 0} \\\\frac{R(I &#043; \\\\phi^\\\\wedge)a &#8211; Ra}{\\\\phi} &#061; -R a^\\\\wedge <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 2.2519em;vertical-align: -0.8804em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord mathnormal\">\u03d5<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8804em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.3171em;vertical-align: -0.8882em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -2.3479em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">\u03d5<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"\"><span class=\"mop\">lim<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8882em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.4289em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03d5<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">I<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03d5<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8804em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8852em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8019em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u8fd9\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u2212Ra\u2227-R a^\\\\wedge<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8352em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2227<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4f1a\u5728\u4f60\u5199\u89c6\u89c9\u91cd\u6295\u5f71\u8bef\u5dee\u3001\u6fc0\u5149\u70b9\u4e91\u5339\u914d\u8bef\u5dee\u7684\u96c5\u53ef\u6bd4\u65f6\u53cd\u590d\u51fa\u73b0\u3002\u8bb0\u4f4f\u8fd9\u4e2a\u6a21\u5f0f&#xff0c;\u80fd\u8ba9\u4f60\u624b\u5199\u4f18\u5316\u5668\u65f6\u4e8b\u534a\u529f\u500d\u3002<\/p>\n<hr 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\u2014\u2014 \u6211\u4eec\u5982\u4f55\u63cf\u8ff0\u7a7a\u95f4\u4e0e\u59ff\u6001&#xff1f;\u5728\u8ba9\u8f66\u52a8\u8d77\u6765\u4e4b\u524d&#xff0c;\u6211\u4eec\u5f97\u5148\u5b9a\u4e49\u6e05\u695a\u201c\u8f66\u5728\u54ea\u513f\u201d\u4ee5\u53ca\u201c<\/p>\n","protected":false},"author":2,"featured_media":100746,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[8232,50,2051],"topic":[],"class_list":["post-100747","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-8232","tag-50","tag-2051"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u81ea\u52a8\u9a7e\u9a76SLAM\u57fa\u7840\uff1a\u51e0\u4f55\u5b66\u4e0e\u8fd0\u52a8\u5b66\u5168\u89e3\u6790 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, 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