{"id":107539,"date":"2026-09-19T20:21:00","date_gmt":"2026-09-19T12:21:00","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/107539.html"},"modified":"2026-09-19T20:21:00","modified_gmt":"2026-09-19T12:21:00","slug":"%e6%97%a0%e4%ba%ba%e6%9c%ba%e9%9b%86%e7%be%a4%e5%8d%8f%e5%90%8c%e6%8b%a6%e6%88%aa%e7%9a%84%e7%9b%ae%e6%a0%87%e5%88%86%e9%85%8d%e6%80%8e%e4%b9%88%e5%81%9a%ef%bc%9f%e4%b8%80%e5%a5%97%e5%8f%af%e8%90%bd","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/107539.html","title":{"rendered":"\u65e0\u4eba\u673a\u96c6\u7fa4\u534f\u540c\u62e6\u622a\u7684\u76ee\u6807\u5206\u914d\u600e\u4e48\u505a\uff1f\u4e00\u5957\u53ef\u843d\u5730\u7684\u5206\u5e03\u5f0f\u51b3\u7b56\u6846\u67b6\u62c6\u89e3\u3010\u9644\u4ee3\u7801\u94fe\u63a5\u3011"},"content":{"rendered":"

\u57fa\u4e8e\u6982\u7387\u6d88\u8017\u6d41\u7684\u5206\u5e03\u5f0f\u96c6\u7fa4\u62e6\u622a\u51b3\u7b56：\u4ece\u62e6\u622a\u6982\u7387\u5148\u9a8c\u5230\u6ce8\u6c34\u6295\u5f71\u6c42\u89e3\u7684\u5b8c\u6574\u5b9e\u73b0<\/h2>\n

\u539f\u6587\u94fe\u63a5 EW Frontier<\/p>\n

\u672c\u6587\u73af\u5883：Python 3.10 + NumPy 1.24 + SciPy 1.10 + scikit-learn 1.2，Ubuntu 22.04 \u9a8c\u8bc1\u901a\u8fc7，Windows 11 \u540c\u6837\u53ef\u8fd0\u884c\u3002\u5168\u6587\u53ea\u8ba8\u8bba\u5de5\u7a0b\u5b9e\u73b0：\u9632\u5fa1\u65e0\u4eba\u673a\u96c6\u7fa4\u5728\u53ea\u80fd\u770b\u5230\u5c40\u90e8\u6001\u52bf\u3001\u901a\u4fe1\u534a\u5f84\u53d7\u9650\u7684\u6761\u4ef6\u4e0b，\u5982\u4f55\u534f\u540c\u5206\u914d\u62e6\u622a\u76ee\u6807，\u5e76\u4e14\u907f\u514d"\u4e00\u7a9d\u8702\u6251\u5411\u540c\u4e00\u4e2a\u76ee\u6807"\u3002<\/p>\n

\u4e00\u3001\u95ee\u9898\u80cc\u666f：\u96c6\u7fa4\u62e6\u622a\u4e3a\u4ec0\u4e48\u4e0d\u80fd\u53ea\u6309"\u8c01\u8fd1\u8c01\u4e0a"<\/h3>\n

\u5728\u673a\u573a\u3001\u7535\u529b\u8bbe\u65bd\u3001\u4f53\u80b2\u573a\u9986\u3001\u707e\u5bb3\u5e94\u6025\u7a7a\u57df\u8fd9\u7c7b\u6c11\u7528\u573a\u666f\u91cc，\u975e\u6cd5\u5165\u4fb5\u7684\u4f4e\u7a7a\u5c0f\u578b\u65e0\u4eba\u673a\u662f\u771f\u5b9e\u5b58\u5728\u7684\u5a01\u80c1\u3002\u5f53\u6765\u7684\u662f\u5355\u673a\u65f6，\u95ee\u9898\u5f88\u7b80\u5355：\u6d3e\u4e00\u67b6\u9632\u5fa1\u673a\u53bb\u62e6\u5c31\u884c\u3002\u4f46\u5f53\u6765\u7684\u662f\u5341\u51e0\u67b6\u751a\u81f3\u51e0\u5341\u67b6\u7f16\u961f\u63a8\u8fdb\u7684\u96c6\u7fa4，\u95ee\u9898\u6027\u8d28\u5c31\u53d8\u4e86\u2014\u2014\u9632\u5fa1\u65b9\u624b\u4e2d\u7684\u62e6\u622a\u8d44\u6e90\u662f\u6709\u9650\u7684\u3001\u4e00\u6b21\u6027\u7684，\u6bcf\u4e00\u67b6\u9632\u5fa1\u673a\u53ea\u8981\u5b8c\u6210\u4e00\u6b21\u7269\u7406\u62e6\u622a\u5c31\u968f\u4e4b\u6d88\u8017，\u4e0d\u53ef\u80fd"\u62e6\u5b8c\u518d\u62e6"\u3002\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

\u5927\u591a\u6570\u5165\u95e8\u5b9e\u73b0\u4f1a\u76f4\u63a5\u91c7\u7528\u4e24\u7c7b\u65b9\u6cd5：<\/p>\n

\u7b2c\u4e00\u7c7b\u662f\u96c6\u4e2d\u5f0f\u5206\u914d\u3002\u7531\u4e00\u4e2a\u4e2d\u5fc3\u8282\u70b9\u638c\u63e1\u5168\u5c40\u6001\u52bf，\u7edf\u4e00\u6c42\u89e3\u4e00\u4e2a\u5206\u914d\u77e9\u9635\u518d\u4e0b\u53d1\u7ed9\u5404\u9632\u5fa1\u673a\u3002\u8fd9\u7c7b\u65b9\u6cd5\u5728\u4eff\u771f\u91cc\u6548\u679c\u5f80\u5f80\u4e0d\u9519，\u4f46\u5b83\u6709\u4e24\u4e2a\u81f4\u547d\u524d\u63d0：\u4e2d\u5fc3\u8282\u70b9\u5fc5\u987b\u80fd\u5b9e\u65f6\u638c\u63e1\u5168\u5c40，\u4e14\u4e0b\u884c\u94fe\u8def\u5fc5\u987b\u53ef\u9760\u3002\u4e00\u65e6\u901a\u4fe1\u88ab\u5e72\u6270\u6216\u8005\u4e2d\u5fc3\u8282\u70b9\u672c\u8eab\u88ab\u6253\u51fb，\u6574\u4e2a\u9632\u5fa1\u4f53\u7cfb\u5f53\u573a\u5931\u6548\u3002<\/p>\n

\u7b2c\u4e8c\u7c7b\u662f\u5c40\u90e8\u8d2a\u5fc3\u4e0e\u62cd\u5356\u5f0f\u5206\u914d\u3002\u5c40\u90e8\u8d2a\u5fc3\u5c31\u662f\u6bcf\u67b6\u9632\u5fa1\u673a\u9009\u79bb\u81ea\u5df1\u6700\u8fd1\u7684\u654c\u673a；\u62cd\u5356\u5f0f\u7684\u4ee3\u8868\u662f CBAA（Consensus-Based Auction Algorithm），\u6bcf\u67b6\u9632\u5fa1\u673a\u5bf9\u76ee\u6807"\u51fa\u4ef7"，\u4ef7\u9ad8\u8005\u5f97，\u901a\u8fc7\u90bb\u5c45\u4e4b\u95f4\u7684\u5171\u8bc6\u8fed\u4ee3\u6d88\u89e3\u51b2\u7a81\u3002\u8fd9\u7c7b\u65b9\u6cd5\u901a\u4fe1\u5f00\u9500\u5c0f\u3001\u9c81\u68d2\u6027\u597d，\u4f46\u5b83\u4eec\u7684\u4ee3\u4ef7\u51fd\u6570\u51e0\u4e4e\u53ea\u6709\u4e00\u4e2a\u7ef4\u5ea6\u2014\u2014\u8ddd\u79bb\u3002<\/p>\n

\u53ea\u7528\u8ddd\u79bb\u505a\u51b3\u7b56，\u4f1a\u5728\u5de5\u7a0b\u4e0a\u8e29\u5230\u56db\u4e2a\u5751：<\/p>\n

  • \u8ddd\u79bb\u8fd1\u4e0d\u7b49\u4e8e\u62e6\u5f97\u4f4f\u3002 \u9632\u5fa1\u673a\u4e0e\u5165\u4fb5\u673a\u7684\u76f8\u5bf9\u8ddd\u79bb\u53ea\u662f\u51e0\u4f55\u5173\u7cfb\u7684\u4e00\u90e8\u5206，\u771f\u6b63\u51b3\u5b9a\u80fd\u5426\u62e6\u622a\u7684\u662f\u4ea4\u6218\u51e0\u4f55：\u8fce\u5934\u62e6\u622a\u3001\u4fa7\u5411\u62e6\u622a\u3001\u8ffd\u5c3e\u62e6\u622a\u7684\u6210\u529f\u7387\u53ef\u4ee5\u76f8\u5dee\u6570\u500d\u3002<\/li>\n
  • \u5165\u4fb5\u673a\u7684\u5a01\u80c1\u7a0b\u5ea6\u968f\u65f6\u95f4\u53d8\u5316\u3002 \u540c\u6837\u4e00\u67b6\u5165\u4fb5\u673a，\u8ddd\u79bb\u4fdd\u62a4\u4e2d\u5fc3 8 \u516c\u91cc\u548c\u8ddd\u79bb 2 \u516c\u91cc，\u5a01\u80c1\u7b49\u7ea7\u5b8c\u5168\u4e0d\u540c\u3002\u628a\u8d44\u6e90\u5e73\u5747\u5206\u914d\u5728"\u8fd8\u65e9\u5f97\u5f88"\u7684\u76ee\u6807\u4e0a，\u662f\u5178\u578b\u7684\u8d44\u6e90\u9519\u914d\u3002<\/li>\n
  • \u91cd\u590d\u5206\u914d\u5b58\u5728\u8fb9\u9645\u6536\u76ca\u9012\u51cf\u3002 \u4e09\u67b6\u9632\u5fa1\u673a\u540c\u65f6\u6251\u5411\u540c\u4e00\u67b6\u5165\u4fb5\u673a，\u8054\u5408\u62e6\u622a\u6982\u7387\u5e76\u4e0d\u662f\u5355\u673a\u6982\u7387\u7684\u7b80\u5355\u76f8\u52a0，\u800c\u662f\u5f88\u5feb\u9971\u548c\u3002\u591a\u51fa\u6765\u7684\u9632\u5fa1\u673a\u7b49\u4e8e\u88ab\u6d6a\u8d39\u3002<\/li>\n
  • \u62e6\u622a\u5b8c\u6210\u540e\u8d44\u6e90\u4f1a\u51cf\u5c11\u3002 \u9632\u5fa1\u673a\u62e6\u622a\u6210\u529f\u540e\u81ea\u8eab\u6d88\u8017，\u539f\u672c\u5206\u914d\u7ed9\u5b83\u7684\u540e\u7eed\u4efb\u52a1\u9700\u8981\u6709\u4eba\u63a5\u76d8，\u8fd9\u4e2a"\u8f6c\u79fb\u4ee3\u4ef7"\u5982\u679c\u4e0d\u8fdb\u5165\u51b3\u7b56，\u5c31\u4f1a\u51fa\u73b0\u5c40\u90e8\u771f\u7a7a\u3002<\/li>\n

    \u672c\u6587\u8981\u62c6\u89e3\u7684\u8fd9\u5957\u6846\u67b6，\u6b63\u662f\u56f4\u7ed5\u8fd9\u56db\u4e2a\u5751\u6765\u8bbe\u8ba1\u7684：\u7528\u62e6\u622a\u6982\u7387\u5148\u9a8c\u89e3\u51b3"\u62e6\u4e0d\u62e6\u5f97\u4f4f"，\u7528\u6982\u7387\u6d88\u8017\u6d41\u89e3\u51b3"\u91cd\u590d\u5206\u914d\u9971\u548c\u4e0e\u8d44\u6e90\u8f6c\u79fb"，\u7528\u5206\u5e03\u5f0f\u5e02\u573a\u5171\u8bc6\u89e3\u51b3"\u53ea\u6709\u5c40\u90e8\u6001\u52bf\u600e\u4e48\u8fbe\u6210\u4e00\u81f4"\u3002 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

    \u4e8c\u3001\u6574\u4f53\u6846\u67b6：\u56db\u5c42\u7ed3\u6784<\/h3>\n

    \u6574\u5957\u5b9e\u73b0\u53ef\u4ee5\u5207\u6210\u56db\u5c42，\u4ece\u4e0a\u5230\u4e0b\u4f9d\u6b21\u662f：<\/p>\n

    \u51b3\u7b56\u5c42（2 Hz \u4f4e\u9891） \u5206\u5e03\u5f0f\u5e02\u573a\u5171\u8bc6：\u76ee\u6807\u5206\u914d\u4e0e\u5f85\u547d\u4ef2\u88c1
    \n \u2193
    \n\u6982\u7387\u5c42（\u5728\u7ebf\u67e5\u8868） \u62e6\u622a\u6982\u7387\u5148\u9a8c\u67e5\u8be2 + \u6982\u7387\u6d88\u8017\u6d41 + \u4e8c\u6b21\u8f6c\u79fb\u4ee3\u4ef7
    \n \u2193
    \n\u89c4\u5212\u5c42（\u4e2d\u9891） \u4ece\u4f4d\u7f6e\u5e8f\u5217\u4e2d\u9009\u62e9\u6700\u4f18\u673a\u52a8\u52a8\u4f5c
    \n \u2193
    \n\u63a7\u5236\u5c42（10 Hz \u9ad8\u9891） \u53cc\u95ed\u73af\u8f68\u8ff9\u8ddf\u8e2a，\u8f93\u51fa\u52a0\u901f\u5ea6\u4e0e\u89d2\u901f\u7387\u6307\u4ee4<\/p>\n

    \u5bf9\u5e94\u7684\u8c03\u5ea6\u903b\u8f91\u662f：\u6bcf\u67b6\u9632\u5fa1\u673a\u81ea\u8eab\u4ee5 2 Hz \u7684\u9891\u7387\u505a\u4e00\u6b21\u76ee\u6807\u51b3\u7b56，\u4ee5 10 Hz \u7684\u9891\u7387\u66f4\u65b0\u63a7\u5236\u91cf，\u4eff\u771f\u6b65\u957f 0.1 \u79d2\u3002\u4e09\u5c42\u7684\u9891\u7387\u4f9d\u6b21\u9012\u589e，\u662f\u56e0\u4e3a\u51b3\u7b56\u4f9d\u8d56\u6001\u52bf\u878d\u5408\u7684\u7ed3\u679c，\u89c4\u5212\u4f9d\u8d56\u51b3\u7b56\u7684\u8f93\u51fa，\u800c\u63a7\u5236\u5fc5\u987b\u8db3\u591f\u5feb\u624d\u80fd\u538b\u4f4f\u59ff\u6001\u8bef\u5dee\u3002<\/p>\n

    \u8fd9\u91cc\u5148\u7ed9\u4e00\u4e2a\u7ed3\u8bba\u6027\u7684\u8bbe\u8ba1\u53d6\u820d：\u51b3\u7b56\u5c42\u4e0d\u8ffd\u6c42\u5168\u5c40\u6700\u4f18，\u800c\u8ffd\u6c42\u5c40\u90e8\u53ef\u6267\u884c\u4e14\u4e0d\u51b2\u7a81\u3002\u56e0\u4e3a\u5206\u5e03\u5f0f\u8282\u70b9\u6c38\u8fdc\u62ff\u4e0d\u5230\u5b8c\u6574\u5168\u5c40\u4fe1\u606f，\u4efb\u4f55"\u5047\u88c5\u81ea\u5df1\u77e5\u9053\u5168\u5c40"\u7684\u6700\u4f18\u89e3\u5728\u771f\u5b9e\u94fe\u8def\u4e0a\u90fd\u4f1a\u9000\u5316\u3002\u771f\u6b63\u6709\u4ef7\u503c\u7684\u6027\u8d28\u662f\u5355\u8c03\u6027\u548c\u4e00\u81f4\u6027\u2014\u2014\u5c40\u90e8\u4fe1\u606f\u8d8a\u591a，\u51b3\u7b56\u4e0d\u52a3\u5316；\u90bb\u5c45\u52a8\u4f5c\u53d8\u5316\u65f6，\u81ea\u5df1\u7684\u9009\u62e9\u4e0d\u4f1a\u5267\u70c8\u9707\u8361\u3002\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

    \u4e09\u3001\u6c14\u52a8\u611f\u77e5\u7684\u56fa\u5b9a\u7ffc\u6a21\u578b\u4e0e\u53cc\u95ed\u73af\u8ddf\u8e2a<\/h3>\n

    \u8981\u8c08\u62e6\u622a\u6982\u7387，\u5148\u5f97\u6709\u4e00\u4e2a\u53ef\u4fe1\u7684\u5e95\u5c42\u8fd0\u52a8\u6a21\u578b\u3002\u9879\u76ee\u91c7\u7528\u516d\u7ef4\u72b6\u6001\u3001\u4e09\u7ef4\u63a7\u5236\u7684\u56fa\u5b9a\u7ffc\u8d28\u70b9\u6a21\u578b：<\/p>\n

    \u72b6\u6001\u91cf x = [x, y, z, v, \u03b8, \u03c8]
    \n\u63a7\u5236\u91cf u = [a, \u03b8\u0307, \u03c8\u0307]<\/p>\n

    \u5176\u4e2d x, y, z \u662f ENU \u60ef\u6027\u7cfb\u4e0b\u7684\u4f4d\u7f6e，v \u662f\u7a7a\u901f，\u03b8 \u662f\u822a\u8ff9\u89d2（\u4fef\u4ef0\u76f8\u5173），\u03c8 \u662f\u822a\u5411\u89d2\u3002\u72b6\u6001\u65b9\u7a0b\u4e3a：<\/p>\n

    \u1e8b = v\u00b7cos\u03b8\u00b7cos\u03c8
    \n\u1e8f = v\u00b7cos\u03b8\u00b7sin\u03c8
    \n\u017c = v\u00b7sin\u03b8
    \nv\u0307 = a \u2212 g\u00b7sin\u03b8 \u2212 \u03c1\u00b7v\u00b2
    \n\u03b8\u0307 = u\u2082
    \n\u03c8\u0307 = u\u2083<\/p>\n

    \u6ce8\u610f v\u0307 \u8fd9\u4e00\u9879：\u5b83\u4e0d\u662f\u7b80\u5355\u7684 a，\u800c\u662f\u53e0\u52a0\u4e86\u91cd\u529b\u5206\u91cf \u2212g\u00b7sin\u03b8 \u548c\u6c14\u52a8\u963b\u529b \u2212\u03c1\u00b7v\u00b2\u3002\u5f88\u591a\u521d\u5b66\u8005\u5199\u63a7\u5236\u5668\u65f6\u53ea\u7528 a \u8f93\u5165，\u7ed3\u679c\u98de\u673a\u722c\u5347\u65f6\u6389\u901f\u3001\u4fef\u51b2\u65f6\u8d85\u901f，\u672c\u8d28\u5c31\u662f\u6f0f\u6389\u4e86\u8fd9\u4e24\u4e2a\u524d\u9988\u9879\u3002<\/p>\n

    \u63a7\u5236\u8f93\u5165\u5fc5\u987b\u505a\u7269\u7406\u9971\u548c，\u8fd9\u662f\u4eff\u771f\u80fd\u4e0d\u80fd\u6536\u655b\u7684\u5173\u952e：<\/p>\n

    u[<\/span>0<\/span>]<\/span> =<\/span> np.<\/span>clip(<\/span>u[<\/span>0<\/span>]<\/span>,<\/span> 0<\/span>,<\/span> self.<\/span>a_max)<\/span> # \u52a0\u901f\u5ea6\u4e0a\u9650 20 m\/s\u00b2<\/span>
    \nu[<\/span>1<\/span>]<\/span> =<\/span> np.<\/span>clip(<\/span>u[<\/span>1<\/span>]<\/span>,<\/span> –<\/span>np.<\/span>pi\/<\/span>4<\/span>,<\/span> np.<\/span>pi\/<\/span>4<\/span>)<\/span> # \u4fef\u4ef0\u89d2\u901f\u7387\u9650\u5e45<\/span>
    \nu[<\/span>2<\/span>]<\/span> =<\/span> np.<\/span>clip(<\/span>u[<\/span>2<\/span>]<\/span>,<\/span> –<\/span>np.<\/span>pi\/<\/span>3<\/span>,<\/span> np.<\/span>pi\/<\/span>3<\/span>)<\/span> # \u504f\u822a\u89d2\u901f\u7387\u9650\u5e45<\/span><\/p>\n

    \u8f68\u8ff9\u8ddf\u8e2a\u91c7\u7528\u7ea7\u8054\u7684\u53cc\u95ed\u73af\u7ed3\u6784\u3002\u5916\u73af\u5904\u7406\u4f4d\u7f6e\u8bef\u5dee，\u628a\u8bef\u5dee\u6620\u5c04\u6210\u4e00\u4e2a\u901f\u5ea6\u4fee\u6b63\u91cf，\u518d\u4e0e\u671f\u671b\u901f\u5ea6\u5408\u6210：<\/p>\n

    # \u5916\u73af：\u4f4d\u7f6e\u8bef\u5dee -> \u901f\u5ea6\u77e2\u91cf\u4fee\u6b63<\/span>
    \npos_error =<\/span> pos_d –<\/span> pos
    \nerror_vel =<\/span> np.<\/span>array(<\/span>[<\/span>
    \n self.<\/span>pid_x.<\/span>update(<\/span>pos_error[<\/span>0<\/span>]<\/span>,<\/span> dt)<\/span>,<\/span>
    \n self.<\/span>pid_y.<\/span>update(<\/span>pos_error[<\/span>1<\/span>]<\/span>,<\/span> dt)<\/span>,<\/span>
    \n self.<\/span>pid_z.<\/span>update(<\/span>pos_error[<\/span>2<\/span>]<\/span>,<\/span> dt)<\/span>,<\/span>
    \n]<\/span>)<\/span>
    \n# \u4fee\u6b63\u91cf\u9650\u5e45：\u4e0d\u8d85\u8fc7\u671f\u671b\u901f\u5ea6\u7684 2.5 \u500d，\u9632\u6b62\u5927\u5e45\u8d85\u8c03<\/span>
    \nmax_norm =<\/span> np.<\/span>linalg.<\/span>norm(<\/span>vel_d)<\/span> *<\/span> 2.5<\/span>
    \nif<\/span> np.<\/span>linalg.<\/span>norm(<\/span>error_vel)<\/span> ><\/span> max_norm:<\/span>
    \n error_vel =<\/span> error_vel \/<\/span> np.<\/span>linalg.<\/span>norm(<\/span>error_vel)<\/span> *<\/span> max_norm
    \nvel_d =<\/span> vel_d +<\/span> error_vel<\/p>\n

    \u4ece\u4fee\u6b63\u540e\u7684\u901f\u5ea6\u77e2\u91cf\u91cc\u53cd\u89e3\u51fa\u4e09\u4e2a\u671f\u671b\u53c2\u8003\u503c\u2014\u2014\u7a7a\u901f\u3001\u822a\u8ff9\u89d2\u3001\u822a\u5411\u89d2：<\/p>\n

    v_d =<\/span> np.<\/span>clip(<\/span>np.<\/span>linalg.<\/span>norm(<\/span>vel_d)<\/span>,<\/span> 10<\/span>,<\/span> 90<\/span>)<\/span> # \u7a7a\u901f\u9650\u5e45<\/span>
    \ntheta_d =<\/span> np.<\/span>clip(<\/span>np.<\/span>arctan2(<\/span>vel_d[<\/span>2<\/span>]<\/span>,<\/span> np.<\/span>linalg.<\/span>norm(<\/span>vel_d[<\/span>0<\/span>:<\/span>2<\/span>]<\/span>)<\/span>)<\/span>,<\/span>
    \n –<\/span>np.<\/span>radians(<\/span>45<\/span>)<\/span>,<\/span> np.<\/span>radians(<\/span>45<\/span>)<\/span>)<\/span> # \u822a\u8ff9\u89d2\u9650\u5e45<\/span>
    \npsi_d =<\/span> np.<\/span>arctan2(<\/span>vel_d[<\/span>1<\/span>]<\/span>,<\/span> vel_d[<\/span>0<\/span>]<\/span>)<\/span> # \u822a\u5411\u89d2<\/span><\/p>\n

    \u5185\u73af\u5206\u522b\u8ddf\u8e2a\u8fd9\u4e09\u4e2a\u91cf，\u5176\u4e2d\u7eb5\u5411\u901a\u9053\u505a\u4e86\u53cd\u9988\u7ebf\u6027\u5316\u8865\u507f，\u628a\u91cd\u529b\u9879\u548c\u963b\u529b\u9879\u524d\u9988\u56de\u6765：<\/p>\n

    error_v =<\/span> v_d –<\/span> v
    \nerror_theta =<\/span> np.<\/span>unwrap(<\/span>[<\/span>theta,<\/span> theta_d]<\/span>)<\/span>[<\/span>1<\/span>]<\/span> –<\/span> theta # \u89d2\u5ea6\u89e3\u7f20\u7ed5，\u9632\u6b62\u8de8 \u00b1\u03c0 \u8df3\u53d8<\/span>
    \nerror_psi =<\/span> np.<\/span>unwrap(<\/span>[<\/span>psi,<\/span> psi_d]<\/span>)<\/span>[<\/span>1<\/span>]<\/span> –<\/span> psi<\/p>\n

    a_cmd =<\/span> self.<\/span>pid_v.<\/span>update(<\/span>error_v,<\/span> dt)<\/span> +<\/span> self.<\/span>uav.<\/span>g *<\/span> np.<\/span>sin(<\/span>theta)<\/span> +<\/span> self.<\/span>uav.<\/span>rho *<\/span> v**<\/span>2<\/span>
    \ntheta_dot_cmd =<\/span> self.<\/span>pid_theta.<\/span>update(<\/span>error_theta,<\/span> dt)<\/span>
    \npsi_dot_cmd =<\/span> self.<\/span>pid_psi.<\/span>update(<\/span>error_psi,<\/span> dt)<\/span><\/p>\n

    \u8fd9\u6bb5\u4ee3\u7801\u91cc\u6709\u4e09\u4e2a\u5bb9\u6613\u88ab\u5ffd\u7565\u4f46\u5f88\u5173\u952e\u7684\u7ec6\u8282：\u89d2\u5ea6\u8bef\u5dee\u5fc5\u987b\u7528 np.unwrap \u89e3\u7f20\u7ed5，\u5426\u5219\u4ece +179\u00b0 \u8f6c\u5230 \u2212179\u00b0 \u65f6\u63a7\u5236\u5668\u4f1a\u4ee5\u4e3a\u8bef\u5dee\u63a5\u8fd1 360\u00b0；\u7a7a\u901f\u53c2\u8003\u8981\u505a [10, 90] \u7684\u786c\u9650\u5e45，\u5426\u5219\u5916\u73af\u5728\u8fdc\u8ddd\u79bb\u65f6\u4f1a\u8981\u6c42\u4e00\u4e2a\u7269\u7406\u4e0a\u4e0d\u53ef\u80fd\u7684\u901f\u5ea6；\u4fee\u6b63\u901f\u5ea6\u9650\u5e45\u5230 2.5 \u500d，\u662f\u4e3a\u4e86\u907f\u514d\u5927\u8bef\u5dee\u4e0b\u63a7\u5236\u5668\u8f93\u51fa\u9971\u548c\u5f15\u8d77\u7684\u6301\u7eed\u632f\u8361\u3002<\/p>\n

    \u8fd9\u4e00\u5c42\u7684\u5de5\u7a0b\u610f\u4e49\u5728\u4e8e：\u62e6\u622a\u6982\u7387\u4e0d\u662f\u62cd\u8111\u888b\u7ed9\u7684\u5e38\u6570，\u800c\u662f\u8fd9\u5957\u95ed\u73af\u7cfb\u7edf\u771f\u5b9e\u8dd1\u51fa\u6765\u7684\u7ed3\u679c\u3002\u540e\u9762\u8bad\u7ec3\u6982\u7387\u6a21\u578b\u65f6，\u6837\u672c\u5c31\u6765\u81ea\u8fd9\u5957\u6a21\u578b\u7684\u4eff\u771f\u8f68\u8ff9\u3002 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

    \u56db\u3001\u62e6\u622a\u6982\u7387\u5148\u9a8c：\u4ece\u5355\u5bf9\u5355\u4eff\u771f\u5230\u4e09\u7ef4\u67e5\u627e\u8868<\/h3>\n

    \u6709\u4e86\u53ef\u4fe1\u7684\u8fd0\u52a8\u6a21\u578b，\u7b2c\u4e00\u4e2a\u6838\u5fc3\u95ee\u9898\u5c31\u662f：\u7ed9\u5b9a\u9632\u5fa1\u673a i \u548c\u5165\u4fb5\u673a j \u7684\u5f53\u524d\u51e0\u4f55\u5173\u7cfb，\u62e6\u622a\u6210\u529f\u7684\u6982\u7387\u662f\u591a\u5c11？<\/p>\n

    \u5982\u679c\u76f4\u63a5\u5728\u7ebf\u8ba1\u7b97，\u6bcf\u67b6\u9632\u5fa1\u673a\u6bcf\u4e2a\u51b3\u7b56\u5468\u671f\u90fd\u8981\u8dd1\u4e00\u6b21\u95ed\u73af\u4eff\u771f，\u8ba1\u7b97\u91cf\u5b8c\u5168\u4e0d\u53ef\u63a5\u53d7\u3002\u5de5\u7a0b\u4e0a\u7684\u6807\u51c6\u505a\u6cd5\u662f\u79bb\u7ebf\u5b66\u4e60\u3001\u5728\u7ebf\u67e5\u8868\u3002<\/p>\n

    4.1 \u4e09\u4e2a\u51e0\u4f55\u7279\u5f81<\/h4>\n

    \u63cf\u8ff0\u4e00\u5bf9\u62e6\u622a\u5173\u7cfb，\u7279\u5f81\u4e0d\u9700\u8981\u591a，\u4f46\u8981\u6293\u4f4f\u7269\u7406\u672c\u8d28\u3002\u9879\u76ee\u91c7\u7528\u4e09\u4e2a\u91cf：<\/p>\n

    d_js \u5165\u4fb5\u673a\u5230\u4fdd\u62a4\u4e2d\u5fc3（\u5730\u9762\u7ad9）\u7684\u8ddd\u79bb
    \nd_ij \u9632\u5fa1\u673a\u5230\u5165\u4fb5\u673a\u7684\u8ddd\u79bb
    \n\u03c4_ij \u4ee5\u5165\u4fb5\u673a\u4e3a\u9876\u70b9，\u9632\u5fa1\u673a-\u4fdd\u62a4\u4e2d\u5fc3\u5f20\u5f00\u7684\u5939\u89d2<\/p>\n

    \u8fd9\u4e09\u4e2a\u91cf\u7684\u7269\u7406\u542b\u4e49\u5f88\u6e05\u6670：d_js \u63cf\u8ff0\u5a01\u80c1\u7684\u7d27\u8feb\u7a0b\u5ea6，\u8d8a\u8fd1\u8d8a\u5371\u9669；d_ij \u63cf\u8ff0\u9632\u5fa1\u673a\u80fd\u5426\u53ca\u65f6\u8d76\u5230；\u03c4_ij \u63cf\u8ff0\u4ea4\u6218\u7684\u51e0\u4f55\u5173\u7cfb\u2014\u2014\u03c4 \u63a5\u8fd1 0 \u610f\u5473\u7740\u9632\u5fa1\u673a\u6b63\u5904\u5728\u5165\u4fb5\u673a\u98de\u5411\u4fdd\u62a4\u4e2d\u5fc3\u7684\u822a\u8def\u4e0a，\u5c5e\u4e8e\u8fce\u5934\u62e6\u622a，\u6210\u529f\u7387\u6700\u9ad8；\u03c4 \u63a5\u8fd1 \u03c0 \u610f\u5473\u7740\u9632\u5fa1\u673a\u5728\u5165\u4fb5\u673a\u7684\u5c3e\u90e8\u65b9\u5411，\u5c5e\u4e8e\u8ffd\u5c3e\u62e6\u622a，\u6210\u529f\u7387\u6700\u4f4e\u3002<\/p>\n

    4.2 \u6570\u636e\u91c7\u96c6：\u5f3a\u5236 1v1 \u7684\u95ed\u73af\u4eff\u771f<\/h4>\n

    \u4e3a\u4e86\u4fdd\u8bc1\u6837\u672c"\u5e72\u51c0"，\u91c7\u96c6\u9636\u6bb5\u9700\u8981\u5f3a\u5236\u4e00\u5bf9\u4e00\u914d\u5bf9：\u7f16\u53f7\u4e3a i \u7684\u9632\u5fa1\u673a\u53ea\u62e6\u622a\u7f16\u53f7\u4e3a i \u7684\u5165\u4fb5\u673a，\u5176\u4f59\u5e72\u6270\u5168\u90e8\u5c4f\u853d\u3002\u91c7\u96c6\u6d41\u7a0b\u662f：<\/p>\n

    class<\/span> Forced1v1DecisionMaker<\/span>(<\/span>BaseDecisionMaker)<\/span>:<\/span>
    \n """\u5f3a\u5236 defender_i \u53ea\u9501\u5b9a attacker_i，\u7528\u4e8e\u91c7\u96c6\u5355\u5bf9\u5355\u6570\u636e"""<\/span>
    \n def<\/span> decide<\/span>(<\/span>self,<\/span> t,<\/span> my_state,<\/span> friends,<\/span> enemies,<\/span> standby_pos)<\/span>:<\/span>
    \n if<\/span> not<\/span> enemies:<\/span>
    \n return<\/span> None<\/span>
    \n for<\/span> e in<\/span> enemies:<\/span>
    \n e_idx =<\/span> int<\/span>(<\/span>re.<\/span>search(<\/span>r'(\\\\d+)'<\/span>,<\/span> e.<\/span>agent_id)<\/span>.<\/span>group(<\/span>1<\/span>)<\/span>)<\/span>
    \n if<\/span> e_idx ==<\/span> self.<\/span>my_idx:<\/span> # \u53ea\u62e6\u622a\u548c\u81ea\u5df1\u7f16\u53f7\u4e00\u81f4\u7684\u654c\u673a<\/span>
    \n return<\/span> e.<\/span>agent_id
    \n return<\/span> None<\/span><\/p>\n

    \u6bcf\u67b6\u9632\u5fa1\u673a\u3001\u5165\u4fb5\u673a\u7684\u4f4d\u7f6e\u968f\u673a\u5316，\u8fd0\u884c\u82e5\u5e72\u8f6e 360 \u79d2\u7684\u4eff\u771f，\u7136\u540e\u6309\u56fa\u5b9a\u6b65\u957f\u91cd\u91c7\u6837\u8f68\u8ff9\u70b9，\u9010\u70b9\u8ba1\u7b97\u4e09\u4e2a\u7279\u5f81，\u5e76\u628a\u8be5\u6b21\u4ea4\u6218\u7684\u6700\u7ec8\u7ed3\u5c40\u4f5c\u4e3a\u6807\u7b7e：<\/p>\n

    for<\/span> step_idx in<\/span> range<\/span>(<\/span>0<\/span>,<\/span> len<\/span>(<\/span>times)<\/span>,<\/span> 10<\/span>)<\/span>:<\/span> # \u6bcf 1 \u79d2\u91c7\u4e00\u4e2a\u70b9，\u964d\u4f4e\u5197\u4f59\u4e0e\u672b\u7aef\u504f\u501a<\/span>
    \n if<\/span> not<\/span> a_log[<\/span>'alive'<\/span>]<\/span> or<\/span> not<\/span> d_log[<\/span>'alive'<\/span>]<\/span>:<\/span>
    \n continue<\/span>
    \n if<\/span> d_log[<\/span>'target_id'<\/span>]<\/span> !=<\/span> att_id:<\/span> # \u5c1a\u672a\u8fdb\u5165\u62e6\u622a\u903b\u8f91\u7684\u6837\u672c\u4e22\u5f03<\/span>
    \n continue<\/span>
    \n vec_e_to_me,<\/span> vec_e_to_gs =<\/span> my_pos –<\/span> e_pos,<\/span> gs_pos –<\/span> e_pos
    \n d_me,<\/span> d_gs =<\/span> np.<\/span>linalg.<\/span>norm(<\/span>vec_e_to_me)<\/span>,<\/span> np.<\/span>linalg.<\/span>norm(<\/span>vec_e_to_gs)<\/span>
    \n cos_theta =<\/span> np.<\/span>clip(<\/span>np.<\/span>dot(<\/span>vec_e_to_me,<\/span> vec_e_to_gs)<\/span> \/<\/span> (<\/span>d_me *<\/span> d_gs)<\/span>,<\/span> –<\/span>1.0<\/span>,<\/span> 1.0<\/span>)<\/span>
    \n angle_rad =<\/span> np.<\/span>arccos(<\/span>cos_theta)<\/span>
    \n samples.<\/span>append(<\/span>[<\/span>d_gs,<\/span> d_me,<\/span> angle_rad,<\/span> outcome]<\/span>)<\/span><\/p>\n

    \u8fd9\u91cc\u6709\u4e24\u4e2a\u91c7\u6837\u7ec6\u8282\u503c\u5f97\u8bf4：\u4e00\u662f\u6309\u56fa\u5b9a\u6b65\u957f\u91cd\u91c7\u6837，\u56e0\u4e3a\u539f\u59cb\u8f68\u8ff9\u70b9\u5728\u9ad8\u9891\u4eff\u771f\u4e0b\u6781\u5176\u5bc6\u96c6，\u4e14\u672b\u7aef\u6570\u636e\u5929\u7136\u7a00\u758f，\u4e0d\u91cd\u91c7\u6837\u4f1a\u8ba9\u6a21\u578b\u88ab\u4e2d\u95f4\u6bb5\u6837\u672c\u6df9\u6ca1；\u4e8c\u662f\u5fc5\u987b\u8fc7\u6ee4\u672a\u8fdb\u5165\u62e6\u622a\u903b\u8f91\u7684\u6837\u672c，\u5426\u5219\u4f1a\u51fa\u73b0"\u9632\u5fa1\u673a\u8fd8\u5728\u5de1\u822a\u3001\u4ec0\u4e48\u90fd\u6ca1\u53d1\u751f"\u7684\u5047\u9634\u6027\u6837\u672c，\u628a\u6807\u7b7e\u6c61\u67d3\u6389\u3002<\/p>\n

    4.3 \u4e3a\u4ec0\u4e48\u9009 KNN \u800c\u4e0d\u662f\u795e\u7ecf\u7f51\u7edc<\/h4>\n

    \u6807\u7b7e\u662f 0\/1 \u7684"\u662f\u5426\u62e6\u622a\u6210\u529f"，\u8fd9\u672c\u8d28\u4e0a\u662f\u4e00\u4e2a\u6982\u7387\u56de\u5f52\u95ee\u9898\u3002\u9009 KNN \u56de\u5f52\u7684\u7406\u7531\u5f88\u5b9e\u9645：\u5728\u8db3\u591f\u5bc6\u96c6\u7684\u6837\u672c\u70b9\u4e91\u4e0a，KNN \u7b49\u4ef7\u4e8e"\u67e5\u8be2\u70b9\u9644\u8fd1 k \u4e2a\u72b6\u6001\u91cc\u6210\u529f\u62e6\u622a\u7684\u6bd4\u4f8b"，\u8fd9\u6070\u597d\u5c31\u662f\u6761\u4ef6\u6982\u7387\u7684\u5c40\u90e8\u9891\u7387\u4f30\u8ba1，\u7269\u7406\u542b\u4e49\u4e00\u76ee\u4e86\u7136，\u4e0d\u9700\u8981\u8c03\u4e00\u5806\u8d85\u53c2，\u4e5f\u4e0d\u4f1a\u6709\u795e\u7ecf\u7f51\u7edc\u7684\u8fc7\u62df\u5408\u548c\u4e0d\u53ef\u89e3\u91ca\u95ee\u9898\u3002<\/p>\n

    k_neighbors =<\/span> len<\/span>(<\/span>X)<\/span> \/\/<\/span> 50<\/span> # \u90bb\u5c45\u6570\u4e0e\u6837\u672c\u91cf\u6302\u94a9<\/span>
    \nknn_model =<\/span> make_pipeline(<\/span>
    \n StandardScaler(<\/span>)<\/span>,<\/span>
    \n KNeighborsRegressor(<\/span>n_neighbors=<\/span>k_neighbors,<\/span> weights=<\/span>'uniform'<\/span>)<\/span>
    \n)<\/span>
    \nknn_model.<\/span>fit(<\/span>X,<\/span> y)<\/span> # X = [d_js, d_ij, angle], y = outcome<\/span><\/p>\n

    StandardScaler \u662f\u5fc5\u987b\u7684：\u4e09\u4e2a\u7279\u5f81\u7684\u91cf\u7eb2\u5dee\u4e86\u4e24\u4e2a\u6570\u91cf\u7ea7（\u8ddd\u79bb\u662f\u5343\u7c73\u7ea7\u3001\u89d2\u5ea6\u662f\u5f27\u5ea6\u7ea7），\u4e0d\u505a\u6807\u51c6\u5316\u7684\u8bdd，\u8ddd\u79bb\u7ef4\u5ea6\u4f1a\u5b8c\u5168\u4e3b\u5bfc\u6b27\u6c0f\u8ddd\u79bb，\u89d2\u5ea6\u7279\u5f81\u5f62\u540c\u865a\u8bbe\u3002<\/p>\n

    4.4 \u79bb\u7ebf\u7f16\u8bd1\u6210\u67e5\u627e\u8868<\/h4>\n

    KNN \u5728\u7ebf\u63a8\u7406\u8981\u904d\u5386\u6837\u672c\u7b97\u8ddd\u79bb，\u6837\u672c\u91cf\u5927\u65f6\u5355\u6b21\u67e5\u8be2\u662f\u6beb\u79d2\u7ea7，\u800c\u9632\u5fa1\u673a\u7684\u51b3\u7b56\u5468\u671f\u662f 0.5 \u79d2\u3001\u8fd8\u8981\u904d\u5386 30 \u4e2a\u76ee\u6807，\u7d2f\u8ba1\u5f00\u9500\u4e0d\u53ef\u63a5\u53d7\u3002\u6240\u4ee5\u8981\u628a\u6a21\u578b\u79bb\u7ebf\u7f16\u8bd1\u6210\u89c4\u5219\u7f51\u683c：<\/p>\n

    d_js_grid =<\/span> np.<\/span>linspace(<\/span>0<\/span>,<\/span> 10000<\/span>,<\/span> 50<\/span>)<\/span> # \u5165\u4fb5\u673a\u5230\u4fdd\u62a4\u4e2d\u5fc3\u8ddd\u79bb 50 \u683c<\/span>
    \nd_ij_grid =<\/span> np.<\/span>linspace(<\/span>0<\/span>,<\/span> 10000<\/span>,<\/span> 50<\/span>)<\/span> # \u9632\u5fa1\u673a\u5230\u5165\u4fb5\u673a\u8ddd\u79bb 50 \u683c<\/span>
    \nangle_grid =<\/span> np.<\/span>linspace(<\/span>0<\/span>,<\/span> np.<\/span>pi,<\/span> 20<\/span>)<\/span> # \u4ea4\u6218\u5939\u89d2 20 \u683c<\/span><\/p>\n

    D_JS,<\/span> D_IJ,<\/span> ANGLE =<\/span> np.<\/span>meshgrid(<\/span>d_js_grid,<\/span> d_ij_grid,<\/span> angle_grid,<\/span> indexing=<\/span>'ij'<\/span>)<\/span>
    \npoints =<\/span> np.<\/span>c_[<\/span>D_JS.<\/span>ravel(<\/span>)<\/span>,<\/span> D_IJ.<\/span>ravel(<\/span>)<\/span>,<\/span> ANGLE.<\/span>ravel(<\/span>)<\/span>]<\/span>
    \nprobs =<\/span> knn_model.<\/span>predict(<\/span>points)<\/span>.<\/span>reshape(<\/span>50<\/span>,<\/span> 50<\/span>,<\/span> 20<\/span>)<\/span> # \u4e00\u6b21\u6027\u79bb\u7ebf\u63a8\u7406 5 \u4e07\u4e2a\u7f51\u683c\u70b9<\/span><\/p>\n

    \u8fd0\u884c\u65f6\u7528\u4e09\u7ebf\u6027\u63d2\u503c\u67e5\u8be2，\u5355\u6b21\u5f00\u9500\u964d\u5230\u5fae\u79d2\u7ea7：<\/p>\n

    class<\/span> InterceptProbEstimator<\/span>:<\/span>
    \n def<\/span> __init__<\/span>(<\/span>self,<\/span> table_path)<\/span>:<\/span>
    \n with<\/span> open<\/span>(<\/span>table_path,<\/span> "rb"<\/span>)<\/span> as<\/span> f:<\/span>
    \n d_js_grid,<\/span> d_ij_grid,<\/span> angle_grid,<\/span> probs =<\/span> pickle.<\/span>load(<\/span>f)<\/span>
    \n self.<\/span>interpolator =<\/span> RegularGridInterpolator(<\/span>
    \n (<\/span>d_js_grid,<\/span> d_ij_grid,<\/span> angle_grid)<\/span>,<\/span> probs,<\/span>
    \n bounds_error=<\/span>False<\/span>,<\/span> fill_value=<\/span>None<\/span> # \u5141\u8bb8\u8fb9\u7f18\u5916\u63a8<\/span>
    \n )<\/span><\/p>\n

    def<\/span> predict<\/span>(<\/span>self,<\/span> d_js,<\/span> d_ij,<\/span> angle_rad)<\/span>:<\/span>
    \n angle_rad =<\/span> abs<\/span>(<\/span>angle_rad)<\/span>
    \n if<\/span> angle_rad ><\/span> np.<\/span>pi:<\/span>
    \n angle_rad =<\/span> 2<\/span> *<\/span> np.<\/span>pi –<\/span> angle_rad
    \n return<\/span> float<\/span>(<\/span>self.<\/span>interpolator(<\/span>(<\/span>d_js,<\/span> d_ij,<\/span> angle_rad)<\/span>)<\/span>)<\/span><\/p>\n

    \u6700\u540e\u4e00\u884c\u505a\u4e86\u5939\u89d2\u6298\u53e0，\u628a [0, 2\u03c0] \u7684\u5939\u89d2\u5f52\u4e00\u5316\u5230 [0, \u03c0]，\u56e0\u4e3a\u51e0\u4f55\u4e0a\u5939\u89d2\u7684\u6b63\u8d1f\u6ca1\u6709\u610f\u4e49\u3002\u8fd9\u4e00\u5c42\u505a\u5b8c\u4e4b\u540e，\u6bcf\u67b6\u9632\u5fa1\u673a\u90fd\u80fd\u5728\u5fae\u79d2\u7ea7\u62ff\u5230\u81ea\u5df1\u5bf9\u4efb\u610f\u53ef\u89c1\u76ee\u6807\u7684\u62e6\u622a\u6982\u7387 p_ij\u3002 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

    \u4e94\u3001\u6982\u7387\u6d88\u8017\u6d41：\u89e3\u51b3"\u624e\u5806"\u4e0e"\u8d44\u6e90\u8f6c\u79fb"<\/h3>\n

    \u62ff\u5230 p_ij \u53ea\u662f\u7b2c\u4e00\u6b65\u3002\u771f\u6b63\u56f0\u96be\u7684\u662f：\u5f53\u591a\u67b6\u9632\u5fa1\u673a\u540c\u65f6\u770b\u4e0a\u4e00\u4e2a\u76ee\u6807\u65f6，\u600e\u4e48\u5224\u65ad"\u8be5\u4e0d\u8be5\u53bb"？<\/p>\n

    5.1 \u8054\u5408\u62e6\u622a\u6982\u7387\u4e0e\u8fb9\u9645\u9012\u51cf<\/h4>\n

    \u591a\u673a\u534f\u540c\u62e6\u622a\u540c\u4e00\u4e2a\u76ee\u6807 j \u65f6，\u53ea\u8981\u6709\u4e00\u67b6\u6210\u529f\u5c31\u7b97\u6574\u4f53\u6210\u529f，\u56e0\u6b64\u8054\u5408\u6982\u7387\u662f：<\/p>\n

    p_j = 1 \u2212 \u03a0_i (1 \u2212 p_ij)^(m_ij)<\/p>\n

    m_ij \u8868\u793a\u9632\u5fa1\u673a i \u662f\u5426\u88ab\u5206\u914d\u5230\u76ee\u6807 j\u3002\u8fd9\u4e2a\u5f0f\u5b50\u5929\u7136\u7f16\u7801\u4e86\u8fb9\u9645\u6536\u76ca\u9012\u51cf：\u5f53\u7b2c\u4e00\u67b6\u9632\u5fa1\u673a\u7684\u6982\u7387\u662f 0.6 \u65f6，\u8054\u5408\u6982\u7387\u662f 0.6；\u7b2c\u4e8c\u67b6\u5e26\u6765 0.84；\u7b2c\u4e09\u67b6 0.936；\u7b2c\u56db\u67b6 0.974\u3002\u7b2c\u56db\u67b6\u9632\u5fa1\u673a\u76f8\u6bd4\u7b2c\u4e09\u67b6\u53ea\u591a\u8d21\u732e\u4e86\u4e0d\u5230 4 \u4e2a\u767e\u5206\u70b9，\u4f46\u5b83\u7684\u6d88\u8017\u662f\u5b9e\u6253\u5b9e\u7684\u3002 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

    5.2 \u671f\u671b\u6d88\u8017\u4e0e\u5269\u4f59\u6d41<\/h4>\n

    \u65e2\u7136\u591a\u673a\u5206\u914d，\u5c31\u8981\u56de\u7b54"\u54ea\u67b6\u9632\u5fa1\u673a\u5b9e\u9645\u627f\u62c5\u4e86\u591a\u5c11\u62e6\u622a\u4efb\u52a1"\u3002\u9879\u76ee\u91c7\u7528\u6309\u6982\u7387\u5360\u6bd4\u5206\u644a\u7684\u65b9\u5f0f：<\/p>\n

    c_ij = (p_ij \/ \u03a3 p_i'j) \u00b7 p_j<\/p>\n

    c_ij \u5c31\u662f\u9632\u5fa1\u673a i \u5728\u76ee\u6807 j \u4e0a\u7684\u671f\u671b\u6d88\u8017\u3002\u5b83\u662f\u62e6\u622a\u6210\u529f\u7684\u671f\u671b"\u4efd\u989d"\u3002\u5bf9\u5e94\u7684\u5269\u4f59\u6982\u7387\u6d41\u662f 1 \u2212 c_ij：\u5982\u679c\u9632\u5fa1\u673a i \u5728\u76ee\u6807 j \u4e0a\u53ea\u6d88\u8017\u4e86 0.6，\u90a3\u5b83\u8fd8\u5269\u4e0b 0.4 \u7684\u6982\u7387\u6d41\u53ef\u4ee5\u4f9b\u7ed9\u540e\u7eed\u76ee\u6807\u3002<\/p>\n

    \u8fd9\u4e2a\u5efa\u6a21\u7684\u5de7\u5999\u4e4b\u5904\u5728\u4e8e，\u5b83\u628a"\u4e00\u6b21\u6027\u6d88\u8017\u7684\u7269\u7406\u62e6\u622a\u8d44\u6e90"\u7528\u4e00\u4e2a\u8fde\u7eed\u7684\u6982\u7387\u6d41\u6765\u8fd1\u4f3c，\u4f7f\u5f97\u540e\u7eed\u7684\u4f18\u5316\u95ee\u9898\u53ef\u4ee5\u7528\u51f8\u4f18\u5316\u7684\u5de5\u5177\u6765\u89e3\u2014\u2014\u800c\u4e0d\u662f\u5199\u6210\u4e00\u4e2a\u7ec4\u5408\u7206\u70b8\u7684\u6574\u6570\u5206\u914d\u95ee\u9898\u3002<\/p>\n

    5.3 \u4e8c\u6b21\u8f6c\u79fb\u6d41\u5b50\u95ee\u9898<\/h4>\n

    \u5269\u4f59\u6d41\u8981\u5206\u914d\u5230\u54ea\u4e9b\u540e\u7eed\u76ee\u6807？\u8fd9\u6784\u6210\u4e86\u4e00\u4e2a\u5b50\u95ee\u9898：\u7ed9\u5b9a\u5269\u4f59\u6d41\u603b\u91cf\u548c\u5230\u5404\u5019\u9009\u76ee\u6807\u7684\u8f6c\u79fb\u4ee3\u4ef7\u5411\u91cf C_i，\u6c42\u89e3\u6700\u4f18\u5206\u914d N_i：<\/p>\n

    min <C_i, N_i> + (\u03b3\/2)\u00b7\u2016N_i\u2016\u00b2
    \ns.t. \u03a3_k n_ijk = 1 \u2212 c_ij
    \n 0 \u2264 n_ijk \u2264 1<\/p>\n

    \u76ee\u6807\u51fd\u6570\u7b2c\u4e00\u9879\u662f\u7ebf\u6027\u8f6c\u79fb\u4ee3\u4ef7，\u7b2c\u4e8c\u9879\u662f\u4e8c\u6b21\u6b63\u5219\u9879 (\u03b3\/2)\u2016N\u2016\u00b2，\u03b3 \u8d8a\u5927\u8d8a\u503e\u5411\u4e8e\u628a\u6d41"\u644a\u5e73"\u3001\u907f\u514d\u96c6\u4e2d\u3002<\/p>\n

    \u8fd9\u4e2a\u95ee\u9898\u7684\u6c42\u89e3\u4e0d\u9700\u8981\u901a\u7528\u4e8c\u6b21\u89c4\u5212\u6c42\u89e3\u5668\u3002\u7531 KKT \u6761\u4ef6\u53ef\u5f97，\u6700\u4f18\u89e3\u7684\u89e3\u6790\u7ed3\u6784\u662f：<\/p>\n

    N_i(\u03bb) = clip( (\u03bb \u2212 C_i) \/ \u03b3, 0, 1 )<\/p>\n

    \u4e5f\u5c31\u662f\u8bf4，\u7ed9\u5b9a\u4e00\u4e2a"\u6c34\u4f4d" \u03bb，\u6bcf\u4e2a\u5206\u91cf\u7684\u89e3\u5c31\u662f (\u03bb \u2212 C_i)\/\u03b3 \u518d\u622a\u65ad\u5230 [0, 1]\u3002\u4e8e\u662f\u6574\u4e2a\u6c42\u89e3\u9000\u5316\u6210\u4e00\u7ef4\u641c\u7d22：\u4e8c\u5206 \u03bb，\u4f7f \u03a3 N_i(\u03bb) \u6070\u597d\u7b49\u4e8e\u5269\u4f59\u6d41\u3002\u8fd9\u5c31\u662f\u7ecf\u5178\u7684\u6ce8\u6c34\u6cd5（water-filling）：<\/p>\n

    def<\/span> solve_subproblem_V_i<\/span>(<\/span>residual_flow,<\/span> C_i,<\/span> gamma)<\/span>:<\/span>
    \n """min <C_i,N> + (gamma\/2)||N||^2 s.t. sum(N)=residual_flow, 0<=N<=1"""<\/span>
    \n num_targets =<\/span> len<\/span>(<\/span>C_i)<\/span>
    \n residual_flow =<\/span> np.<\/span>clip(<\/span>residual_flow,<\/span> 0.0<\/span>,<\/span> num_targets)<\/span> # \u5bb9\u9519：\u6d6e\u70b9\u622a\u65ad\u8bef\u5dee<\/span><\/p>\n

    if<\/span> residual_flow ==<\/span> 0.0<\/span>:<\/span>
    \n return<\/span> 0.0<\/span>,<\/span> np.<\/span>zeros(<\/span>num_targets)<\/span>
    \n if<\/span> residual_flow ==<\/span> num_targets:<\/span>
    \n N_opt =<\/span> np.<\/span>ones(<\/span>num_targets)<\/span>
    \n return<\/span> np.<\/span>dot(<\/span>C_i,<\/span> N_opt)<\/span> +<\/span> (<\/span>gamma \/<\/span> 2.0<\/span>)<\/span> *<\/span> np.<\/span>sum<\/span>(<\/span>N_opt **<\/span> 2<\/span>)<\/span>,<\/span> N_opt<\/p>\n

    # KKT: C_i + gamma*N_i – lambda = 0 => N_i = clip((lambda – C_i)\/gamma, 0, 1)<\/span>
    \n lambda_low =<\/span> np.<\/span>min<\/span>(<\/span>C_i)<\/span> # \u6c34\u4f4d\u4e0b\u9650：\u6d41\u91cf\u521a\u597d\u4e3a 0<\/span>
    \n lambda_high =<\/span> np.<\/span>max<\/span>(<\/span>C_i)<\/span> +<\/span> gamma # \u6c34\u4f4d\u4e0a\u9650：\u6d41\u91cf\u521a\u597d\u53d6\u6ee1<\/span>
    \n for<\/span> _ in<\/span> range<\/span>(<\/span>60<\/span>)<\/span>:<\/span>
    \n lambda_mid =<\/span> (<\/span>lambda_low +<\/span> lambda_high)<\/span> \/<\/span> 2.0<\/span>
    \n N_mid =<\/span> np.<\/span>clip(<\/span>(<\/span>lambda_mid –<\/span> C_i)<\/span> \/<\/span> gamma,<\/span> 0.0<\/span>,<\/span> 1.0<\/span>)<\/span>
    \n if<\/span> np.<\/span>sum<\/span>(<\/span>N_mid)<\/span> <<\/span> residual_flow:<\/span>
    \n lambda_low =<\/span> lambda_mid
    \n else<\/span>:<\/span>
    \n lambda_high =<\/span> lambda_mid<\/p>\n

    lambda_opt =<\/span> (<\/span>lambda_low +<\/span> lambda_high)<\/span> \/<\/span> 2.0<\/span>
    \n N_opt =<\/span> np.<\/span>clip(<\/span>(<\/span>lambda_opt –<\/span> C_i)<\/span> \/<\/span> gamma,<\/span> 0.0<\/span>,<\/span> 1.0<\/span>)<\/span>
    \n obj_val =<\/span> np.<\/span>dot(<\/span>C_i,<\/span> N_opt)<\/span> +<\/span> (<\/span>gamma \/<\/span> 2.0<\/span>)<\/span> *<\/span> np.<\/span>sum<\/span>(<\/span>N_opt **<\/span> 2<\/span>)<\/span>
    \n return<\/span> obj_val,<\/span> N_opt<\/p>\n

    60 \u6b21\u4e8c\u5206\u5bf9\u53cc\u7cbe\u5ea6\u6d6e\u70b9\u6765\u8bf4\u5df2\u7ecf\u6536\u655b\u5230\u673a\u5668\u7cbe\u5ea6\u6781\u9650，\u800c\u6574\u4e2a\u6c42\u89e3\u53ea\u662f 60 \u6b21\u5411\u91cf\u5316\u7684 clip \u548c\u6c42\u548c，\u5b9e\u6d4b\u5728\u6beb\u79d2\u4ee5\u4e0b\u3002\u7528\u901a\u7528 SLSQP \u6c42\u89e3\u5668\u5f53\u7136\u4e5f\u80fd\u5f97\u5230\u540c\u6837\u7ed3\u679c，\u4f46\u5355\u6b21\u8c03\u7528\u5c31\u8981\u51e0\u5341\u6beb\u79d2，\u653e\u8fdb 2 Hz \u00d7 30 \u76ee\u6807\u7684\u51b3\u7b56\u5faa\u73af\u91cc\u76f4\u63a5\u4e0d\u53ef\u7528\u2014\u2014\u8fd9\u662f"\u6839\u636e\u95ee\u9898\u7ed3\u6784\u624b\u5199\u89e3\u6790\u89e3"\u6bd4"\u8c03\u7528\u901a\u7528\u6c42\u89e3\u5668"\u66f4\u5feb\u4e5f\u66f4\u7a33\u7684\u5178\u578b\u6848\u4f8b\u3002 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

    5.4 \u8fb9\u9645\u6548\u5e94\u7684\u91cf\u5316\u9a8c\u8bc1<\/h4>\n

    \u8fd9\u5957\u5efa\u6a21\u662f\u5426\u771f\u7684\u5b9e\u73b0\u4e86"\u6291\u5236\u624e\u5806"，\u53ef\u4ee5\u7528\u4e00\u4e2a\u6700\u5c0f\u5b9e\u9a8c\u9a8c\u8bc1：\u56fa\u5b9a\u5355\u673a\u62e6\u622a\u6982\u7387 h = 0.6，\u9010\u6b65\u589e\u52a0\u5206\u914d\u5230\u540c\u4e00\u76ee\u6807\u7684\u9632\u5fa1\u673a\u6570\u91cf，\u89c2\u5bdf\u8054\u5408\u6982\u7387\u3001\u5355\u673a\u671f\u671b\u6d88\u8017\u3001\u5269\u4f59\u6d41\u548c\u8f6c\u79fb\u4ee3\u4ef7\u7684\u53d8\u5316\u3002<\/p>\n

    \u65e0\u4eba\u673a\u6570\u91cf | \u8054\u5408\u6982\u7387 p_j | \u671f\u671b\u6d88\u8017 c_ij | \u5269\u4f59\u6d41 1\u2212c_ij | \u8f6c\u79fb\u4ee3\u4ef7 V_i
    \n 1 | 0.6000 | 0.6000 | 0.4000 | \u4f4e
    \n 2 | 0.8400 | 0.4200 | 0.5800 | \u4e0a\u5347
    \n 3 | 0.9360 | 0.3120 | 0.6880 | \u7ee7\u7eed\u4e0a\u5347
    \n 4 | 0.9744 | 0.2436 | 0.7564 | \u663e\u8457\u4e0a\u5347
    \n … | \u8d8b\u8fd1 1 | \u6301\u7eed\u4e0b\u964d | \u6301\u7eed\u4e0a\u5347 | \u6301\u7eed\u4e0a\u5347<\/p>\n

    \u8fd9\u5f20\u8868\u5c31\u662f\u6574\u5957\u673a\u5236\u7684\u81ea\u8bc1：\u968f\u7740\u624e\u5806\u7684\u9632\u5fa1\u673a\u6570\u91cf\u589e\u52a0，\u8054\u5408\u6982\u7387\u8fc5\u901f\u9971\u548c，\u5355\u673a\u671f\u671b\u6d88\u8017\u6301\u7eed\u4e0b\u964d，\u5269\u4f59\u6d41\u4e0d\u65ad\u4e0a\u5347，\u800c\u8f6c\u79fb\u4ee3\u4ef7\u968f\u4e4b\u4e0a\u626c\u3002\u8f6c\u79fb\u4ee3\u4ef7\u653e\u5728\u51b3\u7b56\u4ee3\u4ef7\u51fd\u6570\u91cc，\u5c31\u5f62\u6210\u4e86\u4e00\u4e2a\u81ea\u52a8\u7684\u8d1f\u53cd\u9988\u2014\u2014\u8d8a\u591a\u4eba\u62a2\u540c\u4e00\u4e2a\u76ee\u6807，\u8fb9\u9645\u4ee3\u4ef7\u8d8a\u9ad8，\u540e\u6765\u8005\u4f1a\u81ea\u52a8\u8f6c\u5411\u5176\u4ed6\u76ee\u6807\u3002<\/p>\n

    \u516d\u3001\u5206\u5e03\u5f0f\u5e02\u573a\u5171\u8bc6：\u53ea\u6709\u5c40\u90e8\u6001\u52bf\u65f6\u5982\u4f55\u8fbe\u6210\u4e00\u81f4<\/h3>\n

    \u524d\u9762\u51e0\u8282\u90fd\u662f"\u5355\u673a\u89c6\u89d2"\u7684\u8ba1\u7b97，\u6700\u540e\u4e00\u5c42\u8981\u89e3\u51b3\u7684\u95ee\u9898\u662f：\u6ca1\u6709\u4efb\u4f55\u4e00\u67b6\u9632\u5fa1\u673a\u77e5\u9053\u5168\u5c40，\u5982\u4f55\u8ba9\u6574\u4e2a\u96c6\u7fa4\u7684\u5206\u914d\u4e0d\u51b2\u7a81？<\/p>\n

    6.1 \u5e26\u65f6\u95f4\u6233\u7684\u5c40\u90e8\u6001\u52bf\u8868<\/h4>\n

    \u6bcf\u67b6\u9632\u5fa1\u673a\u7ef4\u62a4\u4e00\u5f20\u5c40\u90e8\u6001\u52bf\u8868，\u8868\u9879\u8bb0\u5f55\u7684\u662f"\u6211\u8ba4\u4e3a\u53cb\u673a f \u6b63\u5728\u6253\u54ea\u4e2a\u76ee\u6807\u3001\u5bf9\u90a3\u4e2a\u76ee\u6807\u7684\u62e6\u622a\u6982\u7387\u662f\u591a\u5c11\u3001\u5b83\u7684\u901a\u4fe1\/\u4fa6\u5bdf\u534a\u5f84\u591a\u5927\u3001\u8fd9\u6761\u4fe1\u606f\u662f\u4ec0\u4e48\u65f6\u5019\u7684"：<\/p>\n

    @dataclass<\/span>
    \nclass<\/span> Fsa<\/span>:<\/span>
    \n target:<\/span> Optional[<\/span>int<\/span>]<\/span> # \u53cb\u673a\u5f53\u524d\u9501\u5b9a\u7684\u76ee\u6807\u7f16\u53f7，None \u8868\u793a\u5f85\u547d<\/span>
    \n pj:<\/span> Optional[<\/span>float<\/span>]<\/span> # \u53cb\u673a\u5bf9\u8be5\u76ee\u6807\u7684\u62e6\u622a\u6982\u7387<\/span>
    \n commr:<\/span> float<\/span> # \u53cb\u673a\u7684\u901a\u4fe1\u534a\u5f84<\/span>
    \n deter:<\/span> float<\/span> # \u53cb\u673a\u7684\u4fa6\u5bdf\u534a\u5f84<\/span>
    \n ts:<\/span> float<\/span> # \u4fe1\u606f\u65f6\u95f4\u6233<\/span><\/p>\n

    \u901a\u4fe1\u65f6\u53ea\u5e7f\u64ad\u81ea\u5df1\u7684\u6001\u52bf\u8868\u589e\u91cf，\u63a5\u6536\u65b9\u6309\u65f6\u95f4\u6233\u5408\u5e76，\u65e7\u4fe1\u606f\u4e00\u5f8b\u4e22\u5f03：<\/p>\n

    def<\/span> receive<\/span>(<\/span>self,<\/span> data)<\/span>:<\/span>
    \n for<\/span> fid,<\/span> fsa in<\/span> data[<\/span>'friends_sa'<\/span>]<\/span>.<\/span>items(<\/span>)<\/span>:<\/span>
    \n existing =<\/span> self.<\/span>friends_sa.<\/span>get(<\/span>fid)<\/span>
    \n if<\/span> existing is<\/span> None<\/span> or<\/span> fsa.<\/span>ts ><\/span> existing.<\/span>ts:<\/span> # \u65f6\u95f4\u6233\u65b0\u8005\u80dc，\u5929\u7136\u6297\u4e71\u5e8f<\/span>
    \n self.<\/span>friends_sa[<\/span>fid]<\/span> =<\/span> fsa<\/p>\n

    \u8fd9\u79cd"\u65f6\u95f4\u6233\u53d6\u80dc"\u7684\u5408\u5e76\u89c4\u5219\u6709\u4e09\u4e2a\u597d\u5904：\u4e0d\u9700\u8981\u5168\u5c40\u65f6\u949f\u540c\u6b65\u3001\u4e0d\u9700\u8981\u53ef\u9760\u4f20\u8f93\u3001\u5929\u7136\u62b5\u6297\u6d88\u606f\u4e71\u5e8f\u548c\u91cd\u590d\u3002\u5bf9\u5206\u5e03\u5f0f\u96c6\u7fa4\u6765\u8bf4，\u8fd9\u662f\u6210\u672c\u6700\u4f4e\u7684\u4e00\u81f4\u6027\u673a\u5236\u3002<\/p>\n

    6.2 \u4fe1\u606f\u878d\u5408：\u628a\u90bb\u5c45\u7684\u6982\u7387\u7d2f\u52a0\u8d77\u6765<\/h4>\n

    \u62ff\u5230\u90bb\u5c45\u7684\u6001\u52bf\u540e，\u5148\u505a\u4e24\u4ef6\u4e8b\u3002\u7b2c\u4e00\u4ef6\u662f\u628a\u6240\u6709\u90bb\u5c45\u5bf9\u76ee\u6807 j \u7684\u62e6\u622a\u6982\u7387\u7d2f\u52a0，\u5f97\u5230"\u5df2\u7ecf\u5728\u6253 j \u7684\u53cb\u519b\u6982\u7387\u603b\u548c"：<\/p>\n

    g_p[<\/span>fsa.<\/span>target]<\/span> +=<\/span> fsa.<\/span>pj # \u6982\u7387\u7ebf\u6027\u7d2f\u52a0<\/span>
    \ng_l[<\/span>fsa.<\/span>target]<\/span> +=<\/span> np.<\/span>log(<\/span>1<\/span> –<\/span> fsa.<\/span>pj +<\/span> 1e-9<\/span>)<\/span> # \u5bf9\u6570\u57df\u7d2f\u52a0，\u7528\u4e8e\u8054\u5408\u6982\u7387<\/span><\/p>\n

    \u8fd9\u91cc\u7528\u4e86\u4e00\u4e2a\u5c0f\u6280\u5de7：\u8054\u5408\u5931\u8d25\u6982\u7387\u662f\u5404\u673a\u5931\u8d25\u6982\u7387\u7684\u4e58\u79ef，\u5728\u6570\u503c\u4e0a\u5bb9\u6613\u4e0b\u6ea2，\u6240\u4ee5\u653e\u5230\u5bf9\u6570\u57df\u505a\u7d2f\u52a0，\u9700\u8981\u65f6\u518d\u53d6\u6307\u6570\u3002\u7b2c\u4e8c\u4ef6\u4e8b\u662f\u6536\u96c6\u6240\u6709\u53cb\u519b\u5bf9\u76ee\u6807 j \u7684\u4ee3\u4ef7，\u7528\u4e8e\u8ba1\u7b97"\u51c6\u5165\u95e8\u69db"\u3002<\/p>\n

    6.3 \u51c6\u5165\u95e8\u69db：\u7528\u865a\u62df\u5e2d\u4f4d\u81ea\u52a8\u786e\u5b9a\u7b2c K \u540d<\/h4>\n

    \u8fd9\u662f\u6574\u5957\u65b9\u6cd5\u91cc\u8bbe\u8ba1\u611f\u6700\u5f3a\u7684\u4e00\u5904\u3002\u96c6\u7fa4\u4e0d\u5e94\u8be5\u8ba9\u6240\u6709\u9632\u5fa1\u673a\u6324\u5411\u540c\u4e00\u4e2a\u9ad8\u4ef7\u503c\u76ee\u6807，\u6240\u4ee5\u9700\u8981\u7ed9\u6bcf\u4e2a\u76ee\u6807\u8bbe\u4e00\u4e2a\u62e5\u585e\u95e8\u69db：\u53ea\u6709\u5f53\u81ea\u5df1\u7684\u4ee3\u4ef7\u660e\u663e\u4f4e\u4e8e\u95e8\u69db\u65f6，\u624d\u5141\u8bb8"\u6324\u8fdb\u53bb"\u3002<\/p>\n

    \u95e8\u69db\u600e\u4e48\u5b9a？\u76f4\u89c9\u4e0a\u5e94\u8be5\u662f"\u5f53\u524d\u4e89\u593a\u8fd9\u4e2a\u76ee\u6807\u7684\u6240\u6709\u53cb\u519b\u4e2d，\u7b2c K \u540d\u7684\u4ee3\u4ef7"\u2014\u2014\u56e0\u4e3a\u524d K \u540d\u4ee5\u5185\u662f\u5408\u7406\u8d1f\u8f7d，\u8d85\u51fa K \u540d\u5c31\u5e94\u8be5\u88ab\u529d\u9000\u3002\u4f46\u5206\u5e03\u5f0f\u8282\u70b9\u4e0d\u77e5\u9053\u5168\u5c40\u6392\u540d\u3002\u5b9e\u73b0\u4e0a\u7528\u4e86\u4e00\u4e2a\u5f88\u6734\u7d20\u7684\u5904\u7406：\u628a\u5df2\u7ecf\u6536\u96c6\u5230\u7684\u771f\u5b9e\u4ee3\u4ef7\u548c K \u4e2a\u865a\u62df\u7684\u9ad8\u4ee3\u4ef7\u5e2d\u4f4d（9999.0） \u6df7\u5728\u4e00\u8d77\u6392\u5e8f，\u53d6\u7b2c K \u4e2a\u4f5c\u4e3a\u95e8\u69db：<\/p>\n

    K =<\/span> max<\/span>(<\/span>1<\/span>,<\/span> int<\/span>(<\/span>len<\/span>(<\/span>friends)<\/span> \/<\/span> len<\/span>(<\/span>enemies)<\/span> +<\/span> 0.5<\/span>)<\/span>)<\/span> # \u81ea\u9002\u5e94\u706b\u529b\u5206\u914d\u6bd4\u4f8b，\u56db\u820d\u4e94\u5165<\/span><\/p>\n

    for<\/span> j in<\/span> range<\/span>(<\/span>self.<\/span>NUM_SLOTS +<\/span> 1<\/span>)<\/span>:<\/span>
    \n all_bids =<\/span> sorted<\/span>(<\/span>target_costs_pool[<\/span>j]<\/span> +<\/span> [<\/span>9999.0<\/span>]<\/span> *<\/span> K)<\/span> # \u6df7\u5165 K \u4e2a\u865a\u62df\u9ad8\u4ef7\u5e2d\u4f4d<\/span>
    \n L_i[<\/span>j]<\/span> =<\/span> all_bids[<\/span>K –<\/span> 1<\/span>]<\/span> # \u6392\u5e8f\u540e\u7b2c K \u540d\u5373\u95e8\u69db<\/span><\/p>\n

    \u8fd9\u6837\u505a\u7684\u6548\u679c\u662f：\u5f53\u67d0\u4e2a\u76ee\u6807\u7684\u4e89\u593a\u8005\u4e0d\u8db3 K \u4e2a\u65f6，\u95e8\u69db\u4f1a\u81ea\u52a8\u843d\u5230\u865a\u62df\u5e2d\u4f4d\u7684\u9ad8\u4ef7\u4e0a，\u7b49\u4e8e"\u4e0d\u8bbe\u9650"；\u4e00\u65e6\u4e89\u593a\u8005\u8d85\u8fc7 K \u4e2a，\u95e8\u69db\u5c31\u843d\u5728\u771f\u5b9e\u7684\u7b2c K \u540d\u4ee3\u4ef7\u4e0a，\u540e\u6765\u8005\u53ea\u8981\u4ee3\u4ef7\u9ad8\u4e8e\u5b83\u5c31\u4f1a\u88ab\u529d\u9000\u3002\u7528 K \u4e2a\u865a\u62df\u5e2d\u4f4d\u66ff\u4ee3\u4e86\u5168\u5c40\u6392\u5e8f，\u628a\u4e00\u4e2a\u9700\u8981\u5168\u5c40\u4fe1\u606f\u7684\u5224\u65ad，\u7b80\u5316\u6210\u4e86\u4e00\u6b21\u5c40\u90e8\u6392\u5e8f\u3002<\/p>\n

    6.4 \u8bc4\u4f30\u4ee3\u4ef7\u51fd\u6570：\u4e09\u9879\u52a0\u6743<\/h4>\n

    \u6700\u540e，\u6bcf\u67b6\u9632\u5fa1\u673a\u5bf9\u6bcf\u4e2a\u53ef\u89c1\u76ee\u6807（\u5916\u52a0\u4e00\u4e2a"\u5f85\u547d"\u9009\u9879）\u8ba1\u7b97\u8bc4\u4f30\u4ee3\u4ef7：<\/p>\n

    # \u76f4\u63a5\u4ee3\u4ef7：\u5230\u76ee\u6807\u7684\u8ddd\u79bb<\/span>
    \nterm1 =<\/span> W_i[<\/span>j]<\/span><\/p>\n

    # \u62e5\u585e\u4ee3\u4ef7：\u53ea\u6709\u5f53\u81ea\u5df1\u4ee3\u4ef7\u9ad8\u4e8e\u95e8\u69db\u65f6\u624d\u751f\u6548（ReLU \u5f62\u5f0f）<\/span>
    \nterm2 =<\/span> self.<\/span>parm[<\/span>"lambda_lf"<\/span>]<\/span> *<\/span> (<\/span>W_i[<\/span>j]<\/span> –<\/span> L_i[<\/span>j]<\/span> +<\/span> abs<\/span>(<\/span>W_i[<\/span>j]<\/span> –<\/span> L_i[<\/span>j]<\/span>)<\/span>)<\/span><\/p>\n

    # \u8f6c\u79fb\u4ee3\u4ef7：\u5269\u4f59\u6d41\u5206\u914d\u7684\u6700\u4f18\u503c + \u4e8c\u6b21\u6b63\u5219<\/span>
    \nterm3 =<\/span> np.<\/span>dot(<\/span>C_i[<\/span>j,<\/span> :<\/span>]<\/span>,<\/span> n_row)<\/span> +<\/span> (<\/span>self.<\/span>parm[<\/span>"gamma"<\/span>]<\/span> \/<\/span> 2.0<\/span>)<\/span> *<\/span> np.<\/span>sum<\/span>(<\/span>n_row **<\/span> 2<\/span>)<\/span><\/p>\n

    eval_cost =<\/span> term1 +<\/span> term2 +<\/span> term3<\/p>\n

    \u4e09\u9879\u5206\u522b\u5bf9\u5e94\u4e09\u79cd\u63a7\u5236\u610f\u56fe：term1 \u8ba9\u9632\u5fa1\u673a\u5c31\u8fd1\u62e6\u622a，\u51cf\u5c11\u98de\u884c\u65f6\u95f4 term2 \u6291\u5236\u8fc7\u5ea6\u96c6\u4e2d（x + |x| \u662f ReLU \u7684\u5199\u6cd5，x > 0 \u65f6\u53d6 2x，\u5426\u5219\u4e3a 0，\u5373\u53ea\u6709"\u8d85\u51fa\u95e8\u69db"\u624d\u53d7\u7f5a）；term3 \u628a"\u62e6\u5b8c\u4e4b\u540e\u5269\u4f59\u8d44\u6e90\u53bb\u54ea"\u7684\u4ee3\u4ef7\u63d0\u524d\u7b97\u8fdb\u5f53\u524d\u51b3\u7b56\u3002\u6c42\u6700\u5c0f\u4ee3\u4ef7\u7684\u76ee\u6807，\u82e5\u6700\u5c0f\u7684\u662f"\u5f85\u547d"\u9009\u9879，\u5219\u8fd4\u56de\u8f68\u9053\u9a7b\u7559\u4f4d\u7f6e\u3002<\/p>\n

    6.5 \u51b3\u7b56\u4e3b\u5faa\u73af<\/h4>\n

    \u628a\u4e0a\u9762\u7684\u73af\u8282\u4e32\u8d77\u6765，\u5355\u673a\u7684\u51b3\u7b56\u4f2a\u4ee3\u7801\u662f：<\/p>\n

    \u8f93\u5165: \u81ea\u8eab\u72b6\u6001\u3001\u5c40\u90e8\u53cb\u519b\u6001\u52bf\u8868\u3001\u5c40\u90e8\u654c\u519b\u5217\u8868\u3001\u5f85\u547d\u4f4d\u7f6e
    \n1. \u81ea\u9002\u5e94\u6bd4\u4f8b K \u2190 max(1, round(\u53cb\u519b\u6570 \/ \u654c\u519b\u6570))
    \n2. \u904d\u5386\u53cb\u519b\u6001\u52bf\u8868:
    \n g_p[j] += pj # \u6982\u7387\u7d2f\u52a0
    \n g_l[j] += log(1 – pj) # \u5bf9\u6570\u57df\u7d2f\u52a0
    \n pool[j].append(\u4ee3\u4ef7) # \u6536\u96c6\u4ee3\u4ef7
    \n3. \u8ba1\u7b97\u95e8\u69db L_i[j] \u2190 \u6df7\u5165 K \u4e2a\u865a\u62df\u5e2d\u4f4d\u540e\u7684\u7b2c K \u540d\u4ee3\u4ef7
    \n4. \u5bf9\u6bcf\u4e2a\u53ef\u89c1\u76ee\u6807 j:
    \n P_i[j] \u2190 \u67e5\u627e\u8868\u67e5\u8be2\u62e6\u622a\u6982\u7387（\u542b\u5939\u89d2\u6298\u53e0\u4e0e\u622a\u65ad\u5230 [0.01, 0.99]）
    \n W_i[j] \u2190 \u03bb_a1 \u00d7 0.001 \u00d7 d_ij
    \n C_i[j, :] \u2190 \u03bb_b1 \u00d7 0.001 \u00d7 \u76ee\u6807\u95f4\u8ddd\u79bb
    \n s_val \u2190 \u81ea\u8eab\u6982\u7387\u5360\u6bd4 \u00d7 \u8054\u5408\u6210\u529f\u6982\u7387
    \n n_row \u2190 \u6ce8\u6c34\u6295\u5f71(1 \u2212 s_val, C_i[j,:], \u03b3)
    \n eval_cost \u2190 term1 + term2 + term3
    \n5. \u53d6\u8bc4\u4f30\u4ee3\u4ef7\u6700\u5c0f\u7684\u76ee\u6807；\u82e5\u4e3a"\u5f85\u547d"\u5219\u8fd4\u56de None
    \n6. \u66f4\u65b0\u672c\u673a\u6001\u52bf\u8868\u9879（\u76ee\u6807\u7f16\u53f7\u3001\u62e6\u622a\u6982\u7387\u3001\u65f6\u95f4\u6233），\u4f9b\u90bb\u5c45\u5408\u5e76<\/p>\n

    \u6ce8\u610f\u6700\u540e\u4e00\u6b65\u4f1a\u628a\u81ea\u5df1\u7684\u9009\u62e9\u5199\u8fdb\u6001\u52bf\u8868\u5e76\u5e7f\u64ad\u51fa\u53bb\u3002\u4e0b\u4e00\u8f6e\u51b3\u7b56\u65f6，\u90bb\u5c45\u7684\u6001\u52bf\u8868\u91cc\u5c31\u6709\u4e86\u8fd9\u6761\u4fe1\u606f，g_p\u3001g_l \u548c\u95e8\u69db\u90fd\u4f1a\u968f\u4e4b\u66f4\u65b0\u3002\u6574\u4e2a\u96c6\u7fa4\u5c31\u662f\u901a\u8fc7\u8fd9\u79cd**\u201c\u5404\u81ea\u51b3\u7b56 \u2192 \u5e7f\u64ad\u7ed3\u679c \u2192 \u90bb\u5c45\u5408\u5e76 \u2192 \u91cd\u65b0\u51b3\u7b56\u201d**\u7684\u8fed\u4ee3，\u5728\u6ca1\u6709\u4efb\u4f55\u4e2d\u5fc3\u8282\u70b9\u7684\u60c5\u51b5\u4e0b\u9010\u6b65\u6536\u655b\u5230\u4e92\u4e0d\u51b2\u7a81\u7684\u5206\u914d\u3002<\/p>\n

    \u4e03\u3001\u53c2\u6570\u8bf4\u660e\u4e0e\u8c03\u53c2\u601d\u8def<\/h3>\n

    \u51b3\u7b56\u5668\u66b4\u9732\u7684\u4e3b\u8981\u53c2\u6570\u6709\u4e94\u4e2a，\u542b\u4e49\u548c\u8c03\u53c2\u65b9\u5411\u5982\u4e0b：<\/p>\n\n\u53c2\u6570\u542b\u4e49\u8c03\u5927\u8c03\u5c0f<\/tr>\n\n\n\n\n\n\n
    lambda_a1<\/td>\n\u76f4\u63a5\u8ddd\u79bb\u4ee3\u4ef7\u6743\u91cd<\/td>\n\u66f4\u4fdd\u5b88，\u4f18\u5148\u5c31\u8fd1\u62e6\u622a<\/td>\n\u66f4\u6fc0\u8fdb，\u613f\u610f\u8fdc\u7a0b\u5954\u88ad<\/td>\n<\/tr>\n
    lambda_b1<\/td>\n\u76ee\u6807\u95f4\u8f6c\u79fb\u4ee3\u4ef7\u6743\u91cd<\/td>\n\u66f4\u91cd\u89c6\u62e6\u622a\u540e\u7684\u8d44\u6e90\u63a5\u7eed<\/td>\n\u66f4\u5173\u6ce8\u5f53\u524d\u4e00\u51fb<\/td>\n<\/tr>\n
    lambda_lf<\/td>\n\u62e5\u585e\u60e9\u7f5a\u6743\u91cd<\/td>\n\u5f3a\u70c8\u6291\u5236\u624e\u5806<\/td>\n\u5f31\u5316\u6210\u8fd1\u4f3c\u7eaf\u8d2a\u5fc3<\/td>\n<\/tr>\n
    gamma<\/td>\n\u4e8c\u6b21\u6b63\u5219\u7cfb\u6570<\/td>\n\u5269\u4f59\u6d41\u66f4\u644a\u5e73，\u5206\u6563\u8f6c\u79fb<\/td>\n\u8f6c\u79fb\u66f4\u96c6\u4e2d\u4e8e\u4f4e\u4ee3\u4ef7\u76ee\u6807<\/td>\n<\/tr>\n
    by_b<\/td>\n\u5f85\u547d\u57fa\u51c6\u4ee3\u4ef7<\/td>\n\u66f4\u503e\u5411\u9a7b\u7559\u5f85\u547d\u3001\u4fdd\u5b58\u5b9e\u529b<\/td>\n\u66f4\u503e\u5411\u4e3b\u52a8\u51fa\u51fb<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    \u8c03\u53c2\u7ecf\u9a8c\u4e0a，lambda_lf \u662f\u5f71\u54cd\u6700\u5927\u7684\u4e00\u4e2a：\u5b83\u76f4\u63a5\u51b3\u5b9a"\u5141\u8bb8\u591a\u5c11\u67b6\u9632\u5fa1\u673a\u6253\u540c\u4e00\u4e2a\u76ee\u6807"\u3002\u8c03\u5f97\u592a\u5c0f，\u96c6\u7fa4\u4f1a\u50cf\u7eaf\u8d2a\u5fc3\u4e00\u6837\u624e\u5806；\u8c03\u5f97\u592a\u5927，\u4f1a\u51fa\u73b0\u5927\u91cf\u9632\u5fa1\u673a\u5b81\u53ef\u5f85\u547d\u4e5f\u4e0d\u51fa\u51fb\u3001\u5bfc\u81f4\u6f0f\u9632\u3002\u5b9e\u8df5\u4e2d\u5efa\u8bae\u5148\u56fa\u5b9a lambda_a1 \u548c by_b，\u518d\u7528\u8d1d\u53f6\u65af\u5f0f\u641c\u7d22\u626b lambda_lf \u548c gamma\u3002<\/p>\n

    \u53c2\u6570\u8fd8\u53ef\u4ee5\u901a\u8fc7\u73af\u5883\u53d8\u91cf\u6ce8\u5165，\u65b9\u4fbf\u6279\u91cf\u5b9e\u9a8c：<\/p>\n

    if<\/span> "DDFO_OPT_PARAMS"<\/span> in<\/span> os.<\/span>environ:<\/span>
    \n opt_params =<\/span> json.<\/span>loads(<\/span>os.<\/span>environ[<\/span>"DDFO_OPT_PARAMS"<\/span>]<\/span>)<\/span>
    \n self.<\/span>parm.<\/span>update(<\/span>opt_params)<\/span><\/p>\n

    \u516b\u3001\u8e29\u5751\u8bb0\u5f55<\/h3>\n

    \u5751\u4e00：\u62e6\u622a\u534a\u5f84\u548c\u4eff\u771f\u65f6\u957f\u5fc5\u987b\u4e0e\u7ed3\u8bba\u5bf9\u9f50\u3002 \u8bba\u6587\u5b9e\u9a8c\u914d\u7f6e\u4e0e\u793a\u4f8b\u811a\u672c\u7684\u9ed8\u8ba4\u503c\u5e76\u4e0d\u5b8c\u5168\u4e00\u81f4，\u4f8b\u5982\u62e6\u622a\u5224\u5b9a\u534a\u5f84\u3001\u4eff\u771f\u65f6\u957f（250 \u79d2 vs 100 \u79d2）\u3001\u9ed8\u8ba4\u51b3\u7b56\u7b97\u6cd5（DFMC vs CBAA）\u90fd\u53ef\u80fd\u6709\u5dee\u5f02\u3002\u62ff\u7740\u793a\u4f8b\u811a\u672c\u8dd1\u51fa\u6765\u7684\u6570\u5b57\u53bb\u6838\u5bf9\u8bba\u6587\u8868\u683c，\u51e0\u4e4e\u4e00\u5b9a\u5bf9\u4e0d\u4e0a\u3002\u7ed3\u8bba\u53ea\u80fd\u548c\u4ea7\u751f\u5b83\u7684\u90a3\u5957\u914d\u7f6e\u7ed1\u5b9a，\u8de8\u914d\u7f6e\u6bd4\u8f83\u662f\u6ca1\u6709\u610f\u4e49\u7684\u3002<\/p>\n

    \u5751\u4e8c：\u968f\u673a\u79cd\u5b50\u4e0d\u56fa\u5b9a\u3002 \u573a\u666f\u521d\u59cb\u5316\u3001\u51b3\u7b56\u65f6\u523b\u7684\u6296\u52a8\u3001\u76ee\u6807\u70b9\u91c7\u6837\u90fd\u7528\u4e86\u968f\u673a\u6570\u3002\u4e0d\u56fa\u5b9a\u79cd\u5b50\u7684\u8bdd，\u540c\u4e00\u5957\u7b97\u6cd5\u4e24\u6b21\u8fd0\u884c\u7684\u62e6\u622a\u6570\u53ef\u80fd\u5dee\u51fa\u4e00\u67b6\u4ee5\u4e0a，\u770b\u8d77\u6765\u50cf"\u7b97\u6cd5\u4e0d\u7a33\u5b9a"，\u5176\u5b9e\u53ea\u662f\u91c7\u6837\u566a\u58f0\u3002\u4efb\u4f55\u5bf9\u6bd4\u5b9e\u9a8c\u90fd\u5e94\u8be5\u62a5\u5747\u503c\u548c\u6807\u51c6\u5dee，\u800c\u4e0d\u662f\u5355\u6b21\u7ed3\u679c\u3002<\/p>\n

    \u5751\u4e09：\u6982\u7387\u6a21\u578b\u7684\u5916\u63a8\u98ce\u9669\u3002 \u67e5\u627e\u8868\u5728 fill_value=None \u4e0b\u5141\u8bb8\u5916\u63a8，\u8fd9\u610f\u5473\u7740\u8d85\u51fa\u8bad\u7ec3\u6570\u636e\u8986\u76d6\u8303\u56f4\u7684\u67e5\u8be2\u70b9\u4f1a\u5f97\u5230\u4e00\u4e2a\u7531\u8fb9\u7f18\u503c\u5ef6\u4f38\u51fa\u6765\u7684\u6982\u7387\u3002\u5982\u679c\u76ee\u6807\u8ddd\u79bb\u8fdc\u8d85\u8bad\u7ec3\u65f6\u7684\u91c7\u6837\u8303\u56f4，\u8fd9\u4e2a\u6982\u7387\u5e76\u4e0d\u53ef\u4fe1\u3002\u5de5\u7a0b\u4e0a\u5e94\u8be5\u5728\u67e5\u8be2\u524d\u505a\u8303\u56f4\u68c0\u67e5，\u8d85\u754c\u65f6\u9000\u5316\u4e3a\u4e00\u4e2a\u4fdd\u5b88\u5e38\u6570\u3002<\/p>\n

    \u5751\u56db：\u72ec\u7acb\u6210\u529f\u5047\u8bbe\u3002 \u8054\u5408\u6982\u7387\u516c\u5f0f\u9690\u542b\u4e86"\u5404\u9632\u5fa1\u673a\u7684\u62e6\u622a\u4e8b\u4ef6\u76f8\u4e92\u72ec\u7acb"\u3002\u8fd9\u5728\u4eff\u771f\u91cc\u6210\u7acb，\u4f46\u5728\u771f\u5b9e\u573a\u666f\u4e2d，\u591a\u673a\u5171\u540c\u673a\u52a8\u3001\u5171\u4eab\u7684\u611f\u77e5\u8bef\u5dee\u3001\u6c14\u52a8\u8026\u5408\u90fd\u4f1a\u5f15\u5165\u76f8\u5173\u6027，\u5b9e\u9645\u8054\u5408\u6982\u7387\u4f1a\u4f4e\u4e8e\u516c\u5f0f\u7ed9\u51fa\u7684\u503c\u3002\u8fd9\u5957\u6846\u67b6\u7ed9\u51fa\u7684\u662f\u4e50\u89c2\u4e0a\u754c，\u4e0d\u662f\u7cbe\u786e\u9884\u6d4b\u3002<\/p>\n

    \u5751\u4e94：\u6a21\u578b\u6587\u4ef6\u7684\u5b89\u5168\u6027\u3002 \u6982\u7387\u6a21\u578b\u548c\u67e5\u627e\u8868\u90fd\u662f\u5e8f\u5217\u5316\u5bf9\u8c61，\u52a0\u8f7d\u65f6\u53ef\u80fd\u6267\u884c\u4efb\u610f\u4ee3\u7801\u3002\u751f\u4ea7\u73af\u5883\u5e94\u8be5\u6362\u6210\u5b89\u5168\u7684\u3001\u7ecf\u8fc7\u6821\u9a8c\u7684\u6570\u636e\u683c\u5f0f，\u81f3\u5c11\u8981\u505a\u54c8\u5e0c\u6821\u9a8c\u5e76\u9650\u5b9a\u6765\u6e90\u3002<\/p>\n

    \u5751\u516d：\u89d2\u5ea6\u5904\u7406\u3002 \u5939\u89d2\u5728\u51e0\u4f55\u4e0a\u662f\u5bf9\u79f0\u7684，\u4f46\u539f\u59cb\u8ba1\u7b97\u4f1a\u843d\u5728 [0, 2\u03c0]\u3002\u5982\u679c\u4e0d\u5728\u67e5\u8be2\u524d\u6298\u53e0\u5230 [0, \u03c0]，\u540c\u4e00\u4e2a\u51e0\u4f55\u5173\u7cfb\u4f1a\u56e0\u4e3a\u6b63\u8d1f\u53f7\u4e0d\u540c\u67e5\u5230\u4e24\u4e2a\u4e0d\u540c\u7684\u6982\u7387\u503c，\u8868\u73b0\u4e3a"\u51b3\u7b56\u7ed3\u679c\u6765\u56de\u6296"\u3002<\/p>\n

    \u4e5d\u3001\u7ed3\u679c\u5bf9\u6bd4<\/h3>\n

    \u5728\u540c\u7b49\u4eff\u771f\u914d\u7f6e\u4e0b，\u4e09\u7c7b\u5206\u914d\u7b56\u7565\u7684\u8868\u73b0\u5927\u81f4\u5982\u4e0b（\u6570\u636e\u4e3a\u591a\u6b21\u8fd0\u884c\u7684\u5747\u503c\u4e0e\u6807\u51c6\u5dee）：<\/p>\n\n\u65b9\u6cd5\u5e73\u5747\u62e6\u622a\u5165\u4fb5\u673a\u6570\u91cf\u5e73\u5747\u6bcf\u667a\u80fd\u4f53\u6bcf\u51b3\u7b56\u5468\u671f\u8017\u65f6<\/tr>\n\n\n\n\n
    \u5206\u5e03\u5f0f\u62cd\u5356（CBAA）<\/td>\n9.762 \u00b1 1.137<\/td>\n4.109 \u00b1 0.134 ms<\/td>\n<\/tr>\n
    \u6539\u8fdb\u62cd\u5356（MTCBAA）<\/td>\n10.254 \u00b1 1.208<\/td>\n4.514 \u00b1 0.109 ms<\/td>\n<\/tr>\n
    \u6982\u7387\u6d41\u5171\u8bc6（\u672c\u6587\u6846\u67b6）<\/td>\n10.698 \u00b1 1.190<\/td>\n4.967 \u00b1 0.173 ms<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    \u51e0\u70b9\u89e3\u8bfb：<\/p>\n

      \n
    • \u62e6\u622a\u6570\u91cf\u4e0a，\u6982\u7387\u6d41\u6846\u67b6\u76f8\u5bf9\u57fa\u7840\u62cd\u5356\u63d0\u5347\u7ea6 9.6%，\u76f8\u5bf9\u6539\u8fdb\u62cd\u5356\u63d0\u5347\u7ea6 4.3%\u3002\u63d0\u5347\u5e45\u5ea6\u4e0d\u662f\u6570\u91cf\u7ea7\u7684，\u8fd9\u7b26\u5408\u9884\u671f\u2014\u2014\u5206\u914d\u7b56\u7565\u53ea\u80fd\u4f18\u5316"\u8d44\u6e90\u600e\u4e48\u7528"，\u4e0d\u80fd\u7a81\u7834\u7269\u7406\u62e6\u622a\u80fd\u529b\u7684\u4e0a\u9650\u3002<\/li>\n
    • \u5355\u6b21\u51b3\u7b56\u8017\u65f6\u4ece 4.1 ms \u4e0a\u5347\u5230 5.0 ms，\u589e\u52a0\u4e86\u7ea6 21%\u3002\u8fd9\u662f"\u591a\u7b97\u4e00\u70b9\u6982\u7387\u548c\u8f6c\u79fb\u4ee3\u4ef7"\u6362\u6765\u7684\u4ee3\u4ef7，\u76f8\u5bf9\u4e8e 500 ms \u7684\u51b3\u7b56\u5468\u671f，\u5360\u6bd4\u4e0d\u5230 1%，\u5b8c\u5168\u53ef\u4ee5\u63a5\u53d7\u3002<\/li>\n
    • \u89c4\u6a21\u540c\u6b65\u589e\u5927\u65f6，\u6982\u7387\u6d41\u6846\u67b6\u7684\u62e6\u622a\u7387\u4fdd\u6301\u76f8\u5bf9\u7a33\u5b9a，\u800c\u7eaf\u8ddd\u79bb\u65b9\u6cd5\u4f1a\u968f\u7740\u96c6\u7fa4\u89c4\u6a21\u4e0a\u5347\u800c\u660e\u663e\u9000\u5316\u3002\u539f\u56e0\u5728\u4e8e\u540e\u8005\u7f3a\u4e4f\u6291\u5236\u624e\u5806\u7684\u673a\u5236，\u89c4\u6a21\u8d8a\u5927\u3001\u91cd\u590d\u5206\u914d\u7684\u6d6a\u8d39\u8d8a\u4e25\u91cd\u3002<\/li>\n<\/ul>\n

      \u5341\u3001\u5c40\u9650\u4e0e\u9002\u7528\u8fb9\u754c<\/h3>\n

      \u8fd9\u5957\u5b9e\u73b0\u6709\u660e\u786e\u7684\u9002\u7528\u8fb9\u754c，\u5199\u5728\u8fd9\u91cc\u662f\u4e3a\u4e86\u907f\u514d\u8bef\u7528：<\/p>\n

        \n
      • \u9002\u7528\u5bf9\u8c61\u662f\u4f4e\u7a7a\u3001\u4f4e\u81f3\u4e2d\u7b49\u901f\u5ea6\u7684\u65cb\u7ffc\u6216\u8f7b\u578b\u56fa\u5b9a\u7ffc\u65e0\u4eba\u673a，\u4e0d\u9002\u7528\u4e8e\u9ad8\u901f\u5de1\u822a\u5bfc\u5f39\u3001\u5f39\u9053\u76ee\u6807\u7b49\u8d85\u51fa\u8be5\u7c7b\u65e0\u4eba\u673a\u52a8\u529b\u5b66\u80fd\u529b\u7684\u76ee\u6807\u3002<\/li>\n
      • \u8fd0\u52a8\u6a21\u578b\u548c\u63a7\u5236\u5668\u90fd\u662f\u7b80\u5316\u6a21\u578b，\u4e0d\u80fd\u66ff\u4ee3\u771f\u5b9e\u98de\u63a7\u3001\u907f\u969c\u4e0e\u901a\u4fe1\u534f\u8bae\u6808\u3002<\/li>\n
      • \u6982\u7387\u5148\u9a8c\u4f9d\u8d56\u8bad\u7ec3\u6570\u636e\u7684\u8986\u76d6\u8303\u56f4，\u8d85\u51fa\u5206\u5e03\u7684\u5916\u63a8\u7ed3\u8bba\u9700\u8981\u8c28\u614e\u89e3\u91ca\u3002<\/li>\n
      • \u901a\u4fe1\u4e0e\u6001\u52bf\u878d\u5408\u662f\u8f6f\u4ef6\u5c42\u9762\u7684\u62bd\u8c61，\u4e0d\u7b49\u4ef7\u4e8e\u771f\u5b9e\u65e0\u7ebf\u94fe\u8def（\u6ca1\u6709\u8003\u8651\u4e22\u5305\u3001\u65f6\u5ef6\u6296\u52a8\u3001\u591a\u5f84）\u3002<\/li>\n
      • \u6ca1\u6709\u786c\u4ef6\u5728\u73af\u3001\u5b9e\u673a\u98de\u884c\u6216\u771f\u5b9e\u4f20\u611f\u5668\u9a8c\u8bc1\u3002<\/li>\n
      • \u4eff\u771f\u6b65\u9891 10 Hz\u3001\u51b3\u7b56\u9891\u7387 2 Hz \u662f\u8bba\u6587\u8bbe\u5b9a，\u5b9e\u9645\u7cfb\u7edf\u82e5\u964d\u4f4e\u9891\u7387，\u9700\u91cd\u65b0\u8bc4\u4f30\u6536\u655b\u6027\u3002<\/li>\n<\/ul>\n

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