{"id":67662,"date":"2026-01-29T01:33:29","date_gmt":"2026-01-28T17:33:29","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/67662.html"},"modified":"2026-01-29T01:33:29","modified_gmt":"2026-01-28T17:33:29","slug":"%e6%9c%ba%e5%99%a8%e4%ba%ba%e6%a0%87%e5%87%86dh%ef%bc%88sdh%ef%bc%89%e4%b8%8e%e6%94%b9%e8%bf%9bdh%ef%bc%88mdh%ef%bc%89","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/67662.html","title":{"rendered":"\u673a\u5668\u4eba\u6807\u51c6DH\uff08SDH\uff09\u4e0e\u6539\u8fdbDH\uff08MDH\uff09"},"content":{"rendered":"

\u9996\u5148\u8bf4\u4e00\u4e0b\u4e3a\u4ec0\u4e48\u8981\u5199\u8fd9\u4e00\u7bc7\u535a\u5ba2，\u5c31\u662f\u4e3a\u4e86\u63d0\u9192\u5927\u5bb6\u8981\u660e\u786e\u533a\u5206\u6807\u51c6DH\u548c\u6539\u8fdbDH\u3002\u5f88\u591a\u673a\u5668\u4eba\u521d\u5b66\u8005\u53ea\u77e5\u9053\u7528DH\u6cd5\u5efa\u7acb\u4e32\u8054\u673a\u5668\u4eba\u8fde\u6746\u5750\u6807\u7cfb，\u7136\u540e\u5728\u770b\u4e66\u6216\u8005\u4f7f\u7528DH\u7684\u65f6\u5019\u5f88\u7cca\u6d82\u7684\u5c31\u6a21\u7cca\u4e86\u8fd9\u6807\u51c6DH\u548c\u6539\u8fdbDH\u7684\u533a\u522b，\u6700\u5927\u7684\u5751\u5c31\u662f：\u4e00\u4e9b\u6bd4\u8f83\u8001\u7684\u673a\u5668\u4eba\u5b66\u6559\u79d1\u4e66\u7528\u7684\u662f\u6807\u51c6DH，\u800c\u73b0\u5728\u6bd4\u8f83\u65b0\u7684\u673a\u5668\u4eba\u4e66\u6216\u8005\u8bf4\u6211\u4eec\u5927\u90e8\u5206\u7528\u7684\u90fd\u662f\u6539\u8fdbDH，\u8fd9\u5c31\u5bfc\u81f4\u8001\u7684\u6559\u79d1\u4e66\u91cc\u9762\u7684\u4e00\u4e9b\u516c\u5f0f\u63a8\u5bfc\u548c\u65b0\u7684\u7f51\u4e0a\u627e\u7684\u4ee3\u7801\u4e0d\u4e00\u81f4，\u5c31\u4f1a\u6bd4\u8f83\u9ebb\u70e6\u3002<\/p>\n

\u4e00：\u6539\u8fdbDH\u6cd5<\/h2>\n

\u5efa\u7acb\u8fde\u6746\u5750\u6807\u7cfb：<\/p>\n

\"\"<\/p>\n

\u4f7f\u7528\u6539\u8fdbD-H\u53c2\u6570，\u5c06\"\"\u5750\u6807\u7cfb\u5b9a\u4e49\u5728i\"\"\u8fde\u6746\u7684\u524d\u7aef\u5173\u8282：<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\u4e8c：\u6807\u51c6DH\u4e0e\u6539\u8fdbDH\u6cd5\u7684\u533a\u522b<\/h3>\n

\u6211\u4eec\u77e5\u9053\u4e00\u4e2a\u8fde\u6746\u6709\u4e24\u7aef，\u4e00\u7aef\u79bb\u57fa\u5ea7\u8fd1，\u4e00\u7aef\u79bb\u57fa\u5ea7\u8fdc\u3002\u7b80\u5355\u7684\u6765\u8bf4，\u6807\u51c6DH\u5c06\u5750\u6807\u7cfbi\u5efa\u7acb\u5728\u8fde\u6746i\u79bb\u57fa\u5ea7\u8fd1\u7684\u4e00\u7aef，\u6539\u8fdbDH\u5efa\u7acb\u5728\u79bb\u57fa\u5ea7\u8fdc\u7684\u4e00\u7aef\u3002<\/p>\n

2.1 \u673a\u5668\u4eba\u8fde\u6746\u4e0e\u5173\u8282\u7684\u6807\u53f7<\/p>\n

\u5148\u6807\u53f7，\u518d\u5efa\u7cfb\u3002<\/p>\n

\u8fde\u6746\u7f16\u53f7：\u57fa\u5ea7\u4e3a\u67460，\u4ece\u57fa\u5ea7\u5f80\u540e\u4f9d\u6b21\u5b9a\u4e49\u4e3a\u67461，\u67462，\u2026，\u6746i;<\/p>\n

\u5173\u8282\u7f16\u53f7：\u6746i\u79bb\u57fa\u5ea7\u8fd1\u7684\u4e00\u7aef（\u8fd1\u7aef）\u7684\u5173\u8282\u4e3a\u5173\u8282i，\u8fdc\u7684\u4e00\u7aef（\u8fdc\u7aef）\u4e3a\u5173\u8282i+1\u3002<\/p>\n

\u4e3a\u4fbf\u4e8e\u7406\u89e3，\u8fd9\u91cc\u6211\u628a\u8fde\u6746\u7684\u8fd1\u7aef\u7528\u7eff\u8272\u8868\u793a，\u8fdc\u7aef\u7528\u6a59\u8272\u8868\u793a，\u4e14\u8fdc\u7aef\u9a71\u52a8\u8fd1\u7aef\u8f6c\u52a8\u3002\u5927\u5bb6\u53ea\u8981\u8bb0\u4f4f\u4e00\u53e5\u8bdd，\u8fde\u6746\u8fd1\u7aef\u5173\u8282\u7684\u6807\u53f7\u548c\u8fde\u6746\u6807\u53f7\u662f\u4e00\u81f4\u7684\u3002<\/p>\n

\"\"\u200b<\/p>\n

\u56fe1\u8fde\u6746\u548c\u5173\u8282\u6807\u53f7<\/p>\n

2.2 \u4e24\u79cd\u5efa\u7cfb\u65b9\u6cd5\u7684\u533a\u522b<\/p>\n

\u533a\u522b\u4e00：\u8fde\u6746\u5750\u6807\u7cfb\u5efa\u7acb\u7684\u4f4d\u7f6e\u4e0d\u540c\u3002SDH\u65b9\u6cd5\u5c06\u8fde\u6746i\u7684\u5750\u6807\u7cfb\u56fa\u5b9a\u5728\u8fde\u6746\u7684\u8fdc\u7aef，MDH\u65b9\u6cd5\u628a\u8fde\u6746i\u7684\u5750\u6807\u7cfb\u56fa\u5b9a\u5728\u8fde\u6746\u7684\u8fd1\u7aef\u3002<\/span><\/p>\n

\"\"\u200b<\/p>\n

（a）SDH\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (b)MDH<\/p>\n

\u56fe2 \u5efa\u7cfb\u65b9\u6cd5\u7684\u4e0d\u540c<\/p>\n

\u533a\u522b\u4e8c：\u6267\u884c\u53d8\u6362\u7684\u7684\u987a\u5e8f\u4e0d\u540c\u3002\u6309\u7167SDH\u65b9\u6cd5\u53d8\u6362\u65f6\u56db\u4e2a\u53c2\u6570\u76f8\u4e58\u7684\u987a\u5e8f\u4f9d\u6b21\u4e3ad\u2014>\u03b8\u2014>a\u2014>\u03b1,\u800cMDH\u65b9\u6cd5\u5219\u6309\u7167\u03b1\u2014>a\u2014>\u03b8\u2014>d（\u6b63\u597d\u4e0eSDH\u76f8\u53cd）\u3002<\/p>\n

\u4e09：\u4e3a\u4ec0\u4e48\u8981\u7528\u6539\u8fdbDH\u6cd5，\u800c\u4e0d\u9009\u6807\u51c6DH\u6cd5<\/h4>\n

\u5bf9\u4e8e\u6811\u5f62\u7ed3\u6784\u6216\u8005\u95ed\u94fe\u673a\u6784\u7684\u673a\u5668\u4eba\u6765\u8bf4，\u6309\u7167SDH\u65b9\u6cd5\u5efa\u7acb\u7684\u8fde\u6746\u5750\u6807\u7cfb\u4f1a\u4ea7\u751f\u6b67\u4e49，\u56e0\u4e3aSDH\u7684\u5efa\u7cfb\u539f\u5219\u662f\u628a\u8fde\u6746i\u7684\u5750\u6807\u7cfb\u5efa\u7acb\u5728\u8fde\u6746\u7684\u8fdc\u7aef，\u5982\u56fe3(a)\u6240\u793a，\u8fd9\u5c31\u5bfc\u81f4\u8fde\u67460\u4e0a\u540c\u65f6\u51fa\u73b0\u4e86\u4e24\u4e2a\u5750\u6807\u7cfb\u3002\u800cMDH\u628a\u8fde\u6746\u5750\u6807\u7cfb\u5efa\u7acb\u5728\u6bcf\u4e2a\u8fde\u6746\u7684\u8fd1\u7aef，\u5219\u4e0d\u4f1a\u5750\u6807\u7cfb\u91cd\u5408\u7684\u60c5\u51b5，\u5982\u56fe3(b)\u6240\u793a,\u8fd9\u5c31\u514b\u670d\u4e86SDH\u65b9\u6cd5\u5efa\u7cfb\u7684\u7f3a\u70b9\u3002<\/p>\n

\"\"<\/p>\n

(a)SDH\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0（b）MDH<\/p>\n

\u56fe3 \u5750\u6807\u7cfb\u5206\u914d\u7684\u4e0d\u540c<\/p>\n

\u56db.\u603b\u7ed3<\/h2>\n

1.SDH\u9002\u5408\u5e94\u7528\u4e8e\u5f00\u94fe\u7ed3\u6784\u7684\u673a\u5668\u4eba；<\/p>\n

2.\u5f53\u4f7f\u7528SDH\u8868\u793a\u6811\u72b6\u6216\u95ed\u94fe\u7ed3\u6784\u7684\u673a\u5668\u4eba\u65f6，\u4f1a\u4ea7\u751f\u6b67\u4e49；<\/p>\n

3.MDH\u6cd5\u5bf9\u5f00\u94fe\u3001\u6811\u72b6\u3001\u95ed\u94fe\u7ed3\u6784\u7684\u673a\u5668\u4eba\u90fd\u9002\u7528，\u63a8\u8350\u4f7f\u7528\u3002<\/p>\n

\u4e94.\u6211\u9047\u5230\u7684\u5751<\/h2>\n

\u5728\u4e0b\u9762\u8fd9\u672c\u6559\u6750\u91cc\u9762<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\u663e\u7136\u7528\u7684\u662fDH\u53c2\u6570\u6cd5，\u56e0\u6b64\u5728\u540e\u9762\u63a8\u5bfc\u51e0\u4f55\u96c5\u53ef\u6bd4\u77e9\u9635\u7684\u65f6\u5019<\/p>\n

\"\"<\/p>\n

\u63d0\u5230\"z_{i-1}\"\u548c\"p_{i-1}\"\u5206\u522b\u7531\"R^0_{i-1}\"\u4e0e\"T^0_{i-1}\"\u5f97\u5230：<\/p>\n

\"\"<\/p>\n

\u4f46\u662f\u5982\u679c\u4f60\u7528\u7684\u662f\u6539\u8fdbDH\u53c2\u6570\u6cd5\u8fdb\u884c\u5efa\u6a21，\u6838\u5fc3\u516c\u5f0f（3.30）\u5e94\u8be5\u662f：<\/p>\n

\"\"<\/p>\n

\u539f\u56e0\u662f\u539f\u672c\u7684\u6807\u51c6DH\u7684\u5750\u6807\u7cfb\"i-1\"\u5bf9\u5e94\u7684z\u8f74\"z_{i-1}\"\u5c31\u662f\u6539\u8fdb\u7684DH\u7684\u7684\u5750\u6807\u7cfb\"i\"\u7684z\u8f74\"z_i\"<\/p>\n

\u4e0b\u9762\u662f\u57fa\u4e8e\u6539\u8fdbDH\u8ba1\u7b97\u51e0\u4f55\u96c5\u53ef\u6bd4\u7684\u4ee3\u7801 \u00a0<\/p>\n

function J_geo = geometric_jacobian_from_q_corrected(q)
\n % \u6839\u636e\u5173\u8282\u89d2\u5ea6\u8ba1\u7b97\u51e0\u4f55\u96c5\u53ef\u6bd4\u77e9\u9635，\u5339\u914dMATLAB\u5de5\u5177\u7bb1\u7684\u987a\u5e8f
\n % \u8f93\u5165: q – 7\u00d71\u5173\u8282\u89d2\u5411\u91cf (\u5f27\u5ea6)
\n % \u8f93\u51fa: J_geo – 6\u00d77\u51e0\u4f55\u96c5\u53ef\u6bd4\u77e9\u9635<\/p>\n

% Franka Panda\u7684DH\u53c2\u6570 (Modified DH)
\n % \u683c\u5f0f: [alpha, a, d, theta]
\n MDH = [0, 0, 0.333, q(1);
\n -pi\/2, 0, 0, q(2);
\n pi\/2, 0, 0.316, q(3);
\n pi\/2, 0.0825, 0, q(4);
\n -pi\/2, -0.0825,0.384, q(5);
\n pi\/2, 0, 0, q(6);
\n pi\/2, 0.088, 0.107, q(7)];<\/p>\n

% \u8ba1\u7b97\u6bcf\u4e2a\u5173\u8282\u7684\u53d8\u6362\u77e9\u9635\u548c\u4f4d\u7f6e
\n n = 7;
\n T = eye(4);
\n T_all = cell(n, 1);
\n p_all = zeros(3, n);
\n z_all = zeros(3, n);<\/p>\n

for i = 1:n
\n alpha = MDH(i, 1);
\n a = MDH(i, 2);
\n d = MDH(i, 3);
\n theta = MDH(i, 4);<\/p>\n

% \u6539\u8fdbDH\u53d8\u6362\u77e9\u9635
\n Ti = [cos(theta), -sin(theta), 0, a;
\n sin(theta)*cos(alpha), cos(theta)*cos(alpha), -sin(alpha), -d*sin(alpha);
\n sin(theta)*sin(alpha), cos(theta)*sin(alpha), cos(alpha), d*cos(alpha);
\n 0, 0, 0, 1];<\/p>\n

T = T * Ti;
\n T_all{i} = T;
\n p_all(:, i) = T(1:3, 4);
\n z_all(:, i) = T(1:3, 3);
\n end<\/p>\n

% \u672b\u7aef\u6267\u884c\u5668\u4f4d\u7f6e
\n p_ee = p_all(:, end);<\/p>\n

% \u8ba1\u7b97\u51e0\u4f55\u96c5\u53ef\u6bd4 – \u4fee\u6b63\u5173\u8282\u7f16\u53f7\u5bf9\u5e94\u5173\u7cfb
\n J_geo = zeros(6, n);<\/p>\n

for i = 1:n
\n if i == 1
\n % \u5173\u82821：\u4f7f\u7528\u57fa\u5750\u6807\u7cfb
\n p_i = [0; 0; 0];
\n z_i = [0; 0; 1];
\n else
\n % \u5173\u8282i：\u4f7f\u7528\u8fde\u6746i-1\u7684\u5750\u6807\u7cfb
\n p_i = p_all(:, i); % \u6539\u8fdbDH：\u4f7f\u7528i
\n z_i = z_all(:, i); % \u6539\u8fdbDH：\u4f7f\u7528i
\n end<\/p>\n

% MATLAB\u987a\u5e8f：\u7ebf\u901f\u5ea6\u5728\u524d，\u89d2\u901f\u5ea6\u5728\u540e
\n J_geo(4:6, i) = z_i;
\n J_geo(1:3, i) = cross(z_i, p_ee – p_i);
\n end
\nend<\/p>\n

function T = forward_kinematics_mdh(q)
\n % \u6539\u8fdbDH\u6b63\u8fd0\u52a8\u5b66
\n MDH = [0, 0, 0.333, q(1);
\n -pi\/2, 0, 0, q(2);
\n pi\/2, 0, 0.316, q(3);
\n pi\/2, 0.0825, 0, q(4);
\n -pi\/2, -0.0825,0.384, q(5);
\n pi\/2, 0, 0, q(6);
\n pi\/2, 0.088, 0.107, q(7)];<\/p>\n

T = eye(4);
\n for i = 1:7
\n alpha = MDH(i, 1);
\n a = MDH(i, 2);
\n d = MDH(i, 3);
\n theta = MDH(i, 4);<\/p>\n

Ti = [cos(theta), -sin(theta), 0, a;
\n sin(theta)*cos(alpha), cos(theta)*cos(alpha), -sin(alpha), -d*sin(alpha);
\n sin(theta)*sin(alpha), cos(theta)*sin(alpha), cos(alpha), d*cos(alpha);
\n 0, 0, 0, 1];<\/p>\n

T = T * Ti;
\n end
\nend
\n% <\/p>\n","protected":false},"excerpt":{"rendered":"

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