冗余度机器人在一般限制条件下的最优轨迹规划

Optimal Path Planning of Redundant Robots in General Limit Condition

在讨论冗余度机器人的最优轨迹规划过程中，提出了扩展雅可比矩阵法。将雅可比矩阵和限制条件函数对各关节位置的导数阵联合起来，构成扩展雅可比方阵。讨论了扩展雅可比矩阵的逆，得到了一般限制条件下的最优解与最小范数解的关系，并用此关系进行最优轨迹规划。

A method using extended Jacobian matrices to find the optimal path of a redundant robot is presented. The Jacobian matrices and the derivative matrix of the limit function to joint angles are combined into an extended Jacobian matrix. The inverse matrix of the extended Jacobian matrix is discussed, the relation between an optimal solution in general limit condition and the least-norm solution is obtained, which can be used to find the optimal path