物理受限冗余机械臂逆运动学凸优化求解

Convex Optimization Solution for Inverse Kinematics of a Physically Constrained Redundant Manipulator

针对冗余机械臂逆运动学求解结果极有可能超过机械臂物理限制的问题,提出一种基于凸优化的逆运动学求解方法使得逆解结果满足物理约束.首先分析了关节速度与力矩关系,采用机械臂动能及重复运动为优化指标,以关节速度、关节力矩为优化变量.然后将逆运动学求解问题转化为凸优化问题,进一步转化为二次规划问题,充分利用冗余特性,实现逆运动学求解时避免关节位置、关节速度、关节力矩极限.最后利用7自由度冗余机械臂KUKA LBR iiwa进行仿真,求解关节量结果符合物理极限及优化准则.结果表明本文提出的方法适用于物理受限冗余机械臂的逆运动学求解.

Results of redundant manipulator inverse kinematics are likely to exceed the manipulator＇s physical constraints.To acquire inverse kinematics solution subject to physical bounds, a method using convex optimization is adopted. Firstly,the relation between joint velocity and torque is analyzed, and the manipulator kinetic energy and the repetitive motion are adopted as the optimization criteria, with joint velocity and joint torque as the optimization variables. Then the inverse kinematics problem is transformed into a convex optimization problem and further transformed into a quadratic programming problem. Taking full advantage of the redundancy of the manipulator, physical constraints including the joint position, joint velocity and joint torque are avoided in solving the inverse kinematics. Finally, simulation experiment is carried out on a7-DOF redundant manipulator KUKA LBR iiwa. Results of the obtained joint variables satisfy the physical constraints and the optimization criteria. The result shows that the proposed method is suitable for solving inverse kinematics of physically constrained redundant manipulator.