冗余机器人逆运动学解流形的多目标优化

Multi-objective Optimization for Inverse Kinematics Solution Manifolds of Redundant Robots

针对冗余机器人逆运动学插值优化算法运算量大、实时性差的缺点,提出一种基于流形的多目标优化算法.将冗余机器人逆运动学解空间看作一个光滑流形,对位置工作空间流形和姿态工作空间流形分别进行降维分析,然后结合提出的优化目标函数得到冗余机器人相应的优化逆解.在冗余机器人多目标优化中各个优化性能指标很可能是相互对立矛盾的,这就需要根据优先权的高低进行加权设置,以达到冗余机器人解空间的整体优化,得到的优化逆解往往不是单个的解,而是一个优化的解流形.最后利用飞机S形进气道进行逆运动学仿真验证了所用方法的合理性.

A multi-objective optimization algorithm based on manifolds is proposed to solve the shortcomings of large operand and poor real-time performance of the interpolation optimization algorithm for the inverse kinematics solutions of redundant robots. The solution space of inverse kinematics of the redundant robot is regarded as a smooth manifold, the dimensionality reduction analysis is conducted in the position workspace manifolds and posture workspace manifolds. The optimal inverse solutions of the redundant robot are obtained according to the proposed optimization objective function. The optimal performance indexes may be contradictory in multi-objective optimization of the redundant robot, and thus the weights should be added to each index according to their priorities to realize global optimization of the redundant robot. Generally, the optimal inverse solution is not a single solution, but an optimal solution manifold. Finally, the rationality of the proposed method is demonstrated by inverse kinematics simulation with the plane S-shaped inlet.