基于可操作度优化的冗余机械臂逆运动学求解方法  

Inverse Kinematics Solution of Redundant Manipulator Based on Manipulability Optimization

作　　者：杨晓航 赵智远 李云涛[1] 徐梓淳 赵京东[1] YANG Xiaohang;ZHAO Zhiyuan;LI Yuntao;XU Zichun;ZHAO Jingdong(State Key Laboratory of Robotics and System,Harbin Institute of Technology,Harbin 150001)

机构地区：[1]哈尔滨工业大学机器人技术与系统国家重点实验室,哈尔滨150001

出　　处：《机械工程学报》2024年第7期22-33,共12页Journal of Mechanical Engineering

基　　金：国家自然科学基金资助项目(92148203)。

摘　　要：在运动规划和控制中提升机械臂的灵活性和避免奇异至关重要,一种有效的方法是使可操作度指标最大化。然而可操作度指标是关节角度的非凸函数,优化该指标是一个巨大的挑战,为此提出一种加速度级可操作度最大化(ALMM)方法。首先,通过一种新的多层次同时最小化方案将位置级别的非线性优化问题转化到速度级别和加速度级别,在加速度水平重构最大化可操作度问题。其次,引入最小化速度指标保证系统的稳定性,并使关节角速度维持在较低水平。然后,结合关节的物理极限,将上述问题表述为标准的二次规划(QP)形式进行求解。以SSRMS构型冗余空间机械臂为例进行仿真验证,实验结果表明ALMM方法可以在完成轨迹跟踪任务的同时实现可操作度优化,对比实验证明ALMM方法的有效性和优越性。It is significant to improve flexibility of the manipulator and avoid singularity in the motion planning and control.An effective method is to maximize the manipulability index.However,the manipulability index is a non-convex function of joint angle,and optimizing this index is a great challenge.Therefore,an acceleration level manipulability maximization(ALMM)method is proposed.Firstly,the nonlinear optimization problem in position level is transformed to velocity level and acceleration level by a new multi-level simultaneous minimization scheme,and the problem of maximization manipulability is reconstructed in acceleration level.Secondly,the minimum velocity index is introduced to ensure the stability of the system and keep the joint angular velocity at a low level.Then,combined with the physical limits of the joint,the above problem is formulated as a standard quadratic programming(QP)problem to solve.Taking SSRMS configuration redundant space manipulator as an example,the simulation results show that the ALMM method can achieve the optimization of manipulability while completing the trajectory tracking task,and the comparative experiment proves the effectiveness and superiority of the ALMM method.

关 键 词：冗余机械臂 逆运动学 可操作度 二次规划 

分 类 号：TP242[自动化与计算机技术—检测技术与自动化装置]