冗余机械臂运动学逆解的求解优化方法

doi:10.13229/j.cnki.jdxbgxb.20220099

摘要/Abstract

摘要：

为解决仿人冗余机械臂逆运动学的求解问题，本文提出了一种逆运动学求解优化方法。通过引入臂角参数建立了逆解的解析解公式，根据关节限位进一步分析了不同形式解析解下的臂角可行区间。此外，提出了综合考虑关节避限和能耗最优的目标函数，通过自适应权重参数调节任务优先级，并引入粒子群优化算法得出最优解。实验结果表明，该算法能求出给定臂角的所有解，并且能选出满足关节避限和低能耗的最优解，对于冗余机械臂的轨迹规划有较好的应用意义。

关键词: 冗余机械臂, 逆运动学, 解析解, 关节限位, 能耗最优, 粒子群优化算法

Abstract:

To solve the inverse kinematics of humanoid redundant manipulator， an optimized method was proposed. The analytical solution of the inverse kinematics was established by introducing the arm angle parameters， and the feasible range of the arm angle under different forms of analytical solutions was further analyzed according to the joint limit. In addition， an objective function considering joint limit avoidance and optimal energy consumption was proposed. Tasks， priority was adjusted through adaptive weight parameters， and the particle swarm optimization algorithm was introduced to obtain the optimal solution. Experimental results show that the algorithm can obtain all solutions for a given arm angle and can select the optimal solution that satisfies the joint limit avoidance and low energy consumption. The proposed method has positive application significance for the trajectory movement of the redundant manipulator.

Key words: redundant manipulator, inverse kinematics, analytical solution, joint limit, optimal energy consumption, particle swarm optimization algorithm

中图分类号:

TP242

张铮,朱齐丹,吕晓龙,樊星. 冗余机械臂运动学逆解的求解优化方法[J]. 吉林大学学报(工学版), 2023, 53(12): 3379-3387.

Zheng ZHANG,Qi-dan ZHU,Xiao-long LYU,Xing FAN. Optimized method for solving inverse kinematics of redundant manipulator[J]. Journal of Jilin University(Engineering and Technology Edition), 2023, 53(12): 3379-3387.

图/表 13

图1

表1

DH参数表"

连杆i	$α i / (°)$	$d i / m$	$θ i / (°)$
1	0	d₁	$θ 1$
2	-90	0	$θ 2$
3	90	d₂	$θ 3$
4	-90	0	$θ 4$
5	90	d₃	$θ 5$
6	-90	0	$θ 6$
7	90	d₄	$θ 7$

表1

图2

图3

图4

图5

图6

表2

图7

图8

图9

图10

表3

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组别	关节1	关节2	关节3	关节4	关节5	关节6	关节7
1	92.96	10.39	0	72.92	-124.34	76.96	121.35
2	92.96	10.39	0	72.92	55.66	-76.96	-58.65
3	92.96	10.39	-180	-72.92	55.66	76.96	121.35
4	-87.04	-10.39	-180	72.92	-124.34	76.96	121.35
5	92.96	10.39	-180	-72.92	-124.34	-76.96	-58.65
6	-87.04	-10.39	0	-72.92	55.66	76.96	121.35
7	-87.04	-10.39	-180	72.92	55.66	-76.96	-58.65
8	-87.04	-10.39	0	-72.92	-124.34	-76.96	-58.65

算法	计算时间/ms	平均目标函数值	平均位置误差/10^-7 m
本文	11.26	4.6	7.5
文献［17］	10.39	8.9	8.4