基于自收敛同伦延拓法搜索七自由度机械臂零空间解集  

Searching the null space solution set of 7-DOF manipulator based on self convergence homotopy continuation method

作　　者：吴剑雄 张国庆 李宗道 李清都 WU Jianxiong;ZHANG Guoqing;LI Zongdao;LI Qingdu(Institute of Machine Intelligence,University of Shanghai for Science and Technology,Shanghai 200093,China;School of Health Science and Engineering,USST,University of Shanghai for Science and Technology,Shanghai 200093,China;School of Optical-Electrical and Computer Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学机器智能研究院,上海200093 [2]上海理工大学健康科学与工程学院,上海200093 [3]上海理工大学光电信息与计算机工程学院,上海200093

出　　处：《智能计算机与应用》2024年第8期209-219,共11页Intelligent Computer and Applications

摘　　要：针对七自由度机械臂零空间解集的无穷性,传统数值迭代只能求取单一解,解析法通用性较低,微分映射法精度较低的问题,本文在传统同伦延拓法的基础上采用同伦延拓参数自收敛的方式并加入关节限幅环节以优化延拓空间,并在此基础上,采用余弦函数作为同伦延拓辅助函数为方程组加入扰动。首先,根据改进DH参数法得到正运动学变换矩阵;其次,对自收敛同伦延拓法和传统同伦延拓法的求解时效、求解范围、对求解精度的适应性以及迭代限幅对求解的影响进行对比实验;最后,使用球形包围盒法结合加权取解的方式使得机械臂利用搜索到的零空间解集进行避障运动。经实验证明自收敛法的求解时效要优于传统法,加入关节限幅过程后,两种方法的时效性均有提升。In view of the infinity of the null space solution set of the seven-degree-of-freedom manipulator and the traditional numerical iteration can only obtain a single solution,the analytical method has low versatility,and the differential mapping method has low accuracy.Based on the traditional homotopy continuation method,the self-convergent homotopy continuation parameters and the joint limit are introduced to optimize the continuation space.On this basis,the cosine function is used as a homotopy continuation auxiliary function to add perturbation to the equations.Firstly,the forward kinematics transformation matrix is obtained according to the modified DH parameter method.Then,the solution efficiency,solution range,adaptability to solution accuracy and the influence of joint limit on solution of self-convergence homotopy continuation method and traditional homotopy continuation method are compared.Finally,the spherical bounding box method combined with the method of selecting solutions through weighting is used to make the manipulator use the searched null space solution set to avoid obstacles.Experiments show that the self-convergence method is superior to the traditional method and the efficiency of the two methods is improved after adding the joint limit process.

关 键 词：七自由度机械臂 零空间解集 同伦延拓参数 关节限幅 同伦延拓辅助函数 自收敛同伦延拓法 

分 类 号：TP241[自动化与计算机技术—检测技术与自动化装置]