冗余度机器人自运动中的混沌运动及其控制

Chaotic Motion and Its Control in Self-motion of Redundant Robot

以一个平面 3R刚性冗余度机器人为研究对象 ,采用PD调节器进行工作空间内的负反馈 ,控制机器人末端重复跟踪工作空间内封闭路径 ,对此过程中机器人自运动中可能存在的混沌运动进行了研究 .通过运动仿真和相图 ,以及计算系统的最大李亚普诺夫指数 ,研究发现 ,基于雅可比矩阵的伪逆 ,求解冗余度机器人运动学逆解时其自运动是混沌的 .首次应用延迟反馈控制法对所发现的混沌运动进行控制 ,在适当的参数条件下 ,成功地将混沌运动转变为规则的周期运动 .

In this paper,the possible chaotic motion in the self-motion of a planar 3R redundant robot is discussed under the PD controller when the end-effector traces a closed-path repeatedly in the workspace,by the numerical simulation,phase plot and the largest Lyapunov exponent. The numerical results show that the self-motion is chaotic based on the pseudoinverse of the Jacobian method for solving the inverse kinematics of the redundant robot. The delayed feedback control method is used to control the discovered chaotic motion for the first time. It is shown that the chaotic motion can be turned into regular motion with some appropriate parameters.