基于伪逆的冗余度机械臂关节速度约束方案

Redundant manipulator joint-velocity constraint scheme based on pseudoinverse

针对冗余度机械臂逆运动学求解结果可能超出机械臂物理限制的问题,提出两种基于伪逆算法的冗余度机械臂关节速度约束方案。首先,根据冗余度机械臂末端执行器的跟踪任务,运用伪逆算法在速度层上进行冗余度解析。其次,分别利用设计的两种约束方案对指定的关节速度进行限制与压缩,获得新的速度解并用以执行指定的轨迹跟踪任务。接着,针对末端执行器出现的位置误差,设计误差补偿函数以保证跟踪任务的顺利执行。最后,利用MATLAB软件对六自由度机械臂进行了运动规划仿真实验,并利用Arduino平台对六自由度机械臂进行算法实验验证。实验结果表明,两种约束方案下机械臂的最大跟踪误差均不超过3×10^(-4)m,且时变函数约束方案在限制关节速度时获得更好的速度平稳性。

The pseudoinverse-type solution may exceed the physical limit of a manipulator. To address this problem, two kinds of joint-velocity constraint schemes of redundant manipulator based on the pseudoinverse algorithm are proposed. Firstly, according to the tracking task of the end-effector, the pseudoinverse algorithm is used to analyze the redundancy at the velocity level. Secondly, two constraint schemes are utilized to limit and compress the specified joint velocity. A new velocity solution is obtained to perform the specified trajectory-tracking task. Then, the error compensation function is designed to eliminate the position error of the end-effector to ensure the smooth execution of the tracking task. Finally, simulation results based on the MATLAB software are analyzed and discussed. The algorithm is further evaluated using a six-DOF manipulator which is controlled by the Arduino platform. These results show that the maximum tracking errors do not exceed 3×10^(-4)m with two proposed constrained schemes. And the time-varying function constrained scheme can achieve better velocity stability when the joint velocity is limited.