基于三角函数的机器人手臂轨迹跟踪控制重力补偿算法

摘要

Humanoid manipulator motion control is mainly carried out by trajectory tracking control. As the largest disturbance of a spatial manipulator, gravity force is necessarily compensated to improve the control precision and efficiency. The conventional gravity compensation algorithm requires accurate dynamic parameters and complex matrix transformation operation, which is difficult to be used in real time control. Based on the geometric features and torque balance principle of spatial manipulators, this paper proposed a simple and practical gravity compensation algorithm that does not need complex computation of coordinate transformation and the accurate dynamic models and parameters, only needs the largest gravity torque estimation of manipulator and the calculation of simple trigonometric function, while the algorithm is also suitable for non-parallel axis spatial manipulators with N joints. To verify the gravity compensation control effect, the PD controller with gravity compensation was used to controll the manipulators of two and three joints based on simulation. It was simulated by gravity compensation and without compensation as well as comparison with other compensation methods. Results show that the gravity compensation algorithm can improve the trajectory tracking control with high control precision. The compenstion method can effectively reduce the work burden of a controller and improve the stability of the system. The compensation effect is satisfactory.%机器人手臂的运动控制主要通过轨迹跟踪控制来完成,重力作为空间机械臂中最大的干扰力,有必要通过补偿方法来提高控制精度和效率. 常规的重力补偿算法需要精确的动力学参数和复杂的矩阵变换运算,很难运用到实时控制中. 基于机械臂空间几何特性和扭矩平衡原理提出一种比较简便实用的重力补偿算法,该算法不需要复杂的空间坐标变换计算,不需要获得所有精确的动力学模型和参数,只需要对机械臂的最大重力矩进行估计和简单的三角函数计算,而且该算法可以推广到适用于空间N个关节的非平行轴机械臂. 采用最容易分析的PD控制器加重力补偿控制两关节和三关节机械臂来进行仿真以验证重力补偿后的控制效果. 通过对机械臂进行重力补偿和不补偿以及与其他补偿方法进行仿真对比,结果显示该重力补偿算法能够较好地实现轨迹跟踪控制,控制精度较高,能有效地减轻控制器的工作负担,提高系统的稳定性,补偿效果较好.