基于Udwadia-Kalaba理论的协作机器人轨迹跟踪控制

A Novel Trajectory Tracking Control of Collaborative Robot Based on Udwadia-Kalaba Theory

协作机器人通常应该跟踪给定的轨迹来与人类一起工作,给定轨迹认为是施加于机器人的约束(可能是非理想的)。因此,获得约束力成为核心问题。已有拉格朗日乘数法等多种基于d'Alembert原理的方法来处理这个问题。其缺点为,如果约束是非完整的,动态模型是复杂的,只能得到数值解。这里提出了一种基于Udwadia-Kalaba方法的轨迹跟踪控制的新方法。该方法为具有完整或非完整约束的约束协作机器人系统以及可能是理想的或非理想的约束提供了新颖、简洁和明确的运动方程。在上述基础上,分析不确定性因素的影响并构建自适应律,设计一个产生近似约束的控制器以保持系统稳定性。由于约束力由给定轨迹确定,协作机器人的运动完全符合要求。以一个数值例子来说明实现过程的细节。结果表明,与传统鲁棒控制相比,该方法具有更好的性能和更少的计算量。

Collaborative robot should track given trajectories to work with human in most cases.The given trajectories are regarded as(maybe nonholonomic)constraints applied on the robot.Thus,obtaining the constraint force becomes the core problem.There have been various methods based on d'Alembert principle such as Lagrange multiplier method to deal with this problem in past decades.But the disadvantage is that if the constraint is nonholonomic,the dynamic model is complicate and only numerical solution could be obtained.A novel approach of trajectory tracking control is presented,which is based on Udwadia-Kalaba approach.This approach presents a novel,concise and explicit equation of motion for constrained collaborative robot systems with holonomic and/or nonholonomic constraints as well as constraints that may be ideal or non-ideal.The influence of uncertain factors is analyzed on this basis,the adaptive law is constructed,and a controller with approximate constraints is designed to maintain the stability of the system.Since the constraint force is determined by the given trajectory,the motion of collaborative robot meets the requirements exactly.A numerical example is given to demonstrate the details of implementation procedure.The results show that the proposed approach has better performance and less computation compared to the traditional robust control.