多体系统轨迹跟踪的瞬时最优控制保辛方法

发布时间：2018-03-14 06:36

本文选题：机器人　切入点：多体系统　出处：《力学学报》2016年04期 　论文类型：期刊论文

【摘要】：随着近年来机器人在各行业领域的广泛应用,对机器人的动力学与控制性能不断提出新的要求,特别是对设计越来越复杂、操作越来越灵巧的智能机器人,要求其能够对目标轨迹实现高精度跟踪以满足实际工作需求.因此,针对机器人多体系统对目标轨迹跟踪的任务需求,基于微分代数方程提出瞬时最优控制保辛方法.首先,采用多体动力学绝对坐标建模方法建立机器人系统的普适动力学方程,即微分代数方程;然后,采用保辛方法将连续时间域内的微分代数方程进行离散化,进而得到以当前位置、速度和拉式乘子为未知量的非线性代数方程组;其次,通过引入对目标轨迹跟踪以及对控制加权的瞬时最优性能指标,根据瞬时最优控制理论获得当前最优控制输入;最后,通过离散时间步的更新完成对目标轨迹的跟踪任务.为了验证本文方法的有效性,以双摆轨迹跟踪控制为例进行了数值仿真,结果表明:针对机器人轨迹跟踪任务所提出的瞬时最优控制保辛方法能够实现对目标轨迹的高精度跟踪,且瞬时最优控制由受控微分代数方程推导获得,更具一般性,能够适应其他复杂多体系统的轨迹跟踪控制问题.
[Abstract]:With the wide application of robots in various fields in recent years, new requirements have been put forward for the dynamics and control performance of robots, especially for intelligent robots with more and more complex design and more dexterous operation. It is required that the target trajectory can be tracked with high accuracy to meet the practical requirements. Therefore, aiming at the task requirement of target trajectory tracking in multi-body robot systems, a symplectic preserving method for instantaneous optimal control is proposed based on differential algebraic equations. The universal dynamical equation of robot system, namely differential algebraic equation, is established by using the method of absolute coordinate modeling of multi-body dynamics, and then the differential algebraic equation in continuous time domain is discretized by symplectic preserving method. Then, the nonlinear algebraic equations with the current position, velocity and pull multiplier as unknown variables are obtained. Secondly, the instantaneous optimal performance index of the target trajectory tracking and the control weighting are introduced. According to the instantaneous optimal control theory, the current optimal control input is obtained. Finally, the tracking task of the target trajectory is completed by updating the discrete time step. Numerical simulation is carried out with the example of double pendulum trajectory tracking control. The results show that the symplectic preserving method of instantaneous optimal control for robot trajectory tracking task can achieve high precision tracking of the target trajectory. Moreover, the instantaneous optimal control is derived from the controlled differential algebraic equation, which is more general and can adapt to the trajectory tracking control problem of other complex multi-body systems.
【作者单位】：大连理工大学工程力学系工业装备结构分析国家重点实验室;大连理工大学航空航天学院工业装备结构分析国家重点实验室;
【基金】：国家自然科学基金资助项目(11472069,11472067,11432010)
【分类号】：O313.7

【相似文献】