考虑输出约束的机械臂命令滤波反步控制  

A Backstepping Control Strategy of Command Filtering for Two-Link Flexible Joint Manipulator

作　　者：林孟豪 张蕾[1] 李鹏飞[1] 王晓华[1] 王文杰 LIN Menghao;ZHANG Lei;LI Pengfei;WANG Xiaohua;WANG Wenjie(College of Electronics and Information, Xi’an Polytechnic University, Xi’an 710048, China)

机构地区：[1]西安工程大学电子信息学院,西安710048

出　　处：《西安交通大学学报》2021年第12期70-78,共9页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(51607133);陕西省技术创新引导专项基金资助项目(2020TG-011);陕西省重点研发计划资助项目(2019ZDLGY01-08)。

摘　　要：为了提高双连杆柔性关节机械臂系统的轨迹跟踪响应速度与轨迹跟踪精度,提出一种具有输出约束和误差补偿的双连杆柔性关节机械臂命令滤波反步控制策略(BLF-CFBC)。首先,在反步控制设计中构造对数型障碍李雅普诺夫函数来替代常规的二次型李雅普诺夫函数,使得轨迹跟踪误差被约束在预先设定的误差范围内,从而在加快误差收敛速度的同时保证了轨迹跟踪精度;其次,采用命令滤波器输出子系统递推过程中所需的控制函数及其导数,以避免基于李雅普诺夫理论的常规反步控制方法中由于对控制变量的反复求导而导致的计算爆炸的问题,从而有效降低了计算维度;最后,引入误差补偿机制,利用控制变量与滤波器输出之间的误差来构造系统变量,以降低命令滤波器的误差对机械臂跟踪精度的影响。采用Matlab搭建系统模型进行仿真实验,结果表明,所提控制策略与不考虑输出约束和误差补偿的命令滤波反步控制策略(CFBC)相比,双连杆柔性关节机械臂关节1、2的轨迹跟踪响应速度分别提升了20%、30%,轨迹跟踪误差分别降低了4%、3.5%。A backstepping control strategy of command filtering with output constraint and error compensation for two-link flexible joint manipulator(named BLF-CFBC)is proposed to achieve the control goal of improving the tracking response speed and tracking accuracy of the two-link flexible joint manipulator system.Firstly,a logarithmic barrier Lyapunov function is constructed to replace the conventional quadratic Lyapunov function in the backstepping control design,so that the trajectory tracking error is constrained within the preset range and the trajectory tracking accuracy is ensured while the error convergence speed is accelerated.Secondly,the control signal and its derivative are output from the command filter so as to avoid the problem of computational explosion caused by the repeated derivation of control variables in conventional backstepping control method based on Lyapunov theory,thus effectively reducing the calculation dimension.Finally,an error compensation mechanism is introduced to construct system variables by using the errors between the control signal and the output of the filter,so as to reduce the influence of the error of command filter on the tracking accuracy of the manipulator.A two-link flexible joint manipulator system model is built and simulated in Matlab software.Results and a comparison with the command filter backstepping control strategy(CFBC)without considering output constraint and error compensation show that the proposed control strategy increases the trajectory tracking response speed of joint 1 and joint 2 by 20%and 30%,respectively,and the trajectory tracking error reduces by 4%and 3.5%,respectively.

关 键 词：双连杆柔性关节机械臂 障碍李雅普诺夫函数 命令滤波 滤波误差 

分 类 号：TP241[自动化与计算机技术—检测技术与自动化装置]