作者：宋子浩, 吴斌, 周挺

作者单位：北京交通大学机械与电子控制工程学院, 北京 100044

关键词：球形机器人;轨迹跟踪;输入受限;干扰观测器

摘要：

针对球形机器人在输入受限情况下的轨迹跟踪问题设计控制器。首先，为对位置进行控制的同时给姿态控制回路期望的姿态信号，基于运动学模型设计虚拟控制律；然后，基于含输入受限约束、外扰和不确定性的动力学模型，以虚拟控制量为期望值，基于Lyapunov函数设计力矩控制器，以干扰观测器估计外扰和不确定性，以辅助补偿系统补偿输入力矩限幅。Lyapunov稳定性分析表明，该文所设计的控制器可保证跟踪误差最终一致有界。经直线和圆弧轨迹的仿真，并与现有结构相同的不含限幅补偿的控制算法相比较，说明该文设计的控制器在输入受限的情况下的良好效果。

Trajectory tracking control of a spherical robot under input saturation
SONG Zihao, WU Bin, ZHOU Ting
School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China
Abstract: A control scheme for trajectory tracking of a spherical robot with input saturation is proposed in this paper. Firstly, a virtual controller is designed based on the kinematic model of the robot, meanwhile being the desired attitude signal of the attitude control loop. Then, the torque controller is designed based on the Lyapunov function and the dynamic model with input saturation, disturbances and uncertainties. A compensator is presented for the input saturation. As for the disturbance and uncertainties, an observer is proposed based on the dynamic model. Besides, the stability analysis is given via Lyapunov Theory and all the closed-loop signals are uniformly ultimately bounded. Finally, the performance of the proposed algorithm is shown based on the numerical simulation of linear and circular trajectories and a comparison is made between the proposed algorithm and an existing controller with similar structure to illustrate the effectiveness of the proposed algorithm under input saturation.
Keywords: spherical robot;trajectory tracking;input saturation;disturbance observer
2020, 46(5):120-126  收稿日期: 2019-12-30;收到修改稿日期: 2020-01-28
基金项目: 教育部重点项目（M14GY100020）
作者简介: 宋子浩(1995-),男,辽宁大连市人,硕士研究生,专业方向为球形机器人的运动控制
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