基于质心偏移的移动机器人轨迹跟踪控制

Trajectory Tracking Control of Mobile Robot Based on Centroid Deviation

针对非完整约束下质心偏移的移动机器人,提出了一种改进滑模变结构的轨迹跟踪控制方法,并通过此方法得到一种具有全局渐近稳定性的跟踪控制器。以三轮移动机器人的运动模型为基础,该跟踪控制器的设计分为两部分:第一部分是采用X方向和前向角方向同时具有虚拟反馈变量,通过Lyapunov方法对控制系统进行稳定性分析,设计出切换函数;第二部分是滑模控制器设计,采用指数趋近律,使用S型指数函数代替符号函数,减少了滑模变结构控制的抖动,由此设计出了线速度和角速度的控制律,用来渐近整定移动机器人跟踪误差,实现了对参考轨迹的全局渐近跟踪。实验结果表明:该控制律能够在极短时间内趋于稳定,其跟踪平面坐标误差和前向角误差也能在极短时间内收敛于0,并且移动机器人也能够有效地跟踪期望轨迹,其控制效果具有明显的改善,且具有很好的抗干扰性能。

In order to solve the trajectory tracking problem of mobile robot with centroid deviation under non-holonomic constraints, a trajectory tracking control method for mobile robot with improved sliding mode variable structure is proposed. The tracking controller with global asymptotic stability was also obtained by this method. Based on the motion model of three-wheeled mobile robot, and the tracking controller design was divided into two parts. In the first part, using X direction and forward direction with virtual feedback variable, the stability of the control system was analyzed by Lyapunov method, and the switching function was designed. The second part, the sliding mode controller was designed, which adopts exponential approach law and uses S type exponential function instead of symbol function. Then the jitter of the sliding mode variable structure control was reduced. Then, the control law of linear velocity and angular velocity was designed to asymptotically stabilize the tracking error of mobile robot and to realize the global asymptotic tracking of the reference trajectory. The experimental results show that the control law can be stable in a very short time, and the tracking plane coordinate error and forward angle error can converge to zero in a very short time. Moreover, the mobile robot can track the desired trajectory effectively, and its control effect is obviously improved, and the method has good anti-jamming performance.