Trajectory Tracking Control Of Wheeled Robots

Wheeled mobile robot(WMR)has attracted many research attentions and has been extensively applied in many areas,such as daily life,industrial production,military counter-terrorism,space exploration,et.al,due to its advantages of light weight,heavy load,convenient control and simple operation.Motion control is the key problem to ensure the normal operation of the WMR.As one of the main problems to be solved in the motion control,trajectory tracking has always been a research hotspot.On the other hand,due to mechanical structure,load placement,collision offset,et.al in practice,the center of mass of WMR often does not coincide with the center of the driving wheel axis.Therefore,it is more practical to study the trajectory tracking control under the condition of the displacement of the center of mass and driving axis center.The main contents are summarized as follows:(1)Considering the uncertainty of the distance between the center of mass of WMR and the center of driving wheel axis,an adaptive trajectory tracking control algorithm is designed based on the kinematics model to guarantee the track error converge to zero asymptotically.Firstly,the kinematic model is obtained by considering the displacement of the center of mass and driving axis center under the ideal nonholonomic constraint.Secondly,a new kinematic controller is designed to guarantee the convergence of the tracking error even if the initial error is large.Then,the uncertainty of the displacement is taken into consideration and an adaptive control law is designed.Finally,the effectiveness of control algorithm is verified by simulations.(2)The trajectory tracking control of the WMR is studied under the input saturation constraints based on a new Lyapunov function.Firstly,a new Lyapunov function is proposed and the trajectory tracking controller is designed.Then,it is proved that the saturation constraints is satisfied by choosing the parameters of the controller properly,and then we prove that the tracking error system is asymptotically stable by the Lyapunov theory.Finally,numerical examples are given to illustrate the effectiveness of the propose approach.(3)Considering the simultaneous control of point stabilization and trajectory tracking,a unified controller is designed to eliminate the switching between two different controllers.Firstly,the kinematics model of the tracking error system is obtained in formulation of a chin form via coordinate transformation.Secondly,a kinematic controller that can simultaneously achieve point stabilization and trajectory tracking is designed by introducing a virtual reference variable.Then,the dynamic model of the WMR is derived based on the torque balance equation,and a torque controller is designed to track the linear velocity and the angular velocity output of kinematics controller,the stability of the entire control system is proved through Lyapunov theory.Finally,numerical examples are given to illustrate the effectiveness of the propose approach.