Research On Formation Control Of Leader-Following Robot Based On Second-Order Sliding Mode Algorithm

The issue of multi-robot formation is one of the most important branches of robot control and as a hot research topic in the collaborative research of multi-agents.The formation control of robots has been used in the complex tasks such as military search,submarine formation,and drone formation.The formation of multiple robots in collaboration with each other can complete a variety of complex tasks,improve work efficiency,reduce energy consumption costs,and increase the probability of task completion.This paper takes wheeled mobile robots as the research object and appllies three noval sliding mode control approaches to control the leader-follower formation to realize that the multiple robots maintain a stable and regular formation movement.Firstly,in order to describe the robot formation system accurately,it is necessary to analyze the non-holonomic constraints of the single wheeled mobile robot.The dynamic analysis of the single wheeled robot is performed first,and the state function of the dynamic model is established.Besides,the relations of leader robot and the follower robot are simultaneously expressed on the two-dimensional coordinate plane and establish the state equation for the global system,and control the relative distance and relative phase angle between each follower and the leader by controlling the linear acceleration and angular acceleration of the follower robot.The classical leader-following robot formation system is a complex multi-input multi-output system with many uncertainties and disturbances.Therefore,the requirements of the leader-following robot formation system for the robustness and response performance of the nonlinear controller are harsh.Otherwise,the robot is likely to leave the team or collide during the movement of the robot.Secondly,variable the structure sliding mode control has superior robustness and anti-interference performance to control the nonlinear systems with multiple uncertainties and uncertain disturbances.Applying sliding mode control to the leader-following robot formation system can be processing system uncertainties well.While the traditional first-order and second-order sliding mode control have good robustness,the obvious disadvantage is that the control quantity may overestimate the disturbance,resulting in chattering of the system output.The super-twisting sliding mode controller is used in this paper,which is a kind of second-order sliding mode control.In order to avoid the overestimate and chattering caused by the excessively high control quantity of the controller,adaptive gain super-twisting sliding mode control law is proposed and applied to the robot formation system.This method can effectively adjust the controller gain with the changing of the sliding surface online,which can effectively improve the speed of error convergence and suppressing the chattering.Thirdly,for the multiple uncertainties and disturbances in the system model is always a difficult problem which lead to overshoot of control output and chattering,and reduce the stability of the system.Therefore,this paper proposes two estimators that can estimate the uncertainties of the system.Among them,the STW sliding mode control is based on the extreme learning machine which is the single hidden layer neural network controller essentially.The known states associated with uncertainties and disturbances are the input of the ELM,the weights of the neural network are trained to approximate the uncertainties.The other method is to use a nonlinear state disturbance observer to feedback to the STW sliding mode controller.These two methods for estimating the uncertainty combined with the traditional second-order sliding mode controller can improve the accuracy of the controller for the compensation control of uncertainties,improve the stability of the system,and effectively suppress the chattering phenomenon.Finally,in order to illustrate that the three methods proposed can make the robot formation system track the expected relative distance and relative phase angle within a limited time and remain stable,the proposed control method is also implemented by Lyapunov stability theorem.Lyapunov proof analysis shows that the robotic formation system is stable in adaptive gain super-slip sliding mode control,STW sliding mode control based on ELM and STW sliding mode controller based on NDOB.In additions,in order to reflect the control performance of these three methods,the three methods are simulated on MATLAB respectively,compared with other sliding mode control methods with the same initial conditions and expected values.