Research On Optimal Control For Reconfigurable Robot Systems Based On Two-player Zero-sum Game

The reconfigurable robot uses different combinations of joint modules to change its own structure during the interaction with the environment,and has strong application expansion capabilities,so that the reconfigurable robot is more suitable than the traditional robot to complete relatively complex tasks and work in a non-predetermined environment.The "reconfigurable" characteristics of the reconfigurable robot are not only manifested in the mechanical structure part,but also in the advanced control strategy of the system,which can be applied to different configurations of the robot and can complete non-predefined tasks with high tracking performance.Reconfigurable robots inevitably work in unknown environments,therefore it is necessary to comprehensively consider and ensure the stability,robustness,accuracy,energy saving and efficiency of the system,hence it is necessary to choose the appropriate control strategy.In modern control theory,optimal control is one of the important parts of its research,its main research problem is to find the most suitable control strategy from a class of allowable schemes according to the controlled system,so that when the system is transferred to the target state,the defined system characteristics are optimal.For reconfigurable robot systems that are interfered with the external environment,the two-player zero-sum game theory is introduced into the optimal control of robot systems.The external environment interference term forms a policy with the optimal control law under a certain performance index.The optimal control problem of the reconfigurable robot is converted into a zero-sum game problem for two players under the interference term and the controller as the participant,and then the optimal control strategy needs to solve the Hamilton-Jacobi-Issacs equation.However,this equation is a class of nonlinear partial differential equations that are difficult to obtain optimal solutions using analytical methods.Adaptive dynamic programming is an approximate optimal method emerging from optimal control theory,and it is an important method to solve the optimal control problem of nonlinear systems.In the adaptive dynamic programming method,the function approximation structure is used to approximate the performance index function and control strategy to satisfy the Bellman optimal principle,and then obtain the optimal control strategy and performance index function.Under the premise of ensuring the control accuracy and stability of the reconfigurable robot system under the interference of the external environment,weighing the robust ability of the robot system to face external disturbance and the conservation of energy resources,it has become the goal of scholars to build an optimal control strategy for reconfigurable robots that are more suitable for external environmental interference.This paper combines two-player zero-sum game theory with optimal control theory to study the optimal control problem of reconfigurable robot systems based on two-player zero-sum game,including:(1)Dynamic modeling of reconfigurable robot systemsThe "reconfigurable" characteristics of the reconfigurable robot are analyzed,and two dynamic models suitable for different configurations of the robot system are established by using the Newton-Euler iterative algorithm and the joint torque feedback method.And both dynamic models take into account the robot's individual joints,the force/moment of the connecting rods,and the coupling force/moment between the joints.The individual joints of the reconfigurable robot are decomposed into multiple separate subsystems,and each subsystem builds a corresponding dynamic model.(2)Zero-sum neural optimal control of reconfigurable robots based critic only policy iteration scheme under external collisionsBased on the dynamic model of reconfigurable robot established in this paper,considering the trajectory tracking problem of the optimal position and velocity of the reconfigurable robot under external collision,a zero-sum neural optimal control method of reconfigurable robot based on critic only policy iteration scheme is proposed.Firstly,the adaptive fuzzy control method is used to compensate for the uncertainty of the reconfigurable robot dynamic model,thereby reducing its impact on the stability of the control system.The optimal control problem of the reconfigurable robot is converted into a zero-sum game problem for two player under the interference term and the controller as the participant,and on the basis of the method of policy iteration and adaptive dynamic programming,the Hamilton-Jacobi-Issacs equation is approximated by using a critic only policy iteration scheme to obtain the approximate optimal control law.Then,Lyapunov's theorem is used to prove that the reconfigurable robot system is stable,and finally the simulation results prove the effectiveness of the proposed method.(3)Event-trigger-based approximate optimal control of reconfigurable robot manipulators using zero-sum gameBased on the reconfigurable robot dynamic model of joint torque feedback,a zero-sum game approximation optimal control method of reconfigurable robot system based on event triggering is proposed.The dynamic model of the reconfigurable robot system is described as a collection of joint subsystems containing interconnected dynamic coupling,and the uncertainty terms of the model are compensated by RBF neural network.Establish a performance index function to consider the impact of external interference on system stability.The optimal control problem of the reconfigurable robot is converted into a zerosum game problem for two player under the interference term and the controller as the participant.Based on the adaptive dynamic programming method,the Hamilton-JacobiIssacs equation is estimated to derive the optimal control strategy by using the approximate performance index function of the critic neural network.Introduce the event triggering mechanism into the robot control system,design the event trigger conditions,and update the control law when the system state meets the trigger conditions.The tracking error of the reconfigurable robot system is proved to be uniformly and ultimately bounded by Lyapunov theorem,and verified by the reconfigurable robot experimental platform.