Study On Robot Control Strategy Based On Koopman Operator Theory

The modeling and control of robotic systems have always been a research hotspot in the field of robotics.However,due to its high dimensionality,strong nonlinearity,uncertainty,and strong coupling,the modeling and control of robotic systems are facing great challenges.It is still a difficult task to build accurate models for robotic systems and to control them effectively.The Koopman operator theory can transform the nonlinear system into a linear space for research,reveals the evolution mechanism of the nonlinear system,and provides an effective tool for the modeling and control of the robot nonlinear system.Therefore,this paper will investigate the modeling and control strategies of nonlinear robotic systems based on the Koopman operator theory.The main research contents are as follows:First of all,this paper proposes an LQR control algorithm based on the Koopman operator.By optimizing the construction of the Koopman eigenfunction method to model the typical robotic system of the manipulator,the deep neural network is used to learn the continuous eigenfunction.The LQR optimal control algorithm completes the trajectory tracking control of the manipulator.Through the comparative statistical analysis of the modeling error of the manipulator and the trajectory tracking error of the manipulator in the experimental results,it is shown that the proposed algorithm can accurately describe the robotic arm nonlinear system and the error of trajectory tracking control is smaller.Secondly,for the noise problem,this paper designs an LQR control algorithm based on Kalman-Koopman.On the basis of the original algorithm,the Kalman filter is further added to filter the noise interference of the end effector of the manipulator,which improves the control effect of the algorithm.Through the comparative analysis of the experimental results,it is shown that the proposed algorithm has better robustness,and the effectiveness of the control algorithm can be guaranteed even under the interference of noise.Finally,in order to reduce the influence of model changes on the control policy in complex environments,this paper proposes a model-based reinforcement learning algorithm.The deep Koopman network is used to model the nonlinear robot system in reinforcement learning,and the policy update in reinforcement learning tasks is completed through the iteration of the LQR value function.It can effectively solve the problem that the policy is difficult to solve and the data efficiency is low in the existing reinforcement learning algorithm.By designing a deep neural network with the Koopman operator and combining with LQR optimal control theory,the effectiveness of the algorithm is further improved.The experimental results show that the algorithm can complete the reinforcement learning task,and has a strong advantage in data efficiency.