Trajectory Tracking Control Of Omnidirectional Mobile Manipulator Using Koopman Operator And Gaussian Process Regression

Omnidirectional mobile manipulator is widely used because of its wide working space and flexible operation ability.However,the system itself has the characteristics of high coupling and strong uncertainty,and the modeling process is complex.Taking the omnidirectional mobile manipulator as the research object,this paper uses the combination of Koopman operator and Gaussian process regression(GPR)to generate the data-driven model of the system,and then based on this model,the data-driven trajectory tracking control system is designed by using model predictive control and event trigger control algorithm.Using the method of combining Koopman operator with GPR for system modeling can not only effectively improve the modeling accuracy of traditional Koopman operator,but also compared with black box models such as neural network,the obtained model form is simple and convenient for model-based controller design.The main contents of this paper are as follows:First,the data-driven model of omnidirectional mobile manipulator system is established based on Koopman operator and GPR.The approximate matrix of Koopman operator is obtained by using the extended dynamic mode decomposition method,and the high-dimensional linear state space expression of the system is preliminarily constructed.The input and output data are filtered according to the information maximization criterion,and the data subset rich in information is established.Based on this data set,an off-line Gaussian model is generated by GPR to effectively predict the modeling error of Koopman operator.Finally,the accuracy of the proposed method is verified by simulation and experiment.Then,considering that the system will be affected by uncertain factors such as environmental interference,a model predictive controller based on Koopman model and online GPR is designed to improve the control accuracy and robustness of the control system.Online GPR algorithm is used to adjust the offline Gaussian model online,estimate the internal and external disturbances of the system in real time,and compensate in real time in the predictive controller based on Koopman model.In addition,the calculation time of on-line GPR is shortened by inverse matrix transformation and selective forgetting technology to ensure the real-time performance of system disturbance prediction.Finally,the effectiveness of the proposed algorithm is verified by simulation and experiments.Finally,aiming at the time-consuming problem of online GPR algorithm,event triggered control and extended state observer(ESO)are introduced,and an event triggered model predictive controller based on Koopman model,ESO and offline GPR is designed.The disturbance of the system is estimated in real time by using ESO and off-line GPR and compensated in the predictive controller based on Koopman model.At the same time,the event trigger mechanism is introduced into the controller,and the event trigger conditions are designed on the basis of maintaining the stability of the system,which reduces the calculation times of the controller.Finally,the stability of the whole closed-loop system is analyzed under the event trigger mechanism,and the superiority of the proposed control method is verified by simulation and experiment.