Study On Tracking Control Of Wheeled Mobile Robots: Model Predictive Control Approach

Model predictive control(MPC)has wide applications in process control systems due to its optimized control performance and powerful ability to handle the constraints.Over the past years,many important results on MPC,such as recursive feasibility,closed-loop stability as well as online computation complexity,have been addressed and the MPC theory reaches a relatively mature stage.However,its applications to wheeled mobile robot systems is still an embryonic stage,and lots of difficult but rather important problems still remain to be solved.For example,how to design terminal controller and its corresponding terminal state region in the existence of noholonomic constraint and coupled input constraint;how to make use of external disturbance information to design controllers which guarantee recursive feasibility and closed-loop stability and guarantee a better control performance;and how to further relive the heavy computational load of MPC to meet the real-time performance satisfaction.Motivated by these,this dissertation aims at developing practical MPC schemes for tracking of wheeled mobile robots.The main contents and contributions in this dissertation are summarized as follows.1.An MPC scheme for tracking of wheeled mobile robot subject to coupled input constraint is proposed.The tracking fashion is based on virtual structure.The desired position of the follower is considered to be a virtual structure point with respect to a Frenet-Serret frame fixed on the leader,and the desired control input of the follower depends not only on the input of the leader but also on the separation vector.A sufficient input condition for the leader robot is given to enable the follower to track its desired position while satisfying its inputs constraint.Then an MPC scheme is designed for the follower robot,in which recursive feasibility is guaranteed by developing a diamond-shaped positively invariant terminal-state region and its corresponding controller.Simulation results are provided to verify the effectiveness of the scheme proposed.2.Based on the results above,consider the external disturbances.Two robust MPC schemes are proposed for tracking wheeled mobile robots with input constraint and bounded disturbances: tube-based MPC and nominal robust MPC(NRMPC).In tubebased MPC,the control signal consists of an optimal control action obtained by solving an optimization problem and a nonlinear feedback law based on the deviation of the actual states from the optimal states of a nominal system.It renders the actual trajectory within a tube centered along the optimal trajectory of the nominal system.Recursive feasibility and input-to-state stability are established and the constraints are ensured by tightening the input domain and the terminal region.In NRMPC,an optimal control sequence is obtained by solving an optimization problem based on the current state,and then the first portion of this sequence is applied to the real system in an open-loop manner during each sampling period.The state of the nominal system model is updated by the actual state at each step,which provides additional feedback.By introducing a robust state constraint and tightening the terminal region,recursive feasibility and input-to-state stability are guaranteed.Simulation results demonstrate the effectiveness of both strategies proposed.3.The robust MPC mentioned above,in fact,is designed based on the worst case of the disturbances realization,which aims at achieving the best possible robustness at the sacrifice of nominal performance.Therefore,we develop a disturbance rejection model predictive control(DRMPC)scheme for tracking of nonholonomic robots with matched disturbances.Two disturbance observers(DOBs)are designed to estimate the unknown disturbances and the disturbances with known harmonic frequencies,respectively.By combining the DOB with MPC,DRMPC scheme is presented.Recursive feasibility of the optimization problem is guaranteed by tightening the terminal region and the input constraint.We show that the closed-loop system is input-to-state stable if no information about the disturbance is available and can reach an offset-free tracking performance if the harmonic frequencies of the disturbance are known.Simulations and experiments are provided to show the efficiency of the proposed approaches.4.Considering that traditional MPC requires quite heavy computation,we propose an event-triggered model predictive control(EMPC)for tracking of nonholonomic mobile robot.An event-triggering mechanism is presented by designing a threshold for the error between the actual trajectory and the predicted one,aiming at reducing the frequency of solving the optimization problem.Then an MPC strategy is developed based on the event-triggering mechanism.Recursive feasibility is guaranteed by designing a robust terminal region and the proper parameters.We show that the tracking system is practically stable and also provide an invariant set that the tracking error converges to.The convergence region indicates that the tracking performance is negatively related to the minimal inter-event time as well as the bound of the disturbances.Simulation results show that the computation load is significantly reduced and illustrate the efficiency of our proposed strategy.5.The EMPC approach discussed above are able to alleviate the computation burden to some extent,but it only reduces the frequency of solving the optimization problem.The computational complexity at each update remains high,because the prediction horizon is usually a fixed constant.Consequently,we propose event-based MPC with adaptive prediction horizon approach.We first propose a robust self-triggered MPC with adaptive prediction horizon scheme for a general class of constrained nonlinear discrete-time systems subject to additive disturbances.At each triggering instant,the controller provides an optimal control sequence by solving an optimization problem,and at the same time,determines the next triggering time and prediction horizon.By implementing the algorithm,the average sampling frequency is reduced and the prediction horizon is adaptively decreased as the system state approaches a terminal region.Meanwhile,an upper bound of performance loss is guaranteed when compared with the nominal periodic sampling MPC.Feasibility of the optimization problem and stability of the closed-loop system are established.Simulation results verify the effectiveness of the scheme.Then we apply the method to the tracking problem of wheeled mobile robots,and extend the scheme to eventtriggered case and self-triggered case.The schemes are tested on a networked platform in the laboratory to show their efficiency,which show that the proposed approaches are able to reduce the computational burden from two aspects: reducing the frequency of solving the optimization problem to relive the computational load and decreasing the prediction horizon to decline the computational complexity.At the end of this dissertation,the main results are concluded and the problems to be solved in the future are presented.