Study On Motion Control For Nonholonomic Wheeled Mobile Robots With Control Input Constraints

Nonholonomic systems refer to as systems involving non-integral constraints, whichare in general finite-dimension mechanics such as manipulator, mobile wheeled, sky orsubmarine robots. Certainly, weightless astronauts, diving or gym athletes, which canalso change their position or posture without any help of fixed subject, are regarded asnonholonomic systems in the mathematical sense. In the opinion of control, nonholonomicsystems belong to strong nonlinear systems, and the obtained linear systems of theirJacobi linearization are uncontrollable, so linear control theory is not accessible to solvethe stabilization problem, that is, nonholonomic systems can not be stabilized by smooth(even continuous) static state-feedback control law and require totally nonlinear analysis.Wheeled mobile robots (WMRs) belong to typical nonholonomic systems. WMRs'nonholonomic characteristics is associated with the assumption of pure rolling withoutslipping between the wheels and the ground surface, which means that the motion con-straints are not integral, that is, the constraints can not be written in the form of timedi?erential of general coordinates. Although these nonholonomic constraints reduce theinstantaneous movement the WMRs can perform, WMRs are still globally controllable inthe configuration space. This unique characteristics makes design of feedback controllerfor WMRs a challenging task. WMRs have comprehensive application background inpractice and they are used to such situations as transportation, sweeping bombs, coop-erative rescue in dangerous scenario, vehicles for disabled person and outside washingmachine for high buildings. With the help of WMRs, productivity is enhanced, andWMRs release human being from dangerous so that they bring deep impact on man'sliving and product. At the meanwhile, investigation of the deep sea and deep sky is alsocontributed to the development of mobile robots. Research and development must bedone by the autonomous systems since the environment is unknown or abominable forman to perform task.Classical control strategies for trajectory tracking and stabilization can be classifiedas time-varying law, discontinuous law and hybrid law. The convergent speed is slow under the time-varying control scheme and discontinuous law can reduce this defect but attentionmust be payed to avoid singularity. The torque that actuating wheels is limited since itgenerates from the motor. If the actuator saturation is not taken into account during thedesign of control law, the closed-loop system may be result in performance degenerationand even unstable. Model predictive control(MPC) is a advanced control strategy whichis applied successfully to industrial product. The virtues of MPC include model adaption,convenient parameters adjusting and especially involving the constraints explicitly intooptimization problem easily. Many mobile robots work in a dynamic environment, soMPC has overwhelming merits and can take the actuator saturation into account easily.This thesis mainly studies the trajectory tracking, stabilization and unified trackingand stabilization control law for the WMRs considering the dynamic model with inputconstraints. The control input constraints can be included explicitly in designing themoving horizon optimization controller, and by on-line adjusting controller gains, dy-namic feedback linearization technique is used to design unified tracking and stabiizationconsidering the input constraints. Simulation experiments confirm the validation of thepresenting control law for tracking, stabilization or unified tracking and stabilization onthe representative type (2,0) WMRs.Firstly, a moving horizon stabilization control strategy which gives implicitly a con-trol law satisfying Brockett's theory is presented for dynamic model with friction. Inthe Cartesian frame, a quadratic cost function is chosen but simulation experiment showthat one of position coordinate has steady-state error and the idea of introducing expo-nentially increasing state weighting reduces the steady-state error greatly but remainsa nonzero value. By transform the Cartesian coordinates into Polar ones, the couplebetween position state is eliminated and asymptotically stabilization is obtained. Sim-ulation demonstrates that robot's movement trajectories are smooth, nature. When theconstraints are not asymmetric, moving horizon optimization strategy can deal with thissituation easily.Compared with classical control strategy,it is shown that moving horizoncontrol scheme has better performance.Due to obstruction of Brockett's theory, design of stabilization law for WMRs ischallenging. In the opinion of engineering, trajectory tracking is of practical value sincerobot must follow some trajectory even for the stabilization problem. When WMRs tracka persistent exciting trajectory, the time-varying linear system obtained by Jacobi lin-earization along the trajectory is congruously controllable. Utilizing on-line linearizationto determine the present stabilizing controller and the corresponding terminal region, aquasi-infinite model predictive control strategy is presented for the trajectory tracking ofrobots. Simulation experiments show that robot can reach the desired trajectory in short time and at the same time regarding input constraints. Compared with a control lawwhich does not take saturation into account confirms the presented method's validation.A undesired case may arise is that if the control task changes, control law mustswitch according to the assigned work. It had better that a unified control law canused to tracking and stabilization. Based on di?erential ?atness and dynamic extensiontechnology, this thesis presents a unified tracking and stabilization control law usingdynamic feedback linearizaiton(DFL) and discusses the selection of initial conditions toavoid singularity. On-line adjusting controller gains is used to keep the control input intothe required bounds. Simulation experiments of tracking a sin trajectory and parallelparking from di?erent start point show the validation of presented strategy.Many of the control law design method based on coordinate or input-output trans-formation demonstrate two disadvantages: one is resulting closed-loop trajectory presentsunnecessary oscillatory motions, the other is that control law respecting saturation basedtransformed system doesn't guarantee that the input of original system keep in the bound,so many scholars advocate to design control law based on original systems. This thesispresents a unified tracking and stabilization model predictive control strategy based oncontrol Lyapunov function technique. Terminal controller that guarantees closed-loopstability is designed and the corresponding terminal region is obtained. Good results areshowed by choosing di?erent start point for tracking and stabilization.Certainly, there are some topics that deserve further studying such as consideringmore complicated model although the dynamic description of type (2,0) robot is of rep-resentative and using current of voltage as control input where torques come from.