Uncertain Nonholonomic Kinematic Systems Robust Stabilization

For nonholonomic wheeled mobile robots with uncertainties, we discuss theexponential stabilization problems and the adaptive dynamic feedback trackingproblems in this thesis. Our objective is to propose a few new exciting uncertainchained form models, then design new robust controllers of exponential stabilizationand propose the new tacking controllers for the uncertain systems. The main results andthe innovations for this thesis are shown as follows:1. A few new uncertain chained models are obtained based on visual feedback andstate-input transformations for nonholonomic wheeled mobile robots. The innovationsare that a few new uncertain chained models of four types of nonholonomic wheeledmobile robots and a car with one or n trailers are obtained by using state-inputtransformations and visual feedback of fixed camera with unknown parameters. Then,we derived the more general uncertain chained models from the deduced uncertainmodels. The deduced uncertain chained models are different from those discussed bycontrol experts before. The structures of our new uncertain models do not satisfy theso-called triangularity condition. So the deduced models are a series of novel uncertainchained models.2. For the uncertain chained systems of type (1,1) robots, the exponentialstabilization controllers are addressed in two particular cases. The innovation is that anew exponential stabilization controller in more general case for the uncertain chainedsystem of type (1,1) robot is proposed based on the exponential regulation algorithm inthe particular case. The strict proof is given and the simulation results are shown.3. For the uncertain chained system of type (1,2) robot, four kinds of new controlschemes are presented in four different cases based on the state-scaling, state-inputtransformations and switching strategies. The strict proof is given and the simulationresults are shown for every case which means that the new controllers are effective.4. For the uncertain nonholonomic system of type (2,0) mobile robot, a newdynamic feedback tracking controller is introduced. Then, the new adaptive dynamictracking controller is obtained for type (1,2) robot in particular case. The innovation isthat a new adaptive and dynamic feedback tracking controller is obtained based on thebackstepping method, two transformations and Lyapunov function for the uncertain chained system of type (1,2) nonholonomic wheeled mobile robot. The controller canmake the tracking errors converge to zero asymptotically.To sum up, nonholonomic wheeled mobile robots are kinds of quite complexnonlinear control systems. In practice, precise kinematic models of robots are difficultto obtained due to imprecise measurements, unmodeling and disturbance etc.. Theproposed new uncertain chained models, the new exponential stabilization controllersand the tracking controller for the uncertain chained systems in this thesis not onlyenrich the contents of nonholonomic control theories of uncertain systems but also haveimportant practical significance for the control of wheeled mobile robots.