Motion Control Of Wheeled Mobile Robots

This thesis discusses some issues related to the motion control of wheeled mobile robots. These issues mainly include the unified stabilization and tracking control problem of wheeled mobile robots, the unified control of wheeled mobile robots not satisfying nonholonomic constraint, and the unified control of wheeled mobile robots moving on uncertain uneven surface. In addition, the finite-time control problem of chained systems is also investigated. The main contributions are exhibited by the following aspects:1. A robust unified controller is proposed for wheeled mobile robots that do not satisfying the ideal"rolling without slipping"constraint. Practical trajectory tracking and posture stabilization are achieved in a unified framework. The design procedure is based on Lie group, and the combination of the transverse function method with the Lyapunov redesign technique is utilized. The design is carried out on the perturbed kinematic model of the mobile robot. A bounded transverse function is firstly constructed, by which a corresponding smooth embedded submanifold is defined. After an augmentation procedure applied to the nominal kinematic model of the wheeled mobile robots, we explore the left-invariance property of this model with respect to the standard group operation of the Lie group SE(2), and define the error vector via group operation. Then the nominal error kinematic system is derived. The nominal feedback law is further constructed by employing classical linear control method, which renders the nominal error model practically stable. Finally, an additional control component is constructed to robustify the nominal control laws. The using of the transverse function method makes the whole design process systematic. Moreover, it's no longer needed that the reference trajectory is assumed to be"persistently exciting", which is nearly a standard assumption in trajectory tracking problem. The design method is easily extended to the robot system suffered from some unknown but bounded disturbances.2. Robust unified control framework is proposed for nonholonomic wheeled mobile robots moving on uneven surface that is not exactly known. The proposed control laws render the closed-loop dynamic system practically stable, and robust with respect to the effect of the gravity introduced by the uneven surface. Quadratic surfaces with unknown but bounded coefficients are utilized in the design process to locally approximate the uneven surfaces. The design procedure is also based on the transverse function method, as well as integrator backstepping and Lyapunov redesign technique. Due to the smoothness of the obtained"virtual"control laws, the integrator backstepping technique acts as a bridge between the kinematic and dynamic systems. Driven by the proposed control laws, the wheeled mobile robots have the ability of adaptation to varying surface condition. 3. A unified nonsingular control framework that enables both tracking and stabilization of unicycle type wheeled mobile robots is proposed. With the aid of dynamic feedback linearization and sliding mode control techniques, phase portrait analysis plays a key role in the design method. The influence of different initial state to the Cartesian trajectory of the robot is discussed in detail. Desired paths are properly planned based on the discussion, and suitable control parameters are chosen, as well as initial value of the additional state. Thus the potential singularity of the dynamic compensator is avoided, and a proper eventual orientation of the robot is ensured. The design process is direct and simple, and does not require any complex mathematical skills. The structure of the controller is simple and easy to implement. The control parameters are chosen according to some inequalities, thus the controller is robust with respect to some parameter variations; the employing of the sliding mode renders the close-loop system robust with respect to some external disturbances.4. The finite-time control problem of single chained system is investigated. The principal idea is to exploit the potential linear structure of the n-dimensional chained system, and make use of the finite-time convergence nature of the terminal sliding mode, thus achieves decouple of the control. In detail, the chained system is divided into a scalar subsystem and a (n-1)-dimensional LTV subsystem, then the controllability of the LTV subsystem which has a time-varying function system matrix is proved. A discontinuous feedback control laws is proposed by using the terminal sliding mode control method along with a piecewise control strategy. The chained system is finite-time stabilized by using the terminal sliding mode control technique. When the tracking problem is transformed to a equivalent stabilization problem of the error system, a finite-time tracking scheme is obtained through the proposed design method.