Feedback control strategies for a nonholonomic mobile robot using a nonlinear oscillator

Among control problems for mobile robots, point-to-point stabilization is t he most challenging since it does not admit designs with smooth static stat e feedback laws. Stabilization strategies for mobile robots, and nonholonom ic systems generally, are smooth, time-varying or nonsmooth, time-invariant . Time-varying control strategies are designed with umdamped Linear oscilla tors but their fixed structure offer Limited flexibility in control design. The central theme of this paper lies in use of nonlinear oscillators for m obile robot control. Large numbers of qualitatively different control strat egies can be designed using nonlinear oscillators since stiffness and dampi ng can be functions of robot states. We demonstrate by designing two fundam entally different controllers for two-wheeled mobile robot using two varian ts of a particular nonlinear oscillator. First controller is dynamic and ge nerates smooth control action. Second controller is almost-smooth and time- invariant. While first controller guarantees global asymptotic stability fo r any desired posture of robot, second controller is stable, and converges robot from almost any posture to desired posture. The only gap in posture s pace is unstable equilibrium manifold of measure zero. For both control str ategies we mathematically establish stability and convergence of mobile rob ot to desired posture. Simulation results support theoretical claims. (C) 1 999 John Wiley & Sons, Inc.