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Among control problems for mobile robots, point-to-point stabilization is the most challenging since it does not admit designs with smooth static state feedback laws. Stabilization strategies for mobile robots, and nonholonomic systems generally, are smooth, time-varying or nonsmooth, time-invariant. Time-varying control strategies are designed with umdamped linear oscillators but their fixed structure offer limited flexibility in control design. The central theme of this paper lies in use of nonlinear oscillators for mobile robot control. Large numbers of qualitatively different control strategies can be designed using nonlinear oscillators since stiffness and damping can be functions of robot states. We demonstrate by designing two fundamentally different controllers for two-wheeled mobile robot using two variants of a particular nonlinear oscillator. First controller is dynamic and generates smooth control action. Second controller is almost-smooth and time-invariant. While first controller guarantees global asymptotic stability for any desired posture of robot, second controller is stable, and converges robot from almost any posture to desired posture. The only gap in posture space is unstable equilibrium manifold of measure zero. For both control strategies we mathematically establish stability and convergence of mobile robot to desired posture. Simulation results support theoretical claims. ©1999 John Wiley & Sons, Inc.
Mukherjee et al. (Thu,) studied this question.