Visual regulation of a nonholonomic wheeled mobile robot with two points using Lyapunov functions

For the difficulty represented by the nonholonomic constraints of wheeled mobile robot (WMR), and the lack of stabilization ability via smooth time-invariant control law, all these factors make the visual servoing of WMR attractive research field. It seems that visual-based pose stabilization problem is more challenging than visual-based path following problem for WMR from the point of view of control. In this paper, a position-based visual regulation approach for a unicycle type WMR is proposed. A two-point based state estimation method for the planar motion of WMR is first derived. Based on the state estimation, the kinematics and dynamics of a unicycle type of WMR are expressed in Cartesian coordinate. With a proper choice of the system state variables, we represent the kinematics and dynamics model of the wheeled mobile robot by a polar coordinate system centered at the desired position. Then a feedback control law is derived based on backstepping technique to guarantee asymptotic stabilization of the close loop system in the sense of Lyapunov stability theory. The proof of the stability and convergence are provided based on the error dynamics. The simulation results show the convergence of the proposed approach.