Global asymptotic stabilization control of a lake surface cleaning robot

In this paper an asymptotic stabilization control method for a lake surface cleaning robot (LSCR) is proposed. For the planar motion control, LSCR has a larger degree-of-freedom than the number of control inputs. This kind of system cannot be asymptotically stabilized using any time-invariant smooth feedback control law in Cartesian coordinate since the system violates the well-known Brockett´s necessary condition. To circumvent the constraints, a non-smooth transformation is used in the proposed control law. With a proper choice of the system state variables, we represent the position and orientation of the LSCR by a polar coordinate system centered at the desired position and transform the dynamics equation of the LSCR from the Cartesian coordinates to the polar coordinates. Then a feedback control law is derived based on a vectorial backstepping technique to guarantee global asymptotic stabilization of the close loop system in the sense of Lyapunov stability theory. And with the vectorial backstepping design approach, the position and orientation of the LSCR can be synchronously convergent to the desired configuration. The proof of the stability and convergence and the simulation results are presented.