Variable Structure Control of Pendulum-driven Spherical Mobile Robots

In this paper, we propose a hierarchical sliding mode control approach for a fixed point regulation of pendulum-driven spherical mobile robots. A simplified dynamic model is established for their longitudinal motion and the controller is designed to have double layer structure because the system is divided into two subsystems. In the first layer, the sliding surfaces are hierarchically designed for each subsystem, and in the second layer, the whole sliding surface is designed as the linear combination of the two subsystem surfaces. The asymptotic stability of the whole system is verified by Lyapunov analysis, the stability of sliding surfaces and convergence of output variables are proved utilizing mathematical techniques. Finally, we carry out a simulation to illustrate the effectiveness of the proposed control scheme. Keywords-spherical robots; longitudinal motion; asymptotic stability; sliding mode control; underactuated systems