Variable Structure Control of Pendulum-driven Spherical Mobile Robots

Abstract

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 Omni-directional rolling of spherical mobile robots can be realized by combinations of their longitudinal and lateral motions. Our research in this paper is confined to the longitudinal motion control problems. We propose a hierarchical sliding mode control approach for the pendulum-driven spherical mobile robot system, which is a single-input multi-output nonlinear underactuated system. In the proposed control system, the double layer structure is adopted to guarantee the stability of the whole system. In addition, the sliding surfaces are utilized to drive the output tracking errors to zero. Here, the sliding surfaces of the first layer are designed at each subsystem, while the whole sliding surface is the linear combination of the two subsystem sliding surfaces.