A new decoupled sliding mode control approach for the linear motion of a spherical rolling robot

This paper investigates the dynamics and control aspects of the linear motion of a pendulum-driven spherical rolling robot. The dynamic model is deduced for the linear motion of a spherical robot by using the Euler-Lagrange formulation. By appropriate definitions the equations of motion for the robotic system are transformed into the state space form. A novel decoupled sliding mode control approach is proposed to achieve set-point regulation of the linear motion. This approach consists of the construction of a cascade sliding mode controller and the design of a nonlinear reaching law by using a switching component that dynamically adapts to the variations of the controlled system. The asymptotic stability of the robotic system is verified through Lyapunov analysis, and the validity of the proposed approach is illustrated through numerical simulations.