Path Following Control of a Spherical Robot Rolling on an Inclined Plane

In this paper, the path following control of a spherical robot rolling without slipping on an inclined plane is discussed. We first study the kinematic constraints of the spherical robot and develop the dynamic model of the robot through the constrained Lagrange method. We then present a state space realization of this constrained system through the null space method and using nonlinear feedback. We investigate the path following control algorithms and develop a variable structure approach to the control of this nonholonomic system. By choosing appropriate output equations for path following, we design the sliding surfaces as the functions of the output tracking errors. Using Lyapunov stability theorem and exponential reaching law, we derive the sliding mode control law. The asymptotic stability of the sliding surfaces is theoretically proved, and the validity of the proposed path following method is further validated through MATLAB simulations. Copyright © 2013 IFSA.