Stabilization and Control of a Spherical Robot on an Inclined Plane

In this study, the dynamics and control aspects of a spherical robot rolling without slipping on an inclined plane are investigated. The planar dynamic model of the robot rolling ahead on an inclined plane is derived using Lagrangian dynamics. Based on the equivalent control method and Lyapunov stability theorem, a decoupled sliding mode control approach is presented for stable control of the planar motion. Utilizing the constrained Lagrange method the three-dimensional dynamics of the robot rolling on an inclined plane are deduced. Based on input-output feedback linearization, we develop a trajectory tracking control algorithm for the three-dimensional motion of the robot. The validity of the proposed controllers is demonstrated through numerical simulations.