Approaches to Motion Planning for a Spherical Robot Based on Differential Geometric Control Theory

We present the approaches to motion planning for a spherical robot with a stable platform, which is not a nilpotent system. Firstly, the kinematic equations of the spherical robot are changed into an affine nonlinear control system without drift. The procedure starts by computing a control that steers the given initial configuration to the desired target configuration for an extended system using a Philip Hall basis of the controllability Lie algebra. The motion planning algorithm for the extended system is proposed. The solution to motion planning for the original system is then obtained using the Philip Hall coordinates. An iterative algorithm is given to generate arbitrary precision, and two methods of motion planning for the spherical robot are summarized. Finally, the simulation results of the motion planning examples illustrate the effectiveness of the methods