On the iterative steering of a rolling robot actuated by internal rotors

This chapter deals with a motion planning problem for a spherical rolling robot actuated by two internal rotors that are placed on orthogonal axes. The mathematical model of the robot, represented by a driftless control system, contains a physical singularity corresponding to the motion of the contact point along the equatorial line in the plane of the two rotors. It is shown that steering through the singularity by finding a globally regular valid basis is not applicable to the system under consideration. The solution of the motion planning problem employs the nilpotent approximation of the originally non-nilpotent robot dynamics, and is based on an iterative steering algorithm. At each iteration, the control inputs are constructed with the use of geometric phases. To solve the state-to-state transfer problem, a globally convergent steering algorithm with adjustable step size is implemented and tested under simulation. It is shown that its steering efficiency is not superior to the algorithm with constant iteration step size.