Control of an pseudo-omnidirectional, non-holonomic, mobile robot based on an ICM representation in spherical coordinates

For mobile platforms with steerable standard wheels it is necessary to precisely coordinate rotation and steering angle of their wheels. Especially for redundantly actuated platforms the misalignments of a single wheel directly leads to invalid configurations which may cause degraded motion of the platform and high internal forces. An established approach to deal with this problem is to represent the current state of motion in form of the instantaneous centre of motion (ICM) and to derive a valid trajectory for this point. However, this representation bears severe numerical drawbacks. To remedy those numerical problems an alternative ICM representation based on spherical coordinates is proposed in this work. Furthermore, the relations between ICM and generalized robot velocities are addressed. It is shown, that one receives a basis of a subspace within the kinematical constraints¿ nullspace by decomposing the generalized velocity vector in spherical coordinates. Finally the proposed ICM-based control is particularized and simulative analyzed w.r.t. the Care-O-bot 3 demonstrator.