Singularity avoidance for nonholonomic, omnidirectional wheeled mobile platforms with variable footprint

One characteristic attribute of mobile platforms equipped with a set of independent steering wheels is their omnidirectionality and the ability to realize complex translational and rotational trajectories. An accurate coordination of steering angle and spinning rate of each wheel is necessary for a consistent motion. Since the orientations of the wheels must align to the Instantaneous Center of Rotation (ICR), the current location and velocity of this specific point is essential for describing the state of the platform. However, singular configurations of the controlled system exist depending on the ICR, leading to unfeasible control inputs, i.e., infinite steering rates. Within this work we address and analyze this problem in general. Furthermore, we propose a solution for mobile platforms with variable footprint. An existing controller based on dynamic feedback linearization is augmented by a new potential field-based algorithm for singularity avoidance which uses the tunable leg lengths as an additional control input to minimize deviations from the nominal motion trajectory. Simulations and experimental results on the mobile platform of DLR's humanoid manipulator Justin support our approach.