Kinematic and dynamic singularities of non-holonomic robotic systems

Abstract

We shall study non-holonomic robotic systems represented by either a driftless or a control affine control system with outputs. Two types of singularities are considered: the posture singularities around which the growth vector of the system's distribution is non-constant, and the configuration singularities at which the system's Jacobian is not surjective, related with the singular optimal controls. Using some recent results of sub-Riemannian geometry we provide computational tools for the determination of the configuration singularities. Theoretical arguments are supported by examples of the kinematics of the ball rolling with spinning, and the front wheel driven car with dynamics.