A Proposal for a Unified Concept of Kinematic Singularities for Holonomic and Non-Holonomic Mechanisms

The study of mechanism singularities has traditionally focused on holonomic systems. On the other hand many robotic systems are characterized by non-holonomic constraints, such as mobile platforms and manipulators driven by non-holonomic joints, and a general concept of singularities seems in order. In this paper a possible generalization of the singularity concept is proposed that equally accounts for holonomic and non-holonomic kinematic systems. The central object is the associated kinematic control problem. Singularities are identified as those configurations where the iteration depth of Lie brackets required to compute the accessibility Lie algebra changes. This notion of singularities is applied to serial manipulator and to non-holonomic mobile platforms. It is shown for holonomic manipulators that this is equivalent to the usual Jacobian rank condition. As example the condition is discussed for a Scara manipulator, a 6R manipulator, and for a kinematic car with one or two trailers.