Towards a Unified Notion of Kinematic Singularities for Robot Arms and Non-holonomic Platforms

Abstract

Kinematic singularities are classically defined in terms of the rank of Jacobians of associated maps, such as forward and inverse kinematic mappings. A more inclusive definition should take into account the Lie algebra structure of related tangent spaces. Such a definition is proposed in this paper, initially for serial manipulators and non-holonomic platforms. The definition can be interpreted as a change in the number of successive infinitesimal motions required for the system to reach an arbitrary configuration in the vicinity of the given configuration. More precisely, it is based on the filtration of a controllability distribution.