Self-motion topology for redundant manipulators with joint limits

The topology of self-motion manifolds for serial redundant manipulators in the presence of joint limits is investigated. It is known that the pre-images of singular taskpoints divide the configuration space into regions where self-motion manifolds are homotopic. The authors describe how self-motion manifolds are homotopic. The authors describe how self-motion manifolds rupture moving from one region to the next. The influence of joint limits on those topologies is investigated. This analysis leads to the discovery of the semi-singularity, a new type of singularity introduced by the presence of joint limits in redundant manipulators. As opposed to standard singularities, this type is unidirectional in nature. It has a significant impact in the structure of the kinematic map, as it generates the boundary between regions of different self-motion topologies. A 3-degree-of-freedom planar robot is used to illustrate the phenomena. This analysis is of fundamental importance for global redundancy resolution and path planning, as it describes the connectivity among regions in both the work space and the configuration space, as well as the topology of self-motion manifolds