Singularity-consistent path tracking: a null space based approach

In this paper we develop further the recently proposed null-space method for path tracking at and around kinematic singularities. We consider two types of singularities known as ordinary singularities and bifurcation/isolated-point singularities. A closed-loop kinematic control scheme is introduced, which is able to keep precisely the direction of the specified end-effector path passing arbitrary close to kinematic singularities. The desired velocity magnitude can be maintained at regular points of the kinematic mapping. In the vicinity of singularities, the maximum available joint velocity specified from hardware limits can be applied. Several advantages of the proposed singularity-consistent approach are pointed out when compared with other well-known methods.