  The general inverse kinematics (IK) problem of a manipulator, namely that of
acquiring the self-motion manifold (SMM) of all admissible joint angles for a
desired end-effector pose, plays a vital role in robotics modeling, planning
and control. To efficiently solve the generalized IK, this paper proposes an
interval branch-and-bound-based approach, which is augmented with a fast
numerical IK-solver-enabled search heuristics. In comparison to independent
solutions generated by sampling based methods, our approach generates patches
of neighboring solutions to provide richer information of the inherent geometry
of the SMM for optimal planning and other applications. It can also be utilized
in an anytime fashion to obtain solutions with sub-optimal resolution for
applications within a limited period. The performance of our approach is
verified by numerical experiments on both non-redundant and redundant
manipulators.
