Inverse kinematics of discretely actuated hyper-redundant manipulators using workspace densities

Hyper-redundant manipulators present an alternative to conventional 6 DOF manipulators for inspection, space, and medical applications. The additional degrees of freedom facilitate obstacle avoidance and allow tasks to be performed even if some of the actuators fail. In this paper the authors consider hyper-redundant manipulators that are actuated discretely, e.g. using two-state actuators or motors with finite resolution. The inverse kinematics problem for a discretely actuated manipulator is intrinsically different from the one for its continuously actuated counterpart. The authors present a framework for the discussion of the discretely actuated case and propose an algorithm for the inverse kinematics. The algorithm generates solutions in linear time with respect to the number of manipulator actuators, as opposed to the exponential time required by brute force search.