Coordinating Kinematically Redundant Degrees of Freedom

There are a variety of manifestations of kinematic redundancy in different classes of robotic mechanisms such as manipulator arms, multifingered hands, mobile robots, etc., and while common issues arise in motion planning for such devices, the literature on resolving kinematic redundancy has principally been focused on manipulator arms. The present note will describe the current state of algorithms which resolve kinematic redundancy by optimizing path-integral criteria. This approach has practical advantages in certain application, but it leads to a class of two point boundary value problems which, if solved by standard numerical procedures, are substantially more complex than resolution techniques based on optimizing instantaneous functions of the joint configurations. Our recent work has shown that using the theory of exponential dichotomies we may develop continuation methods which render these problems more manageable while at the same time relating their solution to well understood instantaneous methods.