Design and control of a redundant mechanism for small motion

Redundant manipulators are expected to increase robot performance by reducing the problem of workspace singularities, allowing for obstacle avoidance and providing the opportunity for gross motion optimization. We show that the addition of redundant joints can also increase the dynamic response for small motions of the manipulator at its endpoint. We begin by considering a two link mechanism, which is the simplest redundant system for effecting motion in a single direction. It is shown that the addition of a second link reduces the power required for sinusoidal motion at the mechanism endpoint. A method of choosing the relative link dimensions is then presented. Given a particular choice of link lengths, we show how to allocate motion between the joints to minimize the power required for a specified amplitude of motion. Finally, a strategy is proposed for local control of this redundant system which uses a quick acting mode to respond to disturbances and high bandwidth commands, and a slow acting mode to return the mechanism to a nominal configuration. The implications for control of redundant manipulator systems (i.e. hand and arm systems) are discussed.