Reaction null-space based control of under-actuated manipulators

A general framework for under-actuated manipulator systems is introduced. Within this framework, we show how to decompose the second-order dynamic motion constraint into two orthogonal components. Based on this decomposition, feedback control laws are proposed for motion stabilization to a reactionless-motion equilibrium manifold. Reactionless motion without drift is guaranteed for first-order nonholonomic systems. It is also shown that for a second-order nonholonomic system, reactionless motion in general leads to a drift