Lyapunov-stable position/force control based on dual nature in constraint motion

In the model of the constrained dynamic system of a rigid robot contacting with rigid environment, constrained forces can be expressed as an algebraic function of states (instantaneous process) and a redundancy existing in constraint dynamics (constraint redundancy). Using these results, a force and position control law is proposed by taking the advantages of the redundancy of input generalized forces to the constrained forces and instantaneous process without involving any force sensor, using dual nature of constraint motion stated in this document. Then proof confirming by Lyapunov method that the exerting force equals instantaneously and constantly to desired one and that the motion of robot´s hand in a movable space converges to desired hand´s position. The effectiveness has been confirmed by a 2-link robot in simulations.