Position/force control design for constrained mechanical systems: Lyapunov's direct method

A design procedure for simultaneous position/force control is developed, using Lyapunov's direct method for mechanical systems with holonomic constraints. Many mechanical systems which interact with their environment require the effects of these constraints to be taken into account in the control design. The force applied by the constraint plays a critical role in constrained motion and is, along with displacements and velocities, to be regulated at specified values. Lyapunov's direct method is used to develop a class of decentralized position/force controllers. The approach avoids coordinate transformation and does not require force feedback. The conditions for gain selection demonstrate the importance of the constraints. An example is used to demonstrate this control design method; closed-loop characteristics are indicated by computer simulations