Feedback Linearization of Differential-Algebraic Systems and Force and Position Control of Manipulators

The question of realization and feedback linearization of a class of differential-algebraic systems is considered. Based on nonlinear inversion of an input-output map, an analytical expression for the constraint force vector satisfying the algebraic constraints is derived. In this derivation, certain requirements on the relative degree of the output variables are relaxed. Using a new representation of the system in an extended state space, a control law is derived for the independent control of the chosen output variables satisfying algebraic constraints. These results are applied for the position and force control of robotic manipulators. Simulation results are presented for a three link robotic arm with revolute joints.