On robust adaptive motion/force control of nonholonomic mechanical systems: The Acatastatic Pfaffian constraints case

The contribution of this work relates to two subjects. In the first part of the paper we present a reduced order dynamic description of mechanical (La grangian) systems with Acatastatic nonholonomic constraints. This developme nt was motivated by the need for a convenient anti simple dynamic model for the controller. Essentially, the new element of this development is QR-lik e decomposition of the constraint matrix. Following this decomposition, we have proven a new dynamic property of the considered system (see Property3) . This property allows us to express the system dynamics in terms of a new reduced-order state vector. The second part of the work is concerned with d evelopment of the adaptive position/force controllers for Lagrangian system s with the Acatastatic constraints. The adaptive control law guarantees the uniform ultimate boundness of the tracking error. A detailed numerical exa mple is presented to illustrate the developed method.