Adaptive motion/force control of mechanical systems with nonholonomic Pfaffian constraints

The contribution of this work relates to two subjects. In the first part of the paper the authors present a novel dynamic description of mechanical (Lagrangian) systems with nonholonomic (Pfaffian) constraints. This development was motivated by the need for a convenient and simple dynamic model for the controller. Essentially, the new element of this development is QR decomposition of the constraint matrix. Following this decomposition, the authors have proven a new dynamic property of the considered system. This property allows the authors to express the system dynamics in terms of a new reduced-order state vector. The second part of the work is concerned with development of the adaptive position/force controllers for general Lagrangian systems with Pfaffian constraints. Two cases are elaborated: (i) motion/force tracking control with known system parameters, and (ii) adaptive control in the presence of uncertainties. The adaptive control law guarantees the uniform ultimate boundness of the tracking error