On Robust Adaptive Motion/Force Control of Nonholonomic Mechanical Systems: The Acatastatic Pfaffian Constraints Case

ABSTRACT

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 (Lagrangian) systems with Acatastatic nonholonomic 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-like 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 development of the adaptive position/force controllers for Lagrangian systems with the Acatastatic constraints. The adaptive control law guarantees the uniform ultimate boundness of the tracking error. A detailed numerical example is presented to illustrate the developed method.

Key Words:

• mechanical systems
• nonholonomic constraints
• Acatastatic Pfaffian constraints
• robust adaptive control
• force control