Stability analysis and tracking control of holonomic mechanical systems: a constructive approach

Abstract

This paper proposes a constructive approach for the problem of feedback stabilisation and tracking control of holonomic mechanical systems. The approach is based on the premise that the non-reduced order dynamics of the holonomically constrained system is composed of the unconstrained original dynamics and a term of constraint force. The main stream which links and enables the authors' approach is the technical observation that the constraint force is zero or convergent to zero in closed-loop operation. More importantly, using this stabilisation technique, simple 'global' output feedback tracking control laws can be designed for holonomic mechanical systems with linear original dynamics (e.g., Cartesian structure robots). Furthermore, a discussion is given on the output stability result for general holonomic mechanical systems leading to the introduction of a new linearisation approach based on immersion and static state feedback transformations. Numerical simulations are provided to verify the effectiveness of the main ideas.