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

Authors: K. Melhem, M. Saad, W. Wang, S.C. Abou

Addresses: Department of Mechanical Engineering, Lakehead University, Ontario, Canada. ' Department of Electrical Engineering, Ecole de technologie superieure, Quebec, Canada. ' Department of Mechanical Engineering, Lakehead University, Ontario, Canada. ' Department of Mechanical/Industrial Engineering, University of Minnesota, Duluth, MN, USA

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.

Keywords: output feedback; feedback stabilisation; tracking control; holonomic constraints; mechanical systems; linearisation; nonlinear; modelling; stability analysis; Cartesian robots; simulation.

DOI: 10.1504/IJMIC.2009.023526

International Journal of Modelling, Identification and Control, 2009 Vol.6 No.1, pp.10 - 25

Available online: 26 Feb 2009

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