On mechanical control systems with nonholonomic constraints and symmetries

• Published in: Systems & control letters Vol. 45; no. 2; pp. 133 - 143
• Main Authors: Bullo, Francesco, Žefran, Miloš
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.02.2002; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control of mechanical systems; Control system synthesis; Control theory. Systems; Differential geometric methods; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mechanical systems; Modeling; Nonholonomic constraints; Nonlinear control; Physics; Solid dynamics (ballistics, collision, multibody system, stabilization...); Solid mechanics; Nonholonomic constraints; Mechanical systems; Modeling; Nonlinear control; Differential geometric methods; Locomotion; Lagrangian; Equation of motion; Differential geometry; Mechanical system; Non holonomic system; Mechanical control; Controllability; Lagrangian system; Robotics; Symmetry
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/S0167-6911(01)00173-6

This paper presents a computationally efficient method for deriving coordinate representations for the equations of motion and the affine connection describing a class of Lagrangian systems. We consider mechanical systems endowed with symmetries and subject to nonholonomic constraints and external forces. The method is demonstrated on two robotic locomotion mechanisms known as the snakeboard and the roller racer. The resulting coordinate representations are compact and lead to straightforward proofs of various controllability results.