On mechanical control systems with nonholonomic constraints and symmetries

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. This method is demonstrated on two robotic locomotion mechanisms known as the snake board and the roller racer. The resulting coordinate representations are compact and lead to straightforward proofs of various controllability results.