Planning and Control of Locomotion for a Quadruped: Studying the Curvet Gait

Abstract

In many ways, the simple act of walking is one of the most complex modes of locomotion there is. For control-system scientists the periodic hybrid dynamical nature of walking systems presents a number of unique challenges, many of which still lack satisfying solutions. This thesis applies fairly recent concepts of motion generation and control to generate steps and gaits for such a walking robotic system. The robot, SemiQuad, developed and built at '{E}cole de Nantes in France, is a five degree of freedom, underactuated periodic hybrid dynamical system. This text presents a generic method of reparametrizing a given smooth motion by the use of virtual holonomic constraints, and comments on the conditions required for the method to succeed. It is then shown how virtual holonomic constraints can be generated from scratch, and certain properties of holonomically constrained systems are investigated. From the generated constraints and associated motion, a controller based on the principle of transverse linearization is created, and closed loop characteristics of the system are observed.