On the passive dynamics of quadrupedal running

Abstract

In this thesis, the dynamics of quadrupedal running via the bounding gait is studied. To analyse the properties of the passive dynamics of Scout II, a model consisting of a body and two massless spring-loaded prismatic legs is introduced. A return map is derived to study the existence of periodic system motions. Numerical studies of the return map show that passive generation of cyclic motion is possible. Most strikingly, local stability analysis of the return map shows that the dynamics of the open loop passive system alone can confer stability of the motion. Stability improves at higher speeds, a fact which is in agreement with recent results from biomechanics showing that the dynamics of the body become dominant in determining stability when animals run at high speeds. Furthermore, pronking is found to be more unstable than bounding, which explains why Scout II shows a "preference" for the bounding gait. These results can be used in developing a general control methodology for legged robots, resulting from the synthesis of feed-forward and feedback models that take advantage of the mechanical system.