Quasi-static legged locomotors as nonholonomic systems

We show how motion planning and control ideas for smooth nonholonomic systems can be extended to legged quasi-static locomotion via the notion of "stratified" configuration spaces and "stratified" control theory. We particularly consider "minimalist" legged systems, which are not well handled by conventional theories based on foot placement. We briefly discuss controllability issues, and then present a motion planning algorithm for stratified systems. The method does not depend upon the number of legs, nor is it based on foot placement concepts.