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Why do we move forward when we walk? Our legs undergo periodic motion andthus possess no net change in position; however, our bodies do possess a netchange in position and we are propelled forward. From a geometric perspective,this phenomenon of periodic input producing non-periodic output is holonomy. Toobtain non-zero holonomy and propel forward, we must alternate which leg is incontact with the ground; a non-zero net motion can be obtained by concatenatingarcs that would individually produce no net motion. We develop a framework forcomputing the holonomy group of hybrid systems and analyze their behavior inthe limit as the number of impacts goes to infinity.

How do we walk? Using hybrid holonomy to approximate non-holonomic systems