Beyond Basins of Attraction: Evaluating Robustness of Natural Dynamics

It is commonly accepted that properly designing a system to exhibit favorable natural dynamics can greatly simplify designing or learning the control policy. It is however still unclear what constitutes favorable natural dynamics, and how to quantify its effect. Most studies of simple walking and running models have focused on the basins of attraction of passive limit-cycles, and the notion of self-stability. We emphasize instead the importance of stepping beyond basins of attraction. We show an approach based on viability theory to quantify robustness, valid for the family of all robust control policies. This allows us to evaluate the robustness inherent to the natural dynamics before designing the control policy or specifying a control objective. We illustrate this approach on simple spring mass models of running and show previously unexplored advantages to using a nonlinear leg stiffness. We believe designing robots with robust natural dynamics is partic- ularly important for enabling learning control policies directly in hardware.