Walking With Confidence: Safety Regulation for Full Order Biped Models

Abstract

Safety guarantees are valuable in the control of walking robots, as falling can be both dangerous and costly. Unfortunately, set-based tools for generating safety guarantees (such as sums-of-squares optimization) are typically restricted to simplified, low-dimensional models of walking robots. For more complex models, methods based on hybrid zero dynamics can ensure the local stability of a pre-specified limit cycle, but provide limited guarantees. This letter combines the benefits of both approaches by using sums-of-squares optimization on a hybrid zero dynamics manifold to generate a guaranteed safe set for a ten-dimensional walking robot model. Along with this set, this letter describes how to generate a controller that maintains safety by modifying the manifold parameters when on the edge of the safe set. The proposed approach, which is applied to a bipedal RABBIT model, provides a roadmap for applying sums-of-squares techniques to high-dimensional systems. This opens the door for a broad set of tools that can generate flexible and safe controllers for complex walking robot models.