# Walking with Confidence: Safety Regulation for Full Order Biped Models

## TL;DR

This paper presents a novel method combining sums-of-squares optimization and hybrid zero dynamics to generate safety guarantees for complex 10-dimensional walking robot models, enabling safer control strategies.

## Contribution

It introduces a hybrid approach that applies sums-of-squares verification on a hybrid zero dynamics manifold for high-dimensional walking robots.

## Key findings

- Generated a guaranteed safe set for a 10D walking robot model
- Developed a safety-maintaining controller by adjusting manifold parameters
- Demonstrated the approach on a bipedal Rabbit model

## 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 paper 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 10-dimensional walking robot model. Along with this set, this paper 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 verification techniques to high dimensional systems. This opens the door for a broad set of tools that can generate safety guarantees and regulating controllers for complex walking robot models.