Hybrid system safety guarantees with goal-driven control methods
Hamilton-Jacobi Reachability for Hybrid Systems: Unified Goal-Driven Control with Safety Guarantees
Robotics
Summary
Robots that mix different types of movements and modes, like walking and jumping, can be tricky to control safely. The authors extended a mathematical method called Hamilton-Jacobi reachability to handle these hybrid systems. This helps find safe ways for robots to behave while still achieving their goals, like moving without falling or reaching a target. They tested their approach on a four-legged robot to show it works in real life.
What this means in practice
- •For robotics engineers: Design control systems for legged robots that assure safety during complex movements involving mode switches like walking and jumping.
- •For autonomous vehicle developers: Create safety filters that intervene only when necessary to maintain safe driving modes while pursuing navigation goals involving discrete mode changes.
Authors
Javier Borquez, Shuang Peng, Somil Bansal
Abstract
Hybrid dynamical systems provide a powerful modeling framework for robotic systems, particularly in contact-rich environments. However, ensuring safety and performance in such systems remains challenging due to the intricate coupling between continuous dynamics and discrete mode transitions. In this work, we extend classical Hamilton-Jacobi (HJ) reachability analysis, a formal verification method for continuous-time nonlinear systems, to hybrid dynamical systems. Our framework characterizes safe sets for hybrid systems through a generalized value function defined over both discrete and continuous states while accounting for control constraints and model uncertainty. We additionally provide a numerical algorithm to compute this value function. Building on these safe sets, we propose two different mechanisms to integrate performance objectives. First, we introduce a hybrid least-restrictive safety filter that intervenes on both the discrete and continuous components of a nominal controller only when necessary to avoid unsafe states, thereby preserving nominal behavior whenever possible. Second, we formulate and compute hybrid backward reach-avoid tubes, enabling the simultaneous enforcement of safety and goal-reaching behavior, an extension not previously addressed within hybrid HJ reachability. This enables the synthesis of continuous and discrete control policies that guarantee both safety and task completion. We validate our framework through simulation studies and real-world experiments on a quadrupedal robot, demonstrating its effectiveness in hybrid mode planning and safety-critical applications.