Robotics: Science and Systems XXI

Dynamic Safety in Complex Environments: Synthesizing Safety Filters with Poisson’s Equation

Gilbert Bahati, Ryan M. Bena, Aaron Ames

Abstract:

Synthesizing safe sets for robotic systems operating in complex and dynamically changing environments is a challenging problem. Solving this problem can enable the construction of safety filters that guarantee safe control actions---most notably by employing Control Barrier Functions (CBFs). This paper presents an algorithm for generating safe sets from perception data by leveraging elliptic partial differential equations, specifically Poisson’s equation. Given a local occupancy map, we solve Poisson’s equation subject to Dirichlet boundary conditions, with a novel forcing function. Specifically, we design a smooth guidance vector field, which encodes gradient information required for safety. The result is a variational problem for which the unique minimizer---a safety function---characterizes the safe set. After establishing our theoretical result, we illustrate how safety functions can be used in CBF-based safety filtering. The real-time utility of our synthesis method is highlighted through hardware demonstrations on quadruped and humanoid robots navigating dynamically changing obstacle-filled environments.

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Bibtex:

  
@INPROCEEDINGS{BahatiG-RSS-25, 
    AUTHOR    = {Gilbert Bahati AND Ryan M. Bena AND Aaron Ames}, 
    TITLE     = {{Dynamic Safety in Complex Environments: Synthesizing Safety Filters with Poisson’s Equation}}, 
    BOOKTITLE = {Proceedings of Robotics: Science and Systems}, 
    YEAR      = {2025}, 
    ADDRESS   = {LosAngeles, CA, USA}, 
    MONTH     = {June}, 
    DOI       = {10.15607/RSS.2025.XXI.137} 
}