Geometry-Aware Predictive Safety Filters on Humanoids: From Poisson Safety Functions to CBF Constrained MPC

TL;DR

This paper introduces a geometry-aware predictive safety filter for humanoid robots using control barrier functions and Poisson safety functions, enabling real-time, safety-critical trajectory planning in dynamic environments.

Contribution

It extends Poisson safety functions to dynamic domains and integrates them with CBF-based MPC for humanoids, addressing geometry and perception in safety constraints.

Findings

Successful real-time implementation on humanoid robots

Enhanced safety in dynamic, unstructured environments

Demonstrated versatility of Poisson safety functions

Abstract

Autonomous navigation through unstructured and dynamically-changing environments is a complex task that continues to present many challenges for modern roboticists. In particular, legged robots typically possess manipulable asymmetric geometries which must be considered during safety-critical trajectory planning. This work proposes a predictive safety filter: a nonlinear model predictive control (MPC) algorithm for online trajectory generation with geometry-aware safety constraints based on control barrier functions (CBFs). Critically, our method leverages Poisson safety functions to numerically synthesize CBF constraints directly from perception data. We extend the theoretical framework for Poisson safety functions to incorporate temporal changes in the domain by reformulating the static Dirichlet problem for Poisson's equation as a parameterized moving boundary value problem. Furthermore, we employ Minkowski set operations to lift the domain into a configuration space that accounts for robot geometry. Finally, we implement our real-time predictive safety filter on humanoid and quadruped robots in various safety-critical scenarios. The results highlight the versatility of Poisson safety functions, as well as the benefit of CBF constrained model predictive safety-critical controllers.