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

2025-08-14

AI Summary

Safe, real-time trajectory planning for humanoid robots in unstructured, dynamic environments remains challenging due to their asymmetric geometry and time-varying obstacles. Method: We propose a geometry-aware real-time predictive safety filtering framework. It introduces a Poisson-based safety function to directly construct control barrier function (CBF) constraints from raw perception data, theoretically extended to handle time-varying obstacle domains. By integrating exact robot geometry into the configuration space via Minkowski set operations and coupling it with nonlinear model predictive control (NMPC), the framework enables safe, real-time trajectory generation. Contribution/Results: The method achieves millisecond-level online deployment on both humanoid and quadrupedal robot platforms across diverse complex scenarios. It significantly improves robustness to dynamic obstacles and geometric adaptability, while providing formally verifiable safety guarantees. This establishes a rigorous, deployable safety-critical control paradigm for embodied agents operating autonomously in open real-world environments.

Technology Category

• Humans and AI: Human-Aware Planning and Behavior Prediction
• Natural Language Processing: Safety and Robustness
• Intelligent Robots: Motion and Path Planning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Security and Privacy: Large-scale security measurements

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.

Problem

• Ensuring safety in autonomous navigation for legged robots
• Incorporating robot geometry into safety-critical trajectory planning
• Real-time predictive safety filtering using CBF constrained MPC

Innovation

• Uses CBF constrained MPC for safety
• Leverages Poisson safety functions numerically
• Incorporates Minkowski operations for geometry