Gaussian Process Implicit Surfaces as Control Barrier Functions for Safe Robot Navigation

2025-10-14

AI Summary

This work addresses the challenge of safe robot navigation in complex, uncertain environments. We propose directly modeling Gaussian Process Implicit Surfaces (GPIS) as Control Barrier Functions (CBFs), enabling data-driven, online construction of dynamic safety boundaries. Methodologically, we introduce the first formulation that jointly incorporates the GPIS posterior mean and variance into the CBF constraint, ensuring reliable obstacle avoidance under uncertainty. To overcome the computational bottleneck of standard GPs, we design a sparse Gaussian CBF framework leveraging inducing-point approximations for real-time deployment. Evaluated on 3D collision-avoidance tasks with a 7-DOF manipulator and a quadrotor, our approach successfully rectifies initially unsafe trajectories and achieves millisecond-level safe navigation under both dense and sparse sensing modalities. Results demonstrate significant improvements in adaptability and robustness over conventional CBFs in unknown environments.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

Abstract

Level set methods underpin modern safety techniques such as control barrier functions (CBFs), while also serving as implicit surface representations for geometric shapes via distance fields. Inspired by these two paradigms, we propose a unified framework where the implicit surface itself acts as a CBF. We leverage Gaussian process (GP) implicit surface (GPIS) to represent the safety boundaries, using safety samples which are derived from sensor measurements to condition the GP. The GP posterior mean defines the implicit safety surface (safety belief), while the posterior variance provides a robust safety margin. Although GPs have favorable properties such as uncertainty estimation and analytical tractability, they scale cubically with data. To alleviate this issue, we develop a sparse solution called sparse Gaussian CBFs. To the best of our knowledge, GPIS have not been explicitly used to synthesize CBFs. We validate the approach on collision avoidance tasks in two settings: a simulated 7-DOF manipulator operating around the Stanford bunny, and a quadrotor navigating in 3D around a physical chair. In both cases, Gaussian CBFs (with and without sparsity) enable safe interaction and collision-free execution of trajectories that would otherwise intersect the objects.

Problem

• Unifying implicit surface representation with control barrier functions
• Developing sparse Gaussian process solution for computational efficiency
• Validating safe robot navigation in manipulator and quadrotor scenarios

Innovation

• GPIS defines safety boundaries as control barrier functions
• Sparse Gaussian CBFs address computational scaling limitations
• Posterior variance provides robust safety margins for navigation