Gaussian Process Implicit Surfaces As Control Barrier Functions for Safe Robot Navigation
Mouhyemen Khan, Tatsuya Ibuki, Abhijit Chatterjee
AI summary
Problem
Traditional control barrier functions rely on hand-crafted models or lack hardware validation in 3D, making it difficult to ensure safety in complex, unseen environments. There is a need for a scalable, data-driven method to construct safety boundaries directly from sensor measurements.
Approach
The method models 3D safety boundaries as implicit surfaces using Gaussian Processes, where the posterior mean defines the safety surface and the posterior variance provides a robust safety margin. A sparse GP approximation reduces computational cost, and the resulting function is used in a quadratic program to rectify nominal control inputs for collision avoidance.
Key results
- Unified framework synthesizing GPIS directly as Control Barrier Functions
- Sparse Gaussian CBF method reducing computational complexity while preserving safety guarantees
- Collision-free manipulation of a 7-DOF robot around a Stanford bunny in simulation
- Hardware validation of a quadrotor navigating safely around a physical chair in 3D
Why it matters
Provides a scalable, data-driven safety framework that enables real-world deployment of autonomous robots in complex 3D environments without relying on hand-crafted models.
Abstract
Level set methods underpin modern safety tech- niques 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. The ex- periment video link is: https://youtu.be/1XjaU3ulOVE.