Full-Body Dynamic Safety for Robot Manipulators: 3D Poisson Safety Functions for CBF-Based Safety Filters

TL;DR

This paper introduces a novel framework using 3D Poisson Safety Functions to enforce full-body collision avoidance in high-dimensional robotic manipulators, improving safety in dynamic environments.

Contribution

It presents a new method to synthesize a single, smooth control barrier function for entire manipulators using Poisson's equation, addressing computational challenges.

Findings

Validated on a 7-DOF manipulator in dynamic environments.

Guarantees collision avoidance for the entire robot surface.

Enables real-time safety filtering with a single safety function.

Abstract

Collision avoidance for robotic manipulators requires enforcing full-body safety constraints in high-dimensional configuration spaces. Control Barrier Function (CBF) based safety filters have proven effective in enabling safe behaviors, but enforcing the high number of constraints needed for safe manipulation leads to theoretic and computational challenges. This work presents a framework for full-body collision avoidance for manipulators in dynamic environments by leveraging 3D Poisson Safety Functions (PSFs). In particular, given environmental occupancy data, we sample the manipulator surface at a prescribed resolution and shrink free space via a Pontryagin difference according to this resolution. On this buffered domain, we synthesize a globally smooth CBF by solving Poisson's equation, yielding a single safety function for the entire environment. This safety function, evaluated at each sampled point, yields task-space CBF constraints enforced by a real-time safety filter via a multi-constraint quadratic program. We prove that keeping the sample points safe in the buffered region guarantees collision avoidance for the entire continuous robot surface. The framework is validated on a 7-degree-of-freedom manipulator in dynamic environments.