Representing Robot Geometry as Distance Fields: Applications to Whole-body Manipulation

TL;DR

This paper introduces a novel, differentiable distance field representation for robot geometry that improves collision avoidance and manipulation by enabling smooth, accurate distance queries across joint configurations.

Contribution

It extends signed distance fields to articulated robots using Bernstein polynomials, providing a continuous, differentiable, and efficient geometric representation for manipulation tasks.

Findings

Effective in collision avoidance scenarios

Accurate distance queries in arbitrary configurations

Demonstrated on 7-axis Franka Emika robot

Abstract

In this work, we propose a novel approach to represent robot geometry as distance fields (RDF) that extends the principle of signed distance fields (SDFs) to articulated kinematic chains. Our method employs a combination of Bernstein polynomials to encode the signed distance for each robot link with high accuracy and efficiency while ensuring the mathematical continuity and differentiability of SDFs. We further leverage the kinematics chain of the robot to produce the SDF representation in joint space, allowing robust distance queries in arbitrary joint configurations. The proposed RDF representation is differentiable and smooth in both task and joint spaces, enabling its direct integration to optimization problems. Additionally, the 0-level set of the robot corresponds to the robot surface, which can be seamlessly integrated into whole-body manipulation tasks. We conduct various experiments in both simulations and with 7-axis Franka Emika robots, comparing against baseline methods, and demonstrating its effectiveness in collision avoidance and whole-body manipulation tasks. Project page: https://sites.google.com/view/lrdf/home