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

TL;DR

The paper introduces RDF, a differentiable distance-field representation for articulated robots that extends SDFs to whole-body geometry using per-link Bernstein-polynomial bases and kinematic transformations. By modeling the robot as the minimum over transformed per-link SDFs, the approach enables accurate, gradient-rich distance queries across joint configurations with compact, interpretable parameters and exact gradient computation. The authors demonstrate competitive accuracy and millisecond-scale inference, and validate the method on collision avoidance and dual-arm manipulation tasks, including real-robot experiments. This RDF framework facilitates integration of geometric awareness into optimization-based planning and control for complex, multi-link robotic systems, with demonstrated benefits in safety-critical and contact-rich manipulation scenarios.

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

Figures (6)

• Figure 1: Overview of this work. (a) A precise SDF model of an articulated robot is obtained efficiently by our proposed method. (b) Collision avoidance task based on the SDF representation. (c) Whole-body lifting task with dual-arm.
• Figure 2: Illustration of iterative learning for a two-dimensional SDF from samples at different locations. The weights are initialized to resemble a circular object. Red points are sequentially sampled for weight updates. The contour of the estimated object shape is depicted by the blue curve (0-level set of the SDF).
• Figure 3: We show the smoothness of distance and gradient produced by our approach, in both task space (a) and joint space (b), with comparisons to several baselines. The distance and gradient from point $t=[0,0,z]$ to the surface of link5 with a specific joint are shown in (a). The distance and gradient from a specific point to the robot surface at joint $q=[0,q_2,0,0,0,0,0]$ is shown in (b).
• Figure 4: Collision avoidance experiment in simulation. $g_1$ and $g_2$ represent the target points. Red points on the right arm are sampled with the level set $f=0.05$ to represent the safety threshold surface.
• Figure 5: Real-world collision avoidance experiment. Here, $g$ is the target point for the right arm. Red/black arrows show the reaching velocity with/without collision avoidance. Black dashed circles show the potential collision area.