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

arXiv: https://arxiv.org/abs/2307.00533 · HTML: https://mlsanity.com/paper/2307.00533/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2023.

## Built on by (most cited first, 12 of 12)

- [HIO-SDF: Hierarchical Incremental Online Signed Distance Fields](https://mlsanity.com/paper/2310.09463/) (2023)
- [Neural Configuration-Space Barriers for Manipulation Planning and Control](https://mlsanity.com/paper/2503.04929/) (2025)
- [Neural Implicit Swept Volume Models for Fast Collision Detection](https://mlsanity.com/paper/2402.15281/) (2024)
- [Diffeomorphic Obstacle Avoidance for Contractive Dynamical Systems via Implicit Representations](https://mlsanity.com/paper/2504.18860/) (2025)
- [From Fields to Splats: A Cross-Domain Survey of Real-Time Neural Scene Representations](https://mlsanity.com/paper/2509.23555/) (2025)
- [Physics-Informed Eikonal Caging for Whole-Arm Manipulation Planning](https://mlsanity.com/paper/2606.22143/) (2026)
- [From Distances to Trajectories: Real-Time Signed Distance Function Mapping and Distance-Accelerated Motion Planning for UAVs](https://mlsanity.com/paper/2607.19306/) (2026)
- [RoboEye: Enhancing 2D Robotic Object Identification with Selective 3D Geometric Keypoint Matching](https://mlsanity.com/paper/2509.14966/) (2025)
- [Can Explicit Physical Feasibility Benefit VLA Learning? An Empirical Study](https://mlsanity.com/paper/2604.17896/) (2026)
- [RAM: Reachability Across Morphologies](https://mlsanity.com/paper/2606.09108/) (2026)
- [VERAGMIL: Virtual Environment for Scooping Granular Foods with Imitation Learning Models](https://mlsanity.com/paper/2608.18258/) (2026)
- [WBAG: A Whole-Body and Attached-Geometry Safety Framework for Vision-Language-Action Manipulation](https://mlsanity.com/paper/2610.01083/) (2026)

## Abstract (arXiv)

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