2023/07/02 by Yiming Li, Yan Zhang, Li, Yiming +5 · 19 citations
Computer Science · Engineering · Mathematics · #Algorithm #Artificial intelligence #Computer science #Computer vision #Differentiable function #ENCODE #FOS: Computer and information sciences #Human Pose and Action Recognition #Kinematics #Leverage (statistics) #Mathematics #Mobile robot #Physics #Pure mathematics #Robot #Robot Manipulation and Learning #Robot kinematics #Robotic Path Planning Algorithms #Robotics (cs.RO) #Topology (electrical circuits)
paper · pdf · doi:10.48550/arxiv.2307.00533
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/07/02 · openalex created_date 2023/07/05 · openalex updated_date 2026/07/28
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