ヘルダー符号付き距離：ロボティクスのための微分可能・符号付き・並列化可能な距離指標
Hölder Signed Distance: A Differentiable, Signed, Parallelizable Metric for Robotics
凸多面体間の距離を計算する新しい微分可能な符号付き距離関数を提案し、閉形式で計算できるため収束問題がなくGPU並列化に適している。ロボットマニピュレータの制御実験で有効性を示した。
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著者: Felipe Bartelt, Ali Umut Kaypak, Anthony Tzes, Farshad Khorrami, Luciano C. A. Pimenta, Vinicius M. Gonçalves
分類: cs.RO, cs.CG
原文アブストラクト
Computing distances between sets is essential in robotic motion planning and control, where differentiable gradients enable real-time optimization. The Euclidean Signed Distance Function (SDF), however, is not differentiable everywhere, and existing alternatives often sacrifice differentiability, sign information, or computational efficiency. In this letter, we introduce a novel differentiable signed distance between convex polyhedra. To this end, we first propose differentiable versions of the minimum and maximum operators, termed the Hölder minimum and Hölder maximum. We then replace the original min-max operators in the classical SDF formulation, yielding the Hölder signed distance. Unlike prior differentiable distance formulations that rely on iterative algorithms, our approach is computed in closed form, eliminating convergence issues while remaining naturally amenable to GPU parallelization. We validate the practical advantages and computational performance of the proposed distance through runtime comparisons with existing approaches. We also present a robotic manipulator experiment, demonstrating its suitability for applications in control.