接触運動学の解析的微分による衝突検出
Collision Detection with Analytical Derivatives of Contact Kinematics
形状の曲率がゼロや未定義となる退化配置でも滑らかに微分可能な接触運動学を実現するため、形状を厳密凸な陰的表現に正則化し、陰関数定理で接触距離・位置・法線の解析的微分を導出する衝突検出フレームワークiDCOLを提案。
詳しい要約
1. どんなもの？
2. 先行研究と比べてどこがすごい？
3. 技術・手法の肝は？
4. どうやって有効だと検証した？
5. 議論はある？
6. 次に読むべき論文は？
※ AIが要旨から生成した要約です。正確性は原文をご確認ください。
著者: Anup Teejo Mathew, Anees Peringal, Daniele Caradonna, Frederic Boyer, Federico Renda
分類: cs.RO
原文アブストラクト
Differentiable contact kinematics are essential for gradient-based methods in robotics, yet the mapping from robot state to contact distance, location, and normal becomes non-smooth in degenerate configurations of shapes with zero or undefined curvature. We address this inherent limitation by selectively regularizing such geometries into strictly convex implicit representations, restoring uniqueness and smoothness of the contact map. Leveraging this geometric regularization, we develop iDCOL, an implicit differentiable collision detection and contact kinematics framework. iDCOL represents colliding bodies using strictly convex implicit surfaces and computes collision detection and contact kinematics by solving a fixed-size nonlinear system derived from a geometric scaling-based convex optimization formulation. By applying the Implicit Function Theorem to the resulting system residual, we derive analytical derivatives of the contact kinematic quantities. We develop a fast Newton-based solver for iDCOL and provide an open-source C++ implementation of the framework. The robustness of the approach is evaluated through extensive collision simulations and benchmarking, and applicability is demonstrated in gradient-based kinematic path planning and differentiable contact physics, including multi-body rigid collisions and a soft-robot interaction example.
