対称性が学習ベース動作計画にもたらすもの
What Symmetry Buys a Learned Motion Planner
始点と終点で定まる座標系で軌道と障害物を表現することで、SE(3)の並進3・回転2の自由度を初期化時に除去し、混雑3D環境での衝突回避率を14.6%から51.1%へ改善した。
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？
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分類: cs.RO
原文アブストラクト
Learning-based motion planners pay at training what classical planners pay per query. Trained in world coordinates, they relearn the same motion at every position and orientation. Existing work restores the missing rigid-body equivariance in the training data, in the inference operator, or in the weights, and each carries a cost. We ask how much of that equivariance the planning query supplies for free. A start s and a goal g determine a frame in closed form, with origin at their midpoint and first axis along g-s. Expressing trajectory and obstacles in that frame removes three translations and two rotations of SE(3), at initialisation, for one cross product per query and with no constraint on the architecture. A single rotation about the start-goal axis remains, and no continuous rule removes it. On a cluttered 3D benchmark, holding architecture, data and budget fixed, the frame raises the held-out collision-free rate from 14.60% to 51.10%, where a straight segment from start to goal scores 15.6% and the world-frame model does not beat it. We build all three mechanisms for the residual rotation and each is worth under a point, though the equivariant backbone reaches any given level two to three times sooner. What the representation supplies therefore dominates what any mechanism enforces, and the standard diagnostic does not see the difference: two models with indistinguishable non-equivariance residuals differ by 28 points. Calibrated against a non-symmetry intervention, the frame is not even the largest effect available, since local geometry is worth +40.0 where the frame is worth +36.5.