发表机构
Shanghai Jiao Tong University（上海交通大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出利用起点和终点闭式构造坐标系，在初始化时消除大部分刚体等变性，显著提升学习型运动规划器的无碰撞率，且优于强制等变机制。
AI 中文摘要
基于学习的运动规划器在训练时付出的代价，相当于经典规划器每次查询时付出的代价。由于在世界坐标系中训练，它们会在每个位置和朝向上重新学习相同的运动。现有工作要么在训练数据中、要么在推理算子中、要么在权重中恢复缺失的刚体等变性，而每一种方式都有其代价。我们探究规划查询本身能免费提供多少这种等变性。起点 s 和终点 g 以闭式确定一个坐标系，其原点位于两者中点，第一轴沿 g-s 方向。在该坐标系中表示轨迹和障碍物，可在初始化时消除 SE(3) 的三个平移和两个旋转，每次查询仅需一次叉积，且对架构无任何约束。仅剩绕起点-终点轴的一个旋转，且没有任何连续规则能消除它。在一个杂乱的三维基准测试中，保持架构、数据和预算不变，该坐标系将留出（held-out）无碰撞率从 14.60% 提升至 51.10%，而起点到终点的直线段得分为 15.6%，世界坐标系模型并未超过该得分。我们为剩余旋转构建了全部三种机制，每种机制的贡献均不足一个百分点，尽管等变骨干网络达到任意给定水平的速度要快两到三倍。因此，表示所提供的内容主导了任何机制所强制的内容，而标准诊断方法看不到这种差异：两个非等变性残差无法区分的模型，得分相差 28 个百分点。对照非对称性干预进行校准后，坐标系甚至不是可用的最大效应，因为局部几何的贡献为 +40.0，而坐标系的贡献为 +36.5。
英文摘要
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.
Comments8 pages, 2 figures, 3 tables
