Abstract
Surface manipulation tasks require robots to generate trajectories that comprehensively cover complex 3D surfaces while maintaining precise end-effector poses. Existing ergodic trajectory optimization (TO) methods demonstrate success in coverage tasks, while struggling with point-cloud targets due to the nonconvex optimization landscapes and the inadequate handling of SE(3) constraints in sampling-as-optimization (SAO) techniques. In this work, we introduce a preconditioned SE(3) Stein Variational Gradient Descent (SVGD) approach for SAO ergodic trajectory generation. Our proposed approach comprises multiple innovations. First, we reformulate point-cloud ergodic coverage as a manifold-aware sampling problem. Second, we derive SE(3)-specific SVGD particle updates, and, third, we develop a preconditioner to accelerate TO convergence. Our sampling-based framework consistently identifies superior local optima compared to strong optimization-based and SAO baselines while preserving the SE(3) geometric structure. Experiments on a 3D point-cloud surface coverage benchmark and robotic surface drawing tasks demonstrate that our method achieves superior coverage quality with tractable computation in our setting relative to existing TO and SAO approaches, and is validated in real-world robot experiments.
Abstract (translated)
表面操作任务要求机器人生成全面覆盖复杂三维曲面的轨迹，同时保持末端执行器的精确姿态。现有的遍历轨迹优化（TO）方法在覆盖率任务中表现出色，但在处理点云目标时由于非凸优化景观和采样-优化(SAO)技术对SE(3)约束处理不足而遇到困难。在这项工作中，我们引入了一种预条件化的SE(3) Stein变分梯度下降法（SVGD）用于SAO遍历轨迹生成。我们的方法包含了多项创新：首先，我们将点云遍历覆盖重构为一个关注流形的采样问题；其次，我们推导了适用于SE(3)特性的SVGD粒子更新公式；第三，我们开发了一种预处理器以加速TO收敛性。 基于采样的框架在识别局部最优解方面优于强大的优化基线和SAO方法，同时保留了SE(3)几何结构。实验表明，在一个三维点云表面覆盖基准测试和机器人表面绘图任务中，相较于现有的TO和SAO方法，我们的方法能够在现实世界的机器人实验中实现更高质量的覆盖率，并且计算量是可接受的。
URL
https://arxiv.org/abs/2603.09458
