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.

翻译：曲面操作任务要求机器人能够生成在全面覆盖复杂三维曲面的同时保持精确末端执行器姿态的轨迹。现有的遍历轨迹优化方法在覆盖任务中已展现出成功，但在处理点云目标时却面临挑战，这源于非凸的优化景观以及在采样即优化技术中对SE(3)约束处理不足。本工作中，我们引入了一种预处理的SE(3) Stein变分梯度下降方法，用于采样即优化的遍历轨迹生成。我们提出的方法包含多项创新。首先，我们将点云遍历覆盖重新表述为一个流形感知的采样问题。其次，我们推导了SE(3)特定的SVGD粒子更新规则，并且第三，我们开发了一种预处理器以加速轨迹优化的收敛。与基于优化的强基线方法和采样即优化基线相比，我们基于采样的框架在保持SE(3)几何结构的同时，始终能识别出更优的局部最优解。在三维点云曲面覆盖基准测试和机器人曲面绘制任务上的实验表明，相对于现有的轨迹优化和采样即优化方法，我们的方法在设定条件下以可处理的计算量实现了更优的覆盖质量，并在真实世界的机器人实验中得到了验证。