Stein Variational Ergodic Surface Coverage with SE(3) Constraints

TL;DR

This paper introduces a novel SE(3)-aware Stein Variational Gradient Descent method for ergodic surface coverage, effectively handling complex 3D surfaces and constraints, outperforming existing optimization techniques in quality and efficiency.

Contribution

It develops a preconditioned SE(3) SVGD approach that reformulates surface coverage as a manifold-aware sampling problem, improving convergence and coverage quality.

Findings

Outperforms existing ergodic trajectory optimization methods.

Achieves superior coverage quality on 3D point-cloud benchmarks.

Validated in real-world robotic surface drawing tasks.

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.