Stein Variational Ergodic Surface Coverage with SE(3) Constraints
Jiayun Li, Yufeng Jin, Sangli Teng, Dejian Gong, Georgia Chalvatzaki
AI summary
Problem
Existing ergodic trajectory optimization methods struggle with discrete point-cloud targets due to highly nonconvex optimization landscapes and inadequate handling of SE(3) geometric constraints in sampling-as-optimization techniques.
Approach
The authors reformulate point-cloud ergodic coverage as a manifold-aware sampling problem and derive a preconditioned SE(3) SVGD framework that enables parallel, geometrically consistent trajectory generation.
Key results
- Principled SVGD extension to the SE(3) manifold with parallel transport
- Gauss-Newton preconditioner for accelerated nonlinear least-squares convergence
- Consistent identification of superior local optima over strong baselines on 3D benchmarks
- Successful real-world validation on robotic surface drawing tasks
Why it matters
Enables precise, comprehensive 3D surface manipulation for robots in manufacturing, surgical, and maintenance applications by overcoming geometric and optimization barriers in trajectory planning.
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.