Stein Variational Ergodic Surface Coverage with SE(3) Constraints

2026-03-10

AI Summary

This work addresses the challenge of achieving complete coverage on complex 3D surfaces while respecting SE(3) pose constraints for the end-effector—a task where existing methods often struggle with non-convex optimization and inadequate coverage. To overcome these limitations, the authors propose a manifold-aware Sampling-as-Optimization (SAO) framework that formulates point cloud coverage as a sampling problem on the SE(3) manifold. They derive an SE(3)-specific Stein Variational Gradient Descent (SVGD) update rule and introduce a preconditioner to accelerate convergence while preserving geometric structure. The resulting approach significantly outperforms state-of-the-art trajectory optimization and SAO methods in both coverage quality and computational efficiency, with validation provided through extensive simulations and real-world robotic painting experiments.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Learning & Optimization for ROB
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

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.

Problem

• ergodic trajectory optimization
• SE(3) constraints
• point-cloud coverage
• nonconvex optimization
• robotic surface manipulation

Innovation

• Stein Variational Gradient Descent
• SE(3) constraints
• ergodic trajectory optimization
• manifold-aware sampling
• preconditioning