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Stein Variational Ergodic Surface Coverage with SE(3) Constraints

Jiayun Li, Yufeng Jin, Sangli Teng, Dejian Gong, Georgia Chalvatzaki

TL;DR

This work introduces a preconditioned SE(3) Stein Variational Gradient Descent (SVGD) approach for SAO ergodic trajectory generation and shows that this sampling-based framework consistently identifies superior local optima compared to strong optimization-based and SAO baselines while preserving the SE(3) geometric structure.

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.

Stein Variational Ergodic Surface Coverage with SE(3) Constraints

TL;DR

This work introduces a preconditioned SE(3) Stein Variational Gradient Descent (SVGD) approach for SAO ergodic trajectory generation and shows that this sampling-based framework consistently identifies superior local optima compared to strong optimization-based and SAO baselines while preserving the SE(3) geometric structure.

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.
Paper Structure (16 sections, 20 equations, 5 figures, 1 table)

This paper contains 16 sections, 20 equations, 5 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. RELATED WORK
  3. Ergodic Coverage and Trajectory Optimization
  4. Trajectory Optimization as Inference on SE(3)
  5. Equality-constrained / Manifold SVGD
  6. PRELIMINARY
  7. Ergodic Coverage Optimization Problem
  8. Stein Variational Inference
  9. SE(3) Preliminary
  10. METHOD
  11. Stein Variational Gradient Descent on SE(3)
  12. Ergodic TO as Stein Variational Inference on SE(3)
  13. EXPERIMENT
  14. Benchmark Test
  15. Real World Task
  16. ...and 1 more sections

Figures (5)

  • Figure 1: Robot drawing the letters 'ICRA' followed by a heart symbol on the cylindrical surface of a pot using a pen mounted on its end effector, guided by point cloud input.
  • Figure 2: From left to right, the figure shows a colored point cloud on a torus model, the results after graph diffusion, and the projection onto a graph Fourier basis.
  • Figure 3: The SE(3) SVGD mechanism for sharing gradient information on the manifold: computing the natural gradient (black arrow) and applying parallel transport to obtain the final update direction (red arrow).
  • Figure 4: Six benchmark problems. From left to right: Mustard Bottle (simplified as Must), Pig, Spot, Bunny, Hand, and Torus. The background point cloud is shown in blue, ROIs in green, and the SDF in silver to enhance visualization. The TSVEC-planned trajectory is depicted as a solid line transitioning from light red to dark red, with normal vectors indicating time steps 1–200. Only the Z-axis is shown to avoid visual clutter. The objects are arranged according to ROI curvature variation, from flat to highly curved.
  • Figure 5: Left: SE(3) planning result on the hand-colored point cloud surface. Right: the corresponding sequential IK solution. The viewing angle matches that of Fig. \ref{['fig:real_world_panda']}, allowing a direct comparison between the planned and real-world results.