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.
Ergodic Trajectory Optimization on Generalized Domains Using Maximum Mean Discrepancy
Department of Mechanical Engineering, Yale University（耶鲁大学机械工程系）；School of Computer Science, The University of Sydney（悉尼大学计算机科学学院）；School of Mathematics, The University of Edinburgh（爱丁堡大学数学学院）；NVIDIA
Autonomous Robotic Tissue Palpation and Abnormalities Characterisation via Ergodic Exploration
Department of Information Engineering and Computer Science, University of Trento（信息工程与计算机科学系，特伦托大学）；Department of Industrial Engineering, University of Trento（工业工程系，特伦托大学）
Search at Scale: Improving Numerical Conditioning of Ergodic Coverage Optimization for Multi-Scale Domains
Department of Applied Mathematics, UCLouvain (Université catholique de Louvain)（应用数学系，UCLouvain（比利时列日大学））；Department of Mechanical Engineering, Yale University（机械工程系，耶鲁大学）
Optimizing Start Locations in Ergodic Search for Disaster Response
Robotics Institute, Carnegie Mellon University（机器人研究所，卡内基梅隆大学）；United States Air Force Academy Electrical and Computer Engineering Dept.（美国空军学院电气与计算机工程系）
Constrained multi-agent ergodic area surveying control based on finite element approximation of the potential field
Faculty of Engineering, University of Rijeka（里耶卡大学工程学院）；Center for Advanced Computing and Modelling, University of Rijeka（里耶卡大学高级计算与建模中心）；University of Rijeka（里耶卡大学）
