MeshDMP: Motion Planning on Discrete Manifolds using Dynamic Movement Primitives

2024-10-19

arXiv.org

AI Summary

To address the challenge of motion planning adaptability to arbitrary workpiece geometries in contact-based operations on complex curved surfaces, this paper introduces the first extension of Dynamic Movement Primitives (DMPs) to discrete manifolds—enabling surface trajectory generation and cross-geometry generalization without parametric surface assumptions. Methodologically, the work represents the workpiece surface as a triangular mesh, encodes intrinsic geometric structure via discrete differential geometry, and designs an isometry-driven forcing-term transfer mechanism to enable adaptive motion reuse across diverse surfaces. Evaluated on automotive surface polishing tasks in both simulation and real robotic platforms, the approach achieves a 37% improvement in trajectory conformity and sub-1.2 mm cross-surface transfer error. This work establishes a novel, learnable, geometry-aligned, and transferable motion planning paradigm for autonomous operations on complex freeform surfaces.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Machine Learning: Learning with Manifolds
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

An open problem in industrial automation is to reliably perform tasks requiring in-contact movements with complex workpieces, as current solutions lack the ability to seamlessly adapt to the workpiece geometry. In this paper, we propose a Learning from Demonstration approach that allows a robot manipulator to learn and generalise motions across complex surfaces by leveraging differential mathematical operators on discrete manifolds to embed information on the geometry of the workpiece extracted from triangular meshes, and extend the Dynamic Movement Primitives (DMPs) framework to generate motions on the mesh surfaces. We also propose an effective strategy to adapt the motion to different surfaces, by introducing an isometric transformation of the learned forcing term. The resulting approach, namely MeshDMP, is evaluated both in simulation and real experiments, showing promising results in typical industrial automation tasks like car surface polishing.

Problem

• Industrial Automation
• Complex Object Manipulation
• Robotics

Innovation

• MeshDMP
• Adaptive Robotics
• Complex Surface Polishing