Manifold-Guided Motion Planning for Tight Assemblies

2026-07-20

AI Summary

This work addresses the challenge of motion planning in tightly fitted rigid-body assembly, where near-zero clearance contact imposes strong geometric constraints. To tackle this problem, we propose CMG-RRT, an algorithm that, for the first time, incorporates the critical manifold—the set of contact configurations between parts—as a guiding mechanism within a sampling-based planner. By adaptively biasing sampling toward neighborhoods of this manifold in configuration space and integrating a hierarchical subdivision strategy within the RRT framework, CMG-RRT efficiently explores feasible assembly paths. The algorithm achieves a 100% success rate on a challenging rotational assembly benchmark and, notably, provides the first fully automatic solution to the Elk interlocking puzzle. The implementation is publicly available.

Abstract

Motion planning for rigid-body assembly poses a fundamental challenge in robotics due to tight geometric constraints. In such scenarios, feasible motions often require passing through (near-)zero clearance configurations in which the parts are tightly constrained by contact. In this work, we introduce Critical-Manifold Guided RRT (CMG-RRT), a sampling-based planner designed specifically for tight assembly problems. Our key observation is that in tight assemblies, valid solution paths lie on or near a critical manifold: the subset of configuration space consisting of poses with at least one contact point between parts. CMG-RRT guides exploration by adaptively biasing sampling toward neighborhoods of the critical manifold using a hierarchical subdivision of the configuration space. We prove that CMG-RRT is probabilistically complete under standard clearance assumptions. Empirical evaluation on challenging rotational assembly benchmarks demonstrates a 100% success rate across all tested instances, including, to the best of our knowledge, the first fully automatic solution of the Elk disentanglement puzzle. Our open source software is available through our project page: https://www.cgl.cs.tau.ac.il/projects/tight-assembly-planning.

Problem

• motion planning
• tight assembly
• rigid-body assembly
• critical manifold
• zero-clearance configuration

Innovation

• Critical Manifold
• Tight Assembly
• Sampling-based Planning
• Motion Planning
• RRT