Manifold-Guided Motion Planning for Tight Assemblies
2026-07-20 • Robotics
Robotics
AI summaryⓘ
The authors address a hard problem in robotics: planning how to move and fit together rigid parts that need to navigate very tight spaces with almost no room to spare. They developed a new method called Critical-Manifold Guided RRT (CMG-RRT) that smartly focuses its search on configurations where parts touch, which are crucial for solving these tight assembly tasks. Their method is proven to find a solution if one exists under normal conditions and worked perfectly in tests, including a very tricky puzzle known as the Elk disentanglement. They also made their software freely available for others to use.
Motion PlanningRigid-Body AssemblyConfiguration SpaceSampling-Based PlannerCritical ManifoldRapidly-exploring Random Tree (RRT)Probabilistic CompletenessGeometric ConstraintsAssembly PuzzleContact Configuration
Authors
Dror Livnat, Michael M. Bilevich, Michal Kleinbort, Dan Halperin
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.