Backward Layout Search for Sequence-Constrained Robotic Assembly

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.

Assembly using robots often requires specially designed fixtures, or relies on top-down only assembly strategies. Using multiple robots, we can avoid using fixtures and make robotic assembly more flexible. Planning assembly sequences for multiple robots is challenging due to the high number of possible task assignments and orders. In addition, we need to reason over forces that occur during the assembly process, e.g., to decide if multiple robots are required for support, or if external support such as a table should be used. We present Wrap, a multi-robot assembly planner for multi-part assemblies, given the inter-part ordering-dependencies, the part meshes, and their initial state. We formulate a linear program to reason about valid grasps for supporting the forces that occur during assembly. The search leverages the assembly sequence, and greedily finds a feasible solution per assembly step by computing a heuristic via a cheap backwards search, and using the heuristic in the more expensive forward search. We then solve the multi-robot, multi-goal motion planning problem, and for execution, we split the plan into contact-rich assembly skills, and free space motion. We benchmark the planner on a variety of multi-part assemblies, and apply the planner to groups of robots differing in size and kinematics. We validate the work both in a physics simulation, and in real. Videos and code are available at https://www.vhartmann.com/wrap.

Assembly Sequence Planning (ASP) remains a challenging problem due to its combinatorial nature, making exhaustive planning approaches impractical for complex industrial assemblies. Furthermore, many CAD models lack reliable semantic contact information or require extensive manual preprocessing, limiting the applicability of existing methods. This paper presents a hybrid ASP framework combining learning-based relation extraction with geometric-symbolic reasoning to generate feasible robotic disassembly sequences from imperfect CAD data. A neural network predicts semantic geometric relations from point clouds, while human-in-the-loop verification enables correction of uncertain predictions and planning failures. Extracted relations are transformed into a symbolic assembly graph, enabling a geometric-symbolic planner to efficiently compute locally valid sets of robotic manipulation primitives. A visibility-based ray-casting strategy guides the search for feasible disassembly directions without requiring an exhaustive combinatorial search, while the local solution space enables efficient sequence optimization. The framework is evaluated on an introduced assembly dataset and on the ASAP test dataset. On the ASAP test dataset, the proposed planner achieves an 85.83% planning success rate while reducing the median planning time by more than one order of magnitude across all assembly sizes and by more than a factor of 50 for assemblies with more than 30 components compared to the baseline. The results demonstrate that the proposed hybrid framework enables efficient robotic assembly sequence planning from imperfect CAD data while substantially reducing planning time. By combining learning-based feature segmentation, human-in-the-loop verification, and geometric-symbolic reasoning, the framework provides a practical foundation for scalable and adaptable robotic assembly and disassembly planning.