Reconfiguration-Complete Motion Primitives with Constructive Planning for Deformable Planar Modular Robots

• URL: http://arxiv.org/abs/2608.17324v1
• Date: Tue, 18 Aug 2026 03:34:54 GMT
• Title: Reconfiguration-Complete Motion Primitives with Constructive Planning for Deformable Planar Modular Robots
• Abstract summary: This letter introduces a square-cell abstraction that maps deformable rhombus modules to fixed-size grid cells.<n>We prove that every non-straight edge-connected configuration with $N geq 7$ can be transformed to a fixed staircase canonical using only admissible primitive motions.
• Score: 12.157600704536533
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The continuously deformable geometry of modular robots makes it difficult to define a fixed representation for reconfiguration planning and analysis. This letter introduces a square-cell abstraction that maps deformable rhombus modules to fixed-size grid cells while retaining physically interpretable local motions through two primitives, pivoting and shearing. Under this abstraction, we prove that every non-straight edge-connected configuration with $N \geq 7$ can be transformed to a fixed canonical staircase using only admissible primitive motions. Since these motions are reversible, any two configurations in this class are mutually reconfigurable. The proof is constructive and directly yields a staircase-canonicalization planner that transports removable boundary modules while preserving connectivity. As a practical enhancement, we further introduce a boundary-to-delivery lookahead selector that ranks admissible high level choices without affecting the completeness guarantee. Experiments demonstrate the constructive reconfiguration process and show that the selector substantially reduces planning time, while reference comparisons indicate lower planning times than the prior framework over the shared module counts.

Related papers

• A Compositional Theory of Causally Masked Transformers [50.88598486616582]
  We develop a formalization that derives expressivity directly from the model's implemented dynamics.<n>Each attention head updates its own state independently within a layer.<n>A modified form of soft attention supports irreversible, checklist-like state.
  arXiv  Detail & Related papers  (2026-07-29T14:47:19Z)
• Coupled Routing and Configuration Optimization for Multi-Viewpoint Robotic Inspection [4.164290233214403]
  We present a unified framework that turns a set of 6-DoF inspection viewpoints into a time-optimal, collision-free route for a 9-DoF robotic system.<n>Unlike modular pipelines that fix a single inverse-kinematics (IK) configuration per viewpoint, build an all-pairs travel-time map, and then route, our method jointly optimize the visiting order and the per-viewpoint configuration in a single global search.
  arXiv  Detail & Related papers  (2026-06-17T17:14:54Z)
• Learning Unions of Convex Sets via Invertible Latent Decomposition for Path Planning [19.14344979340464]
  Invertible Latent Decomposition (ILD) is a framework that learns an invertible mapping and a union of explicit convex polytopes in the resulting latent space.<n>ILD achieves broader coverage, better inter-set connectivity, and higher path-planning success rates than prior baselines.<n>On a 14-DoF bimanual manipulator, we demonstrate real-time collision-free planning, with test-time refinement adapting to scene-geometry changes.
  arXiv  Detail & Related papers  (2026-06-10T12:49:47Z)
• CellScientist: Dual-Space Hierarchical Orchestration for Closed-Loop Refinement of Virtual Cell Models [62.281480231694]
  Virtual Cell Modeling (VCM) requires models that not only predict perturbation responses, but also support targeted revision when predictions fail.<n>Current LLM-assisted modeling face a refinement-routing problem: prediction discrepancies are observed through executable implementations.<n>We propose CellScientist, a dual-space hierarchical framework that couples a high-level hypothesis space with a low-level executable implementation space.
  arXiv  Detail & Related papers  (2026-05-08T06:40:24Z)
• Second-Order, First-Class: A Composable Stack for Curvature-Aware Training [1.2891210250935148]
  We introduce Somax, a composable Optax-native stack that treats curvature-aware training as a single JIT-compiled step governed by a static plan.<n>Somax exposes first-class modules behind a single step interface and composes with Optax by applying standard gradient transformations.<n>We report system-oriented ablations showing that composition choices materially affect scaling behavior and time-to-accuracy.
  arXiv  Detail & Related papers  (2026-03-26T23:36:37Z)
• PRISM: Parallel Residual Iterative Sequence Model [52.26239951489612]
  We propose PRISM (Parallel Residual Iterative Sequence Model) to resolve this tension.<n>PRISM introduces a solver-inspired inductive bias that captures key structural properties of multi-step refinement in a parallelizable form.<n>We prove that this formulation achieves Rank-$L$ accumulation, structurally expanding the update manifold beyond the single-step Rank-$1$ bottleneck.
  arXiv  Detail & Related papers  (2026-02-11T12:39:41Z)
• Self-Reconfiguration Planning for Deformable Quadrilateral Modular Robots [9.249285433601205]
  lattice modular self-reconfigurable robots (MSRRs)<n>Maintaining stable connections during reconfiguration is crucial for physical feasibility and deployability.<n>This letter presents a novel self-reconfiguration planning algorithm for deformable quadrilateral MSRRs that guarantees stable connection.
  arXiv  Detail & Related papers  (2026-01-27T11:32:04Z)
• Light-SQ: Structure-aware Shape Abstraction with Superquadrics for Generated Meshes [60.92139345612904]
  We present Light-SQ, a novel superquadric-based optimization framework.<n>We propose a block-regrow-fill strategy guided by structure-aware volumetric decomposition.<n>Experiments demonstrate that Light-SQ enables efficient, high-fidelity, and editable shape abstraction with superquadrics.
  arXiv  Detail & Related papers  (2025-09-29T16:18:32Z)
• DepGraph: Towards Any Structural Pruning [68.40343338847664]
  We study general structural pruning of arbitrary architecture like CNNs, RNNs, GNNs and Transformers. We propose a general and fully automatic method, emphDependency Graph (DepGraph), to explicitly model the dependency between layers and comprehensively group parameters for pruning. In this work, we extensively evaluate our method on several architectures and tasks, including ResNe(X)t, DenseNet, MobileNet and Vision transformer for images, GAT for graph, DGCNN for 3D point cloud, alongside LSTM for language, and demonstrate that, even with a
  arXiv  Detail & Related papers  (2023-01-30T14:02:33Z)
• Multi-agent Soft Actor-Critic Based Hybrid Motion Planner for Mobile Robots [16.402201426448002]
  The planner is model-free and can realize the end-to-end mapping of multi-robot state and observation information to final smooth and continuous trajectories. The design of the back-end trajectory optimization module is based on the minimal snap method with safety zone constraints.
  arXiv  Detail & Related papers  (2021-12-13T12:23:30Z)
• Frame Averaging for Equivariant Shape Space Learning [85.42901997467754]
  A natural way to incorporate symmetries in shape space learning is to ask that the mapping to the shape space (encoder) and mapping from the shape space (decoder) are equivariant to the relevant symmetries. We present a framework for incorporating equivariance in encoders and decoders by introducing two contributions.
  arXiv  Detail & Related papers  (2021-12-03T06:41:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.