Reconfiguration-Complete Motion Primitives with Constructive Planning for Deformable Planar Modular Robots
arXiv:2608.17324v1 Announce Type: new 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.
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[Submitted on 18 Aug 2026]
Title:Reconfiguration-Complete Motion Primitives with Constructive Planning for Deformable Planar Modular Robots
View a PDF of the paper titled Reconfiguration-Complete Motion Primitives with Constructive Planning for Deformable Planar Modular Robots, by Jie Gu and 6 other authors
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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.
Comments: Jie Gu and Tingting Wang contributed equally to this work
Subjects:
Robotics (cs.RO)
Cite as: arXiv:2608.17324 [cs.RO]
(or arXiv:2608.17324v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2608.17324
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Gu Jie [view email] [v1] Tue, 18 Aug 2026 03:34:54 UTC (1,651 KB)
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