Self-Reconfiguration Planning for Deformable Quadrilateral Modular Robots

TL;DR

The paper tackles stable, deployable reconfiguration planning for deformable quadrilateral MSRRs by introducing morphpivoting as a robust motion primitive. It couples a virtual-graph based action generation phase with a Dependence-based Reverse Tree (DRTree) to produce executable, conflict-free reconfiguration sequences, complemented by a Bidirectional Isomorphism Tree to bridge start and goal configurations via graph isomorphism. A key theoretical result shows that for $n \ge 7$, all non-linear configurations are isotypic, guaranteeing reconfigurability between any two such configurations, and practical validation with hardware demonstrates the method’s stability and efficiency compared to a modified BiRRT. The approach offers a fast, reliable pathway to morphable modular robots, enabling scalable deployments and informing future extensions to broader polygonal systems.

Abstract

For lattice modular self-reconfigurable robots (MSRRs), maintaining stable connections during reconfiguration is crucial for physical feasibility and deployability. This letter presents a novel self-reconfiguration planning algorithm for deformable quadrilateral MSRRs that guarantees stable connection. The method first constructs feasible connect/disconnect actions using a virtual graph representation, and then organizes these actions into a valid execution sequence through a Dependence-based Reverse Tree (DRTree) that resolves interdependencies. We also prove that reconfiguration sequences satisfying motion characteristics exist for any pair of configurations with seven or more modules (excluding linear topologies). Finally, comparisons with a modified BiRRT algorithm highlight the superior efficiency and stability of our approach, while deployment on a physical robotic platform confirms its practical feasibility.

Figures (10)

• Figure 1: The hardware platform. The standard square module with four sides capable of connecting to other modules. (b) The rhombus shape obtained by morphing the module in (a) along its diagonal.
• Figure 2: Morphpivoting: definition and comparison with conventional pivoting. (a) The proposed quadrilateral MSRR model achieves reconfiguration through morphing combined with necessary connection and disconnection operations. (b) Reconfiguration via pivoting, demonstrated using the ElectroVoxel system.
• Figure 3: (a) The canonical and non-canonical forms of a six-module configuration graph. The latter is obtained from the former by adding $e_{24}$ and $e_{36}$. (b) The tree generated from the two forms in (a).
• Figure 4: Three counterexamples that violate the above constraints.
• Figure 5: Illustration of the virtual graph generation process.