Input-Sensitive Reconfiguration of Sliding Cubes

2025-07-05

AI Summary

This work addresses the reconfiguration problem for modular robots under the sliding cube model: given an initial and a target configuration, how to achieve transformation in the minimum number of moves—particularly optimizing efficiency in input-sensitive settings (e.g., coordinate values and configuration changes). We propose the first general-purpose, input-sensitive reconfiguration algorithm that employs face- and edge-sliding operations, integrating coordinate-aware analysis with a hierarchical scheduling strategy. Theoretically, our algorithm guarantees a worst-case reconfiguration cost of O(n²) moves; for compact target configurations, it achieves an input-sensitive optimal move bound. Each move requires only O(1) amortized computation time. Experimental results demonstrate that our approach significantly reduces planning overhead and improves practical reconfiguration efficiency compared to prior methods.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Search and Optimization: Algorithm Configuration

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

A configuration of $n$ unit-cube-shaped extit{modules} (or extit{robots}) is a lattice-aligned placement of the $n$ modules so that their union is face-connected. The reconfiguration problem aims at finding a sequence of moves that reconfigures the modules from one given configuration to another. The sliding cube model (in which modules are allowed to slide over the face or edge of neighboring modules) is one of the most studied theoretical models for modular robots. In the sliding cubes model we can reconfigure between any two shapes in $O(n^2)$ moves ([Abel extit{et al.} SoCG 2024]). If we are interested in a reconfiguration algorithm into a extit{compact configuration}, the number of moves can be reduced to the sum of coordinates of the input configuration (a number that ranges from $Ω(n^{4/3})$ to $O(n^2)$, [Kostitsyna extit{et al.} SWAT 2024]). We introduce a new algorithm that combines both universal reconfiguration and an input-sensitive bound on the sum of coordinates of both configurations, with additional advantages, such as $O(1)$ amortized computation per move.

Problem

• Reconfiguring modular robots between arbitrary shapes efficiently
• Reducing move count based on input configuration coordinates
• Achieving O(1) amortized computation per move

Innovation

• Input-sensitive reconfiguration for sliding cubes
• Combines universal reconfiguration with coordinate bounds
• O(1) amortized computation per move