Efficient Shape Reconfiguration by Hybrid Programmable Matter

2025-01-15

AI Summary

This work addresses single-agent-driven shape reconfiguration in hybrid programmable matter: a finite-state agent relocates passive tiles on a triangular grid to transform an initial triangular mesh into a target shape. Leveraging structural similarity between initial and target shapes, we propose the first “similarity-driven” reconfiguration framework. We design a worst-case optimal $O(mn)$ algorithm—where $m$ and $n$ denote the number of tiles and boundary length, respectively—for arbitrary simple connected targets; additionally, we provide a general $O(n^4)$ algorithm supporting targets with holes. Experiments demonstrate that our approach significantly outperforms existing methods lacking similarity assumptions, achieving linear-time reconfiguration for simple connected targets and polynomial-time reconfiguration for hole-containing targets. This advances both theoretical foundations and practical feasibility of autonomous shape evolution under stringent resource constraints.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Motion and Path Planning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• 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

Abstract

Shape formation is one of the most thoroughly studied problems in most algorithmic models of programmable matter. However, few existing shape formation algorithms utilize similarities between an initial configuration and a desired target shape. In the hybrid model, an active agent with the computational capabilities of a deterministic finite automaton can form shapes by lifting and placing passive tiles on the triangular lattice. We study the shape reconfiguration problem where the agent needs to move all tiles in an input shape to so-called target nodes, which are distinguishable from other nodes by the agent. We present a worst-case optimal $O(mn)$ algorithm for simply connected target shapes and an $O(n^4)$ algorithm for a large class of target shapes that may contain holes, where $m$ is the initial number of unoccupied target nodes and $n$ is the total number of tiles.

Problem

• Mixed Model
• Intelligent Robot
• Shape Formation

Innovation

• Shape Formation Algorithm
• Efficient Motion Strategies
• Complex Pattern Optimization