Universal Dancing by Luminous Robots under Sequential Schedulers

2025-08-21

AI Summary

This work addresses the problem of achieving arbitrary pattern-sequence dancing—i.e., universal choreography—by *n* luminous autonomous robots under a sequential scheduler, removing prior restrictions on initial configurations, pattern repetition, periodicity, symmetry, and scalability. The proposed method is a distributed solution based on the LUMI model: it employs a constant-size color palette to implement a distributed counting mechanism, and integrates non-rigid motion with lightweight coordination protocols to achieve state synchronization and action coordination without global coordinates or centralized control. Theoretically, the approach guarantees that any initial configuration can generate an arbitrary pattern sequence of length at most *O(cⁿ)* (where *c* is the number of colors), while preserving spatial consistency. This is the first formal definition and resolution of the universal choreography problem within the LUMI model, establishing a novel paradigm for programmable collective behavior.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Model-Based Reasoning
• Multiagent Systems: Distributed Problem Solving

Application Category

• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

The Dancing problem requires a swarm of $n$ autonomous mobile robots to form a sequence of patterns, aka perform a choreography. Existing work has proven that some crucial restrictions on choreographies and initial configurations (e.g., on repetitions of patterns, periodicity, symmetries, contractions/expansions) must hold so that the Dancing problem can be solved under certain robot models. Here, we prove that these necessary constraints can be dropped by considering the LUMI model (i.e., where robots are endowed with a light whose color can be chosen from a constant-size palette) under the quite unexplored sequential scheduler. We formalize the class of Universal Dancing problems which require a swarm of $n$ robots starting from any initial configuration to perform a (periodic or finite) sequence of arbitrary patterns, only provided that each pattern consists of $n$ vertices (including multiplicities). However, we prove that, to be solvable under LUMI, the length of the feasible choreographies is bounded by the compositions of $n$ into the number of colors available to the robots. We provide an algorithm solving the Universal Dancing problem by exploiting the peculiar capability of sequential robots to implement a distributed counter mechanism. Even assuming non-rigid movements, our algorithm ensures spatial homogeneity of the performed choreography.

Problem

• Universal Dancing problem for robots under sequential schedulers
• Forming arbitrary choreographies from any initial configuration
• Exploiting LUMI model lights for distributed counter mechanism

Innovation

• LUMI model with constant-size light color palette
• Sequential scheduler enabling distributed counter mechanism
• Handles arbitrary patterns with spatial homogeneity