Programmable Synchronization Graphs for Adaptive and Fault-Tolerant Modular Miniature Robots
Authors: Okan Kulekcioglu, Arqam Bin Ahmad, Ines Garcia, Filipe Serra Alves, Onur Ozcan, M. Selim Hanay
Organizations: Department of Mechanical Engineering, Bilkent University; Ankara, Türkiye. · International Iberian Nanotechnology Laboratory (INL); Braga, Portugal.
Modular miniature robots could provide scalable function in constrained environments, but coordinating many imperfect modules remains difficult when computation, communication and reliability are limited. A central robotics challenge is to coordinate many actuator-sensor modules without assigning a privileged leader, prescribing a fixed gait template, or relying on dense communication. Here we introduce a programmable synchronization-graph framework for modular miniature robots in which each actuator-sensor pair is represented as a network node and locomotor coordination is encoded through graph coupling. Fixed intra-subgraph links synchronize heterogeneous actuator groups, whereas a small number of signed inter-subgraph links program phase relationships between groups. In physical robot collectives with up to nine modules, graph coupling drives the emergence of synchronization, signed links tune the phase difference from in-phase to out-of-phase motion, and floor experiments produce gallop-like and trot-like contact patterns in a five-module robot assembly. Replacing dense all-to-all coupling with sparse d-regular topologies preserves synchronization while reducing the coupling burden. The same graph representation also captures fault tolerance: increasing graph degree increases the number of module deactivations tolerated before desynchronization. Finally, an upper-confidence-bound edge-selection algorithm learns inter-subgraph links that drive the system toward target phase states. In a separate deactivation benchmark, the graph-based controller avoids the leader-specific failure mode observed in centralized leader-follower control and reduces worst-case phase error by about threefold. These results establish programmable network topology as a compact control layer for gait phase programming, online adaptation and robustness to unit loss in modular miniature robots.
Communication graph rigidity is a fundamental requirement in many multi robot formation control approaches. However, ensuring and maintaining a rigid communication topology becomes challenging in practice due to limited sensing ranges and dynamic operating conditions. This paper provides a method for achieving an inter robot collision free, rigid time varying communication graph, where communication links are established or broken according to limited sensing ranges, without assuming an initial rigid graph. In addition, the proposed approach guarantees the realization of a rigid graph for heterogeneous nonlinear multi robot systems. A computationally lean, distributed quadratic optimization-based controller is developed for a leader follower architecture, acquiring rigidity based on hierarchical second-order consensus among robots. Follower agents do not require global absolute positions of any agent, including their own. The proposed method is validated through both simulations and hardware experiments in a motion-capture environment, demonstrating reliable performance under the limited sensing capabilities of individual robots.
Collective behavior arises when locally interacting units produce coordinated global organization, from synchronization in dynamical systems to task-relevant information flow on graphs. The central challenge is not only to explain how collective behavior emerges, but to design local interaction rules that can produce desired global organization and generalize across graphs, dynamics and tasks.To address this challenge, we introduce the Swarm-Inspired Emergent Synchronizer (SIES), a graph-dynamical framework that learns generalizable local-interaction laws for controllable collective organization. Each node is an agent-like dynamical unit with a state and task cue, and signed source-target-conditioned attention acts as an adaptive coupling term inside an explicit evolution model. Therefore, SIES combines an explicit dynamical engine with local agent intelligence, similar to biological swarms. For synchronization control, SIES learns a generalizable coupling operator that produces prescribed synchronization patterns for CDSs across untrained network scales, target phase relations, and intrinsic node dynamics without retraining. The learned operator also reaches gait-related modes faster than three oscillator baselines and generalizes synchronization-driven locomotion to simulated multi-legged robots of different scales and a physical hexapod after leg disablement. For graph representation learning, SIES applies the same signed interaction principle to message passing and achieves the highest performance among the compared methods on heterophilous node-classification benchmarks. Together, these results position SIES as a generalizable and learnable graph-dynamical interaction framework with promise for synchronization control, adaptive robot coordination, and heterophilous graph representation learning.
In multi-robot systems, maintaining persistent communication graph connectivity is often overly restrictive, especially when robots have limited communication ranges but operate in large environments. Instead, allowing robots to temporarily disconnect and later reconnect is often more desirable for efficient task execution while still ensuring timely information sharing across the team. In this paper, we propose an adaptive prescribed-time control barrier function (adaptive PT-CBF) framework that enables robots to temporarily disconnect and re-enter the communication range within an adjustable and feasible prescribed time. Moreover, we introduce a reconnection triggering mechanism that jointly considers task execution and reconnection urgency, thereby providing a principled way to decide when reconnection should occur. Theoretical analysis justifies convergence to the satisfying reconnection within a prescribed finite time. Experimental results validate the performance of our proposed adaptive PT-CBF with improved task efficiency and satisfying reconnections.