[Paper Review] Stochastic Broadcast Control of Multi-Agent Swarms

Ilana Segall, Alfred M. Bruckstein⋆|arXiv (Cornell University)|Jul 17, 2016

Distributed Control Multi-Agent Systems15 references3 citations

TL;DR

This paper proposes a stochastic broadcast control framework for multi-agent swarms where only a random subset of agents receive external control signals, becoming ad-hoc leaders. Using a linear local agreement protocol with uniform or scaled influence models, the swarm asymptotically aligns and moves cohesively in the direction of the control signal, achieving collective motion speed proportional to the fraction of leaders when the visibility graph is complete, but dependent on topology when incomplete.

ABSTRACT

We present a model for controlling swarms of mobile agents via broadcast control, assumed to be detected by a random set of agents in the swarm. The agents that detect the control signal become ad-hoc leaders of the swarm. The agents are assumed to be velocity controlled, identical, anonymous, memory-less units with limited capabilities of sensing their neighborhood. Each agent is programmed to behave according to a linear local gathering process, based on the relative position of all its neighbors. The detected exogenous control, which is a desired velocity vector, is added by the leaders to the local gathering control. The graph induced by the agents adjacency is referred to as the visibility graph. We show that for piece-wise constant system parameters and a connected visibility graph, the swarm asymptotically aligns in each time-interval on a line in the direction of the exogenous control signal, and all the agents move with identical speed. These results hold for two models of pairwise influence in the gathering process, uniform and scaled. The impact of the influence model is mostly evident when the visibility graph is incomplete. These results are conditioned by the preservation of the connectedness of the visibility graph. In the second part of the report we analyze sufficient conditions for preserving the connectedness of the visibility graph. We show that if the visibility graph is complete then certain bounds on the control signal suffice to preserve the completeness of the graph. However, when the graph is incomplete, general conditions, independent of the leaders topology, could not be found.

Motivation & Objective

• To model and analyze collective motion in multi-agent swarms under stochastic broadcast control, where only a subset of agents detect external control signals.
• To investigate how different neighbor influence models—uniform and scaled—affect the swarm's alignment and collective speed.
• To derive sufficient conditions for preserving connectivity of the visibility graph during motion, ensuring sustained group cohesion.
• To quantify the relationship between control signal strength, network topology, and the resulting collective velocity of the swarm.
• To provide analytical and simulation-based validation of swarm behavior under piecewise constant control inputs and varying visibility graph structures.

Proposed method

• Model agents as velocity-controlled, memoryless, anonymous units with limited sensing range, using a linear local gathering process based on relative positions.
• Integrate exogenous control signals (desired velocity vectors) only into agents that detect the broadcast, designating them as ad-hoc leaders.
• Define the visibility graph as the adjacency graph of agents within sensing range, and analyze its role in determining collective dynamics.
• Apply two influence models: uniform (equal weight to all neighbors) and scaled (weight proportional to inverse distance), and compare their impact on convergence and speed.
• Use matrix theory and Laplacian eigenvalue analysis (standard and normalized) to study connectivity preservation and stability of the system.
• Derive sufficient conditions on control signal magnitude and agent distribution to maintain graph connectivity, especially under incomplete visibility graphs.

Experimental results

Research questions

• RQ1 How does the swarm’s collective motion align with the exogenous control signal when only a subset of agents detect it?
• RQ2 What is the impact of the influence model (uniform vs. scaled) on the achieved collective speed when the visibility graph is incomplete?
• RQ3 Under what conditions is the visibility graph preserved during motion, ensuring sustained connectivity and cohesion?
• RQ4 How does the topology of the visibility graph affect the convergence and deviation behavior of the swarm in 2D space?
• RQ5 Can general connectivity preservation conditions be derived for incomplete visibility graphs independent of leader topology?

Key findings

• For a connected visibility graph and piecewise constant control, the swarm asymptotically aligns along a line in the direction of the exogenous control signal and moves with uniform speed.
• When the visibility graph is complete, the ratio of achieved collective speed to desired speed equals the ratio of leaders to total agents, regardless of influence model.
• With incomplete visibility graphs, the scaled influence model makes the collective speed dependent on the specific topology and leader placement, not just the number of leaders.
• For uniform influence, the collective speed ratio remains equal to the leader fraction even when the graph is incomplete.
• Sufficient conditions for preserving graph connectivity are derived: for complete graphs, bounded control signals maintain completeness; for incomplete graphs, no general conditions independent of topology exist.
• Edge addition increases algebraic connectivity in the uniform model, while eigenvalue interlacing properties differ in the scaled influence model, affecting stability and convergence.