Emergent Behavior Models in Multi-Agent Systems for Large-Scale Space Exploration

This research examines how localized agent interactions within swarms give rise to emergent behaviors enabling robust coordination and adaptability in expansive space exploration scenarios.

Chris Adams, Brian Nguyen, Vivek Bakshi

Arboria Research, Alpharetta, GA/United States

Corresponding Author email(s): cadams@arborialabs.com, [private], [private]

ORCID - Christopher Adams

Abstract

We investigate emergent behaviors in large-scale space-exploration swarms by integrating density-modulated Boids (DMB) and task-field Ant Colony Optimization (TF-ACO) policies in Gossamer and evaluating at up to $5×10^5$ agents in the Leviathan Engine. We characterize phase transitions in alignment, coverage, and collision rate as functions of agent density, sensing radius, and noise. DMB introduces adaptive rule weights based on local density and obstacle potential fields; TF-ACO lays stigmergic gradients on task fields to coordinate coverage and revisit schedules. Across asteroid-belt survey scenarios, DMB improved alignment order parameter by 19% and reduced collision rate by 46% relative to fixed-weight Boids, while TF-ACO increased unique coverage by 24% with 0.7× messages vs a greedy assignment baseline. We observe a supercritical density threshold beyond which naive policies collapse due to oscillations; DMB+TF-ACO delays this transition by 1.6× in density and sustains coverage under noise. Maneuver.Map orchestrations reveal stable pattern regimes and failure modes. These findings suggest emergent coordination can be tuned for robust exploration without centralized control, informing mission designs for belts, rings, and crater fields.

(1) Context/Background: Briefly introduce the broader problem area (e.g., challenges of interstellar exploration, orbital debris management). (2) Problem Statement: Clearly state the specific gap or challenge this research addresses (e.g., need for scalable coordination algorithms under latency, lack of robust debris tracking methods). (3) Methodology: Briefly describe your core approach/framework (e.g., developed a novel distributed algorithm using Gossamer, simulated million-agent swarms in Leviathan). Mention key theoretical underpinnings or unique aspects. (4) Key Results: Summarize the most important findings quantitatively if possible (e.g., achieved X% coherence improvement, demonstrated Y% reduction in collision risk, scaled efficiently up to Z agents). (5) Conclusion/Implications: State the main conclusion and briefly mention the significance or potential impact of the work (e.g., enabling feasibility studies for interstellar missions, improving space situational awareness).]_

Keywords

Emergent Behavior, Boids, Ant Colony Optimization, Coverage, Multi-Agent Systems, Space Exploration

1. Introduction

1.1. Background and Motivation:
- Space exploration demands robust, scalable sensing over vast, obstacle-rich domains (asteroid belts, ring systems). Swarm emergent behaviors offer adaptable coordination from local rules but degrade at high densities and under noise.
- The gap is a principled mapping from local interaction parameters to global performance and failure regimes at scale, guiding safe operating envelopes.
1.2. Problem Statement and Research Questions/Hypotheses:
- Problem: Quantify and improve emergent alignment, coverage, and safety at scale under density, noise, and obstacle fields.
- Hypotheses: (H1) Density-modulated Boids (DMB) increases alignment and reduces collisions vs fixed weights; (H2) TF-ACO improves coverage with lower message overhead than greedy assignment.
1.3. Proposed Approach and Contributions:
- We implement DMB and TF-ACO in Gossamer and evaluate in Leviathan across asteroid-belt analogs, with Maneuver.Map orchestrating sweeps.
- Contributions:
  - Density-modulated Boids (adaptive rule weights by local density and obstacle potential).
  - Task-field ACO (stigmergic coverage gradients with revisit decay and noise robustness).
  - Phase-diagram characterization of alignment, coverage, and collision regimes up to $5×10^5$ agents.
  - Comparative analysis vs fixed-weight Boids and greedy tasking.
1.4. Paper Outline:
- Section 2 reviews background. Section 3 details DMB and TF-ACO. Section 4 describes the setup. Section 5 presents results. Section 6 discusses implications. Section 7 concludes and future work.

Emergence in swarms arises from local rules (Reynolds’ Boids) and stigmergy (ACO). At scale, density and noise induce phase changes affecting global order.
2.1. Swarm Intelligence Fundamentals:
- Boids: separation, alignment, cohesion; ACO: pheromone deposition/evaporation; PSO: velocity-coupled optimization. Limitations: fixed parameters struggle across densities.
2.2. Distributed Systems Principles:
- Local communication, gossip, and bounded-degree graphs mitigate broadcast storms; DTN patterns help when contacts are sparse.
2.3. Swarm Robotics in Space:
- Prior work demonstrates small-team coordination; few quantify phase transitions at >1e5 agents in sparse, obstacle-filled environments.
2.4. Existing Coordination Techniques:
- Fixed-weight Boids and greedy tasking are simple but brittle; MARL scales poorly in sample complexity without strong priors.
2.5. Positioning of Current Work:
- We provide scalable, parameter-robust emergent policies with empirical phase maps guiding safe density/noise envelopes.

3. Methodology / Proposed Framework / System Design

We detail DMB and TF-ACO and their integration in Gossamer.
3.1. Conceptual Overview:
- Agents run DMB steering and TF-ACO coverage fields; Leviathan advances physics and obstacles; Maneuver.Map orchestrates sweeps and logging.
- Terms: order parameter ψ, coverage ratio χ, collision rate ρ_c.
3.2. Density-Modulated Boids (DMB):
- Rule weights w_sep, w_align, w_coh adapt with local density d via sigmoid schedules, reducing oscillations at high d.

w_{\text{align}}(d)=\frac{w_a^0}{1+e^{\alpha(d-d_0)}},\quad w_{\text{sep}}(d)=w_s^0\,\left(1+e^{\beta(d-d_1)}\right)

Obstacle potential field U guides repulsion; steering v’ normalized and clamped by max acceleration.
Implemented as gossamer.algorithms.flocking.dmb_step.
3.3. Task-Field ACO (TF-ACO):
- Agents deposit pheromone on under-sampled cells; evaporation λ enforces revisit cadence; selection probability ∝ pheromone×heuristic (distance/uncertainty).
- Implemented as a lattice overlay; messages limited to local neighbors; parameters tuned via Maneuver.Map evolution.
3.4. Mathematical Modeling:

Order parameter $\psi=\frac{1}{N}\left\|\sum_k \hat v_k\right\|\,;\quad \text{coverage}\ \chi=\frac{|\text{unique cells visited}|}{|\text{total cells}|}.$

Collision rate $\rho_c=\frac{\text{collisions}}{N\,T}.$
3.5. Theoretical Analysis:
- DMB reduces eigenvalues of local linearized dynamics, dampening oscillations; TF-ACO balances exploration/exploitation via λ.

4. Experimental Setup / Simulation Environment

All experiments were reproducible via Leviathan configs and Maneuver.Map runs.
4.1. Simulation Platform:
- Leviathan Engine with obstacle fields; Gossamer v0.4; Maneuver.Map for orchestration and logging.
4.2. Scenario Design:
- Asteroid-belt analog: 1,000×1,000×50 km, $10^4–5×10^5$ agents, obstacles as inverse-square repulsive fields.
- Agent speed 5–15 m/s; neighbor radius 100–500 m; noise $σ_v∈[0,0.2]$ .
4.3. Input Data:
- Synthetic obstacle maps and initial seeds at /nas/experiments/emergence/inputs/*.
4.4. Baseline Methods / Comparative Analysis:
- Fixed-weight Boids; Greedy nearest-task assignment; MARL (small-scale ablation) for reference.
4.5. Performance Metrics:
- Alignment $ψ$ , coverage $χ$ , collision rate $ρ_c$ , message overhead (KB/agent·h), runtime/step.
4.6. Experimental Procedure:
- 15 seeds per condition; sweeps over density, neighbor radius, and noise. MLflow tracked runs at /nas/experiments/emergence.

5. Results

We report $ψ, χ, ρ_c$ across policies and densities.

5.1. Alignment and Safety:
- DMB increased $ψ$ by 19% and reduced $ρ_c$ by 46% vs fixed Boids at density $0.3$ $agents/m^3$ ; $p<0.01$ .
5.2. Scalability:
- Runtime/step scaled linearly with $N$ ; message overhead remained $O(1)$ per agent via local neighborhoods.
5.3. Robustness:
- DMB+TF-ACO sustained $χ$ under noise $σ_v$ up to 0.15, with $<8$ % drop; fixed Boids degraded by 25%.
5.4. Comparative Analysis:
- TF-ACO achieved $χ=0.82$ vs Greedy $χ=0.66$ at equal steps; messages $0.7×$ Greedy.
(Figures and Tables):
- Table 1: $ψ$ and $ρ_c$ vs policy at density $0.3$ $agents/m^3$ .

Table 1: Alignment and collision rate

Policy	ψ (↑ better)	ρ_c (×1e-4)
Fixed Boids	0.58	7.2
DMB (ours)	0.69	3.9
DMB+TF-ACO	0.71	3.8

6. Discussion

DMB and TF-ACO tune emergent behavior for safer, more coherent exploration without centralized planning.
6.1. Interpretation of Key Findings: H1 and H2 are supported; adaptive weights and stigmergy provide robustness at scale with modest overhead.
6.2. Comparison with Related Work: Confirms Boids’ sensitivity to density; extends ACO to 3D coverage with revisit decay.
6.3. Implications of the Work: Provides phase maps to set safe densities and sensing radii for belts/rings; guides parameter choices.
6.4. Impact of Framework/Tools: Leviathan scaled to $5×10^5$ agents; Gossamer enabled rapid policy variants; Maneuver.Map revealed regime shifts.

7. Limitations and Future Work

Limitations include simplified sensing and obstacle models; no comms latency modeled here.

7.1. Limitations:
- [Acknowledge simplifying assumptions made in your models or simulations (e.g., “Our energy model did not account for…”, “The simulation assumed perfect sensor data…”, “The study was limited to 2D environments…”).]
- [Discuss constraints on the experimental setup (e.g., limited scale tested due to computational resources, specific scenarios considered).]
- [Mention aspects of the problem not addressed by your current work.]
7.2. Future Work:
- [Suggest specific, concrete directions for future research based on your findings and limitations.]
- [Propose extensions to your algorithms or framework (e.g., incorporating machine learning, adding new agent capabilities).]
- [Suggest new experiments or scenarios to explore (e.g., testing in more complex environments, hardware validation).]
- [Identify open questions that arise from your work.]

8. Conclusion

We showed adaptive local rules (DMB) and stigmergic coverage (TF-ACO) yield robust emergent patterns at scale, improving alignment, safety, and coverage with modest overhead. These insights provide actionable phase maps and parameter choices for space-swarm deployments in belts and rings.

Acknowledgements

We thank the Arboria Visualization Team for Maneuver.Map support.

Data and Code Availability

Input maps and configs at /nas/experiments/emergence/inputs and /nas/experiments/emergence/configs; outputs at /nas/experiments/emergence/outputs. Policies in Gossamer are proprietary; analysis scripts available upon request.

References

Reynolds, C. (1987); Dorigo, M. (1999); Vicsek, T. (1995) emergent order; additional references available upon request.

(Optional Sections:)

Appendix / Supplementary Material

[Include material that is too detailed for the main paper but supports the research.]

[Detailed mathematical proofs.]

[Extended algorithm pseudocode.]

[Additional figures, tables, or simulation results.]

_[Links to videos (e.g., Maneuver.Map visualizations).] _

[Detailed configuration files.]

[List of simulation parameters.]