DynaSwarm: Adaptive Swarm Dynamics

• DynaSwarm is a comprehensive framework that defines dynamic scaling, decentralized adaptation, and emergent collective behaviors across biological, robotic, and multi-agent AI systems.
• It employs methodologies such as real-time graph optimization, phased coordination in robot swarms, and adaptive task allocation strategies to ensure robust performance in dynamic environments.
• Empirical evaluations show that DynaSwarm achieves faster reconfiguration, improved multi-target tracking, and responsive behavior at the edge-of-chaos, highlighting its potential across diverse application domains.

DynaSwarm comprises a suite of algorithmic and modeling paradigms capturing the dynamics, coordination, and adaptability of swarms in both natural and artificial domains. It encompasses frameworks for biological collective behavior, distributed robotics, multi-agent AI, adversarial swarms, and dynamic task allocation, each characterized by mechanisms for decentralized adaptation, efficient information flow, and robust collective response to environmental changes or internal objectives.

1. Foundations and Definitions

DynaSwarm first emerged as a descriptive term for a novel universality class identified in collective motion of natural swarms, where dynamic scaling and non-exponential relaxation behaviors were observed in activity correlations of large insect clouds (Cavagna et al., 2016). More recently, the label has been appropriated in robotics, AI, and control to denote frameworks for dynamic swarm management: adaptive coordination, real-time graph structure optimization, and distributed task allocation in environments with dynamic objectives and constraints (Leong et al., 31 Jul 2025, Prasertying et al., 14 Nov 2025, Gupta et al., 2021, Qamar et al., 2022, Balachandran et al., 2024).

Across all these instantiations, DynaSwarm connotes a departure from static, predesigned control or collaboration architectures, in favor of methodologies that allow decentralized agents (biological, robotic, or artificial) to reorganize, adapt, and select their collective coordination structure in response to the current task, input, or environmental observation.

2. DynaSwarm in Biological Swarms: Dynamic Scaling and Universality

The DynaSwarm concept originated with the identification of emergent dynamic scaling in midges swarms (Cavagna et al., 2016). Key features include:

• Spatio-temporal Correlation Structure: Define single-insect velocity fluctuations as $\delta v_i(t)=v_i(t)-V(t)$ (removing center-of-mass translation, rotation, and dilation), normalized to dimensionless $\delta\hat v_i(t)$. The space-time correlation,

$$C(r, t) = \left\langle \sum_{i,j} \delta\hat v_i(t_0) \cdot \delta\hat v_j(t_0 + t) \, \delta[r - |r_i(t_0) - r_j(t_0 + t)|] \right\rangle_{t_0}$$

demonstrates that correlations propagate over long distances and persist over long timescales, governed by a single scaling function.

• Dynamic Scaling Ansatz: The normalized Fourier-transformed correlation function $\hat C(k, t) = C(k, t) / C(k, 0)$ collapses via

$\hat C(k, t) = f(k^z t),$

with characteristic time $\tau_k \propto k^{-z}$. In natural swarms, the critical dynamic exponent $z \approx 1$, indicating much faster propagation of correlations than in canonical (e.g., Vicsek/Model A) models where $z \approx 2$.

• Implications: Natural swarms exhibit non-exponential relaxation, with initial correlation decay markedly flatter than predicted by first-order models. This is interpreted as evidence for persistent spin-wave–like modes and necessitates second-order, inertial dynamics in the effective theory.

A summary comparison is given below:

Feature	Natural Swarms (DynaSwarm)	Vicsek Model/Model A
Dynamic exponent $z$	$\approx 1$	$\delta\hat v_i(t)$0
Correlation decay	Non-exponential, flat at $\delta\hat v_i(t)$1	Purely exponential
Necessary dynamics	Second-order (inertial)	First-order (relaxational)

The emergence of DynaSwarm dynamics thus represents a distinct universality class for active matter.

3. Robotic DynaSwarm: Distributed Shape Formation and Control

Robotic DynaSwarm frameworks operationalize dynamic adaptation in real-world multi-robot control. The main paradigm combines centralized assignment with distributed execution to achieve rapid, collision-free shape transitions (Prasertying et al., 14 Nov 2025).

• Phased Coordination: Each robot proceeds through sequential phases—instantaneous positional check (claiming a grid cell if target proximity allows), axis-aligned navigation to a designated starting line (row/side partitioned), and a final, staggered approach to its assigned target cell. Row-sequenced activation and time-staggering prevent inter-robot conflicts.
• Geometric Assignment: Shape is encoded as a finite set $\delta\hat v_i(t)$2 of target coordinates. Robots are partitioned into rows (e.g., $\delta\hat v_i(t)$3 per row) and assigned starting sides. Within rows, assignments prioritize Euclidean proximity to the shape centroid, and waypoints are offset to prevent congestion at region boundaries.
• Control and Collision Avoidance: Each robot implements cascaded 1D PD controllers for axis-aligned trajectory tracking and local velocity-obstacle logic for dynamic collision avoidance, with formal guarantees for controller stability and convergence under bounded inter-robot communication.
• Localization Under Uncertainty: Odometry and GPS readings are fused via a complementary filter, yielding bounded localization error according to

$\delta\hat v_i(t)$4

• Scalability and Robustness: Computational complexity is $\delta\hat v_i(t)$5 offline, $\delta\hat v_i(t)$6 per robot during control updates. Experimental results with $\delta\hat v_i(t)$7 demonstrate robust, 55% faster reconfiguration than centralized or gradient-based baselines, with fill accuracy below $\delta\hat v_i(t)$8cm and tolerant performance under up to 10% packet loss.

4. Dynamic Graph Structures in LLM-based Multi-Agent Systems

The DynaSwarm paradigm also applies to coordination in LLM-based multi-agent systems (MAS), where the challenge is selecting optimal inter-agent graph topologies per query (Leong et al., 31 Jul 2025).

• Graph Optimization via RL: Rather than using a fixed collaboration DAG, DynaSwarm parameterizes edges with probabilities $\delta\hat v_i(t)$9 and samples candidate graphs $$C(r, t) = \left\langle \sum_{i,j} \delta\hat v_i(t_0) \cdot \delta\hat v_j(t_0 + t) \, \delta[r - |r_i(t_0) - r_j(t_0 + t)|] \right\rangle_{t_0}$$0. Optimization uses A2C (Advantage Actor-Critic) instead of REINFORCE, yielding stable, low-variance gradient updates for sampling high-utility graphs.
• Input-Conditional Graph Selection: After A2C yields a population of $$C(r, t) = \left\langle \sum_{i,j} \delta\hat v_i(t_0) \cdot \delta\hat v_j(t_0 + t) \, \delta[r - |r_i(t_0) - r_j(t_0 + t)|] \right\rangle_{t_0}$$1 strong candidate graphs, a lightweight “graph selector” (LLM+LoRA modules, pooler, and linear-sigmoid head) predicts, for each input, which graph is optimal. Training employs a listwise ranking loss emphasizing preserving ground-truth utility ordering among graphs.
• Performance: Evaluations on crosswords, Game-of-24, MMLU, and HumanEval benchmarks show DynaSwarm delivers 2–4% higher accuracy than static-graph or single-agent MAS baselines across multiple LLM backbones, without incurring latency increases. Ablations confirm gains from both A2C (vs. REINFORCE) and graph selection (vs. best fixed graph).
• Implication: Per-input architectural flexibility enables MAS to adapt to input-specific reasoning patterns, paralleling in-context example selection in prompting, and suggests a general shift toward sample-aware architectures in LLM-based agent design.

5. Dynamic Task Allocation and Search in Unknown Environments

DynaSwarm encompasses distributed algorithms for dynamic task allocation in settings where tasks appear stochastically in unknown locations (Balachandran et al., 2024). Key strategies include:

• Propagation-based (PROP): Each grid vertex runs a propagator agent that disseminates task information periodically within radius $$C(r, t) = \left\langle \sum_{i,j} \delta\hat v_i(t_0) \cdot \delta\hat v_j(t_0 + t) \, \delta[r - |r_i(t_0) - r_j(t_0 + t)|] \right\rangle_{t_0}$$2 and maximal distance $$C(r, t) = \left\langle \sum_{i,j} \delta\hat v_i(t_0) \cdot \delta\hat v_j(t_0 + t) \, \delta[r - |r_i(t_0) - r_j(t_0 + t)|] \right\rangle_{t_0}$$3. Followers query local propagators to probabilistically select tasks to service (guided by current residual demand and spatial proximity).
• Lévy Random Walk (RW) Baseline: Follower agents perform random walks with Lévy-distributed step lengths ($$C(r, t) = \left\langle \sum_{i,j} \delta\hat v_i(t_0) \cdot \delta\hat v_j(t_0 + t) \, \delta[r - |r_i(t_0) - r_j(t_0 + t)|] \right\rangle_{t_0}$$4) for efficient spatial coverage, committing to tasks upon proximity.
• Division of Labor (DL) and Hybrid: A fraction $$C(r, t) = \left\langle \sum_{i,j} \delta\hat v_i(t_0) \cdot \delta\hat v_j(t_0 + t) \, \delta[r - |r_i(t_0) - r_j(t_0 + t)|] \right\rangle_{t_0}$$5 of followers use PROP, the rest RW. Hybrid switches agents between PROP and RW based on cycling or dwell time, balancing local exploitation and exploration.
• Performance: At low task-arrival rates ($$C(r, t) = \left\langle \sum_{i,j} \delta\hat v_i(t_0) \cdot \delta\hat v_j(t_0 + t) \, \delta[r - |r_i(t_0) - r_j(t_0 + t)|] \right\rangle_{t_0}$$6), PROP excels; at high $$C(r, t) = \left\langle \sum_{i,j} \delta\hat v_i(t_0) \cdot \delta\hat v_j(t_0 + t) \, \delta[r - |r_i(t_0) - r_j(t_0 + t)|] \right\rangle_{t_0}$$7, RW is superior. DL and Hybrid configurations produce up to 25% lower mean completion time at intermediate loads. Tuning rules are provided, including $$C(r, t) = \left\langle \sum_{i,j} \delta\hat v_i(t_0) \cdot \delta\hat v_j(t_0 + t) \, \delta[r - |r_i(t_0) - r_j(t_0 + t)|] \right\rangle_{t_0}$$8, $$C(r, t) = \left\langle \sum_{i,j} \delta\hat v_i(t_0) \cdot \delta\hat v_j(t_0 + t) \, \delta[r - |r_i(t_0) - r_j(t_0 + t)|] \right\rangle_{t_0}$$9 and $\hat C(k, t) = C(k, t) / C(k, 0)$0 based on marginal efficiency gains, and hybrid switches at $\hat C(k, t) = C(k, t) / C(k, 0)$1.

6. Decentralized Deep Reinforcement Learning for Swarm Coordination

DynaSwarm frameworks for autonomous agent navigation and target tracking implement decentralized learning and real-time adaptation in high-dimensional environments (Qamar et al., 2022).

• MDP and Reward Structure: Each agent's observation encodes geodesic distances to targets, histogrammed neighbor distributions (via HVC), and obstacle sensor readings. Actions are continuous 3D velocity vectors. Composite rewards incentivize shortest-path navigation, swarm cohesion, and collision avoidance, with additional multi-swarm averaging for split subswarms.
• Policy Architecture and Training: The policy is realized using LSTM-augmented deep actor-critic networks, trained with custom PPO/TPPO/SAC implementations. Hyperparameters are specified for update frequency, batch size, entropy bonus, and buffer sizes.
• Island Modeling: When multiple dynamic targets are present, the full swarm splits into subswarms assigned to individual targets, and merges as targets converge or disappear. This is achieved through per-agent target ID updates and reward redistribution.
• Empirical Efficacy: Over 55 million steps, the system achieves >95% multi-target tracking success in cluttered 3D scenarios, with ablations confirming the necessity of island modeling and HVC-based neighbor encoding for optimal performance.

7. DynaSwarm in Adversarial and Edge-of-Chaos Swarm Dynamics

DynaSwarm also denotes agent-based adversarial swarms exhibiting edge-of-chaos dynamics (Gupta et al., 2021). Here, Attackers strive to breach a defended goal while Defenders seek to block access. Key technical features are:

• Agent Dynamics: Each agent obeys second-order ODEs including Morse intra-swarm forces, inter-swarm interactions (repulsive or attractive depending on zone), linear goal attraction, and Rayleigh friction, numerically integrated with RK4.
• Dynamical Complexity: The system operates at the “edge of chaos,” as established by phase-space embedding, Lyapunov spectrum computations, and the presence of multiple attractors. Multiscale entropy (MSE) metrics consistently indicate the defender swarm has higher randomness/adaptivity due to constrained multi-attractor motion.
• Practical Implications: The model provides a template for tuning swarm interaction parameters ($\hat C(k, t) = C(k, t) / C(k, 0)$2, $\hat C(k, t) = C(k, t) / C(k, 0)$3, $\hat C(k, t) = C(k, t) / C(k, 0)$4, $\hat C(k, t) = C(k, t) / C(k, 0)$5, $\hat C(k, t) = C(k, t) / C(k, 0)$6, $\hat C(k, t) = C(k, t) / C(k, 0)$7) to achieve responsive, robust behavior regimes straddling order and chaos.

8. Synthesis and Outlook

DynaSwarm encapsulates a paradigmatic shift in swarm algorithmics and theory: collective systems that eschew static architectures in favor of adaptively selected, input-, task-, or environment-dependent coordination strategies. Core themes recur across domains:

• Dynamic scaling, non-exponential relaxation, and new universality in biological swarms;
• Formal decentralized control laws and robust distributed assignment for robotic shape formation;
• RL-based, per-input structural selection in AI multi-agent systems;
• Adaptive, parameterized search and task allocation in unknown or stochastic environments;
• Deep-RL architectures with real-time subswarm splitting/merging for dynamic target pursuit;
• Edge-of-chaos operation yielding optimal responsiveness in adversarial settings.

A plausible implication is that DynaSwarm methodologies will underpin next-generation biological modeling, swarm robotics, and distributed AI, with benchmarks including adaptability, scalability, and robust collective performance in non-stationary and partially observed environments (Cavagna et al., 2016, Leong et al., 31 Jul 2025, Prasertying et al., 14 Nov 2025, Gupta et al., 2021, Qamar et al., 2022, Balachandran et al., 2024).