Beacon-Based Agent Selection

• Beacon-Based Agent Selection is a methodology that employs fixed reference points (beacons) to efficiently control agent formations, coverage, and task allocation in distributed systems.
• It integrates convex combination control laws, submodular optimization, and geometric algorithms to balance local dynamics with global objectives.
• This approach underpins robust coordination in applications ranging from robotic station-keeping and sensor localization to decentralized orchestration in networked systems.

Beacon-Based Agent Selection refers to a suite of methodologies, control laws, and algorithmic frameworks in which “beacons”—fixed points, deployed nodes, or agents with special status—are used as references to influence, select, or control the behavior or selection of other agents within multi-agent or distributed systems. The beacon concept appears in control theory (formation and pursuit), algorithmic coverage and routing, distributed robotics, wireless networks, and emerging settings such as decentralized LLM orchestration. Beacon-based mechanisms exploit locality, attraction patterns, or capability matching to achieve efficient agent deployment, motion, coverage, selection, or task allocation.

1. Beacon-Referenced Control in Multi-Agent Systems

Beacon-referenced pursuit has become a central paradigm for controlling agent formations, particularly for robotic station-keeping and collective behavior. In classical cyclic pursuit, each agent maintains a constant offset (bearing) with respect to a single neighbor. The beacon-referenced version augments this by introducing an external reference: each agent’s control input is a convex combination of a neighbor-chasing term and a beacon-tracking term:

$$u_i = (1-\lambda) u_\mathrm{CB}^i + \lambda u_\mathrm{B}^i,\quad \lambda \in [0,1]$$

where $u_\mathrm{CB}^i$ and $u_\mathrm{B}^i$ represent the control efforts associated with neighbor pursuit and beacon referencing, respectively, typically modulated by parameters (e.g., offsets $\alpha_i$, $\alpha_0$ and gain $\mu$) (Galloway et al., 2015, Galloway et al., 2017, Galloway et al., 2017, Galloway et al., 2019).

The closed-loop system admits “circling equilibria”: agents arrange themselves around the stationary beacon at a radius and with angular spacing dictated by the control parameters.

• For $n$ agents, necessary equilibrium conditions impose
  • beacon bearing $\kappa_{ib} = \pm \frac{\pi}{2}$
  • inter-agent bearing $\theta_{i+1} = \pi - \kappa_i$
• Explicit formulas relate the steady-state distances to $\lambda,$ the offset angles, and the feedback gain.
• Rigorous stability analysis for the 2-agent (and extended n-agent) cases is performed using linearization; with appropriate parameter choices (e.g., positive $\sin\alpha_0$ and average offset), all non-geometric eigenvalues have strictly negative real parts, implying local asymptotic stability.

The design flexibility allows systematic selection of which (and how many) agents are entrained in the desirable formation, simply by adjusting control weights and offset angles, which modulate the tradeoff between inter-agent cohesion and station-keeping on the reference (Galloway et al., 2015).

2. Beacon-Based Coverage and Routing in Geometric Domains

Beacon attraction models—where agents or points are “pulled” in greedy fashion toward active beacons, sliding along obstacles as needed—have motivated combinatorial coverage, guarding, and routing problems in computational geometry.

In planar rectilinear polygons, tight combinatorial bounds are established:

• Coverage: $\left\lfloor n/6 \right\rfloor$ beacons suffice and are sometimes necessary to cover a simple $n$-vertex rectilinear polygon ($n=2r+4$; $r$ = number of reflex vertices), equivalent to covering each “corner” region of spiral polygons. Placement at reflex vertices is optimal (Bae et al., 2015).
• Routing: To guarantee greedy paths between all pairs of points, $\left\lfloor (3n-4)/8 \right\rfloor-1$ beacons suffice, with lower bounds at $\left\lceil n/4 \right\rceil-1$.

These bounds are operationalized via safe partition strategies (using “normal cuts” and recursive decomposition), and new algorithms achieve linear time complexity for computing the so-called beacon kernel $K(P)$—the locus from which a beacon attracts every point. In three dimensions, similar principles extend, using the tetrahedral decomposition of polyhedra—now requiring up to $\left\lfloor (m+1)/3 \right\rfloor$ beacons, $m$ being tetrahedra in a partition (Cleve et al., 2017).

3. Algorithmic Optimization for Beacon Placement in Localization

Beacon-based localization leverages beacons as anchors for distance or signal measurements, and their selection critically affects localization accuracy. Modern approaches employ information-theoretic and data-driven optimization:

• The D-optimality criterion (maximizing $\log\det(\mathrm{FIM})$) is used to formulate beacon placement as a submodular set-function maximization problem, with provable $(1-1/e)$ approximation guarantees for the greedy algorithm (Sequeira et al., 19 May 2024).
• MAP estimation includes both data-fidelity and prior terms, with Fisher Information Matrix (FIM) contributions weighted by measurement variances:

$f(S) = \log\det (\mathrm{FIM}(S) + \mathrm{FIM}_0)$

• Open-source implementations and simulation tools are provided for practical deployment, spanning application domains from indoor WiFi localization to factory robotics. Comparison with random, brute-force, and purely coverage-maximizing heuristics consistently shows the superiority (in RMSE) of information-driven beacon placement.

Alternative strategies (e.g., grid-mapping approaches with received signal strength (RSS) binarization) support the search for optimal beacon count and transmission radius (Bharadwaj et al., 2015). Bayesian filtering (e.g., Kalman, particle, and kernel density estimators) can further boost proximity estimation accuracy up to 40% over simple averaging (Mackey et al., 2020).

4. Beacon-Based Distributed Protocols for Agent Selection, Coverage, and Formation

Beyond static placement, in dynamic or decentralized agent collectives, beacon “roles” are assigned algorithmically to support exploration, coverage, or structure formation:

• Settling agents as beacons: In coverage/exploration swarms, agents that settle in new locations become beacons, broadcasting local “step counts” that establish a virtual potential gradient, causing mobile agents to fill uncovered regions efficiently. When all regions are filled, backward propagating closure (BPC) signals deterministically terminate exploration, sharply reducing redundant agent activity and energy consumption (Rappel et al., 2022).
• Gradient and potential field propagation: In distributed structure formation, settled “beacon” agents at the structure frontier propagate a gradient throughout the partially formed shape. Free agents follow the gradient to reach the frontier, then undergo a local bidding protocol to settle, ensuring scalable and robust assembly even in 3D environments (Mina et al., 2023).
• Stagnation recovery mechanisms: Local rules and finite state machines manage transitions between search, gradient-following, bidding, and settling states, including forced random-walk resampling when agents are caught in geometric deadlocks.

Simulation studies confirm that these protocols scale linearly in termination time with region size and minimize active agent count and energy consumption compared to naively layered coverage.

5. Beacon-Driven Selection in Networked Systems and Decentralized Orchestration

Beacon-based agent selection principles have been generalized to task allocation and orchestration in multi-agent computational frameworks, particularly in decentralized and privacy-preserving contexts for LLM-based systems:

• Beacon-Selection Protocol: In decentralized frameworks such as Symphony, a “beacon” is broadcast for each sub-task (in a chain-of-thought decomposition), expressing the task's requirement vector. Each agent computes a local match:

$s_j(t_{i,k}) = \varphi(c_j, r(t_{i,k})) \in [0,1]$

using, for example, cosine similarity between local capabilities $c_j$ and sub-task requirements $r(\cdot)$ (Wang et al., 27 Aug 2025).

• Decentralized Ledger: Agent capabilities are registered (e.g., as capability vectors and DID-backed credentials) in a decentralized ledger that dynamically updates as agents join, exit, or change state. This forms the backbone for resilience and real-time agent selection.
• Weighted Voting by Chains of Thought (CoT): For each query, multiple planning agents generate reasoning chains; the final answer is selected via a weighted majority vote over candidate outputs, with weights proportional to confidence (aggregate match scores) along the CoT:

$$\hat{a} = \arg\max_{a\in\mathcal{A}} \sum_{i=1}^M \mathbb{1}(a_i = a) \cdot w_i$$

This process, empirically, produces substantial accuracy and robustness gains on complex benchmarks relative to direct and random allocation baselines.

• Scalability and Adaptability: Symphony achieves horizontal scalability without centralized orchestration, easily adapting to variable agent pools and consumer hardware, and incurring low orchestration overhead ($<5\%$ of inference latency).

6. Theoretical and Algorithmic Principles

Core algorithmic and mathematical elements that recur in beacon-based agent selection include:

• Convex combination control laws: Weighting terms for neighbor and beacon influence ($\lambda$ parameter), enabling interpolation between local and global objectives.
• Submodularity in selection and coverage: The diminishing returns property in log-determinant objectives ensures efficiency and bounded suboptimality of greedy beacon selection.
• Gradient, kernel, and region constructs: Use of gradients (virtual or physical), kernel-based uncertainty quantification, and definition of attraction, inverse attraction, and kernel regions underpin analytical and algorithmic developments (Kostitsyna et al., 2018).
• Inductive and recursive geometric arguments: For coverage/routing, proofs employ safe cuts, recursive splitting, and dual-graph pruning to construct minimal beacon sets with combinatorial optimality guarantees (Bae et al., 2015, Cleve et al., 2017).

7. Broader Impact and Open Directions

Beacon-based agent selection encompasses a broad array of applications, including autonomous surveillance, indoor localization, sensor network deployment, wireless network bootstrapping, formation control, and decentralized AI orchestration. Research continues to refine combinatorial and optimization frameworks for non-rectilinear and dynamically evolving domains, integrate sensor noise and communication constraints, and generalize protocols for heterogeneous agent collectives and adversarial environments. The unifying insight is that references—physical, informational, or virtual—can be leveraged both as attractors for distributed coordination and as decision primitives for scalable, efficient agent selection across domains.