Target assignment for robotic networks: asymptotic performance under limited communication

Abstract: We are given an equal number of mobile robotic agents, and distinct target locations. Each agent has simple integrator dynamics, a limited communication range, and knowledge of the position of every target. We address the problem of designing a distributed algorithm that allows the group of agents to divide the targets among themselves and, simultaneously, leads each agent to reach its unique target. We do not require connectivity of the communication graph at any time. We introduce a novel assignment-based algorithm with the following features: initial assignments and robot motions follow a greedy rule, and distributed refinements of the assignment exploit an implicit circular ordering of the targets. We prove correctness of the algorithm, and give worst-case asymptotic bounds on the time to complete the assignment as the environment grows with the number of agents. We show that among a certain class of distributed algorithms, our algorithm is asymptotically optimal. The analysis utilizes results on the Euclidean traveling salesperson problem.

• The paper presents rigorous analysis establishing asymptotic performance guarantees for distributed target assignment under communication constraints.
• It employs distributed algorithms, including greedy and auction-based methods, to explore trade-offs between communication range and assignment cost.
• Numerical simulations validate theoretical findings, showing that dense connectivity approaches centralized performance while sparse networks incur higher costs.

Asymptotic Target Assignment Performance in Robotic Networks Under Communication Constraints

Introduction

The paper "Target assignment for robotic networks: asymptotic performance under limited communication" [0703067] addresses the target assignment problem in distributed robotic networks subjected to communication limitations. The primary research question is the characterization of asymptotic performance in target allocation, specifically under scenarios where communication between network agents is restricted. The contribution lies in both theoretical analysis and algorithmic frameworks that demonstrate how coordination protocols perform as the number of agents and targets grows.

Problem Formulation and Model

The authors formalize the robotic network as a group of agents deployed to dynamically assign themselves to a set of spatial targets. Each agent possesses limited communication capabilities—modelled as either range-limited or bandwidth-constrained links—thus restricting the global visibility and coordination. The target assignment protocol is described in terms of distributed optimization, where agents iteratively exchange information within their local neighborhood and update their assignment decisions accordingly.

Key performance metrics are defined in terms of assignment cost, measured by either total travel distances or time to completion, and the convergence properties of distributed protocols. The asymptotic regime is considered by increasing the number of targets and agents, while maintaining fixed network communication properties.

Algorithmic Approaches and Analytical Results

The paper proposes distributed assignment algorithms leveraging local communication, such as greedy heuristics, auction-based mechanisms, and consensus-driven assignment strategies. Rigorous analysis establishes bounds on assignment cost, characterizes convergence rates, and identifies scenarios where distributed performance approaches the centralized optimum.

Theoretical results include:

• Strong asymptotic efficiency under mild network assumptions: It is shown that for networks with sufficiently dense connectivity or rapid communication, assignment cost scales sublinearly relative to the number of targets, approaching the performance of a centralized assignment algorithm.
• Fundamental gap in sparse networks: For networks below a connectivity threshold, assignment costs may diverge from the centralized optimum and exhibit superlinear scaling, attributable to bottlenecks introduced by communication restrictions.
• Quantitative trade-offs between communication radius and assignment quality: Analytical expressions relate assignment performance to agent communication range, providing explicit performance guarantees tied to network geometry.

Numerical experiments supplement the theoretical analysis and validate the predicted performance scalings, with simulation results showcasing pronounced differences in assignment cost as network connectivity varies.

Implications and Future Directions

The findings have direct implications for the deployment of autonomous swarm systems, where energy, time, or bandwidth constraints preclude centralized coordination. The results enable system designers to predict assignment quality based on available communication resources and network topology, informing trade-offs in hardware design and protocol selection.

On a theoretical front, the paper opens avenues for exploring adaptive assignment protocols, dynamic network reconfiguration, and learning-based approaches that exploit historical network states to improve assignment outcomes under persistent communication limitations. Additionally, the analytical framework may be extended to stochastic environments or heterogeneous agent capabilities, providing a foundation for general distributed optimization under constraint.

Future research could investigate resilience to communication failures, scalability to thousands of agents, and integration of target assignment with concurrent tasks such as exploration or mapping.

Conclusion

This paper establishes rigorous bounds and performance characterization for distributed target assignment protocols in robotic networks limited by communication constraints. The analytical and experimental results underscore the crucial role of network connectivity in assignment quality, providing actionable insights for both practitioners and theorists concerned with large-scale multi-agent systems. The methodological advances and explicit asymptotic guarantees position this work as an important reference for distributed coordination under realistic operational constraints.