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A Global Games-Inspired Approach to Multi-Robot Task Allocation for Heterogeneous Teams

Logan Beaver

TL;DR

This work tackles multi-robot task allocation for heterogeneous teams by framing the problem as a global-games mechanism design. A linear utility $u_i(a, \mathbf{n}, \mathbf{s})$ drives robots to distribute across tasks based on a per-task signal $s_k(t)$ and current occupancy, yielding a mixed Nash equilibrium that favors more capable robots and balanced task coverage. The authors derive explicit NE solutions for homogeneous cases and extend to heterogeneous groups through a reduction to tractable linear systems, accompanied by an efficient iterative-elimination algorithm with $O(M\cdot g)$ complexity. Simulations in colony maintenance and persistent monitoring demonstrate dynamic, robust allocations with resilience to robot addition/removal and without explicit inter-robot communication. The approach offers scalable MRTA with real-time adaptability and theoretical guarantees under the global-games framework, with future work aimed at hardware validation and richer dynamics.

Abstract

In this article we propose a game-theoretic approach to the multi-robot task allocation problem using the framework of global games. Each task is associated with a global signal, a real-valued number that captures the task execution progress and/or urgency. We propose a linear objective function for each robot in the system, which, for each task, increases with global signal and decreases with the number assigned robots. We provide conditions on the objective function hyperparameters to induce a mixed Nash equilibrium, i.e., solutions where all robots are not assigned to a single task. The resulting algorithm only requires the inversion of a matrix to determine a probability distribution over the robot assignments. We demonstrate the performance of our algorithm in simulation and provide direction for applications and future work.

A Global Games-Inspired Approach to Multi-Robot Task Allocation for Heterogeneous Teams

TL;DR

This work tackles multi-robot task allocation for heterogeneous teams by framing the problem as a global-games mechanism design. A linear utility drives robots to distribute across tasks based on a per-task signal and current occupancy, yielding a mixed Nash equilibrium that favors more capable robots and balanced task coverage. The authors derive explicit NE solutions for homogeneous cases and extend to heterogeneous groups through a reduction to tractable linear systems, accompanied by an efficient iterative-elimination algorithm with complexity. Simulations in colony maintenance and persistent monitoring demonstrate dynamic, robust allocations with resilience to robot addition/removal and without explicit inter-robot communication. The approach offers scalable MRTA with real-time adaptability and theoretical guarantees under the global-games framework, with future work aimed at hardware validation and richer dynamics.

Abstract

In this article we propose a game-theoretic approach to the multi-robot task allocation problem using the framework of global games. Each task is associated with a global signal, a real-valued number that captures the task execution progress and/or urgency. We propose a linear objective function for each robot in the system, which, for each task, increases with global signal and decreases with the number assigned robots. We provide conditions on the objective function hyperparameters to induce a mixed Nash equilibrium, i.e., solutions where all robots are not assigned to a single task. The resulting algorithm only requires the inversion of a matrix to determine a probability distribution over the robot assignments. We demonstrate the performance of our algorithm in simulation and provide direction for applications and future work.
Paper Structure (14 sections, 7 theorems, 47 equations, 8 figures, 2 tables, 1 algorithm)

This paper contains 14 sections, 7 theorems, 47 equations, 8 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Notation
  3. Problem Formulation
  4. Solution Approach
  5. Homogeneous Systems
  6. Idle Task Feasible, Homogeneous
  7. Idle Task Infeasible, Homogeneous
  8. Heterogeneous Systems
  9. Idle Task Feasible, Heterogeneous.
  10. Idle Task Infeasible, Heterogeneous.
  11. Simulation Results
  12. Colony Maintenance
  13. Persistent Monitoring
  14. Conclusion

Key Result

Lemma 1

If $0\in\delta$, i.e., doing nothing is a feasible action, then each robot $i$ assigns itself to task $k\in\delta\setminus\{0\}$ with probability,

Figures (8)

  • Figure 1: The simulation state at (left to right) $t=100, 200, 400$ seconds; these show the initial configuration, configuration after half the robots are removed, and final configuration of the robots.
  • Figure 2: Energy level for the colony (red) and entire system (black, dashed) during the colony maintenance simulation.
  • Figure 3: Amount of undelivered cargo at each time step, the vertical steps correspond to the arrival and delivery of cargo, respectively.
  • Figure 4: Caption
  • Figure 5: Caption
  • ...and 3 more figures

Theorems & Definitions (23)

  • Definition 1
  • Definition 2
  • Definition 3: Strictly Dominant Strategy
  • Definition 4: Mixed Strategy
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Definition 5
  • Lemma 3
  • ...and 13 more