Multi-Robot Task Allocation using Global Games with Negative Feedback: The Colony Maintenance Problem

TL;DR

This paper tackles multi-robot task allocation for maintaining a centralized colony's energy by casting the problem as a global games framework with a negative feedback term in the robots' utility to avoid trivial all-foraging or all-idle equilibria. Robots decide to forage based on the global energy signal $s(t)$ (with $\theta(t)=1-s(t)$) and the current number of foragers, yielding a nontrivial mixed-strategy Nash equilibrium within a defined $\theta$ interval. The authors derive the marginal utility $\pi(n,\theta) = -c_a+\kappa+\lambda e^{-(n+1)}+\theta$ and show it decreases in $n$, providing resilience to removal or external recruitment and enabling adaptive long-duration autonomy. A Matlab simulation with $N=12$ demonstrates robustness to agent removal and corroborates the theoretical equilibrium, supporting the method's practicality for dynamic MRTA tasks.

Abstract

In this article we address the multi-robot task allocation problem, where robots must cooperatively assign themselves to accomplish a set of tasks. We consider the colony maintenance problem as an example, where a team of robots are tasked with continuously maintaining the energy supply of a central colony. We model this as a global game, where each robot measures the energy level of the colony, and the current number of assigned robots, to determine whether or not to forage for energy sources. The key to our approach is introducing a negative feedback term into the robots' utility, which also eliminates the trivial solution where foraging or not foraging are strictly dominant strategies. We compare our approach qualitatively to existing an global games approach, where a positive positive feedback term admits threshold-based decision making that encourages many robots to forage. We discuss how positive feedback can lead to a cascading failure when robots are removed from the system, and we demonstrate the resilience of our approach in simulation.

Figures (5)

• Figure 1: The marginal utility of our proposed mechanism. Robots do not consider the actions of others when $\theta$ falls beyond the shaded green area.
• Figure 2: Switching system that describes the behavior of the robots. Each robot is idle until the marginal utility of foraging is positive, and they continue to forage until they return with an energy source.
• Figure 3: Snapshots of the simulation environment at $t = 800$ and $t=901$, just before and after $6$ of the $12$ robots are removed from the domain. Red and blue circles are robots, dashed circles denote the sensing radius, and straight lines point from a robot to its stored memory location.
• Figure 4: Energy of the colony (red) and the total energy $J$ (black, dashed). The blue vertical line is the instant where half the robots are removed from the system.
• Figure 5: The expected, actual, and maximum number of robots foraging during the simulation.

Theorems & Definitions (16)

• Definition 1
• Remark 1
• Definition 2: Strictly Dominant Strategy
• Definition 3: Mixed Strategy
• Lemma 1
• proof
• Theorem 1
• proof
• Remark 2
• Remark 3