Uncertainty-Aware Multi-Robot Task Allocation With Strongly Coupled Inter-Robot Rewards

Abstract

Allocating tasks to heterogeneous robot teams in environments with uncertain task requirements is a fundamentally challenging problem. Redundantly assigning multiple robots to such tasks is overly conservative, while purely reactive strategies risk costly delays in task completion when the uncertain capabilities become necessary. This paper introduces an auction-based task allocation algorithm that explicitly models uncertain task requirements, leveraging a novel strongly coupled formulation to allocate tasks such that robots with potentially required capabilities are naturally positioned near uncertain tasks. This approach enables robots to remain productive on nearby tasks while simultaneously mitigating large delays in completion time when their capabilities are required. Through a set of simulated disaster relief missions with task deadline constraints, we demonstrate that the proposed approach yields up to a 15% increase in expected mission value compared to redundancy-based methods. Furthermore, we propose a novel framework to approximate uncertainty arising from unmodeled changes in task requirements by leveraging the natural delay between encountering unexpected environmental conditions and confirming whether additional capabilities are required to complete a task. We show that our approach achieves up to an 18% increase in expected mission value using this framework compared to reactive methods that don't leverage this delay.

Figures (4)

• Figure 1: A disaster relief scenario with uncertain task requirements. Debris tasks can always be completed by a debris robot, whereas search tasks require a search robot and may require additional support from a debris robot with some probability. While other methods assign the debris robot either to the nearest debris task or directly to an uncertain search task, our approach strategically selects a more distant debris task, balancing both timely debris task completion and quick assistance for either search task.
• Figure 2: Total expected value loss and average missed tasks for an 8-robot, 12-task (4 HVUTs) mission with known uncertainty, where the uncertainty realization time is $\mathcal{T}=50$. We compare performance across a range of probabilities that search tasks require debris-clearing assistance. The results show that AURA consistently achieves the lowest value loss, meeting nearly all high-value deadlines while completing more regular-value tasks within their deadlines than redundancy-based approaches.
• Figure 3: Total value loss and number of missed tasks as the problem size increases. We assume a fixed team of 3 search robots and 3 debris robots and maintain a ratio of approximately 2:1 debris tasks to search tasks. As the number of tasks grows, AURA consistently achieves the highest performance, satisfying as many HVUT deadlines as the redundancy-based methods while maintaining a level of regular-value deadline completion comparable to the non-proactive approach.
• Figure 4: Runtime analysis as the number of tasks increases. On a log-scale plot, all greedy methods exhibit linear growth, indicating the expected polynomial-time complexity. In contrast, CTAS exhibits exponential growth and reaches the 600 second time-limit for larger problem sizes.

Theorems & Definitions (10)

• Lemma 1
• proof
• Lemma 2
• proof
• Theorem 1
• proof
• Lemma 3
• proof
• Theorem 2
• proof