This article considers the problem of assigning mobile robots to goals on transport networks with uncertain and potentially correlated information about travel times. Our aim is to produce optimal assignments such that the average waiting time at destinations is minimized. Since noisy travel time estimates result in suboptimal assignments, we propose a method that offers robustness to uncertainty by making use of redundant robot assignments. However, solving the redundant assignment problem optimally is strongly NP-hard. Hence, we exploit the structural properties of our mathematical problem formulation to propose a polynomial-time, near-optimal solution. We demonstrate that our problem can be reduced to minimizing a supermodular cost function subject to a matroid constraint. This allows us to develop a greedy assignment algorithm, for which we derive suboptimality bounds. We demonstrate the effectiveness of our approach with simulations on transport networks with correlated uncertain edge costs and uncertain node positions that lead to noisy travel time estimates. Comparisons to benchmark algorithms show that our method performs near-optimally and significantly better than the nonredundant assignment. Finally, our findings include results on the benefit of diversity and complementarity in redundant robot coalitions; these insights contribute toward providing resilience to uncertainty through the targeted composition of robot coalitions. Note to Practitioners-This article is motivated by the problem of assigning mobile robots (e.g., vehicles and drones) to goals when travel times from robot origins to goal locations are uncertain. Existing robust assignment methods deal with uncertainty by minimizing risk or by predefining acceptable risk thresholds. In this article, we propose a complementary method that offers robustness to uncertainty by making use of robot redundancy. In other words, we assign more robots than necessary to a given goal, in the expectation that one of the redundant robots will reach the goal faster (than the originally assigned robot). However, solving this redundant assignment problem is computationally intractable for large systems. By characterizing the mathematical problem, we show how the redundant assignment problem can be solved efficiently. We apply our assignment algorithm to transport network problems to reduce the average waiting times at goal locations when travel times from vehicle origins to destinations are uncertain and potentially also correlated. Our results show that exploiting robot redundancy is an effective approach to reducing waiting times. In this work, we build on the premise that time is the primary commodity, and we do not explicitly model the additional cost of utilizing redundant robots. Future work should more explicitly address the tradeoff between the cost of providing redundancy (e.g., travel costs and robot costs) and performance gains.

中文翻译：

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在行程时间不确定的运输网络上使用冗余机器人进行鲁棒分配


本文考虑了将移动机器人分配给运输网络上的目标的问题，其中包含有关旅行时间的不确定且潜在相关的信息。我们的目标是制定最佳分配方案，最大限度地减少目的地的平均等待时间。由于嘈杂的行程时间估计会导致分配不理想，因此我们提出了一种通过使用冗余机器人分配来提供对不确定性的鲁棒性的方法。然而，最优地解决冗余分配问题是非常NP困难的。因此，我们利用数学问题公式的结构特性来提出多项式时间的、接近最优的解决方案。我们证明我们的问题可以简化为最小化受拟阵约束的超模成本函数。这使我们能够开发一种贪婪分配算法，并为此得出次优边界。我们通过对运输网络进行模拟来证明我们的方法的有效性，该运输网络具有相关的不确定边缘成本和不确定的节点位置，从而导致嘈杂的旅行时间估计。与基准算法的比较表明，我们的方法的性能接近最优，并且明显优于非冗余分配。最后，我们的研究结果包括冗余机器人联盟中多样性和互补性的好处；这些见解有助于通过有针对性的机器人联盟组成来提供对不确定性的抵御能力。从业者注意事项 - 本文的动机是当从机器人起点到目标位置的行进时间不确定时，将移动机器人（例如车辆和无人机）分配给目标的问题。现有的稳健分配方法通过最小化风险或预先定义可接受的风险阈值来处理不确定性。 在本文中，我们提出了一种补充方法，通过利用机器人冗余来提供对不确定性的鲁棒性。换句话说，我们为给定目标分配了超出必要数量的机器人，期望其中一个冗余机器人能够更快地到达目标（比最初分配的机器人）。然而，对于大型系统来说，解决这种冗余分配问题在计算上是困难的。通过描述数学问题的特征，我们展示了如何有效地解决冗余分配问题。当从车辆出发地到目的地的行驶时间不确定且可能相关时，我们将分配算法应用于运输网络问题，以减少目标位置的平均等待时间。我们的结果表明，利用机器人冗余是减少等待时间的有效方法。在这项工作中，我们的前提是时间是主要商品，并且我们没有明确模拟使用冗余机器人的额外成本。未来的工作应该更明确地解决提供冗余的成本（例如，旅行成本和机器人成本）和性能增益之间的权衡。