Robust Assignment Using Redundant Robots on Transport Networks With Uncertain Travel Time

Abstract

This paper 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 sub-optimal 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 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 sub-optimality 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 non-redundant assignment. Finally, our findings include results on the benefit of diversity and complementarity in redundant robot coalitions; these insights contribute towards providing resilience to uncertainty through targeted composition of robot coalitions. Note to Practitioners-This paper is motivated by the problem of assigning mobile robots (e.g., vehicles, drones, etc.) 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 pre-defining acceptable risk thresholds. In this work, 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 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 trade-off between the cost of providing redundancy (e.g., travel costs, robot costs) and performance gains.

Optimization of Web Service-Based Data-Collection System With Smart Sensor Nodes for Balance Between Network Traffic and Sensing Accuracy

“…Thirty replications of the simulation are performed in total, the same as the field experiments. The 30 simulation results consist of three parts and are concluded, respectively, as the 10 The hotspot (smartphone) always consumes network traffic even though there is no estimate-submission due to the reason that some built-in applications cannot be completely shut down and always lead to network traffic cost. The network data corresponding to such consumption and the estimate-submissions jointly produce data blocks.…”

“…This means that C without = 1000 × 10 = 10 000 B and n ε = 55 (see footnote 10). 10 In the test, we measured C with = 10 055 B, so we have ε ≈ (10 055 − 10 000)/55 = 1 B. To emulate the real scenario, simulations and field experiments share the same c and ε and are both carried out by the following three parts.…”

Pursuer Assignment and Control Strategies in Multi-Agent Pursuit-Evasion Under Uncertainties

“…We first consider the assignment problem from the perspective of the pursuers-with the evaders represented by probability distributions {p j } j∈Cy , what's the best pursuer-to-evader assigment? In a probabilistic setup, where the costs (capture times) are stochastic variables (see Section 3.3.2), and there are excess pursuers, this needs to be solved in two stages (Prorok, 2020): First we need to determine an initial assignment of each evader to one pursuer. Following that we determine the assignment of the remaining (redundant) pursuers so as to minimize the (total or maximum) expected capture time.…”

“…After computation of an initial assignment, A 0 , we determine the assignment of the remaining pursuers using the method proposed in (Prorok, 2020). Formally, we first consider the problem of selecting a set of redundant pursuer-evader matchings, Ā , that minimizes the total expected travel time to evaders, under the constraint that any pursuer is only assigned once:…”

Resilient Active Information Gathering with Mobile Robots

“…But most robotics research places no emphasis on robustifying information acquisition against attacks (or failures) that may temporarily disable the robots' sensors; e.g., smokecloud attacks that can block temporarily the field of view of multiple sensors. For example, [21] focuses on formation control, instead of information acquisition; [22] focuses on state estimation against byzantine attacks, i.e., attacks that corrupt the robots' sensors with adversarial noise, instead of disabling them; and [23] focuses on a trajectory scheduling in transportation networks when travel times can be uncertain, instead on trajectory planning for information acquisition. An exception is [16], which however is limited to multi-target tracking based on myopic planning, instead of non-myopic.…”