Redundant Robot Assignment on Graphs with Uncertain Edge Costs

We provide a framework for the assignment of multiple robots to goal locations, when robot travel times are uncertain. Our premise is that time is the most valuable asset in the system. Hence, we make use of redundant robots to counter the effect of uncertainty and minimize the average waiting time at destinations. We apply our framework to transport networks represented as graphs, and consider uncertainty in the edge costs (i.e., travel time). Since solving the redundant assignment problem is strongly NP-hard, we exploit structural properties of our problem to propose a polynomial-time solution with provable sub-optimality bounds. Our method uses distributive aggregate functions, which allow us to efficiently (i.e., incrementally) compute the effective cost of assigning redundant robots. Experimental results on random graphs show that the deployment of redundant robots through our method reduces waiting times at goal locations, when edge traversals are uncertain

Right Place, Right Time:Proactive Multi-Robot Task Allocation Under Spatiotemporal Uncertainty

For many multi-robot problems, tasks are announced during execution, where task announcement times and locations are uncertain. To synthesise multi-robot behaviour that is robust to early announcements and unexpected delays, multi-robot task allocation methods must explicitly model the stochastic processes that govern task announcement. In this paper, we model task announcement using continuous-time Markov chains which predict when and where tasks will be announced. We then present a task allocation framework which uses the continuous-time Markov chains to allocate tasks proactively, such that robots are near or at the task location upon its announcement. Our method seeks to minimise the expected total waiting duration for each task, i.e. the duration between task announcement and a robot beginning to service the task. Our framework can be applied to any multi-robot task allocation problem where robots complete spatiotemporal tasks which are announced stochastically. We demonstrate the efficacy of our approach in simulation, where we outperform baselines which do not allocate tasks proactively, or do not fully exploit our task announcement models