Collaborative delivery with energy-constrained mobile robots

Andreas Bärtschi*, Jérémie Chalopin, Shantanu Das, Yann Disser, Barbara Geissmann, Daniel Graf, Arnaud Labourel, Matúš Mihalák

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


We consider the problem of collectively delivering some package from a specified source to a designated target location in a graph, using multiple mobile agents. Each agent has limited energy which constrains the distance it can move. Hence multiple agents need to collaborate to move the package, each agent handing over the package to the next agent to carry it forward. Given the positions of the agents in the graph and their respective budgets, the problem of finding a feasible movement schedule for the agents can be challenging. We consider two variants of the problem: in non-returning delivery, the agents can stop anywhere; whereas in returning delivery, each agent needs to return to its starting location, a variant which has not been studied before.

We first provide a polynomial-time algorithm for returning delivery on trees, which is in contrast to the known (weak) NP-hardness of the non-returning version. In addition, we give resource-augmented algorithms for returning delivery in general graphs. Finally, we give tight lower bounds on the required resource augmentation for both variants of the problem. In this sense, our results close the gap left by previous research. (C) 2017 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)2-14
Number of pages13
JournalTheoretical Computer Science
Publication statusPublished - 2 Mar 2020


  • Budget
  • Delivery
  • Limited battery
  • Mobile agents
  • Resource augmentation

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