{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T17:07:22Z","timestamp":1767373642035,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2021,12,18]],"date-time":"2021-12-18T00:00:00Z","timestamp":1639785600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"RoboCup Federation and Mathworks","award":["RoboCup Federation and Mathworks 2021 Research Projects"],"award-info":[{"award-number":["RoboCup Federation and Mathworks 2021 Research Projects"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>Currently, there is a lack of developer-friendly software tools to formally address multi-robot coordination problems and obtain robust, efficient, and predictable strategies. This paper introduces a software toolbox that encapsulates, in one single package, modeling, planning, and execution algorithms. It implements a state-of-the-art approach to representing multi-robot systems: generalized Petri nets with rewards (GSPNRs). GSPNRs enable capturing multiple robots, decision states, action execution states and respective outcomes, action duration uncertainty, and team-level objectives. We introduce a novel algorithm that simplifies the model design process as it generates a GSPNR from a topological map. We also introduce a novel execution algorithm that coordinates the multi-robot system according to a given policy. This is achieved without compromising the model compactness introduced by representing robots as indistinguishable tokens. We characterize the computational performance of the toolbox with a series of stress tests. These tests reveal a lightweight implementation that requires low CPU and memory usage. We showcase the toolbox functionalities by solving a multi-robot inspection application, where we extend GSPNRs to enable the representation of heterogeneous systems and system resources such as battery levels and counters.<\/jats:p>","DOI":"10.3390\/app112412087","type":"journal-article","created":{"date-parts":[[2021,12,19]],"date-time":"2021-12-19T20:41:55Z","timestamp":1639946515000},"page":"12087","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Petri Net Toolbox for Multi-Robot Planning under Uncertainty"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8842-8989","authenticated-orcid":false,"given":"Carlos","family":"Azevedo","sequence":"first","affiliation":[{"name":"Institute For Systems and Robotics, Instituto Superior T\u00e9cnico, University of Lisbon, 1049-001 Lisboa, Portugal"}]},{"given":"Ant\u00f3nio","family":"Matos","sequence":"additional","affiliation":[{"name":"Institute For Systems and Robotics, Instituto Superior T\u00e9cnico, University of Lisbon, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8962-8050","authenticated-orcid":false,"given":"Pedro U.","family":"Lima","sequence":"additional","affiliation":[{"name":"Institute For Systems and Robotics, Instituto Superior T\u00e9cnico, University of Lisbon, 1049-001 Lisboa, Portugal"}]},{"given":"Jose","family":"Avenda\u00f1o","sequence":"additional","affiliation":[{"name":"The MathWorks, Natick, MA 01760, USA"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ohradzansky, M.T., Rush, E.R., Riley, D.G., Mills, A.B., Ahmad, S., McGuire, S., Biggie, H., Harlow, K., Miles, M.J., and Frew, E.W. 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