Multi-level spatial modeling for stochastic distributed robotic systems
Open accessAbstract
We propose a combined spatial and non-spatial probabilistic modeling methodology motivated by an inspection task performed by a group of miniature robots. Our models explicitly consider spatiality and yield accurate predictions on system performance. An agent’s spatial distribution over time is modeled by the Fokker—Planck diffusion model and complements current non-spatial microscopic and macroscopic models that model the discrete state distribution of a distributed robotic system. We validate our models on a microscopic level based on sub-microscopic, embodied robot simulations as well as real robot experiments. Subsequently, using the validated microscopic models as our template, abstraction is raised to the level of macroscopic difference equations. We discuss the dependency of the modeling performance on the distance from the robot origin (drop-off location) and temporal convergence of the team distribution. Also, using an asymmetric setup, we show the necessity of spatial modeling methodologies for environments where the robotic platform underlies drift phenomena.
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The simulation-reality gap problem is particularly important in swarm robotics where it is exacerbated by the fact that many robots have to interact with each other.
“This problem is particularly important in swarm robotics where it is exacerbated by the fact that many robots have to interact with each other [44].”
From Swarm Robotics: Past, Present, and Future [Point of View] (2021) · cites this paper as [44]
Cites
Bonabeau, E. W., Dorigo, M., & Guy Theraulaz, A. (1999) · Oxford University Press eBooks · doi:10.1093/oso/9780195131581.001.0001 · Cited by 6,588 · see citing works
Self-Organization in Biological Systems
Sneyd, J., Theraula, G., Bonabeau, E., Deneubourg, J.-L., & Franks, N. R. (2001) · doi:10.1515/9780691212920 · Cited by 2,949 · see citing works
(1999) · Choice Reviews Online · doi:10.5860/choice.36-5109 · Cited by 2,533 · see citing works
Berg, H. C. (1984) · Princeton University Press eBooks · doi:10.1515/9780691279886 · Cited by 2,400 · see citing works
Vehicles: Experiments in Synthetic Psychology.
Dennett, D. C., & Braitenberg, V. (1986) · The Philosophical Review · doi:10.2307/2185146 · Cited by 1,626 · see citing works
Vehicles: Experiments in synthetic psychology
Stefik, M. (1985) · Artificial Intelligence · doi:10.1016/0004-3702(85)90057-8 · Cited by 1,346 · see citing works
Cyberbotics Ltd. Webots <sup>™</sup> : Professional Mobile Robot Simulation
Michel, O. (2004) · International Journal of Advanced Robotic Systems · doi:10.5772/5618 · Cited by 1,261 · see citing works
Coverage for robotics – A survey of recent results
Choset, H. (2001) · Annals of Mathematics and Artificial Intelligence · doi:10.1023/a:1016639210559 · Cited by 1,213 · see citing works
Data collection, storage, and retrieval with an underwater sensor network
Vasilescu, I., Kotay, K. D., Rus, D. L., Dunbabin, M. D., & Corke, P. (2005) · ACM Conference on Embedded Networked Sensor Systems (SenSys) · doi:10.1145/1098918.1098936 · Cited by 619 · see citing works
(1999) · Kybernetes · doi:10.1108/k.1999.28.1.107.3 · Cited by 537 · see citing works
An overview of spatial microscopic and accelerated kinetic Monte Carlo methods
Chatterjee, A., & Vlachos, D. G. (2007) · Journal of Computer-Aided Materials Design · doi:10.1007/s10820-006-9042-9 · Cited by 466 · see citing works
Arkin, R. C. (1998) · Cited by 457 · see citing works
2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2010)
中尾学 (2011) · Journal of the Robotics Society of Japan · doi:10.7210/jrsj.29.443a2 · Cited by 410 · see citing works
Modeling Swarm Robotic Systems: a Case Study in Collaborative Distributed Manipulation
Martinoli, A., Easton, K., & Agassounon, W. (2004) · The International Journal of Robotics Research · doi:10.1177/0278364904042197 · Cited by 273 · see citing works
Self-citationMathematical Model of Foraging in a Group of Robots: Effect of Interference
Lerman, K., & Galstyan, A. (2002) · Autonomous Robots · doi:10.1023/a:1019633424543 · Cited by 182 · see citing works
Elements of Green's Functions and Propagation: Potentials, Diffusion, and Waves
Barton, G. (1989) · CERN Document Server (European Organization for Nuclear Research) · Cited by 169 · see citing works
SwisTrack - A Flexible Open Source Tracking Software for Multi-Agent Systems
Lochmatter, T., Roduit, P., Cianci, C. M., Correll, N., Jacot, J., & Martinoli, A. (2008) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros.2008.4650937 · Cited by 157 · see citing works
Self-citationA framework of space–time continuous models for algorithm design in swarm robotics
Hamann, H., & Wörn, H. (2008) · Swarm Intelligence · doi:10.1007/s11721-008-0015-3 · Cited by 134 · see citing works
A Survey of Numerical Methods for Parabolic Differential Equations
Douglas, J. J. (1961) · Advances in computers · doi:10.1016/s0065-2458(08)60140-0 · Cited by 128 · see citing works
WebotsTM: Professional Mobile Robot SimulationPreprint
Michel, O. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.cs/0412052 · Cited by 119 · see citing works
Mobile micro-robots ready to use: Alice
Caprari, G., & Siegwart, R. (2005) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros.2005.1545568 · Cited by 97 · see citing works
Makeev, A. G., Maroudas, D., Panagiotopoulos, A. Z., & Kevrekidis, I. G. (2002) · The Journal of Chemical Physics · doi:10.1063/1.1512274 · Cited by 91 · see citing works
Aerial Shepherds: Coordination among UAVs and Swarms of Robots
Chaimowicz, L., & Kumar, V. (2008) · Springer eBooks · doi:10.1007/978-4-431-35873-2_24 · Cited by 90 · see citing works
Gelten, R. J., Jansen, A. P. J., van Santen, R. A., Lukkien, J. J., Segers, J., & Hilbers, P. A. J. (1998) · The Journal of Chemical Physics · doi:10.1063/1.476003 · Cited by 89 · see citing works
Rudnick, J., & Gaspari, G. (2004) · Cambridge University Press eBooks · doi:10.1017/cbo9780511610912 · Cited by 76 · see citing works
Modelling a wireless connected swarm of mobile robots
Winfield, A. F. T., Liu, W., Nembrini, J., & Martinoli, A. (2008) · Swarm Intelligence · doi:10.1007/s11721-008-0018-0 · Cited by 71 · see citing works
Self-citationCollective Inspection of Regular Structures using a Swarm of Miniature Robots
Correll, N., & Martinoli, A. (2006) · Springer tracts in advanced robotics · doi:10.1007/11552246_36 · Cited by 62 · see citing works
Self-citationAgassounon, W., Martinoli, A., & Easton, K. (2004) · Autonomous Robots · doi:10.1023/b:auro.0000033971.75494.c8 · Cited by 60 · see citing works
Self-citation13th International Symposium on Distributed Autonomous Robotic Systems (DARS 2016)
Giuggioli, L., Arye, I., Robles, A. H., & Kaminka, G. A. (2016) · Distributed Autonomous Robotic Systems · Cited by 31 · see citing works
System Identification of Self-Organizing Robotic Swarms
Correll, N., & Martinoli, A. (2007) · Springer eBooks · doi:10.1007/4-431-35881-1_4 · Cited by 29 · see citing works
Self-citationModeling and Optimization of a Swarm-Intelligent Inspection System
Correll, N., & Martinoli, A. (2008) · Springer eBooks · doi:10.1007/978-4-431-35873-2_36 · Cited by 28 · see citing works
Self-citationNumber of times a site is visited in two-dimensional random walks
Ferraro, M., & Zaninetti, L. (2001) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.64.056107 · Cited by 12 · see citing works
Flagged first, then by citations
1 of the 34 references couldn’t be matched to a known paper.
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Swarm robotics: a review from the swarm engineering perspective
Brambilla, M., Ferrante, E., Birattari, M., & Dorigo, M. (2013) · Swarm Intelligence · doi:10.1007/s11721-012-0075-2 · Cited by 1,791 · see citing works
Swarm Robotics: Past, Present, and Future [Point of View]
Dorigo, M., Theraulaz, G., & Trianni, V. (2021) · Proceedings of the IEEE · doi:10.1109/jproc.2021.3072740 · Cited by 401 · see citing works
Anonymous Hedonic Game for Task Allocation in a Large-Scale Multiple Agent System
Jang, I., Shin, H.-S., & Tsourdos, A. (2018) · IEEE Transactions on Robotics · doi:10.1109/tro.2018.2858292 · Cited by 129 · see citing works
Beal, J., Dulman, S., Usbeck, K., Mirko Viroli, D., & Correll, N. (2012) · IGI Global eBooks · doi:10.4018/978-1-4666-2092-6.ch016 · Cited by 121 · see citing works
Self-citationMean-field models in swarm robotics: a survey
Elamvazhuthi, K., & Berman, S. (2019) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/ab49a4 · Cited by 110 · see citing works
Collective dynamics in entangled worm and robot blobs
Ozkan-Aydin, Y., Goldman, D. I., & Bhamla, M. S. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2010542118 · Cited by 89 · see citing works
The Impact of Diversity on Optimal Control Policies for Heterogeneous Robot Swarms
Prorok, A., Hsieh, M. A., & Kumar, V. (2017) · IEEE Transactions on Robotics · doi:10.1109/tro.2016.2631593 · Cited by 83 · see citing works
Self-citationBeyond Robustness: A Taxonomy of Approaches towards Resilient Multi-Robot SystemsPreprint
Prorok, A., Malencia, M., Carlone, L., Sukhatme, G. S., Sadler, B. M., & Kumar, V. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2109.12343 · Cited by 63 · see citing works
Self-citationHamann, H. (2013) · Swarm Intelligence · doi:10.1007/s11721-013-0080-0 · Cited by 56 · see citing works
Provable self-organizing pattern formation by a swarm of robots with limited knowledge
Coppola, M., Guo, J., Gill, E. K. A., & de Croon, G. (2019) · Swarm Intelligence · doi:10.1007/s11721-019-00163-0 · Cited by 46 · see citing works
Optimal control of stochastic coverage strategies for robotic swarms
Elamvazhuthi, K., & Berman, S. (2015) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra.2015.7139435 · Cited by 44 · see citing works
Hamann, H., Khaluf, Y., Botev, J., Soorati, M. D., Ferrante, E., Kosak, O., Montanier, J.-M., Mostaghim, S., Redpath, R., Timmis, J., et al. (2016) · Frontiers in Robotics and AI · doi:10.3389/frobt.2016.00014 · Cited by 41 · see citing works
Steering a Swarm of Particles Using Global Inputs and Swarm Statistics
Shahrokhi, S., Lin, L. S., Ertel, C., Wan, M., & Becker, A. T. (2017) · IEEE Transactions on Robotics · doi:10.1109/tro.2017.2769094 · Cited by 41 · see citing works
Towards a PDE-based large-scale decentralized solution for path planning of UAVs in shared airspace
Radmanesh, R., Kumar, M., French, D. A., & Casbeer, D. W. (2020) · Aerospace Science and Technology · doi:10.1016/j.ast.2020.105965 · Cited by 38 · see citing works
PDE-based optimization for stochastic mapping and coverage strategies using robotic ensembles
Elamvazhuthi, K., Kuiper, H. J., & Berman, S. (2018) · Automatica · doi:10.1016/j.automatica.2018.06.007 · Cited by 37 · see citing works
Effects of Spatiality on Value-Sensitive Decisions Made by Robot Swarms
Reina, A., Bose, T., Trianni, V., & Marshall, J. A. R. (2018) · Springer proceedings in advanced robotics · doi:10.1007/978-3-319-73008-0_32 · Cited by 32 · see citing works
Dynamic UAV Swarm Deployment for Non-Uniform Coverage
Albani, D., Manoni, T., Nardi, D., & Trianni, V. (2018) · Adaptive Agents and Multi-Agents Systems · doi:10.65109/zlsf2164 · Cited by 32 · see citing works
Formalizing the impact of diversity on performance in a heterogeneous swarm of robots
Prorok, A., Hsieh, M. A., & Kumar, V. R. (2016) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra.2016.7487748 · Cited by 30 · see citing works
Self-citationDecentralized stochastic control of robotic swarm density: Theory, simulation, and experiment
Li, H., Feng, C., Ehrhard, H., Shen, Y., Cobos, B., Zhang, F., Elamvazhuthi, K., Berman, S., Haberland, M., & Bertozzi, A. L. (2017) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros.2017.8206299 · Cited by 30 · see citing works
Derivation of a Micro-Macro Link for Collective Decision-Making Systems
Hamann, H., Valentini, G., Khaluf, Y., & Dorigo, M. (2014) · Lecture notes in computer science · doi:10.1007/978-3-319-10762-2_18 · Cited by 26 · see citing works
Sartoretti, G., Hongler, M.-O., de Oliveira, M. E., & Francesco Mondada, C. (2014) · Swarm Intelligence · doi:10.1007/s11721-014-0101-7 · Cited by 26 · see citing works
Towards Swarm Calculus: Universal Properties of Swarm Performance and Collective Decisions
Hamann, H. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-32650-9_15 · Cited by 25 · see citing works
Multiscale Modelling and Analysis of Collective Decision Making in Swarm Robotics
Vigelius, M., Meyer, B. E., & Pascoe, G. (2014) · PLoS ONE · doi:10.1371/journal.pone.0111542 · Cited by 25 · see citing works
Berman, S., Nagpal, R., & Halász, Á. (2011) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros.2011.6094771 · Cited by 21 · see citing works
Dantu, K., Berman, S., Kate, B., & Nagpal, R. (2012) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros.2012.6386233 · Cited by 20 · see citing works
A Data-Driven Soft Sensor for Swarm Motion Speed Prediction Using Ensemble Learning Methods
Khaldi, B., Harrou, F., Benslimane, S. M., & Sun, Y. (2021) · IEEE Sensors Journal · doi:10.1109/jsen.2021.3087342 · Cited by 20 · see citing works
Probabilistic Modeling of Swarming Systems
Correll, N., & Hamann, H. (2015) · Springer eBooks · doi:10.1007/978-3-662-43505-2_74 · Cited by 19 · see citing works
Self-citationPerformance Bounds on Spatial Coverage Tasks by Stochastic Robotic Swarms
Zhang, F., Bertozzi, A. L., Elamvazhuthi, K., & Berman, S. (2017) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2017.2747769 · Cited by 19 · see citing works
Garattoni, L., & Birattari, M. (2016) · Wiley Encyclopedia of Electrical and Electronics Engineering · doi:10.1002/047134608x.w8312 · Cited by 19 · see citing works
The PageRank algorithm as a method to optimize swarm behavior through local analysis
Coppola, M., Guo, J., Gill, E. K. A., & de Croon, G. (2019) · Swarm Intelligence · doi:10.1007/s11721-019-00172-z · Cited by 17 · see citing works
Swarm Modeling With Dynamic Mode Decomposition
Hansen, E., Brunton, S. L., & Song, Z. (2022) · IEEE Access · doi:10.1109/access.2022.3179414 · Cited by 16 · see citing works
Modeling Self-Assembly Across Scales: The Unifying Perspective of Smart Minimal Particles
Mastrangeli, M., Mermoud, G., & Martinoli, A. (2011) · Micromachines · doi:10.3390/mi2020082 · Cited by 16 · see citing works
Self-citationFratzl, P., Friedman, M., Krauthausen, K., & Schäffner, W. (2021) · De Gruyter eBooks · doi:10.1515/9783110562064 · Cited by 15 · see citing works
Opinion Dynamics With Mobile Agents: Contrarian Effects by Spatial Correlations
Hamann, H. (2018) · Frontiers in Robotics and AI · doi:10.3389/frobt.2018.00063 · Cited by 14 · see citing works
An Enzyme-Inspired Approach to Stochastic Allocation of Robotic Swarms Around Boundaries
Pavlic, T. P., Wilson, S., Kumar, G. P., & Berman, S. (2016) · Springer tracts in advanced robotics · doi:10.1007/978-3-319-28872-7_36 · Cited by 12 · see citing works
Efficient quantitative assessment of robot swarms: coverage and targeting Lévy strategies
Duncan, S., Estrada-Rodriguez, G., Stocek, J., Dragone, M., Vargas, P. A., & Gimperlein, H. (2022) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/ac57f0 · Cited by 12 · see citing works
Nonlinear Generalizations of Diffusion-Based Coverage by Robotic Swarms
Elamvazhuthi, K., & Berman, S. (2018) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.2018.8618889 · Cited by 11 · see citing works
Crystallization-Inspired Design and Modeling of Self-Assembly Lattice-Formation Swarm Robotics
Pan, Z., Wen, G., Yin, H., Yin, S., & Tan, Z. (2024) · Sensors · doi:10.3390/s24103081 · Cited by 7 · see citing works
A Deep Recurrent Neural Network Framework for Swarm Motion Speed Prediction
Khaldi, B., Harrou, F., Dairi, A., & Sun, Y. (2023) · Journal of Electrical Engineering and Technology · doi:10.1007/s42835-023-01446-7 · Cited by 6 · see citing works
Risk-Aware Motion Planning for Very-Large-Scale Robotics Systems Using Conditional Value-at-Risk
Yang, X., Gao, H., Zhu, P., & Liu, C. (2023) · Lecture notes in computer science · doi:10.1007/978-981-99-6498-7_44 · Cited by 5 · see citing works
Intrusion detection for stochastic task allocation in robot swarms
Kennel-Maushart, F., Prorok, A., Hsieh, M. A., & Kumar, V. (2017) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros.2017.8205998 · Cited by 5 · see citing works
Self-citationSalamat, B., & Elsbacher, G. (2022) · Aerospace · doi:10.3390/aerospace9110702 · Cited by 4 · see citing works
Controllability to equilibria of the 1-D fokker-planck equation with zero-flux boundary condition
Elamvazhuthi, K., Kuiper, H. J., & Berman, S. (2017) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.2017.8264014 · Cited by 4 · see citing works
Radmanesh, M., Kumar, M., & French, D. A. (2019) · Journal of Dynamic Systems Measurement and Control · doi:10.1115/1.4045797 · Cited by 3 · see citing works
Sorting boxes with a robotic swarm: An analysis by means of experiment, simulation and model
Kettler, A., & Wörn, H. (2011) · IEEE International Conference on Robotics and Biomimetics (ROBIO) · doi:10.1109/robio.2011.6181396 · Cited by 2 · see citing works
The Role of Largest Connected Components in Collective Motion
Hamann, H. (2018) · Lecture notes in computer science · doi:10.1007/978-3-030-00533-7_23 · Cited by 2 · see citing works
Baumann, C., & Martinoli, A. (2022) · Frontiers in Robotics and AI · doi:10.3389/frobt.2022.961053 · Cited by 1 · see citing works
Self-citationGated Recurrent Unit Based Short-Term Network for Robot Swarm Motion Forecasting
Khaldi, B., Harrou, F., Dairi, A., & Sun, Y. (2022) · IEEE International Forum on Research and Technology for Society and Industry (RTSI) · doi:10.1109/rtsi55261.2022.9905085 · Cited by 1 · see citing works
Modeling Swarm Systems and Formal Design Methods
Hamann, H. (2018) · Springer eBooks · doi:10.1007/978-3-032-10584-4_7 · Cited by 1 · see citing works
Spectral Gap Optimization of Divergence Type Diffusion Operators
Biswal, S., Elamvazhuthi, K., Mittelmann, H. D., & Berman, S. (2020) · European Control Conference (ECC) · doi:10.23919/ecc51009.2020.9143621 · Cited by 1 · see citing works
Goswami, D., & Hamann, H. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1410.5738 · Cited by 1 · see citing works
Interview with Nikolaus Correll: Robotic Materials
Correll, N., Friedman, M., & Krauthausen, K. (2021) · De Gruyter eBooks · doi:10.1515/9783110562064-010 · Cited by 1 · see citing works
Self-citationCollective protection and transport in entangled biological and robotic active matterPreprint
Ozkan-Aydin, Y., Goldman, D. I., & Bhamla, M. S. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.05.25.114736
Salamat, B., Starck, C. J., & Hamann, H. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2108.10153
Ding, W., Yao, L., Wang, Z., Chen, G., & Qin, L. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5888406
Meifan, R., & Syifa, F. T. (2026) · JURNAL ILMIAH TEKNIK INDUSTRI DAN INOVASI · doi:10.59024/jisi.v4i3.2451
- Authors
- Prorok, A., Correll, N., & Martinoli, A.
- Affiliations
- École Polytechnique Fédérale de Lausanne (CH)
- University of Colorado Boulder (US)
- Venue
- The International Journal of Robotics Research
- Publisher
- SAGE Publications
- Published
- 2011-02-08
- Volume
- 30
- Issue
- 5
- Pages
- 574-589
- ISSN
- 0278-3649 (ISSN-L)
- 1741-3176
- OpenAlex
- W2023510972
- Cited by
- 56
- References
- 34
- Citations by year
- 2025: 1 · 2024: 1 · 2023: 2 · 2022: 5 · 2021: 7 · 2020: 3 · 2019: 4 · 2018: 8 · 2017: 7 · 2016: 4 · 2015: 2 · 2014: 4 · 2013: 2 · 2012: 3
- FWCI
- 6.80
- Type
- journal article
- Language
- en
- Open access
- green
- infoscience.epfl.ch
- Licence
- Locations
- The International Journal of Robotics Research (publishedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion)
- Funders
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
- Topics
- Physical Sciences › Engineering › Mechanical Engineering › Modular Robots and Swarm Intelligence
- Physical Sciences › Computer Science › Computer Networks and Communications › Distributed Control Multi-Agent Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Robotics and Automated Systems
- Keywords
- distributed robotics, stochastic modeling, recurrence relations, small robots, inspection tasks
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