# Distributed matroid-constrained submodular maximization for multi-robot exploration: theory and practice

- 419 Downloads
- 1 Citations

**Part of the following topical collections:**

## Abstract

This work addresses the problem of efficient online exploration and mapping using multi-robot teams via a new distributed algorithm for multi-robot exploration, distributed sequential greedy assignment (DSGA), which is based on sequential greedy assignment (SGA). While SGA permits bounds on suboptimality, robots must execute planning steps sequentially. Rather than plan for each robot sequentially as in SGA, DSGA assigns plans to subsets of robots using a fixed number of sequential planning rounds. DSGA retains the same suboptimality bounds as SGA with the addition of a term that describes the additional suboptimality incurred when assigning multiple plans at once. We use this result to extend a single-robot planner based on Monte-Carlo tree search to the multi-robot domain and evaluate the resulting planner in simulated exploration of a confined and cluttered environment. The experimental results show that for teams of 4–32 robots suboptimality due to redundant sensor information introduced in the distributed planning rounds remains small in practice given only two or three distributed planning rounds while providing a 2–8 times speedup over SGA. We also incorporate aerial robots with inter-robot collision constraints and non-trivial dynamics and address subsequent impacts on safety and optimality. Real-time simulation and experimental results for teams of quadrotors demonstrate online planning for multi-robot exploration and indicate that collision constraints have limited impacts on exploration performance.

## Keywords

Multi-robot Exploration Informative planning Submodular Matroid## Notes

## References

- Atanasov, N.A., Le Ny, J., Daniilidis, K., & Pappas, G.J. (2015). Decentralized active information acquisition: Theory and application to multi-robot SLAM. In
*Proceedings of the IEEE international conference on robotics and automation, Seattle, WA*.Google Scholar - Barbosa, RdP., Ene, A., Nguyen, H.L., & Ward, J. (2016). A new framework for distributed submodular maximization. In
*Proceedings of the IEEE annual symposium on foundations of computer science, New Brunswick, NJ*.Google Scholar - Best, G., Cliff, O. M., Patten, T., Mettu, R. R., & Fitch, R. (2016). Decentralised Monte Carlo tree search for active perception. In
*Algorithmic foundation robotics*. San Francisco, CAGoogle Scholar - Browne, C., Powley, E., Whitehouse, D., Lucas, S., Cowling, P. I., Rohlfshagen, P., et al. (2012). A survey of Monte Carlo tree search methods.
*IEEE Transactions on Computational Intelligence and AI in Games*,*4*(1), 1–43.CrossRefGoogle Scholar - Calinescu, G., Chekuri, C., Pal, M., & Vondrák, J. (2011). Maximizing a monotone submodular function subject to a matroid constraint.
*SIAM Journal on Computing*,*40*(6), 1740–1766.MathSciNetCrossRefzbMATHGoogle Scholar - Charrow, B. (2015).
*Information-theoretic active perception for multi-robot teams*. Ph.D. thesis, University of Pennsylvania.Google Scholar - Charrow, B., Kumar, V., & Michael, N. (2014). Approximate representations for multi-robot control policies that maximize mutual information.
*Autonomous Robots*,*37*(4), 383–400.CrossRefGoogle Scholar - Charrow, B., Kahn, G., Patil, S., Liu, S., Goldberg, K., Abbeel, P., Michael, N., & Kumar, V. (2015a). Information-theoretic planning with trajectory optimization for dense 3D mapping. In
*Proceedings of robotics: science and systems, Rome, Italy*.Google Scholar - Charrow, B., Liu, S., Kumar, V., & Michael, N. (2015b). Information-theoretic mapping using Cauchy-Schwarz quadratic mutual information. In
*Proceedings 1990 IEEE international conference on robotics and automation, Seattle, WA*.Google Scholar - Chaslot, G. (2010).
*Monte-Carlo tree search*. Ph.D. thesis, Universiteit Maastricht.Google Scholar - Chekuri, C., & Martin, P. (2005). A recursive greedy algorithm for walks in directed graphs. In
*Proceedings of the IEEE annual symposium on foundations of computer science*, pp 245–253.Google Scholar - Choi, H. L., Brunet, L., & How, J. P. (2009). Consensus-based decentralized auctions for robust task allocation.
*IEEE Transactions on Robotics*,*25*(4), 912–926.CrossRefGoogle Scholar - Corah, M., & Michael, N. (2017). Efficient online multi-robot exploration via distributed sequential greedy assignment. In
*Proceedings of robotics: science and system, Cambridge, MA*.Google Scholar - Corah, M., & Michael, N. (2018). Distributed submodular maximization on partition matroids for planning on large sensor networks. In
*Proceedings of the IEEE conference on decision and control. Miami, FL*(**submitted for publication**).Google Scholar - Cover, T. M., & Thomas, J. A. (2012).
*Elements of information theory*. New York, NY: Wiley.zbMATHGoogle Scholar - Elfes, A. (1989). Using occupancy grids for mobile robot perception and navigation.
*IEEE Computer Society*,*22*(6), 46–57.CrossRefGoogle Scholar - Filmus, Y., & Ward, J. (2012). A tight combinatorial algorithm for submodular maximization subject to a matroid constraint. In
*Proceedings of the IEEE annual symposium on foundations of computer science, New Brunswick, NJ*.Google Scholar - Gharan, S.O., & Vondrák, J. (2011). Submodular maximization by simulated annealing. In
*Proceedings of the symposium on discrete algorithms, Philadelphia, PA*.Google Scholar - Gharesifard, B., & Smith, S.L. (2017). Distributed submodular maximization with limited information.
*IEEE Transactions on Control of Network Systems*. https://doi.org/10.1109/TCNS.2017.2740625. - Goundan, P. R., & Schulz, A. S. (2007). Revisiting the greedy approach to submodular set function maximization.
*Optim Online*,*1984*, 1–25.Google Scholar - Grimsman, D., Ali, M.S., Hespanha, P., & Marden, J.R. (2017). Impact of information in greedy submodular maximization. In
*Proceedings of the IEEE conference on decision and control, Melbourne, Australia*.Google Scholar - Jadidi, M.G., Miro, J.V., & Dissanayake, G. (2015). Mutual information-based exploration on continuous occupancy maps. In
*Proceedings of the IEEE/RSJ international conference on intelligent robots and systems, Hamburg, Germany*.Google Scholar - Jorgensen, S., Chen, R.H., Milam, M.B., & Pavone, M. (2017). The matroid team surviving orienteers problem: Constrained routing of heterogeneous teams with risky traversal. In
*Proceedings of the IEEE/RSJ international conference on intelligent robots and systems, Vancouver, Canada*.Google Scholar - Julian, B. J., Karaman, S., & Rus, D. (2014). On mutual information-based control of range sensing robots for mapping applications.
*The International Journal of Robotics Research*,*33*(10), 1357–1392.CrossRefGoogle Scholar - Krause, A., & Guestrin, C.E. (2005). Near-optimal nonmyopic value of information in graphical models. In
*Proceedings of the conference on uncertainty in artificial intelligence, Edinburgh, Scotland*.Google Scholar - Krause, A., Singh, A., & Guestrin, C. (2008). Near-optimal sensor placements in Gaussian processes: Theory, efficient algorithms and empirical studies.
*Journal of Machine Learning Research*,*9*, 235–284.zbMATHGoogle Scholar - Ladner, R. E., & Fischer, M. J. (1980). Parallel prefix computation.
*Journal of the ACM (JACM)*,*27*(4), 831–838.MathSciNetCrossRefzbMATHGoogle Scholar - Lauri, M., & Ritala, R. (2016). Planning for robotic exploration based on forward simulation.
*Robotics and Autonomous Systems*,*83*, 15–31.CrossRefGoogle Scholar - Mahony, R., Kumar, V., & Corke, P. (2012). Multirotor aerial vehicles: Modeling, estimation, and control of quadrotor.
*IEEE Robotics and Automation Magazine*,*19*(3), 20–32.CrossRefGoogle Scholar - Mirzasoleiman, B., Karbasi, A., Sarkar, R., & Krause, A. (2013). Distributed submodular maximization: Identifying representative elements in massive data. In C. J. C. Burges, L. Bottou, M. Welling, Z. Ghahramani & K. Q. Weinberger (Eds.),
*Procdeedings of the advances in neural information processing systems*(Vol. 26, pp. 2049–2057). Stateline, Nevada: Curran Associates, Inc. http://papers.nips.cc/HrBpaper/5039-distributed-submodular-maximization-identifying-reHrBpresentative-elements-in-massivedata.pdf. - Nelson, E., & Michael, N. (2015). Information-theoretic occupancy grid compression for high-speed information-based exploration. In
*Proceedings of the IEEE/RSJ international conference on intelligent robots and systems, Hamburg, Germany*.Google Scholar - Nemhauser, G. L., & Wolsey, L. A. (1978). Best algorithms for approximating the maximum of a submodular set function.
*Mathematics of Operations Research*,*3*(3), 177–188.MathSciNetCrossRefzbMATHGoogle Scholar - Nemhauser, G. L., Wolsey, L. A., & Fisher, M. L. (1978a). An analysis of approximations for maximizing submodular set functions-I.
*Mathematics Program*,*14*(1), 265–294.MathSciNetCrossRefzbMATHGoogle Scholar - Nemhauser, G. L., Wolsey, L. A., & Fisher, M. L. (1978b). An analysis of approximations for maximizing submodular set functions-II.
*Polyhedral Combinatorics*,*8*, 73–87.MathSciNetCrossRefzbMATHGoogle Scholar - Patten, T. (2017).
*Active object classification from 3D range data with mobile robots*. Ph.D. thesis, The University of Sydney.Google Scholar - Quigley, M., Gerkey, B., Conley, K., Faust, J., Foote, T., Leibs, J., et al. (2009). ROS: An open-source robot operating system. In
*ICRA workshop on open source software, Kobe, Japan*Google Scholar - Rawlings, J. B., & Muske, K. R. (1993). The stability of constrained receding horizon control.
*IEEE Transactions on Automatic Control*,*38*(10), 1512–1516.MathSciNetCrossRefzbMATHGoogle Scholar - Regev, T., & Indelman, V. (2016). Multi-robot decentralized belief space planning in unknown environments via efficient re-evaluation of impacted paths. In
*Proceedings of the IEEE/RSJ international conference on intelligent robots and systems, Daejeon, Korea*.Google Scholar - Singh, A., Krause, A., Guestrin, C., & Kaiser, W. J. (2009). Efficient informative sensing using multiple robots.
*Journal of Artificial Intelligence Research*,*34*, 707–755.MathSciNetCrossRefzbMATHGoogle Scholar - Tabib, W., Corah, M., Michael, N., & Whittaker, R. (2016). Computationally efficient information-theoretic exploration of pits and caves. In
*Proceedings of the IEEE/RSJ international conference on intelligent robots and systems, Daejeon, Korea*.Google Scholar - Williams, J.L. (2007).
*Information theoretic sensor management*. Ph.D. thesis, Massachusetts Institute of Technology.Google Scholar - Williams, R.K., Gasparri, A., & Ulivi, G. (2017). Decentralized matroid optimization for topology constraints in multi-robot allocation problems. In
*Proceedings of the IEEE international conference on robotics and automation, Singapore*.Google Scholar - Yamauchi, B. (1997). A frontier-based approach for autonomous exploration. In
*Proceedings of the international symposium on computer intelligence in robotics and automation, Monterey, CA*.Google Scholar - Zhou, T., Ouyang, H., Chang, Y., Bilmes, J., & Guestrin, C. (2017). Scaling submodular maximization via pruned submodularity graphs.
*Proceedings of Machine Learning Research*,*54*, 316–324.Google Scholar