Skip to main content
SpringerLink
Log in

Robust rendezvous for multi-robot system with random node failures: an optimization approach

  • Published:
Autonomous Robots Aims and scope Submit manuscript

Abstract

In this paper, we consider the problem of designing distributed control algorithms to solve the rendezvous problem for multi-robot systems with limited sensing, for situations in which random nodes may fail during execution. We first formulate a distributed solution based upon averaging algorithms that have been reported in the consensus literature. In this case, at each stage of execution a one-step sequential optimal control (i.e., näive greedy algorithm) is used. We propose a distributed stochastic optimal control algorithm that minimizes a mean–variance cost function for each stage, given that the probability distribution for possible node failures is known a priori, as well as a minimax version of the problem when the prior probability distribution is not known. We demonstrate via extensive numerical simulations that our proposed algorithm provides statistically better rendezvous task performance than contemporary algorithms in cases for which failures occur.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Notes

  1. For example, \(\mathbf {u}_i^0\) can be set to a \(d \times 1\) vector with 0s.

  2. The form of the construct is similar to that found in Shapiro and Ahmed (2004).

References

  • Ando, H., Oasa, Y., Suzuki, I., & Yamashita, M. (1999). Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Transactions on Robotics and Automation, 15(5), 818–828.

    Article  Google Scholar 

  • Ando, H., Suzuki, I., & Yamashita, M. (1995). Formation and agreement problems for synchronous mobile robots with limited visibility. In Proceedings of the 1995 IEEE international symposium on intelligent control (pp. 453–460), 1995, IEEE.

  • Ben-Tal, A., & Nemirovski, A. (2002). Robust optimization-methodology and applications. Mathematical Programming, 92(3), 453–480.

    Article  MathSciNet  Google Scholar 

  • Beyer, H. G., & Sendhoff, B. (2007). Robust optimization—A comprehensive survey. Computer Methods in Applied Mechanics and Engineering, 196(33), 3190–3218.

    Article  MathSciNet  Google Scholar 

  • Bullo, F., Cortés, J., & Martinez, S. (2009). Distributed control of robotic networks: A mathematical approach to motion coordination algorithms. Princeton: Princeton University Press.

    Book  Google Scholar 

  • Chen, W. (1998). Quality utility—A compromise programming approach to robust design. Ph.D. thesis, University of Illinois.

  • Cortés, J., Martínez, S., & Bullo, F. (2006). Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions. IEEE Transactions on Automatic Control, 51(8), 1289–1298.

    Article  MathSciNet  Google Scholar 

  • Doudou, A., & Schiper, A. (1997). Muteness detectors for consensus with byzantine processes. Tech. rep. In Proceedings of the 17th ACM symposium on principle of distributed computing (Puerto).

  • Feng, Z., Sun, C., & Hu, G. (2016). Robust connectivity preserving rendezvous of multi-robot systems under unknown dynamics and disturbances. In IEEE transactions on control of network systems.

  • Flocchini, P., Prencipe, G., & Santoro, N. (2012). Distributed computing by oblivious mobile robots. Synthesis Lectures on Distributed Computing Theory, 3(2), 1–185.

    Article  Google Scholar 

  • Franceschelli, M., Giua, A., & Pisano, A. (2014). Finite-time consensus on the median value by discontinuous control. In American Control Conference (ACC) (pp. 946–951), 2014, IEEE.

  • Gusrialdi, A., Qu, Z., & Simaan, MA. (2014). Robust design of cooperative systems against attacks. In American Control Conference (ACC) (pp. 1456–1462), 2014, IEEE.

  • Homem-de Mello, T., & Bayraksan, G. (2014). Monte carlo sampling-based methods for stochastic optimization. Surveys in Operations Research and Management Science, 19(1), 56–85.

    Article  MathSciNet  Google Scholar 

  • Jadbabaie, A., Lin, J., & Morse, A. (2003). Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control, 48(6), 988–1001.

    Article  MathSciNet  Google Scholar 

  • Ji, M., & Egerstedt, M. (2007). Distributed coordination control of multi-agent systems while preserving connectedness. IEEE Transactions on Robotics (T-RO), 23(4), 693–703.

    Article  Google Scholar 

  • LeBlanc, H. J., Zhang, H., Koutsoukos, X., & Sundaram, S. (2013). Resilient asymptotic consensus in robust networks. IEEE Journal on Selected Areas in Communications, 31(4), 766–781.

    Article  Google Scholar 

  • LeBlanc, H. J., Zhang, H., Sundaram, S., & Koutsoukos, X. (2012). Consensus of multi-agent networks in the presence of adversaries using only local information. In Proceedings of the 1st international conference on High Confidence Networked Systems, ACM (pp. 1–10).

  • Lin, J., Morse, A., & Anderson, B. (2003). The multi-agent rendezvous problem. In 42nd IEEE conference on decision and control, 2003. Proceedings, IEEE (Vol. 2, pp. 1508–1513).

  • Lin, J., Morse, A. S., & Anderson, B. D. (2007). The multi-agent rendezvous problem. Part 1: The synchronous case. SIAM Journal on Control and Optimization, 46(6), 2096–2119.

    Article  MathSciNet  Google Scholar 

  • Lorenz, J. (2007). Repeated averaging and bounded confidence-modeling, analysis and simulation of continuous opinion dynamics. Ph.D. thesis, University of Bremen, Germany. Available at http://nbn-resolving.de/urn:nbn:de:gbv:46-diss000106688.

  • Markowitz, H. (1952). Portfolio selection*. The Journal of Finance, 7(1), 77–91.

    Google Scholar 

  • Mathew, N., Smith, S. L., & Waslander, S. L. (2013). A graph-based approach to multi-robot rendezvous for recharging in persistent tasks. In 2013 IEEE International Conference on Robotics and Automation (ICRA), IEEE (pp. 3497–3502).

  • Mendes, H., & Herlihy, M. (2013). Multidimensional approximate agreement in Byzantine asynchronous systems. In Proceedings of the forty-fifth annual ACM symposium on theory of computing, ACM (pp. 391–400).

  • Meskin, N., & Khorasani, K. (2009). Actuator fault detection and isolation for a network of unmanned vehicles. IEEE Transactions on Automatic Control, 54(4), 835–840.

    Article  MathSciNet  Google Scholar 

  • Moreau, L. (2005). Stability of multiagent systems with time-dependent communication links. IEEE Transactions on Automatic Control, 50(2), 169–182.

    Article  MathSciNet  Google Scholar 

  • Mulvey, J. M., Vanderbei, R. J., & Zenios, S. A. (1995). Robust optimization of large-scale systems. Operations Research, 43(2), 264–281.

    Article  MathSciNet  Google Scholar 

  • Olfati-Saber, R., & Murray, R. M. (2004). Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 49(9), 1520–1533.

    Article  MathSciNet  Google Scholar 

  • Park, H., & Hutchinson, S. (2014). A distributed optimal strategy for rendezvous of multi-robots with random node failures. In 2014 IEEE/RSJ international conference on intelligent robots and systems (IROS), IEEE (pp. 1155–1160).

  • Park, H., & Hutchinson, S. (2015). A distributed robust convergence algorithm for multi-robot systems in the presence of faulty robots. In 2015 IEEE/RSJ international conference on intelligent robots and systems (IROS), IEEE (pp. 2980–2985).

  • Park, H., & Hutchinson, S. (2016). An efficient algorithm for fault-tolerant rendezvous of multi-robot systems with controllable sensing range. In 2016 IEEE international conference on robotics and automation (ICRA), IEEE (pp. 358–365).

  • Park, H., & Hutchinson, S. (2017). Fault-tolerant rendezvous of multirobot systems. In IEEE transactions on robotics.

    Article  Google Scholar 

  • Parlangeli, G. (2013). A fault compensation strategy for consensus networks subject to transient and intermittent faults. In: 2013 21st mediterranean conference on control and automation (MED), IEEE (pp. 46–53).

  • Pasqualetti, F., Bicchi, A., & Bullo, F. (2012). Consensus computation in unreliable networks: A system theoretic approach. IEEE Transactions on Automatic Control, 57(1), 90–104.

    Article  MathSciNet  Google Scholar 

  • Rebennack, S. (2016). Combining sampling-based and scenario-based nested benders decomposition methods: Application to stochastic dual dynamic programming. Mathematical Programming, 156(1–2), 343–389.

    Article  MathSciNet  Google Scholar 

  • Ren, W., Beard, R. W., & Atkins, E. M. (2007). Information consensus in multivehicle cooperative control. IEEE Control Systems, 27(2), 71–82.

    Article  Google Scholar 

  • Roumeliotis, S. I., Sukhatme, G. S., & Bekey, G. A. (1998). Fault detection and identification in a mobile robot using multiple-model estimation. In 1998 IEEE international conference on robotics and automation, 1998. Proceedings, IEEE (Vol. 3, pp. 2223–2228).

  • Roy, N., & Dudek, G. (2001). Collaborative robot exploration and rendezvous: Algorithms, performance bounds and observations. Autonomous Robots, 11(2), 117–136.

    Article  Google Scholar 

  • Shapiro, A., & Ahmed, S. (2004). On a class of minimax stochastic programs. SIAM Journal on Optimization, 14(4), 1237–1249.

    Article  MathSciNet  Google Scholar 

  • Shapiro, A., & Kleywegt, A. (2002). Minimax analysis of stochastic problems. Optimization Methods and Software, 17(3), 523–542.

    Article  MathSciNet  Google Scholar 

  • Shiliang, S., Ting, W., Chen, Y., Xiaofan, L., & Hai, Z. (2014). Distributed fault detection and isolation for flocking in a multi-robot system with imperfect communication. International Journal of Advanced Robotic Systems, 11(6), 86.

    Article  Google Scholar 

  • Sundaram, S., Revzen, S., & Pappas, G. (2012). A control-theoretic approach to disseminating values and overcoming malicious links in wireless networks. Automatica, 48(11), 2894–2901.

    Article  MathSciNet  Google Scholar 

  • Vaidya, N. H. (2014). Iterative Byzantine vector consensus in incomplete graphs. In Distributed computing and networking (pp. 14–28). Berlin: Springer.

    Chapter  Google Scholar 

  • Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., & Shochet, O. (1995). Novel type of phase transition in a system of self-driven particles. Physical Review Letters, 75(6), 1226.

    Article  MathSciNet  Google Scholar 

  • Zhang, H., Fata, E., & Sundaram, S. (2015). A notion of robustness in complex networks. IEEE Transactions on Control of Network Systems, 2(3), 310–320.

    Article  MathSciNet  Google Scholar 

  • Zhang, H., & Sundaram, S. (2012). A simple median-based resilient consensus algorithm. In: 2012 50th annual Allerton conference on communication, control, and computing (Allerton), IEEE (pp. 1734–1741).

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Michigan, Ann Arbor, 48109, MI, USA

    Hyongju Park

  2. Department of Electrical and Computer Engineering, University of Illinois, Urbana, 61801, IL, USA

    Seth Hutchinson

Authors
  1. Hyongju Park
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Seth Hutchinson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hyongju Park.

Additional information

This is one of several papers published in Autonomous Robots comprising the “Special Issue on Distributed Robotics: From Fundamentals to Applications”.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Park, H., Hutchinson, S. Robust rendezvous for multi-robot system with random node failures: an optimization approach. Auton Robot 42, 1807–1818 (2018). https://doi.org/10.1007/s10514-018-9715-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10514-018-9715-8

Keywords

Search

Navigation