Abstract
We are interested in securing the operation of robot swarms composed of heterogeneous agents that collaborate by exploiting aggregation mechanisms. Since any given robot type plays a role that may be critical in guaranteeing continuous and failure-free operation of the system, it is beneficial to conceal individual robot types and, thus, their roles. In our work, we assume that an adversary gains access to a description of the dynamic state of the swarm in its non-transient, nominal regime. We propose a method that quantifies how easy it is for the adversary to identify the type of any of the robots, based on this observation. We draw from the theory of differential privacy to propose a closed-form expression of the leakage of the system at steady-state. Our results show how this model enables an analysis of the leakage as system parameters vary; they also indicate design rules for increasing privacy in aggregation mechanisms.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Side information can be understood as a prior probability distribution over the database [14].
- 2.
In our context of a robotic swarm, an example of side information could be the number of manufacturing parts ordered to build the swarm. If different robot species are made of different parts, such information can be used to construct an initial guess about the number of robots per species. Thus, one would be able to derive the probability of a robot belonging to a given species.
- 3.
We assume a snapshot adversary that gains system-level information at a specific time. This system-level information is a design variable, called the observable system-level state.
- 4.
The symbol \(\mathbf {x}\) denotes the discrete state, whereas \(\mathsf {x} \) denotes the average population.
References
Agrawal, R., Srikant, R.: Privacy-preserving data mining. ACM Sigmod Record 29(2), 439–450 (2000)
Anderson, D.F., Craciun, G., Kurtz, T.G.: Product-form stationary distributions for deficiency zero chemical reaction networks. Bull. Math. Biol. 1–23 (2010)
Cheng, J., Cheng, W., Nagpal, R.: Robust and self-repairing formation control for swarms of mobile agents. AAAI (2005)
Correll, N., Martinoli, A.: Modeling self-organized aggregation in a swarm of miniature robots. In: IEEE International Conference Robotics and Automation (ICRA) (2007)
Dorigo, M., Floreano, D., Gambardella, L.M., Mondada, F., Nolfi, S., et al.: Swarmanoid: a novel concept for the study of heterogeneous robotic swarms. IEEE Robot. Autom. Mag. 20(4), 60–71 (2013)
Dwork, C.: Differential privacy: a survey of results. In: Theory and Applications of Models of Computation, pp. 1–19. Springer, Berlin (2008)
Dwork, C.: Differential privacy. In: Encyclopedia of Cryptography and Security, pp. 338–340 (2011)
Evfimievski, A., Gehrke, J., Srikant, R.: Limiting privacy breaches in privacy preserving data mining. In: the Twenty-second ACM SIGMOD-SIGACT-SIGART Symposium, pp. 211–222. ACM Press, New York (2003)
Feinberg, M.: Some recent results in chemical reaction network theory. In: Patterns and Dynamics in Reactive Media, pp. 43–70. Springer, New York (1991)
Garnier, S., Jost, C., Gautrais, J., Asadpour, M., Caprari, G., Jeanson, R., Grimal, A., Theraulaz, G.: The embodiment of cockroach aggregation behavior in a group of micro-robots. Artif. Life 14(4), 387–408 (2008)
Groß, R., Dorigo, M.: Self-assembly at the macroscopic scale. Proc. IEEE 96(9), 1490–1508 (2008)
Halloy, J., Sempo, G., Caprari, G., Rivault, C., Asadpour, M., Tache, F., Said, I., Durier, V., Canonge, S., Ame, J.M., Detrain, C., Correll, N., Martinoli, A., Mondada, F., Siegwart, R., Deneubourg, J.L.: Social integration of robots into groups of cockroaches to control self-organized choices. Science 318(5853), 1155–1158 (2007)
Hosokawa, K., Shimoyama, I., Miura, H.: Dynamics of self-assembling systems: analogy with chemical kinetics. Artif. Life 1(4), 413–427 (2010)
Kasiviswanathan, S.P., Smith, A.: A note on differential privacy: Defining resistance to arbitrary side information. CoRR abs. (2008)
Klavins, E., Burden, S., Napp, N.: Optimal rules for programmed stochastic self-assembly. In: Robotics: Science and Systems (2006)
Martinoli, A., Ijspeert, A.J., Gambardella, L.M.: A probabilistic model for understanding and comparing collective aggregation mechanisms. In: Advances in Artificial Life, pp. 575–584. Springer, Berlin (1999)
Matthey, L., Berman, S., Kumar, V.: Stochastic strategies for a swarm robotic assembly system. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 1953–1958. IEEE, New York (2009)
Parrish, J.K., Edelstein-Keshet, L.: Complexity, pattern, and evolutionary trade-offs in animal aggregation. Science 284(5411), 99–101 (1999)
Prorok, A., Hsieh, A.M., Kumar, V.: Formalizing the impact of diversity on performance in a heterogeneous swarm of robots. In: IEEE International Conference on Robotics and Automation (ICRA) (2016)
Prorok, A., Kumar, V.: A macroscopic privacy model for heterogeneous robot swarms. In: International Conference on Swarm Intelligence (2016)
Siegel, D., MacLean, D.: Global stability of complex balanced mechanisms. J. Math. Chem. 27, 89–110 (2000)
Acknowledgements
The authors would like to thank the anonymous referees for their constructive feedback. We gratefully acknowledge the support of ONR grants N00014-15-1-2115 and N00014-14-1-0510, ARL grant W911NF-08-2-0004, NSF grant IIS-1426840, and TerraSwarm, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Prorok, A., Kumar, V. (2018). Towards Differentially Private Aggregation of Heterogeneous Robots. In: Groß, R., et al. Distributed Autonomous Robotic Systems. Springer Proceedings in Advanced Robotics, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-73008-0_41
Download citation
DOI: https://doi.org/10.1007/978-3-319-73008-0_41
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73006-6
Online ISBN: 978-3-319-73008-0
eBook Packages: EngineeringEngineering (R0)