Analyzing human-swarm interactions using control Lyapunov functions and optimal control

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September 2015, 10(3): 609-630. doi: 10.3934/nhm.2015.10.609

Analyzing human-swarm interactions using control Lyapunov functions and optimal control

Jean-Pierre de la Croix ^1, and Magnus Egerstedt ^1,

1.	School of Electrical and Computer Engineering, Georgia Institute of Technology, 777 Atlantic Drive NW, Atlanta, GA 30332-0250, United States, United States

Received November 2014 Revised February 2015 Published July 2015

Abstract
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A number of different interaction modalities have been proposed for human engagement with networked systems. In this paper, we establish formal guarantees for whether or not a given human-swarm interaction (HSI) strategy is appropriate for achieving particular multi-robot tasks, such as guiding a swarm of robots into a particular geometric configuration. In doing so, we define what it means to impose an HSI control structure on a multi-robot system. Control Lyapunov functions are used to establish feasibility for a user to achieve a particular geometric configuration with a multi-robot system under some selected HSI control structure. Several examples of multi-robot systems with unique HSI control structures are provided to illustrated the use of CLFs to establish feasibility. Additionally, we also uses these examples to illustrate how to use optimal control tools to compute three metrics for evaluating an HSI control structure: attention, effort, and scalability.

Keywords: control theory, Networked systems, human-swarm interactions..

Mathematics Subject Classification: Primary: 93C85; Secondary: 37B25, 49N0.

Citation: Jean-Pierre de la Croix, Magnus Egerstedt. Analyzing human-swarm interactions using control Lyapunov functions and optimal control. Networks and Heterogeneous Media, 2015, 10 (3) : 609-630. doi: 10.3934/nhm.2015.10.609

References:

[1]	S. Bashyal and G. K. Venayagamoorthy, Human swarm interaction for radiation source search and localization, in Swarm Intelligence Symposium (SIS), IEEE, 2008, 1-8. doi: 10.1109/SIS.2008.4668287.
[2]	A. Becker, C. Ertel and J. McLurkin, Crowdsourcing swarm manipulation experiments: A massive online user study with large swarms of simple robots, in Robotics and Automation (ICRA), 2014 IEEE International Conference on, 2014, 2825-2830. doi: 10.1109/ICRA.2014.6907264.
[3]	S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004. doi: 10.1017/CBO9780511804441.
[4]	R. W. Brockett, Minimum attention control, in Proceedings of the 36th IEEE Conference on Decision and Control, Vol. 3, IEEE, 1997, 2628-2632. doi: 10.1109/CDC.1997.657776.
[5]	A. E. Bryson, Applied Optimal Control: Optimization, Estimation and Control, CRC Press, 1975.
[6]	J. Casper and R. R. Murphy, Human-robot interactions during the robot-assisted urban search and rescue response at the world trade center, Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, 33 (2003), 367-385. doi: 10.1109/TSMCB.2003.811794.
[7]	S. Chopra and M. Egerstedt, Heterogeneous multi-robot routing, in American Control Conference (ACC), IEEE, 2014, 5390-5395. doi: 10.1109/ACC.2014.6859368.
[8]	J.-P. de la Croix and M. Egerstedt, A separation signal for heterogeneous networks, in 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton), IEEE, 2013, 254-261.
[9]	J.-P. de la Croix and M. Egerstedt, A control lyapunov function approach to human-swarm interactions, American Control Conference, to appear.
[10]	M. Diana, J.-P. de la Croix and M. Egerstedt, Deformable-medium affordances for interacting with multi-robot systems, in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE, 2013, 5252-5257. doi: 10.1109/IROS.2013.6697116.
[11]	F. Dorfler and B. Francis, Geometric analysis of the formation problem for autonomous robots, IEEE Transactions on Automatic Control, 55 (2010), 2379-2384. doi: 10.1109/TAC.2010.2053735.
[12]	F. Gao and M. L. Cummings, Barriers to Robust and Effective Human-Agent Teamwork, AAAI Spring Symposium Series, 2014.
[13]	M. A. Goodrich, B. Pendleton, P. Sujit and J. Pinto, Toward human interaction with bio-inspired robot teams, in IEEE International Conference on Systems, Man, and Cybernetics (SMC), IEEE, 2011, 2859-2864. doi: 10.1109/ICSMC.2011.6084115.
[14]	M. Hägele, W. Schaaf and E. Helms, Robot assistants at manual workplaces: Effective co-operation and safety aspects, in Proceedings of the 33rd ISR (International Symposium on Robotics), 2002, 7-11.
[15]	D. Kahneman, Attention and Effort, Englewood Cliffs, N7T, Prentice-Hall, 1973.
[16]	H. K. Khalil and J. Grizzle, Nonlinear Systems, Vol. 3, Prentice Hall Upper Saddle River, 2002.
[17]	Z. Kira and M. A. Potter, Exerting human control over decentralized robot swarms, in 4th International Conference on Autonomous Robots and Agents (ICRA), IEEE, 2009, 566-571. doi: 10.1109/ICARA.2000.4803934.
[18]	A. Kolling, K. Sycara, S. Nunnally and M. Lewis, Human swarm interaction: An experimental study of two types of interaction with foraging swarms, Journal of Human-Robot Interaction, 2 (2013), 103-128. doi: 10.5898/JHRI.2.2.Kolling.
[19]	S. Lee, G. Sukhatme, J. Kim and C.-M. Park, Haptic control of a mobile robot: A user study, in IEEE/RSJ International Conference on Intelligent Robots and Systems, Vol. 3, IEEE, 2002, 2867-2874.
[20]	J. McLurkin, J. Smith, J. Frankel, D. Sotkowitz, D. Blau and B. Schmidt, Speaking swarmish: Human-robot interface design for large swarms of autonomous mobile robots., in AAAI Spring Symposium: To Boldly Go Where No Human-Robot Team Has Gone Before, 2006, 72-75.
[21]	M. Mesbahi and M. Egerstedt, Graph Theoretic Methods in Multi-Agent Networks, Princeton University Press, 2010.
[22]	J. Nagi, H. Ngo, A. Giusti, L. M. Gambardella, J. Schmidhuber and G. A. Di Caro, Incremental learning using partial feedback for gesture-based human-swarm interaction, in RO-MAN, IEEE, 2012, 898-905. doi: 10.1109/ROMAN.2012.6343865.
[23]	R. Olfati-Saber, J. A. Fax and R. M. Murray, Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95 (2007), 215-233. doi: 10.1109/JPROC.2006.887293.
[24]	R. Olfati-Saber and R. M. Murray, Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control, 49 (2004), 1520-1533. doi: 10.1109/TAC.2004.834113.
[25]	G. Podevijn, R. O'Grady and M. Dorigo, Self-organised feedback in human swarm interaction, in Proceedings of the Workshop on Robot Feedback in Human-robot Interaction: How to make a Robot Readable for a Human Interaction Partner (RO-MAN), 2012.
[26]	E. Schoof, A. Chapman and M. Mesbahi, Bearing-compass formation control: A human-swarm interaction perspective, in American Control Conference (ACC), IEEE, 2014, 3881-3886. doi: 10.1109/ACC.2014.6859380.
[27]	E. D. Sontag, Control-lyapunov functions, in Open problems in mathematical systems and control theory, Springer, 1999, 211-216.

show all references

References:

[1]	S. Bashyal and G. K. Venayagamoorthy, Human swarm interaction for radiation source search and localization, in Swarm Intelligence Symposium (SIS), IEEE, 2008, 1-8. doi: 10.1109/SIS.2008.4668287.
[2]	A. Becker, C. Ertel and J. McLurkin, Crowdsourcing swarm manipulation experiments: A massive online user study with large swarms of simple robots, in Robotics and Automation (ICRA), 2014 IEEE International Conference on, 2014, 2825-2830. doi: 10.1109/ICRA.2014.6907264.
[3]	S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004. doi: 10.1017/CBO9780511804441.
[4]	R. W. Brockett, Minimum attention control, in Proceedings of the 36th IEEE Conference on Decision and Control, Vol. 3, IEEE, 1997, 2628-2632. doi: 10.1109/CDC.1997.657776.
[5]	A. E. Bryson, Applied Optimal Control: Optimization, Estimation and Control, CRC Press, 1975.
[6]	J. Casper and R. R. Murphy, Human-robot interactions during the robot-assisted urban search and rescue response at the world trade center, Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, 33 (2003), 367-385. doi: 10.1109/TSMCB.2003.811794.
[7]	S. Chopra and M. Egerstedt, Heterogeneous multi-robot routing, in American Control Conference (ACC), IEEE, 2014, 5390-5395. doi: 10.1109/ACC.2014.6859368.
[8]	J.-P. de la Croix and M. Egerstedt, A separation signal for heterogeneous networks, in 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton), IEEE, 2013, 254-261.
[9]	J.-P. de la Croix and M. Egerstedt, A control lyapunov function approach to human-swarm interactions, American Control Conference, to appear.
[10]	M. Diana, J.-P. de la Croix and M. Egerstedt, Deformable-medium affordances for interacting with multi-robot systems, in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE, 2013, 5252-5257. doi: 10.1109/IROS.2013.6697116.
[11]	F. Dorfler and B. Francis, Geometric analysis of the formation problem for autonomous robots, IEEE Transactions on Automatic Control, 55 (2010), 2379-2384. doi: 10.1109/TAC.2010.2053735.
[12]	F. Gao and M. L. Cummings, Barriers to Robust and Effective Human-Agent Teamwork, AAAI Spring Symposium Series, 2014.
[13]	M. A. Goodrich, B. Pendleton, P. Sujit and J. Pinto, Toward human interaction with bio-inspired robot teams, in IEEE International Conference on Systems, Man, and Cybernetics (SMC), IEEE, 2011, 2859-2864. doi: 10.1109/ICSMC.2011.6084115.
[14]	M. Hägele, W. Schaaf and E. Helms, Robot assistants at manual workplaces: Effective co-operation and safety aspects, in Proceedings of the 33rd ISR (International Symposium on Robotics), 2002, 7-11.
[15]	D. Kahneman, Attention and Effort, Englewood Cliffs, N7T, Prentice-Hall, 1973.
[16]	H. K. Khalil and J. Grizzle, Nonlinear Systems, Vol. 3, Prentice Hall Upper Saddle River, 2002.
[17]	Z. Kira and M. A. Potter, Exerting human control over decentralized robot swarms, in 4th International Conference on Autonomous Robots and Agents (ICRA), IEEE, 2009, 566-571. doi: 10.1109/ICARA.2000.4803934.
[18]	A. Kolling, K. Sycara, S. Nunnally and M. Lewis, Human swarm interaction: An experimental study of two types of interaction with foraging swarms, Journal of Human-Robot Interaction, 2 (2013), 103-128. doi: 10.5898/JHRI.2.2.Kolling.
[19]	S. Lee, G. Sukhatme, J. Kim and C.-M. Park, Haptic control of a mobile robot: A user study, in IEEE/RSJ International Conference on Intelligent Robots and Systems, Vol. 3, IEEE, 2002, 2867-2874.
[20]	J. McLurkin, J. Smith, J. Frankel, D. Sotkowitz, D. Blau and B. Schmidt, Speaking swarmish: Human-robot interface design for large swarms of autonomous mobile robots., in AAAI Spring Symposium: To Boldly Go Where No Human-Robot Team Has Gone Before, 2006, 72-75.
[21]	M. Mesbahi and M. Egerstedt, Graph Theoretic Methods in Multi-Agent Networks, Princeton University Press, 2010.
[22]	J. Nagi, H. Ngo, A. Giusti, L. M. Gambardella, J. Schmidhuber and G. A. Di Caro, Incremental learning using partial feedback for gesture-based human-swarm interaction, in RO-MAN, IEEE, 2012, 898-905. doi: 10.1109/ROMAN.2012.6343865.
[23]	R. Olfati-Saber, J. A. Fax and R. M. Murray, Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95 (2007), 215-233. doi: 10.1109/JPROC.2006.887293.
[24]	R. Olfati-Saber and R. M. Murray, Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control, 49 (2004), 1520-1533. doi: 10.1109/TAC.2004.834113.
[25]	G. Podevijn, R. O'Grady and M. Dorigo, Self-organised feedback in human swarm interaction, in Proceedings of the Workshop on Robot Feedback in Human-robot Interaction: How to make a Robot Readable for a Human Interaction Partner (RO-MAN), 2012.
[26]	E. Schoof, A. Chapman and M. Mesbahi, Bearing-compass formation control: A human-swarm interaction perspective, in American Control Conference (ACC), IEEE, 2014, 3881-3886. doi: 10.1109/ACC.2014.6859380.
[27]	E. D. Sontag, Control-lyapunov functions, in Open problems in mathematical systems and control theory, Springer, 1999, 211-216.

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