zbMATH — the first resource for mathematics

Coordination of nonholonomic mobile robots for diffusive threat defense. (English) Zbl 1412.93059
Summary: This paper studies coordination of a team of nonholonomic mobile robots with smart actuators for defending against invasive threat to a planar convex area. The threat refers to a kind of harmful substance such as chemical pollutant appearing outside and moving towards the area. The invasion of threat can be modeled by a 2D unsteady reaction-diffusion process. To reflect the adverse effect of threat on the area, a so-called risk intensity field is introduced. The value of risk intensity is equal to the concentration of threat measured by a static mesh sensor network. Based on this risk intensity field, a coordination control scenario using Voronoi tessellation is formulated. In order to minimize the actuator performance loss and reduce the total average risk intensity simultaneously, a generalized centroidal Voronoi tessellation (CVT) algorithm including optimal motion control and risk mitigation control is designed. The proposed algorithm is gradient-based and guides mobile robots to track their optimal trajectories asymptotically. Meanwhile, two conditions of choosing control gains are derived to keep the total average risk intensity below a safety level. Several simulation examples with different cases of threat invasion are provided and the advantage of proposed algorithm over traditional control method is presented.

93C85 Automated systems (robots, etc.) in control theory
93C20 Control/observation systems governed by partial differential equations
70F25 Nonholonomic systems related to the dynamics of a system of particles
Full Text: DOI
[1] Conradt, L.; Roper, T. J., Group decision-making in animals, Nature, 421, 691, 155-158, (2003)
[2] Ren, W.; Beard, R. W.; Atkins, E. M., Information concensus in multivehicle cooperative control, IEEE Control. Syst. Mag., 27, 2, 71-82, (2007)
[3] Dong, L.; Chai, S.; Zhang, B.; Nguang, S. K.; Li, X., Cooperative relay tracking strategy for multi-agent systems with assistance of Voronoi diagrams, J. Frankl. Inst., 353, 17, 4422-4441, (2016) · Zbl 1349.93013
[4] Guan, Z. H.; Liu, Z. W.; Feng, G.; Jian, M., Impulsive consensus algorithms for second-order multi-agent networks with sampled information, Automatica, 48, 7, 1397-1404, (2012) · Zbl 1246.93007
[5] Martinez, S.; Cortes, J.; Bullo, F., Motion coordination with distributed information, IEEE Control Syst. Mag., 27, 4, 75-88, (2007)
[6] Qi, H.; Iyengar, S. S.; Chakrabarty, K., Distributed sensor networks-a review of recent research, J. Frankl. Inst., 338, 6, 655-668, (2001) · Zbl 1169.93314
[7] Haugen, J.; Imsland, L., Monitoring an advection-diffusion process using aerial mobile sensors, Unmanned Syst., 3, 03, 221-238, (2015)
[8] Qu, Y.; Xu, S.; Song, C.; Ma, Q.; Chu, Y.; Zou, Y., Finite-time dynamic coverage for mobile sensor networks in unknown environments using neural networks, J. Frankl. Inst., 351, 10, 4838-4849, (2014) · Zbl 1395.93066
[9] Miah, S.; Nguyen, B.; Bourque, F. A.; Spinello, D., Nonuniform deployment of autonomous agents in harbor-like environments, Unmanned Syst., 2, 4, 377-389, (2014)
[10] Demetriou, M. A., Guidance of mobile actuator-plus-sensor networks for improved control and estimation of distributed parameter systems, IEEE Trans. Autom. Control, 55, 7, 1570-1584, (2010) · Zbl 1368.93268
[11] Demetriou, M. A., Adaptive control of 2-D PDEs using mobile collocated actuator/sensor pairs with augmented vehicle dynamics, IEEE Trans. Autom. Control, 57, 12, 2979-2993, (2012) · Zbl 1369.93270
[12] Fridman, E.; Blighovsky, A., Robust sampled-data control of a class of semilinear parabolic systems, Automatica, 48, 5, 826-836, (2012) · Zbl 1246.93076
[13] Selivanov, A.; Fridman, E., Distributed event-triggered control of diffusion semilinear PDEs, Automatica, 68, 344-351, (2016) · Zbl 1334.93120
[14] Cortes, J.; Martinez, S.; Karatas, T.; Bullo, F., Coverage control for mobile sensing networks, IEEE Trans. Robot. Autom., 20, 2, 243-255, (2004)
[15] Chao, H.; Chen, Y.; Ren, W., Consensus of information in distributed control of a diffusion process using centroidal Voronoi tessellations, Proceedings of the 46th IEEE Conference on Decision Control, 1441-1446, (2007)
[16] Chen, Y.; Wang, Z.; Liang, J., Optimal dynamic actuator location in distributed feedback control of a diffusion process, Int. J. Sensor Netw., 2, 3-4, 169-178, (2007)
[17] Chen, J.; Zhuang, B.; Chen, Y.; Cui, B., Diffusion control for a tempered anomalous diffusion system using fractional-order PI controllers, ISA Trans., (2017)
[18] Franco, C.; López-Nicolás, G.; Sagüés, C.; Llorente, S., Adaptive action for multi-agent persistent coverage, Asian J. Control, 18, 2, 419-432, (2016) · Zbl 1346.93017
[19] Kamel, M.; Stastny, T.; Alexis, K.; Siegwart, R., Model predictive control for trajectory tracking of unmanned aerial vehicles using robot operating system, (Koubaa, A., Robot Operating System (ROS)-The Complete Reference, 2, (2017), Springer: Springer Cham, Switzerland)
[20] Ivić, S.; Crnković, B.; Mezić, I., Ergodicity-based cooperative multiagent area coverage via a potential field, IEEE Trans. Cybern., 47, 8, 1983-1993, (2017)
[21] Mavrommati, A.; Tzorakoleftherakis, E.; Abraham, I.; Murphey, T. D., Real-time area coverage and target localization using receding-horizon ergodic exploration, IEEE Trans. Rob., 34, 1, 62-80, (2018)
[22] Cortes, J.; Martinez, S.; Karatas, T., Coverage control for mobile sensing networks: variations on a theme, Proceedings of the 10th Mediterranean Conference on Control and Automation, Lisbon, Portugal, 1-9, (2002)
[23] Pimenta, L. C.; Schwager, M.; Lindsey, Q.; Kumar, V.; Rus, D.; Mesquita, R. C.; Pereira, G. A., Simultaneous coverage and tracking (SCAT) of moving targets with robot networks, Proceedings of the Eighth International Workshop on the Algorithmic Foundations of Robotics, 57, 85-99, (2009), Springer: Springer Berlin Heidelberg · Zbl 1215.93101
[24] Lekien, F.; Leonard, N. E., Nonuniform coverage and cartograms, SIAM J. Control Optimiz., 48, 1, 351-372, (2009) · Zbl 1182.93109
[25] Lee, S. G.; Diaz-Mercado, Y.; Egerstedt, M., Multirobot control using time-varying density functions, IEEE Trans. Robot., 31, 2, 489-493, (2015)
[26] Du, Q.; Gunzburger, M. D.; Ju, L., Constrained centroidal Voronoi tessellations for surfaces, SIAM J. Sci. Comput., 24, 5, 1488-1506, (2003) · Zbl 1036.65101
[27] Du, Q.; Faber, V.; Gunzburger, M., Centroidal Voronoi tessellations: applications and algorithms, SIAM Rev., 41, 4, 637-676, (1999) · Zbl 0983.65021
[28] Guruprasad, K. R.; Ghose, D., Heterogeneous locational optimisation using a generalised Voronoi partition, Int. J. Control, 86, 6, 977-993, (2013) · Zbl 1278.93034
[29] Patankar, S., Numerical Heat Transfer and Fluid Flow, (1980), CRC Press · Zbl 0521.76003
[30] Liu, Y.; Wang, W.; Levy, B.; Sun, F.; Yan, D. M.; Lu, L.; Yang, C., On centroidal Voronoi tessellationenergy smoothness and fast computation, ACM Trans. Graph., 28, 4, 101, (2009)
[31] Edwards, C.; Spurgeon, S., Sliding Mode Control: Theory and Applications, (1998), CRC Press
[32] Lee, S. G.; Egerstedt, M., Controlled coverage using time-varying density functions, IFAC Proc., 46, 27, 220-226, (2013)
[33] Du, Q.; Emelianenko, M., Acceleration schemes for computing centroidal Voronoi tessellations, Numer. Linear Algebra Appl., 13, 2/3, 173-192, (2006) · Zbl 1174.05323
[34] Dubins, L. E., On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and tangents, Am. J. Math., 79, 3, 497-516, (1957) · Zbl 0098.35401
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.