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A survey on routing problems and robotic systems

Published online by Cambridge University Press:  06 August 2018

Douglas G. Macharet  and
Mario F. M. Campos
Douglas G. Macharet*
Affiliation:
Computer Vision and Robotics Laboratory, Department of Computer Science, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil. E-mail: mario@dcc.ufmg.br
Mario F. M. Campos
Affiliation:
Computer Vision and Robotics Laboratory, Department of Computer Science, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil. E-mail: mario@dcc.ufmg.br
*
*Corresponding author. E-mail: doug@dcc.ufmg.br
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Summary

Planning paths that are length or time optimized or both is an age-long problem for which numerous approaches have been proposed with varied degree of success depending on the imposed constraints. Among classical instances in the literature, the Traveling Salesman Problem and the Vehicle Routing Problem have been widely studied and frequently considered in the realm of mobile robotics. Understandably, the classical formulation for such problems do not take into account many different issues that arise in real-world scenarios, such as motion constraints and dynamic environments, commonly found in actual robotic systems, and consequently the solutions have been generalized in several ways. In this work, we present a broad and comprehensive review of the classical works and recent breakthroughs regarding the routing techniques ordinarily used in robotic systems and provide references to the most fundamental works in the literature.

Keywords

Traveling Salesman ProblemVehicle Routing ProblemDubins vehicleDubins TSPTSP with neighborhoodsk-TSPDynamic VRP
Type
Articles
Information
Robotica , Volume 36 , Issue 12 , December 2018 , pp. 1781 - 1803
Copyright
Copyright © Cambridge University Press 2018 

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References

1. Aggarwal, A., Coppersmith, D., Khanna, S., Motwani, R. and Schieber, B., “The Angular-Metric Traveling Salesman Problem,” Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms SODA1997, Philadelphia, PA, USA, Society for Industrial and Applied Mathematics (1997) pp. 221–229.Google Scholar
2. Alatartsev, S., Mersheeva, V., Augustine, M. and Ortmeier, F., “On Optimizing A Sequence of Robotic Tasks,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems IROS (2013).Google Scholar
3. Alves Neto, A., Macharet, D. G. and Campos, M. F. M., “Feasible RRT-Based Path Planning Using Seventh Order Bézier Curves,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems IROS2010 (Oct. 2010) pp. 1445–1450.Google Scholar
4. Applegate, D. L., Bixby, R. E., Chvatal, V. and Cook, W. J., The Traveling Salesman Problem: A Computational Study, Princeton Series in Applied Mathematics (Princeton University Press, Princeton, NJ, USA, 2007).Google Scholar
5. Arkin, E. M. and Hassin, R., “Approximation algorithms for the geometric covering salesman problem,” Discrete Appl. Math. 55, 197–218 (Dec. 1994).Google Scholar
6. Arsie, A., Savla, K. and Frazzoli, E., “Efficient routing algorithms for multiple vehicles with no explicit communications,” IEEE Trans. Autom. Control 54 (10), 2302–2317 (Oct. 2009).Google Scholar
7. Arslan, G., Marden, J. R. and Shamma, J. S., “Autonomous vehicle-target assignment: A game-theoretical formulation,” J. Dyn. Syst. Meas. Control 129 (5), 584–596 (2007).Google Scholar
8. Ausiello, G., Bonifaci, V. and Laura, L., “The on-line asymmetric traveling salesman problem,” J. Discrete Algorithms 6 (2mo), 290–298 (2008). Selected papers from CompBioNets 2004 - Algorithms and Computational Methods for Biochemical and Evolutionary Networks.Google Scholar
9. Ausiello, G., Feuerstein, E., Leonardi, S., Stougie, L. and Talamo, M., “Algorithms for the on-line travelling salesman,” Algorithmica 29, 560–581 (2001).Google Scholar
10. Bednowitz, N., Batta, R. and Nagi, R., “Dispatching and loitering policies for unmanned aerial vehicles,” J. Simul. 8 (1), 9–24 (Feb. 2012).Google Scholar
11. Bektas, T., “The multiple traveling salesman problem: An overview of formulations and solution procedures,” Omega 34 (3), 209–219 (2006).Google Scholar
12. Bertsimas, D. J. and van Ryzin, G., “A stochastic and dynamic vehicle routing problem in the Euclidean plane,” Oper. Res. 39 (4), 601–615 (1991).Google Scholar
13. Bertsimas, D. J. and van Ryzin, G., “Stochastic and dynamic vehicle routing in the Euclidean plane with wultiple capacitated vehicles,” Oper. Res. 41 (1), 60–76 (1993).Google Scholar
14. Bhadauria, D., Tekdas, O. and Isler, V., “Robotic data mules for collecting data over sparse sensor fields,” J. Field Robot. 28 (3), 388–404 (2011).Google Scholar
15. Bopardikar, S., Smith, S., Bullo, F. and Hespanha, J., “Dynamic vehicle routing for translating demands: Stability analysis and receding-horizon policies,” IEEE Trans. Autom. Control 55 (11), 2554–2569 (Nov. 2010).Google Scholar
16. Borenstein, J. and Koren, Y., “The vector field histogram-fast obstacle avoidance for mobile robots,” IEEE Trans. Robot. Autom. 7 (3), 278–288 (Jun. 1991).Google Scholar
17. Bullo, F., Frazzoli, E., Pavone, M., Savla, K. and Smith, S., “Dynamic vehicle routing for robotic systems,” Proc. IEEE 99 (9), 1482–1504 (Sep. 2011).Google Scholar
18. Chakravarthy, A. and Ghose, D., “Obstacle avoidance in a dynamic environment: A collision cone approach,” IEEE Trans. Syst. Man, Cybern. - Part A: Syst. Humans 28 (5), 562–574 (Sep. 1998).Google Scholar
19. Choset, H., Lynch, K. M., Hutchinson, S., Kantor, G., Burgard, W., Kavraki, L. E. and Thrun, S., Principles of Robot Motion: Theory, Algorithms, and Implementations (MIT Press, Cambridge, MA, Jun. 2005).Google Scholar
20. Christofides, N., “Technical note–bounds for the travelling-salesman problem,” Oper. Res. 20 (5), 1044–1056 (1972).Google Scholar
21. Cobano, J., Conde, R., Alejo, D. and Ollero, A., “Path Planning Based on Genetic Algorithms and the Monte-Carlo Method to Avoid Aerial Vehicle Collisions Under Uncertainties,” Proceedings of the IEEE International Conferenceon Robotics and Automation ICRA2011 (May 2011) pp. 4429–4434.Google Scholar
22. Comarela, G., Gonçalves, K., Pappa, G. L., Almeida, J. and Almeida, V., “Robot Routing in Sparse Wireless Sensor Networks with Continuous Ant Colony Optimization,” Proceedings of the 13th Annual Conference Companion on Genetic and Evolutionary Computation GECCO2011, New York, NY, USA: ACM (2011).Google Scholar
23. Dantzig, G. B. and Ramser, J. H., “The truck dispatching problem,” Manag. Sci. 6 (1), 80–91 (1959).Google Scholar
24. de Berg, M., Gudmundsson, J., Katz, M. J., Levcopoulos, C., Overmars, M. H. and van der Stappen, A. F., “TSP with neighborhoods of varying size,” J. Algorithms 57, 22–36 (Sep. 2005).Google Scholar
25. Desai, J. P. and Kumar, V., “Motion planning for cooperating mobile manipulators,” J. Robot. Syst. 16 (10), 557–579 (1999).Google Scholar
26. 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).Google Scholar
27. Dumitrescu, A. and Mitchell, J. S., “Approximation algorithms for TSP with neighborhoods in the plane,” J. Algorithms 48 (1), 135–159 (2003). Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms.Google Scholar
28. Elbassioni, K., Fishkin, A. and Sitters, R., “On Approximating the TSP with Intersecting Neighborhoods,” In: Algorithms and Computation (Asano, T., ed.) Lecture Notes in Computer Science, vol. 4288 (Springer, Berlin, Heidelberg, 2006) pp. 213–222.Google Scholar
29. Elbassioni, K. M., Fishkin, A. V., Mustafa, N. H. and Sitters, R., “Approximation Algorithms for Euclidean Group TSP,” In: Automata, Languages and Programming (Caires, L., Italiano, G. F., Monteiro, L., Palamidessi, C. and Yung, M., eds.) Lecture Notes in Computer Science, vol. 3580 (Springer, Berlin, Heidelberg, 2005) pp. 1115–1126.Google Scholar
30. Enright, J. and Frazzoli, E., “Cooperative UAV Routing with Limited Sensor Range,” Proceedings of the AIAA Conference on Guidance, Navigation and Control, Keystone, CO, USA (2006).Google Scholar
31. Enright, J. J., Savla, K., Frazzoli, E. and Bullo, F., “Stochastic and dynamic routing problems for multiple UAVs,” AIAA J. Guidance, Control, Dyn. 32 (4), 1152–1166 (2009).Google Scholar
32. Fiorini, P. and Shiller, Z., “Motion planning in dynamic environments using velocity obstacles,” Int. J. Robot. Res. 17 (7), 760–772 (1998).Google Scholar
33. Fox, D., Burgard, W. and Thrun, S., “The dynamic window approach to collision avoidance,” IEEE Robot. Autom. Mag. 4 (1), 23–33 (1997).Google Scholar
34. Frazzoli, E. and Bullo, F., “Decentralized Algorithms for Vehicle Routing in a Stochastic Time-Varying Environment,” Proceedings of the 43rd IEEE Conference on Decision and Control CDC2004, vol. 4 (Dec. 2004) pp. 3357–3363.Google Scholar
35. Frederickson, G. N., Hecht, M. S. and Kim, C. E., “Approximation algorithms for some routing problems,” SIAM J. Comput. 7 (2), 178–193 (1978).Google Scholar
36. Gal, O., Shiller, Z. and Rimon, E., “Efficient and Safe on-Line Motion Planning in Dynamic Environments,” Proceedings of the IEEE International Conference on Robotics and Automation (2009) pp. 88–93.Google Scholar
37. Gentilini, I., Margot, F. and Shimada, K., “The travelling salesman problem with neighbourhoods: MINLP solution,” Optim. Methods Softw. 28 (2), 364–378 (2013).Google Scholar
38. Gudmundsson, J. and Levcopoulos, C., “A fast approximation algorithm for TSP with neighborhoods,” Nordic J. Comput. 6, 469–488 (Dec. 1999).Google Scholar
39. Hota, S. and Ghose, D., “Optimal Path Planning for an Aerial Vehicle in 3D Space,” Proceedings of IEEE Conference on Decision and Control CDC (Dec. 2010) pp. 4902–4907.Google Scholar
40. Isaacs, J. T., Klein, D. J. and Hespanha, J. P., “Algorithms for the Traveling Salesman Problem With Neighborhoods Involving a Dubins Vehicle,” Proceedings of the IEE American Control Conference ACC2011 (2011), pp. 1704–1709.Google Scholar
41. Isaiah, P. and Shima, T., “Motion planning algorithms for the Dubins travelling salesperson problem,” Automatica 53 (0), 247–255 (2015).Google Scholar
42. Jaillet, L., Cortés, J. and Siméon, T., “Sampling-based path planning on configuration-space costmaps,” IEEE Trans. Robot. 26 (4), 635–646 (2010).Google Scholar
43. Jaillet, P. and Wagner, M. R., “Online Vehicle Routing Problems: A Survey,” In: The Vehicle Routing Problem: Latest Advances and New Challenges (Golden, B., Raghavan, S., Wasil, E., Sharda, R. and Voß, S., eds.) Operations Research/Computer Science Interfaces Series, vol. 43 (Springer, USA, 2008) pp. 221–237.Google Scholar
44. Karaman, S. and Frazzoli, E., “Optimal Kinodynamic Motion Planning Using Incremental Sampling-Based Methods,” Proceedings of the IEEE Conference on Decision and Control CDC2010 (Dec. 2010) pp. 7681–7687.Google Scholar
45. Khatib, O., “Real-time obstacle avoidance for manipulators and mobile robots,” Int. J. Robot. Res. 5 (1), 90–98 (1986).Google Scholar
46. Kim, D., Uma, R., Abay, B., Wu, W., Wang, W. and Tokuta, A., “Minimum latency multiple data MULE trajectory planning in wireless sensor networks,” IEEE Trans. Mobile Comput. 13 (4), 838–851 (Apr. 2014).Google Scholar
47. Koren, Y. and Borenstein, J., “Potential Field Methods and their Inherent Limitations for Mobile Robot Navigation,” Proceedings of the IEEE International Conference on Robotics and Automation (1991) pp. 1398–1404.Google Scholar
48. Kuwata, Y., Fiore, G., Teo, J., Frazzoli, E. and How, J., “Motion Planning for Urban Driving Using RRT,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems IROS2008 (Sep. 2008) pp. 1681–1686.Google Scholar
49. LaValle, S. M., Planning Algorithms (Cambridge University Press, New York, NY, USA, 2006).Google Scholar
50. LaValle, S. M. and Kuffner, J., J. J., “Randomized Kinodynamic Planning,” Proceedings of the International Conference on Robotics and Automation (1999) pp. 473–479.Google Scholar
51. Le Ny, J., Performance Optimization for Unmanned Vehicle Systems Ph.D. Thesis (Cambridge, MA: Massachusetts Institute of Technology, 2008).Google Scholar
52. Le Ny, J. and Feron, E., “An Approximation Algorithm for the Curvature-Constrained Traveling Salesman Problem,” Proceedings of the 43rd Annual Allerton Conference on Communications, Control and Computing (2005).Google Scholar
53. Le Ny, J., Feron, E. and Frazzoli, E., “On the dubins traveling salesman problem,” IEEE Trans. Autom. Control 57 (1), 265–270 (Jan. 2012).Google Scholar
54. Le Ny, J., Frazzoli, E. and Feron, E., “The Curvature-Constrained Traveling Salesman Problem for High Point Densities,” Proceedings of the 46th IEEE Conference on Decision and Control CDC2007 (Dec. 2007) pp. 5985–5990.Google Scholar
55. Lin, S. and Kernighan, B. W., “An effective heuristic algorithm for the traveling-salesman problem,” Oper. Res. 21 (2), 498–516 (1973).Google Scholar
56. Lozano-Pérez, T. and Wesley, M. A., “An algorithm for planning collision-free paths among polyhedral obstacles,” Commun. ACM 22 (10), 560–570 (1979).Google Scholar
57. Ma, X. and Castañón, D. A., “Receding Horizon Planning for Dubins Traveling Salesman Problems,” Proceedings of the 45th IEEE Conference on Decision and Control CDC2006 (Dec. 2006) pp. 5453–5458.Google Scholar
58. Macharet, D. G., Alves Neto, A. and Campos, M. F. M., “Feasible UAV Path Planning Using Genetic Algorithms and Bézier Curves,” Proceedings of the 20th Brazilian Conference on Advances in Artificial Intelligence SBIA2010 Berlin, Heidelberg: Springer-Verlag (2010) pp. 223–232.Google Scholar
59. Macharet, D. G., Alves Neto, A., da Camara Neto, V. F. and Campos, M. F. M., “Nonholonomic Path Planning Optimization for Dubins' Vehicles,” Proceedings of the IEEE International Conference on Robotics and Automation ICRA2011 (May 2011) pp. 4208–4213.Google Scholar
60. Macharet, D. G., Alves Neto, A., da Camara Neto, V. F. and Campos, M. F. M., “An Evolutionary Approach for the Dubins' Traveling Salesman Problem with Neighborhoods,” Proceedings of the 21th Genetic and Evolutionary Computation Conference GECCO (2012).Google Scholar
61. Macharet, D. G., Alves Neto, A., da Camara Neto, V. F. and Campos, M. F. M., “Efficient Target Visiting Path Planning for Multiple Vehicles with Bounded Curvature,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems IROS (Nov. 2013) pp. 3830–3836.Google Scholar
62. Macharet, D. G., Monteiro, J. W., Mateus, G. R. and Campos, M. F., “Bi-objective data gathering path planning for vehicles with bounded curvature,” Comput. Oper. Res. 84, 195–204 (2017).Google Scholar
63. Macharet, D. G., Monteiro, J. W. G., Mateus, G. R. and Campos, M. F. M., “Time-Optimized Routing Problem for Vehicles with Bounded Curvature,” Proceedings of the XIII Latin American Robotics Symposium and IV Brazilian Robotics Symposium LARS/SBR (Oct. 2016).Google Scholar
64. Macharet, D. G., Neto, A., da Camara Neto, V. and Campos, M., “Data Gathering Tour Optimization for Dubins' Vehicles,” Proceedings of the IEEE Congress on Evolutionary Computation CEC (Jun. 2012) pp. 1–8.Google Scholar
65. Mahmoodi, M., Alipour, K. and Mohammadi, H. B., “KidVO: A kinodynamically consistent algorithm for online motion planning in dynamic environments,” Ind. Robot: Int. J. 43 (1), 33–47 (01 2016).Google Scholar
66. Marble, J. D. and Bekris, K., “Towards Small Asymptotically Near-Optimal Roadmaps,” Proceedings of the IEEE International Conference on Robotics and Automation ICRA (2012) pp. 2557–2562.Google Scholar
67. Mata, C. S. and Mitchell, J. S. B., “Approximation Algorithms for Geometric Tour and Network Design Problems,” Proceedings of the 11th Annual Symposium on Computational Geometry SCG1995, New York, NY, USA: ACM (1995) pp. 360–369.Google Scholar
68. Medeiros, A. and Urrutia, S., “Discrete optimization methods to determine trajectories for Dubins' vehicles,” Electron. Notes Discrete Math. 36, 17–24 (2010). ISCO 2010 - International Symposium on Combinatorial Optimization.Google Scholar
69. Mitchell, J. S. B., “A PTAS for TSP with Neighborhoods Among Fat Regions in the Plane,” Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms SODA2007, Philadelphia, PA, USA, Society for Industrial and Applied Mathematics (2007) pp. 11–18.Google Scholar
70. Moore, B. and Passino, K., “Distributed task assignment for mobile agents,” IEEE Trans. Autom. Control 52 (4), 749–753 (Apr. 2007).Google Scholar
71. Moscato, P. and Cotta, C., “A Modern Introduction to Memetic Algorithms,” In: Handbook of Metaheuristics (Gendreau, M. and Potvin, J.-Y., eds.) International Series in Operations Research & Management Science, vol. 146, (Springer, USA, 2010) pp. 141–183.Google Scholar
72. Noon, C. E. and Bean, J. C., “An efficient transformation of the generalized traveling salesman problem. Technical Report Technical Report 91-26, University of Michigan (1991).Google Scholar
73. Obermeyer, K. J., “Path planning for a UAV Performing Reconnaissance of Static Ground Targets in Terrain,” Proceedings of the AIAA Conference on Guidance, Navigation and Control, Chicago, IL, USA (Aug. 2009).Google Scholar
74. Obermeyer, K. J., Oberlin, P. and Darbha, S., “Sampling-Based Roadmap Methods for a Visual Reconnaissance UAV,” Proceedings of the AIAA Conference on Guidance, Navigation and Control, Toronto, ON, Canada (Aug. 2010).Google Scholar
75. Owen, M., Beard, R. and McLain, T., “Implementing Dubins Airplane Paths on Fixed-Wing UAVs,” In: Handbook of Unmanned Aerial Vehicles (Valavanis, K. P. and Vachtsevanos, G. J., eds.) (Springer, Netherlands, 2014) pp. 1677–1701.Google Scholar
76. Pavone, M., Bisnik, N., Frazzoli, E. and Isler, V., “A stochastic and dynamic vehicle routing problem with time windows and customer impatience,” Mobile Netw. Appl. 14, 350–364 (Jun. 2009).Google Scholar
77. Pavone, M. and Frazzoli, E., “Dynamic Vehicle Routing with Stochastic Time Constraints,” Proceedings of IEEE International Conference on Robotics and Automation ICRA2010 (May 2010) 1460–1467.Google Scholar
78. Pavone, M., Frazzoli, E. and Bullo, F., “Adaptive and distributed algorithms for vehicle routing in a stochastic and dynamic environment,” IEEE Trans. Autom. Control 56 (6), 1259–1274 (Jun. 2011).Google Scholar
79. Psaraftis, H. N., “Dynamic Vehicle Routing Problems,” In: Vehicle Routing: Methods and Studies (Golden, B. L. and Assad, A. A., eds.) Studies in Management Science and Systems, vol. 16 (North-Holland, Amsterdam, 1988) pp. 223–248.Google Scholar
80. Rathinam, S., Sengupta, R. and Darbha, S., “A resource allocation algorithm for multivehicle systems with nonholonomic constraints,” IEEE Trans. Autom. Sci. Eng. 4 (1), 98–104 (Jan. 2007).Google Scholar
81. Reeds, J. A. and Shepp, L. A., “Optimal paths for a car that goes both forwards and backwards. Pac. J. Math. 145 (2), 367–393 (1990).Google Scholar
82. Rosen, K. H., Discrete Mathematics and Its Applications, 7th ed. (McGraw-Hill Higher Education, Boston, 2012).Google Scholar
83. Safra, S. and Schwartz, O., “On the complexity of approximating TSP with neighborhoods and related problems,” Comput. Complexity 14, 281–307 (Mar. 2006).Google Scholar
84. Savla, K., Bullo, F. and Frazzoli, E., “On Traveling Salesperson Problems for Dubins' Vehicle: Stochastic And Dynamic Environments,” Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference CDC-ECC2005 (Dec. 2005) pp. 4530–4535.Google Scholar
85. Savla, K., Frazzoli, E. and Bullo, F., “On the Point-to-Point and Traveling Salesperson Problems for Dubins' Vehicle,” Proceedings of the IEE American Control Conference ACC2005, vol. 2 (Jun. 2005) pp. 786–791.Google Scholar
86. Shima, T., Rasmussen, S. and Gross, D., “Assigning micro UAVs to task tours in an Urban terrain,” IEEE Trans. Control Systems Technol. 15 (4), 601–612 (Jul. 2007).Google Scholar
87. Shkel, A. M. and Lumelsky, V., “Classification of the Dubins set,” Robot. Auton. Syst. 34 (4), 179–202 (2001).Google Scholar
88. Siegwart, R., Nourbakhsh, I. R. and Scaramuzza, D., Introduction to Autonomous Mobile Robots, 2nd ed. (MIT Press, Cambridge, MA, USA, 2011).Google Scholar
89. Smith, S., Bopardikar, S. and Bullo, F., “A Dynamic Boundary Guarding Problem with Translating Targets,” Proceedings of the 48th IEEE Conference on Decision and Control held jointly with the 28th Chinese Control Conference CDC/CCC2009 (Dec. 2009) pp. 8543–8548.Google Scholar
90. Smith, S. L., Pavone, M., Bullo, F. and Frazzoli, E., “Dynamic Vehicle Routing with Priority Classes of Stochastic Demands,” SIAM J. Control Optim. 48 (5), 3224–3245 (2010).Google Scholar
91. Snape, J., van den Berg, J., Guy, S. J. and Manocha, D., “The hybrid reciprocal velocity obstacle,” IEEE Trans. Robot. 27 (4), 696–706 (2011).Google Scholar
92. Sofge, D., Schultz, A. and DeJong, K., “Evolutionary Computational Approaches to Solving the Multiple Traveling Salesman Problem Using a Neighborhood Attractor Schema,” Proceedings of the Applications of Evolutionary Computing on EvoWorkshops 2002: EvoCOP, EvoIASP, EvoSTIM/EvoPLAN, London, UK: Springer-Verlag (2002) pp. 153–162.Google Scholar
93. Takahashi, O. and Schilling, R. J., “Motion planning in a plane using generalized voronoi diagrams,” IEEE Trans. Robot. Autom. 5 (2), 143–150 (Apr. 1989).Google Scholar
94. Tang, Z. and Özgüner, Ü., “Motion planning for multitarget surveillance with mobile sensor agents,” IEEE Trans. Robot. 21 (5), 898–908 (Oct. 2005).Google Scholar
95. Tekdas, O., Isler, V., Lim, J. and Terzis, A., “Using mobile robots to harvest data from sensor fields,” IEEE Wireless Commun. 16 (1), 22–28 (Feb. 2009).Google Scholar
96. Todorov, E. and Li, W., “A Generalized Iterative LQG Method for Locally-Optimal Feedback Control of Constrained Nonlinear Stochastic Systems,” Proceedings of the American Control Conference ACC, vol. 1 (Jun. 2005) pp. 300–306.Google Scholar
97. Toth, P. and Vigo, D., eds., The Vehicle Routing Problem (Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2001).Google Scholar
98. Valle, C. A., da Cunha, A. S., Aioffi, W. M. and Mateus, G. R., “Algorithms for Improving The Quality of Service in Wireless Sensor Networks with Multiple Mobile Sinks,” Proceedings of the 11th International Symposium on Modeling, Analysis and Simulation of Wireless and Mobile Systems MSWiM2008, New York, NY, USA: ACM (2008) pp. 239–243.Google Scholar
99. Van Den Berg, J., Guy, S. J., Lin, M. and Manocha, D., “Optimal Reciprocal Collision Avoidance for Multi-Agent Navigation,” Proceedings of the IEEE International Conference on Robotics and Automation (2010).Google Scholar
100. van den Berg, J., Guy, S. J., Lin, M. and Manocha, D., “Reciprocal n-Body Collision Avoidance. In: Robotics Research: The 14th International Symposium ISRR (Pradalier, C., Siegwart, R. and Hirzinger, G., eds.) (Springer, Berlin Heidelberg, 2011).Google Scholar
101. van den Berg, J., Lin, M. and Manocha, D., “Reciprocal Velocity Obstacles for Real-Time Multi-Agent Navigation,” Proceedings of the IEEE International Conference on Robotics and Automation (2008) pp. 1928–1935.Google Scholar
102. Váňa, P., Path Planning for Non-Holonomic Vehicle in Surveillance Missions Master's Thesis (Czech Republic: Czech Technical University in Prague, 2015).Google Scholar
103. Vána, P. and Faigl, J., “On the Dubins Traveling Salesman Problem with Neighborhoods,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems IROS (Sep. 2015) pp. 4029–4034.Google Scholar
104. Wilkie, D., Van den Berg, J. and Manocha, D., “Generalized Velocity Obstacles,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (2009) pp. 5573–5578.Google Scholar
105. Wu, F.-J., Huang, C.-F. and Tseng, Y.-C., “Data Gathering by Mobile Mules in a Spatially Separated Wireless Sensor Network,” Proceedings of the 10th International Conference on Mobile Data Management: Systems, Services and Middleware MDM2009, Washington, DC, USA: IEEE Computer Society (2009) pp. 293–298.Google Scholar
106. Yu, X. and Hung, J. Y., “A Genetic Algorithm for the Dubins Traveling Salesman Problem,” Proceedings of the IEEE International Symposium on Industrial Electronics ISIE (May 2012) pp. 1256–1261.Google Scholar
107. Yuan, B., Orlowska, M. and Sadiq, S., “Finding the Optimal Path in 3D Spaces Using EDAs — The Wireless Sensor Networks Scenario,” Proceedings of the 8th International Conference on Adaptive and Natural Computing Algorithms, Part I ICANNGA2007 (Springer-Verlag, Berlin, Heidelberg, 2007) pp. 536–565.Google Scholar
108. Yuan, B., Orlowska, M. and Sadiq, S., “On the optimal robot routing problem in wireless sensor networks,” IEEE Trans. Knowl. Data Eng. 19 (9), 1252–1261 (Sep. 2007).Google Scholar