Abstract
Swarm robotic systems comprising members with limited onboard localization capabilities rely on employing collaborative motion-control strategies to successfully carry out multi-task missions. Such strategies impose constraints on the trajectories of the swarm and require the swarm to be divided into worker robots that accomplish the tasks at hand, and support robots that facilitate the movement of the worker robots. The consideration of the constraints imposed by these strategies is essential for optimal mission-planning. Existing works have focused on swarms that use leader-based collaborative motion-control strategies for mission execution and are divided into worker and support robots prior to mission-planning. These works optimize the plan of the worker robots and, then, use a rule-based approach to select the plan of the support robots for movement facilitation – resulting in a sub-optimal plan for the swarm. Herein, we present a mission-planning methodology that concurrently optimizes the plan of the worker and support robots by dividing the mission-planning problem into five stages: division-of-labor, task-allocation of worker robots, worker robot path-planning, movement-concurrency, and movement-allocation. The proposed methodology concurrently searches for the optimal value of the variables of all stages. The proposed methodology is novel as it (1) incorporates the division-of-labor of the swarm into worker and support robots into the mission-planning problem, (2) plans the paths of the swarm robots to allow for concurrent facilitation of multiple independent worker robot group movements, and (3) is applicable to any collaborative swarm motion-control strategy that utilizes support robots. A unique pre-implementation estimator, for determining the possible improvement in mission execution performance that can achieved through the proposed methodology was also developed to allow the user to justify the additional computational resources required by it. The estimator uses a machine learning model and estimates this improvement based on the parameters of the mission at hand. Extensive simulated experiments showed that the proposed concurrent methodology improves the mission execution performance of the swarm by almost 40% compared to the competing sequential methodology that optimizes the plan of the worker robots first and, then, the plan of the support robots. The developed pre-implementation estimator was shown to achieve an estimation error of less than 5%.
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References
Brambilla, M., Ferrante, E., Birattari, M., Dorigo, M.: Swarm robotics: A review from the swarm engineering perspective. Swarm Intell. 7(1), 1–41 (2013)
Şahin, E.: Swarm robotics: From sources of inspiration to domains of application. In: Şahin, E., Spears, W.M. (eds.) Swarm Robotics, 3342, pp. 10–20. Springer, Berlin, Heidelberg (2004)
Schranz, M., Umlauft, M., Sende, M., Elmenreich, W.: Swarm robotic behaviors and current applications. Front. Robot. AI 7, 36 (2020)
Macwan, A., Nejat, G., Benhabib, B.: Target-motion prediction for robotic search and rescue in wilderness environments. IEEE Trans. Syst. Man Cybern. Part B. Cybern. 41(5), 1287–1298 (2011)
Bakhtari, A., Naish, M.D., Eskandari, M., Croft, E.A., Benhabib, B.: Active-vision-based multisensor surveillance - An implementation. IEEE Trans. Syst. Man Cybern. Part C. Appl. Rev. 36(5), 668–680 (2006)
Eschke, C., Heinrich, M. K., Wahby, M., and Haman, H.: Self-organized adaptive paths in multi-robot manufacturing: Reconfigurable and pattern-independent fibre deployment. In: IEEE/RSJ Int. Conf. Intel. Robot. Syst., pp. 4086–4091 (2019)
Nunes, E., Manner, M., Mitiche, H., Gini, M.: A taxonomy for task allocation problems with temporal and ordering constraints. Robot. Auton. Syst. 90, 55–70 (2017)
Gerkey, B.P., Matarić, M.J.: A formal analysis and taxonomy of task allocation in multi-robot systems. Int. J. Robot. Res. 23(9), 939–954 (2004)
Koes, M., Nourbakhsh, I., and Sycara, K.: Heterogeneous multirobot coordination with spatial and temporal constraints. In: Proc. Nat. Conf. Art. Intel. 3, pp. 1292–1297 (2005)
Yao, W., Qi, N., Liu, Y., Xu, S., Du, D.: Homotopic approach for robot allocation optimization coupled with path constraints. IEEE Robot. Autom. Lett. 5(1), 88–95 (2020)
Motes, J., Sandström, R., Lee, H., Thomas, S., Amato, N.M.: Multi-robot task and motion planning with subtask dependencies. IEEE Robot. Autom. Lett. 5(2), 3338–3345 (2020)
Henkel, C., Abbenseth, J., and Toussaint, M.: An optimal algorithm to solve the combined task allocation and path finding problem. In: IEEE/RSJ Int. Conf. Intell. Robots Syst., pp. 4140–4146 (2019)
Banfi, J., Messing, A., Kroninger, C., Stump, E., Hutchinson, S., Roy, N.: Hierarchical planning for heterogeneous multi-robot routing problems via learned subteam performance. IEEE Robot. Autom. Lett. 7(2), 4464–4471 (2022)
Messing, A., Neville, G., Chernova, S., Hutchinson, S., Ravichandar, H.: GRSTAPS: Graphically recursive simultaneous task allocation, planning, and scheduling. Int. J. Robot. Res. 41(2), 232–256 (2022)
Jones, E.G., Dias, M.B., Stentz, A.: Time-extended multi-robot coordination for domains with intra-path constraints. Auton. Robots 30(1), 41–56 (2011)
Jones, E. G., Dias, M. B., and Stentz, A.: Tiered auctions for multi-agent coordination in domains with precedence constraints: In Proc. 26th Army Sci. Conf., pp. 1–8 (2008)
Parker, L.E., Tang, F.: Building multirobot coalitions through automated task solution synthesis. Proc. IEEE 94(7), 1289–1305 (2006)
Zhang, Y. and Parker, L. E.: IQ-ASyMTRe: Synthesizing coalition formation and execution for tightly-coupled multirobot tasks. In: IEEE/RSJ Int. Conf. Intell. Robots Syst., pp. 5595–5602 (2010)
Zhang, Y., Parker, L.E.: IQ-ASyMTRe: Forming executable coalitions for tightly coupled multirobot tasks. IEEE Trans. Robot. 29(2), 400–416 (2013)
Tang, F. and Parker, L. E.: A Complete Methodology for Generating Multi-Robot Task Solutions using ASyMTRe-D and Market-Based Task Allocation. In: Proc. IEEE Int. Conf. Robot. Autom., pp. 3351–3358 (2007)
Korsah, G.A., Stentz, A., Dias, M.B.: A comprehensive taxonomy for multi-robot task allocation. Int. J. Robot. Res. 32(12), 1495–1512 (2013)
Choi, H.-L., Brunet, L., How, J.P.: Consensus-based decentralized auctions for robust task allocation. IEEE Trans. Robot. 25(4), 912–926 (2009)
Nayak, S., Yeotikar, S., Carrillo, E., Rudnick-Cohen, E., Jaffar, M.K.M., Patel, R., Azarm, S., Herrmann, J.W., Xu, H., Otte, M.: Experimental comparison of decentralized task allocation algorithms under imperfect communication. IEEE Robot. Autom. Lett. 5(2), 572–579 (2020)
Khamis, A.M., Elmogy, A.M., Karray, F.O.: Complex task allocation in mobile surveillance systems. J. Intell. Robot. Syst. 64(1), 33–55 (2011)
Ansari, I., Mohamed, A., Flushing, E. F., and Razak, S.: Cooperative and load-balancing auctions for heterogeneous multi-robot teams dealing with spatial and non-atomic tasks. In: IEEE Int. Symp. Safety, Sec., Resc. Robot., pp. 213–220 (2020)
Jones, E. G., Bernardine Dias, M., and Stentz, A.: Learning-enhanced market-based task allocation for oversubscribed domains. In: IEEE/RSJ Int. Conf. Intell. Robots Syst., pp. 2308–2313 (2007)
Berman, S., Halasz, A., Hsieh, M.A., Kumar, V.: Optimized stochastic policies for task allocation in swarms of robots. IEEE Trans. Robot. 25(4), 927–937 (2009)
Lee, W., Vaughan, N., Kim, D.: Task allocation into a foraging task with a series of subtasks in swarm robotic system. IEEE Access 8, 107549–107561 (2020)
Pang, B., Song, Y., Zhang, C., Wang, H., Yang, R.: Autonomous task allocation in a swarm of foraging robots: An approach based on response threshold sigmoid model. Int. J. Control Autom. Syst. 17(4), 1031–1040 (2019)
De Lope, J., Maravall, D., Quiñonez, Y.: Response threshold models and stochastic learning automata for self-coordination of heterogeneous multi-task distribution in multi-robot systems. Robot. Auton. Syst. 61(7), 714–720 (2013)
Mayya, S., Wilson, S., Egerstedt, M.: Closed-loop task allocation in robot swarms using inter-robot encounters. Swarm Intell. 13(2), 115–143 (2019)
Jevtic, A., Gutierrez, Á., Andina, D., Jamshidi, M.: Distributed bees algorithm for task allocation in swarm of robots. IEEE Syst. J. 6(2), 296–304 (2012)
Jha, D. K.: Algorithms for task allocation in homogeneous swarm of robots. In: IEEE/RSJ Int. Conf. Intell. Robots Syst., pp. 3771–3776 (2018)
Jang, I., Shin, H.-S., Tsourdos, A.: Anonymous hedonic game for task allocation in a large-scale multiple agent system. IEEE Trans. Robot. 34(6), 1534–1548 (2018)
Mazdin, P., Rinner, B.: Distributed and communication-aware coalition formation and task assignment in multi-robot systems. IEEE Access 9, 35088–35100 (2021)
Nedjah, N., de Mendonça, R.M., de Macedo Mourelle, L.: PSO-based distributed algorithm for dynamic task allocation in a robotic swarm. Procedia Comput. Sci. 51, 326–335 (2015)
Dutta, A. and Asaithambi, A.: One-to-many bipartite matching based coalition formation for multi-robot task allocation. In: IEEE Int. Conf. Robot. Autom., pp. 2181–2187 (2019)
Chen, J., Yan, X., Chen, H., and Sun, D.: Resource constrained multirobot task allocation with a leader-follower coalition method. In: IEEE/RSJ Int. Conf. Intell. Robots Syst., pp. 5093–5098 (2010)
Chandarana, M., Hughes, D., Lewis, M., Sycara, K., and Scherer, S.: Hybrid model for a priori performance prediction of multi-job type swarm search and service missions. In: Int. Conf. Adv. Robot., pp. 714–719 (2019)
Chandarana, M., Lewis, M., Sycara, K., and Scherer, S.: Determining effective swarm sizes for multi-job type missions. In: IEEE/RSJ Int. Conf. Intell. Robots Syst., pp. 4848–4853 (2018)
Luna, M. A., Refaat Ragab, A., Ale Isac, M. S., Flores Peña, P., and Cervera, P. C.: A new algorithm using hybrid UAV swarm control system for firefighting dynamical task allocation. In: IEEE Int. Conf. Syst. Man Cyber., pp. 655–660 (2021)
Capezzuto, L., Tarapore, D., and Ramchurn, S. D.: Large-scale, dynamic and distributed coalition formation with spatial and temporal constraints. In: Proc. European Conf. Mult. Agent Syst., pp. 108–125 (2021)
Hsieh, M.A., Halász, Á., Berman, S., Kumar, V.: Biologically inspired redistribution of a swarm of robots among multiple sites. Swarm Intell. 2(2), 121–141 (2008)
Dutta, A., Ufimtsev, V., and Asaithambi, A.: Correlation clustering based coalition formation for multi-robot task allocation. In: Proc. ACM/SIGAPP Symp. Appl. Comp., pp. 906–913 (2019)
Dutta, A., Ufimtsev, V., Said, T., Jang, I., and Eggen, R.: Distributed hedonic coalition formation for multi-robot task allocation. In: IEEE Int. Conf. Autom. Sci. Eng., pp. 639–644 (2021)
Autenrieb, J., Strawa, N., Shin, H.-S., and Hong, J.-H.: A mission planning and task allocation framework for multi-UAV swarm coordination. In: Work. Res. Ed. Dev. Unman. Aer. Syst., pp. 297–304 (2019)
Atay, N. and Bayazit, B.: Mixed-integer linear programming solution to multi-robot task allocation problem. All Comput. Sci. Eng. Res. Report Number: WUCSE-2006–54, (2006)
Sheridan, P.K., Gluck, E., Guan, Q., Pickles, T., Balcıog, B., Benhabib, B.: The dynamic nearest neighbor policy for the multi-vehicle pick-up and delivery problem. Transp. Res. Part Policy Pract. 49, 178–194 (2013)
Notomista, G., Mayya, S., Emam, Y., Kroninger, C., Bohannon, A., Hutchinson, S., Egerstedt, M.: A resilient and energy-aware task allocation framework for heterogeneous multirobot systems. IEEE Trans. Robot. 38(1), 159–179 (2022)
Mayya, S., D’antonio, D.S., Saldaña, D., Kumar, V.: Resilient task allocation in heterogeneous multi-robot systems. IEEE Robot. Autom. Lett. 6(2), 1327–1334 (2021)
Viguria, A., Maza, I., and Ollero, A.: S+T: An algorithm for distributed multirobot task allocation based on services for improving robot cooperation. In: IEEE Int. Conf. Robot. Autom., pp. 3163–3168 (2008)
Croft, E.A., Benhabib, B., Fenton, R.G.: Near-time optimal robot motion planning for on-line applications. J. Robot. Syst. 12(8), 553–567 (1995)
Irfan, M. and Farooq, A.: Auction-based task allocation scheme for dynamic coalition formations in limited robotic swarms with heterogeneous capabilities. In: Int. Conf. Intell. System. Eng., pp. 210–215 (2016)
Vig, L., Adams, J.A.: Multi-robot coalition formation. IEEE Trans. Robot. 22(4), 637–649 (2006)
Nam, C., Shell, D.A.: Robots in the huddle: Upfront computation to reduce global communication at run time in multirobot task allocation. IEEE Trans. Robot. 36(1), 125–141 (2020)
Emam, Y., Mayya, S., Notomista, G., Bohannon, A., and Egerstedt, M.: Adaptive Task Allocation for Heterogeneous Multi-Robot Teams with Evolving and Unknown Robot Capabilities. In: IEEE Int. Conf. Robot. Autom., pp. 7719–7725 (2020)
Borg, J.M., Mehrandezh, M., Fenton, R.G., Benhabib, B.: Navigation-guidance-based robotic interception of moving objects in industrial settings. J. Intell. Robot. Syst. 33(1), 1–23 (2002)
Hujic, D., Croft, E.A., Zak, G., Fenton, R.G., Mills, J.K., Benhabib, B.: The robotic interception of moving objects in industrial settings: strategy development and experiment. IEEE/ASME Trans. Mechatron. 3(3), 225–239 (1998)
Luo, L., Chakraborty, N., Sycara, K.: Provably-good distributed algorithm for constrained multi-robot task assignment for grouped tasks. IEEE Trans. Robot. 31(1), 19–30 (2015)
Wu, D., Zeng, G., Meng, L., Zhou, W., Li, L.: Gini coefficient-based task allocation for multi-robot systems with limited energy resources. J. Autom. Sin. 5(1), 155–168 (2018)
Korsah, G. A., Kannan, B., Browning, B., Stentz, A., and Dias, M. B.: xBots: An approach to generating and executing optimal multi-robot plans with cross-schedule dependencies. In: IEEE Int. Conf. Robot. Autom., pp. 115–122 (2012)
Lemaire, T., Alami, R., and Lacroix, S.: A distributed tasks allocation scheme in multi-UAV context. In: IEEE Int. Conf. Robot. Autom., 4, pp. 3622- 3627 (2004)
Suslova, E. and Fazli, P.: Multi-robot task allocation with time window and ordering constraints. In: IEEE/RSJ Int. Conf. Intell. Robots Syst., pp. 6909–6916 (2020)
Ayari, E., Hadouaj, S., and Ghedira, K.: A dynamic decentralised coalition formation approach for task allocation under tasks priority constraints. In: Int. Conf. Adv. Robot., pp. 250–255 (2017)
Mouradian, C., Sahoo, J., Glitho, R. H., Morrow, M. J., and Polakos, P. A.: A coalition formation algorithm for multi-robot task allocation in large-scale natural disasters. In: Int. Wireless Comm. Mob. Comp. Conf., pp. 1909–1914 (2017)
Kim, J.Y., Kashino, Z., Colaco, T., Nejat, G., Benhabib, B.: Design and implementation of a millirobot for swarm studies – mROBerTO. Robotica 36(11), 1591–1612 (2018)
Kim, J. Y., Colaco, T., Kashino, Z., Nejat, G., and Benhabib, B.: mROBerTO: A modular millirobot for swarm-behavior studies. In: IEEE/RSJ Int. Conf. Intell. Robots Syst., pp. 2109–2114 (2016)
Eshaghi, K., Li, Y., Kashino, Z., Nejat, G., Benhabib, B.: mROBerTO 2 0 – An autonomous millirobot with enhanced locomotion for swarm robotics. Robot. Autom. Let 5(2), 962–969 (2020)
Pickem, D., Lee, M., and Egerstedt, M.: The GRITSBot in its natural habitat - A multi-robot testbed. In: IEEE Int. Conf. Robot. Autom., pp. 4062–4067 (2015)
Rubenstein, M., Ahler, C., and Nagpal, R.: Kilobot: A low cost scalable robot system for collective behaviors. In: IEEE Int. Conf. Robot. Autom., pp. 3293–3298 (2012)
Sabelhaus, A. P., Mirsky, D., Hill, L. M., Martins, N. C., and Bergbreiter, S.: TinyTeRP: A tiny terrestrial robotic platform with modular sensing. In: IEEE Int. Conf. Robot. Autom., pp. 2600–2605 (2013)
Arvin, F., Murray, J., Zhang, C., Yue, S.: Colias: An autonomous micro robot for swarm robotic applications. Int. J. Adv. Robot. Syst. 11(7), 1–10 (2014)
Kim, J.Y., Kashino, Z., Pineros, L.M., Bayat, S., Colaco, T., Nejat, G., Benhabib, B.: A high-performance millirobot for swarm-behaviour studies: Swarm-topology estimation. Int. J. Adv. Robot. Syst. 16(6), 1–18 (2019)
Pires, A. G., Macharet, D. G., and Chaimowicz, L.: Exploring heterogeneity for cooperative localization in swarm robotics. In: Int. Conf. Adv. Robot., pp. 407–414 (2015)
Li, W., Xiong, Z., Sun, Y., and Xiong, J.: Cooperative positioning algorithm of swarm UAVs based on posterior linearization belief propagation. In: IEEE Inf. Tech. Network. Electron. Autom. Conf. Conf., pp. 1277–1282 (2019)
Song, Z. and Mohseni, K.: A distributed localization hierarchy for an AUV swarm. In: American Conf. Conf., pp. 4721–4726 (2014).
Loefgren, I., Ahmed, N., Frew, E., Heckman, C., and Humbert, S.: Scalable event-triggered data fusion for autonomous cooperative swarm localization. In: Int. Conf. Inf. Fusion, pp. 1–8 (2019)
Yoon, H.J., Eshaghi, K., Nejat, G., Benhabib, B.: Localization and topology estimation of robot swarms using Kalman filters. J. Inst. Control Robot. Syst. 28(6), 622–631 (2022)
Cornejo, A., Nagpal, R.: Distributed range-based relative localization of robot swarms. In: Akin, H.L., Amato, N.M., Isler, V., van der Stappen, A.F. (eds.) Algorithmic Foundations of Robotics XI, 107, pp. 91–107. Springer International Publishing, Cham, Switzerland (2015)
Eshaghi, K., Kashino, Z., Yoon, H.J., Nejat, G., Benhabib, B.: An inchworm-inspired motion strategy for robotic swarms. Robotica 39(12), 2283–2305 (2021)
Eshaghi, K., Rogers, A., Nejat, G., Benhabib, B.: Closed-loop motion control of robotic swarms – A tether-based strategy. IEEE Trans. Robot. 38(6), 3564–3581 (2022)
Tutsoy, O., Barkana, D.E., Balikci, K.: A novel exploration-exploitation-based adaptive law for intelligent model-free control approaches. IEEE Trans. Cybern. 53(1), 329–337 (2023)
Tutsoy, O.: COVID-19 epidemic and opening of the schools: Artificial intelligence-based long-term adaptive policy making to control the pandemic diseases. IEEE Access 9, 68461–68471 (2021)
Haykin, S.: Neural Networks: A Comprehensive Foundation, 2nd ed. Upper Saddle River, NJ, United States: Prentice Hall PTR (1998)
Katoch, S., Chauhan, S.S., Kumar, V.: A review on genetic algorithm: past, present, and future. Multimed. Tools Appl. 80(5), 8091–8126 (2021)
Mohamed, S.C., Fung, A., Nejat, G.: A multirobot person search system for finding multiple dynamic users in human-centered environments. IEEE Trans. Cybern. 53(1), 628–640 (2023)
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This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), and the Canada Research Chairs program (CRC).
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This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), NSERC CRD, and the Canada Research Chairs program (CRC).
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Conceptualization: K.E. and B.B.; Material preparation and data collection: K.E., Analysis: K.E., G.N., B.B., Writing – original draft preparation: K.E.; Writing—review and editing: K.E., G.N., and B.B.; Funding acquisition: G.N. and B.B.; Supervision: G.N. and B.B. All authors read and approved the final manuscript.
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Appendix 1: A Descriptive Example
Appendix 1: A Descriptive Example
The implementation of the proposed swarm mission-planning methodology is detailed herein for a mission comprising \({n}_{V}=5\) tasks. The position of the tasks, as well as their number of required worker robots and task working times are shown in Fig. 15. The swarm at hand comprises \({n}_{R}=50\) (homogeneous) robots, each of which can operate in either a worker or support role. Furthermore, the environment includes one connectivity point at home base that is used to provide connectivity for the adopted tether-based motion control strategy. The simplicity of the example allows us to present the optimal solutions in graphical form.
1.1 Estimating the Improvement in Mission-completion time
The proposed MLP detailed in Section 4.1, and trained through the process detailed in Section 5.1, was applied to the mission at hand, and used to decide whether a concurrent planning methodology would be necessary. In this example, the user defined minimum improvement was set as 30%. Since the estimation model estimated an improvement of about 32% for this mission, the concurrent planning methodology was deemed beneficial, and applied to plan the mission of the worker and support robots.
1.2 Division-of-Labor
For the mission at hand, the minimum (total) number of necessary worker robots is \({n}_{Wmin}=30\), calculated as the maximum number of robots required for any one of the tasks. The minimum (total) number of required support robots is \({n}_{Smin}=10\), based on the length of the longest tether that would be used for swarm motion-control. This leaves ten (= 50-30-10) swarm robots whose role can be selected to minimize the mission-completion time.
In this example, the proposed mission-planning methodology selected \({n}_{W}^{*}=35\) worker robots, leaving \({n}_{S}^{*}=15\) support robots for facilitating the workers’ motion.
1.3 Task-Allocation and Path-Planning for Worker Robots
The mission of the worker robots is planned by determining the optimal formation of the coalitions for the tasks at hand. It also involves determining the optimal paths that the sub-coalitions take to reach their destinations.
The proposed mission-planning methodology allocated the \({n}_{W}^{*}=35\) worker robots to the task at hand through:
The optimal task-allocation is shown graphically in Fig. 16.
For the optimal task-allocation shown in Fig. 16, the optimal paths of the \({n}_{C}=8\) sub-coalitions were determined as:
These paths are shown graphically in Fig. 17, where each distinct color represents the path of a sub-coalition.
1.4 Movement-Concurrency, Movement-Allocation, and Path-Planning for Support Robots
Mission-planning for the support robots, in turn, involves optimizing the concurrent execution of the movements at hand and the allocation of the support robots to these movements. This is, then, followed by optimal path planning for the support robots based on the adopted tether-based swarm motion-control strategy.
As was shown through Fig. 17 above, there are four path segments that share the same pick-up and drop-off task locations. These four segments require the worker robots to be (1) picked-up at \({V}_{0}\) and dropped-off at \({V}_{3}\), (2) picked-up at \({V}_{3}\) and dropped-off at \({V}_{5}\), (3) picked-up at \({V}_{5}\) and dropped-off at \({V}_{1}\), and (4) picked-up at \({V}_{1}\) and dropped-off at \({V}_{2}\). The plan determined that all movements associated with these four segments should be facilitated concurrently – \({M}_{{c}_{03}1}\) and \({M}_{{c}_{05}1}\), \({M}_{{c}_{05}2}\) and \({M}_{{c}_{35}1}\), \({M}_{{c}_{52}1}\) and \({M}_{{c}_{51}1}\), and \({M}_{{c}_{52}2}\) and \({M}_{{c}_{12}1}\) were planned for concurrent execution, Eq. (45), where the movements are ordered along the rows (left to right) and columns (top to bottom) as: \({M}_{0}\), \({M}_{{c}_{03}1}\), \({M}_{{c}_{05}1}\), \({M}_{{c}_{05}2}\), \({M}_{{c}_{12}1}\), \({M}_{{c}_{34}1}\), \({M}_{{c}_{35}1}\), \({M}_{{c}_{41}1}\), \({M}_{{c}_{51}1}\), \({M}_{{c}_{52}1}\), \({M}_{{c}_{52}2}\).
For the optimal movement-concurrency detailed above, the optimal allocation of the \({n}_{S}^{*}=15\) support robots to the movements at hand was determined as Eq. (46), where the movements are ordered along the rows and columns as detailed above.
The optimal movement-concurrency and the optimal movement-allocation are shown graphically in Fig. 18, where the nodes with multiple movements represent movements that are planned for concurrent facilitation.
As the final step, the paths of the support robots were planned to allow for collaboration with the worker robots through the tether-based motion control strategy, where the paths of the support robots are planned to form the shortest tethers for connecting the worker robots to the connectivity point at home base. Figure 19 illustrates example tethers formed for the connectivity of the swarm to the home base.
1.5 Robot Trajectory-Planning
As the final step to mission-planning, the trajectories of all (worker and support) robots were planned based on the execution rules detailed in Section 4.5. These rules allow the swarm robots to follow their planned paths, and to synchronize their motion for effective collaboration.
For the optimal division-of-labor and the optimal mission plan of the worker and support robots, the planned trajectories achieved the task completion times shown in Table 2 below. In this example, the optimal mission-completion time, as found through the proposed concurrent methodology, was determined as \({t}_{CC}=142 s\).
In contrast, the application of the sequential methodology resulted in a mission-completion time of \({t}_{CS}=217 s\). This indicates an improvement of 35% for the proposed concurrent solution over the sequential one. As expected through the estimated improvement in Section 5.2.1, this is above the minimum user defined threshold. An animation of the mission execution for the plans found through the proposed concurrent and competing sequential planning methodologies can be found at https://youtu.be/gmM8D8FWOc0.
For an in-depth analysis, let us examine the motion of the sub-coalition of 5 worker robots that leave task \({V}_{5}\) and are allocated to task \({V}_{2}\). This sub-coalition is represented as \({c}_{52}\), and is shown through \({a}_{52}\) of the optimal task-allocation solution, \({{\varvec{A}}}^{*}\), Eq. (43), Fig. 16. The path of this sub-coalition was selected to visit task \({V}_{1}\) when moving from \({V}_{5}\) to \({V}_{2}\), \({p}_{{pc}_{52}}^{*}=\left\{{V}_{5},{V}_{1},{V}_{2}\right\}\), Eq. (44). This path is completed in two movements: \({M}_{{c}_{52}1}\) and \({M}_{{c}_{52}2}\), respectively.
Movement \({M}_{{c}_{52}1}\) was selected to be executed concurrently with the movement of sub-coalition \({c}_{51}\) from \({V}_{5}\) to \({V}_{1}\), \({M}_{{c}_{51}1}\), Eq. (45), Fig. 18. These two movements begin as soon as \({V}_{5}\) is completed at \(t=62 s\), and the associated workers, part of sub-coalitions \({c}_{52}\) and \({c}_{51}\), arrive at \({V}_{1}\) at \(t=95 s\). The movements require five support robots. The path of these support robots as they concurrently facilitate movements \({M}_{{c}_{52}1}\) and \({M}_{{c}_{51}1}\) is shown in Fig. 20(a).
The second movement of sub-coalition \({c}_{52}\), \({M}_{{c}_{52}2}\), is planned to be concurrently executed with the movement of sub-coalition \({c}_{12}\) from \({V}_{1}\) to \({V}_{2}\), \({M}_{{c}_{12}1}\), Eq. (45), Fig. 18. Thus, the worker robots of \({c}_{52}\) must wait until \({V}_{1}\) is completed at \(t=107 s\), before they can begin moving to their next task, \({V}_{2}\). Movements \({M}_{{c}_{52}2}\) and \({M}_{{c}_{12}1}\) begin at \(t=107 s\), and the associated worker robots reach task \({V}_{2}\) at \(t=127 s\). The movements require 10 support robots. The path of these support robots used to concurrently facilitate these two movements is shown in Fig. 20(b).
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Eshaghi, K., Nejat, G. & Benhabib, B. A Concurrent Mission-Planning Methodology for Robotic Swarms Using Collaborative Motion-Control Strategies. J Intell Robot Syst 108, 15 (2023). https://doi.org/10.1007/s10846-023-01881-8
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DOI: https://doi.org/10.1007/s10846-023-01881-8