Abstract
This work aims to enable distributed robot systems to follow time-varying paths safely. Artificial Vector Fields offer a viable alternative for addressing path-following challenges, yet collision avoidance among agents guided by such fields remains an open problem. To address this, we have designed a Model Predictive Control (MPC) setup that integrates an Artificial Vector Field reference with prominent collision avoidance methods, such as Optimal Reciprocal Collision Avoidance (ORCA) and Control Barrier Functions (CBF), to produce real-time, safe solutions. Our work involves a direct comparison between different MPC-based collision avoidance methods, and we have obtained results from various simulation scenarios as well as experiments on real robotic systems (Crazyflie 2.1). We aim to assess the applicability and limitations of these techniques through extracted metrics and insights.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
Data availability
Experimental data can be made available upon acceptance and publication.
Code Availability
Algorithms can be made available upon acceptance and publication.
Materials Availability
Not applicable.
References
Chung, S.-J., Paranjape, A.A., Dames, P., Shen, S., Kumar, V.: A survey on aerial swarm robotics. IEEE Trans. Rob. 34(4), 837–855 (2018). https://doi.org/10.1109/TRO.2018.2857475
Rezende, A.M.C., Gonçalves, V.M., Nunes, A.H.D., Pimenta, L.C.A.: Robust quadcopter control with artificial vector fields. In: 2020 IEEE International Conference on Robotics and Automation (ICRA), pp. 6381–6387 (2020). https://doi.org/10.1109/ICRA40945.2020.9196605 . IEEE
Rezende, A.M.C., Goncalves, V.M., Pimenta, L.C.A.: Constructive time-varying vector fields for robot navigation. IEEE Trans. Robot. 38(2), 852–867 (2021). https://doi.org/10.1109/TRO.2021.3093674
Miranda, V.R., Rezende, A., Rocha, T.L., Azpúrua, H., Pimenta, L.C., Freitas, G.M.: Autonomous navigation system for a delivery drone. J. Control Autom. Electr. Syst. 33(1), 141–155 (2022). https://doi.org/10.1007/s40313-021-00828-4
Rezende, A.M., Miranda, V.R., Machado, H.N., Chiella, A.C., Gonçalves, V.M., Freitas, G.M.: Autonomous system for a racing quadcopter. In: 2019 19th International Conference on Advanced Robotics (ICAR), pp. 1–6 (2019). https://doi.org/10.1109/ICAR46387.2019.8981660. IEEE
Santos, M.A., Ferramosca, A., Raffo, G.V.: Set-point tracking mpc with avoidance features. Autom. 159, 111390 (2024) https://doi.org/10.1016/j.automatica.2023.111390
Santos, M.A., Ferramosca, A., Raffo, G.V.: Nonlinear model predictive control schemes for obstacle avoidance. J. Control Autom. Electr. Syst. 34(5), 891–906 (2023). https://doi.org/10.1007/s40313-023-01024-2
Pereira, J.C., Leite, V.J., Raffo, G.V.: Nonlinear model predictive control on se (3) for quadrotor aggressive maneuvers. J. Intell. Robot. Syst. 101, 1–15 (2021) https://doi.org/10.1007/s10846-021-01310-8
Sánchez, I., D’Jorge, A., Raffo, G.V., González, A.H., Ferramosca, A.: Nonlinear model predictive path following controller with obstacle avoidance. J. Intell. Robot. Syst. 102, 1–18 (2021) https://doi.org/10.1007/s10846-021-01373-7
Huang, S., Teo, R.S.H., Tan, K.K.: Collision avoidance of multi unmanned aerial vehicles: A review. Ann. Rev. Control 48, 147–164 (2019). https://doi.org/10.1016/j.arcontrol.2019.10.001
Nikolos, I.K., Valavanis, K.P., Tsourveloudis, N.C., Kostaras, A.N.: Evolutionary algorithm based offline/online path planner for uav navigation. IEEE Trans. Syst. Man Cybern. B Cybern. 33(6), 898–912 (2003). https://doi.org/10.1109/TSMCB.2002.804370
Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. Int. J. Robot. Res. 5(1), 90–98 (1986). https://doi.org/10.1177/027836498600500106
Chakravarthy, A., Ghose, D.: Obstacle avoidance in a dynamic environment: A collision cone approach. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 28(5), 562–574 (1998). https://doi.org/10.1109/3468.709600
Fiorini, P., Shiller, Z.: Motion planning in dynamic environments using the relative velocity paradigm. Proc. IEEE Int. Conf. Robot. Autom. 560–565 (1993). https://doi.org/10.1109/robot.1993.292038
Berg, J., Ming Lin, Manocha, D.: Reciprocal velocity obstacles for real-time multi-agent navigation. 2008 IEEE Int. Conf. Robot. Autom. 23, 1928–1935 (2008). https://doi.org/10.1109/ROBOT.2008.4543489
Berg, J., Guy, S.J., Lin, M., Manocha, D.: Reciprocal n-body collision avoidance. In: Pradalier, C., Siegwart, R., Hirzinger, G. (eds.) Robotics Research, pp. 3–19. Springer, Berlin, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19457-3_1
Alejo, D., Cobano, J.A., Heredia, G., Ollero, A.: Optimal reciprocal collision avoidance with mobile and static obstacles for multi-uav systems. In: 2014 International Conference on Unmanned Aircraft Systems (ICUAS), pp. 1259–1266 (2014). https://doi.org/10.1109/ICUAS.2014.6842383
Conroy, P., Bareiss, D., Beall, M., Berg, J.: 3-D Reciprocal Collision Avoidance on Physical Quadrotor Helicopters with On-Board Sensing for Relative Positioning (2014)
Wang, L., Ames, A.D., Egerstedt, M.: Safety barrier certificates for collisions-free multirobot systems. IEEE Trans. Rob. 33(3), 661–674 (2017). https://doi.org/10.1109/TRO.2017.2659727
Vangasse, A.D.C., Raffo, G.V., Pimenta, L.C.A.: Mpc-cbf strategy for multi-robot collision-free path-following. In: 2023 Latin American Robotics Symposium (LARS), 2023 Brazilian Symposium on Robotics (SBR), and 2023 Workshop on Robotics in Education (WRE), pp. 284–289 (2023). https://doi.org/10.1109/LARS/SBR/WRE59448.2023.10332984
Freitas, E.J.R., Vangasse, A.D.C., Raffo, G.V., Pimenta, L.C.A.: Decentralized multi-robot collision-free path following based on time-varying artificial vector fields and mpc-orca. In: 2023 Latin American Robotics Symposium (LARS), 2023 Brazilian Symposium on Robotics (SBR), and 2023 Workshop on Robotics in Education (WRE), pp. 212–217 (2023). https://doi.org/10.1109/LARS/SBR/WRE59448.2023.10333004
Nunes, A.H.D., Rezende, A.M.C., Cruz, G.P., Freitas, G.M., Gonçalves, V.M., Pimenta, L.C.A.: Vector field for curve tracking with obstacle avoidance. In: 2022 IEEE 61st Conference on Decision and Control (CDC), pp. 2031–2038 (2022). https://doi.org/10.1109/CDC51059.2022.9992435
Nunes, A.H.D., Raffo, G.V., Pimenta, L.C.A.: Integrated vector field and backstepping control for quadcopters. In: 2023 IEEE International Conference on Robotics and Automation (ICRA), pp. 1256–1262 (2023). https://doi.org/10.1109/ICRA48891.2023.10160824
Cheng, H., Zhu, Q., Liu, Z., Xu, T., Lin, L.: Decentralized navigation of multiple agents based on orca and model predictive control. In: 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 3446–3451 (2017). https://doi.org/10.1109/IROS.2017.8206184
Borrmann, U., Wang, L., Ames, A.D., Egerstedt, M.: Control barrier certificates for safe swarm behavior. IFAC-PapersOnLine. 48(27), 68–73 (2015). https://doi.org/10.1016/j.ifacol.2015.11.154. Analysis and Design of Hybrid Systems ADHS
Lawrence, D., Frew, W., Pisano, W.: Lyapunov vector fields for autonomous uav flight control 1. (2007). https://doi.org/10.2514/6.2007-6317
Frew, E.W., Lawrence, D., Morris, S.: Coordinated standoff tracking of moving targets using lyapunov guidance vector fields. J. Guid. Control. Dyn. 31(2), 290–306 (2008). https://doi.org/10.2514/1.30507
Gonçalves, V.M., Pimenta, L.C., Maia, C.A., Dutra, B.C., Pereira, G.A.: Vector fields for robot navigation along time-varying curves in \( n \)-dimensions. IEEE Trans. Rob. 26(4), 647–659 (2010)
Wu, C., Chen, J., Jeltsema, D., Dai, C.: Guidance vector field encoding based on contraction analysis, 282–287 (2018). https://doi.org/10.23919/ECC.2018.8550301
Yao, W., Marina, H.G., Lin, B., Cao, M.: Singularity-free guiding vector field for robot navigation. IEEE Trans. Rob. 37(4), 1206–1221 (2021)
Watanabe, Y., Calise, A., Johnson, E., Evers, J.: Minimum-effort guidance for vision-based collision avoidance. In: AIAA Atmospheric Flight Mechanics Conference and Exhibit, p. 6641 (2006)
Mujumdar, A., Padhi, R.: Reactive collision avoidance of using nonlinear geometric and differential geometric guidance. J. Guid. Control. Dyn. 34(1), 303–311 (2011)
Ames, A.D., Coogan, S., Egerstedt, M., Notomista, G., Sreenath, K., Tabuada, P.: Control barrier functions: Theory Appl. 3420–3431 (2019). https://doi.org/10.23919/ECC.2019.8796030
Nagumo, M.: über die lage der integralkurven gewöhnlicher differentialgleichungen. (1942). https://api.semanticscholar.org/CorpusID:118866209
Prajna, S., Jadbabaie, A.: Safety verification of hybrid systems using barrier certificates. In: International Workshop on Hybrid Systems: Comput. Control pp. 477–492 (2004). Springer
Prajna, S.: Barrier certificates for nonlinear model validation. Autom. 42(1), 117–126 (2006)
Tee, K.P., Ge, S.S., Tay, E.H.: Barrier lyapunov functions for the control of output-constrained nonlinear systems. Autom. 45(4), 918–927 (2009)
Wieland, P., Allgöwer, F.: Constructive safety using control barrier functions. IFAC Proc. Vol. 40(12), 462–467 (2007)
Romdlony, M.Z., Jayawardhana, B.: Uniting control lyapunov and control barrier functions. In: 53rd IEEE Conference on Decision and Control, pp. 2293–2298 (2014). IEEE
Nascimento, T.P., Dórea, C.E.T., Gonçalves, L.M.G.: Nonholonomic mobile robots’ trajectory tracking model predictive control: a survey. Robot. 36(5), 676–696 (2018). https://doi.org/10.1017/S0263574717000637
Zhou, H., Liu, C.: Distributed motion coordination using convex feasible set based model predictive control. arXiv. (2021). https://doi.org/10.48550/ARXIV.2101.07994
Soria, E., Schiano, F., Floreano, D.: Distributed predictive drone swarms in cluttered environments. IEEE Robot. Autom. Lett. 7(1), 73–80 (2022). https://doi.org/10.1109/LRA.2021.3118091
Pacheco, G.V., Pimenta, L.C.A., Raffo, G.V.: Distributed parameterized predictive control for multi-robot curve tracking. IFAC-PapersOnLine. 53(2), 3144–3149 (2020). https://doi.org/10.1016/j.ifacol.2020.12.1054
Pereira, L.A.A., Nunes, A.H.D., Rezende, A.M.C., Gonçalves, V.M., Raffo, G.V., Pimenta, L.C.A.: Collision-free vector field guidance and mpc for a fixed-wing uav. In: 2021 IEEE International Conference on Robotics and Automation (ICRA), pp. 176–182 (2021). https://doi.org/10.1109/ICRA48506.2021.9560850
Leite, G.R., C. Vangasse, A., B. Q. Araujo, Savino, H.J.: Collision avoidance with differential drive robots using mpc-orca. Vol. 1 No 1 (2021): SBAI 2021. (2021). https://doi.org/10.20906/sbai.v1i1.2774
Arul, S.H., Manocha, D.: Dcad: Decentralized collision avoidance with dynamics constraints for agile quadrotor swarms. IEEE Robot. Autom. Lett. 5(2), 1191–1198 (2020). https://doi.org/10.1109/LRA.2020.2967281
Mao, R., Gao, H., Guo, L.: A novel collision-free navigation approach for multiple nonholonomic robots based on orca and linear mpc. Mathematical Problems in Engineering. 2020, 1–16 (2020). https://doi.org/10.1155/2020/4183427
Ames, A.D., Grizzle, J.W., Tabuada, P.: Control barrier function based quadratic programs with application to adaptive cruise control. In: 53rd IEEE Conference on Decision and Control, pp. 6271–6278 (2014). https://doi.org/10.1109/CDC.2014.7040372
Preiss\(*\), J.A., Hönig\(*\), W., Sukhatme, G.S., Ayanian, N.: Crazyswarm: A large nano-quadcopter swarm. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 3299–3304. IEEE, (2017). https://doi.org/10.1109/ICRA.2017.7989376. Software available at https://github.com/USC-ACTLab/crazyswarm
Quigley, M., Conley, K., Gerkey, B., Faust, J., Foote, T., Leibs, J., Wheeler, R., Ng, A.Y., et al.: Ros: an open-source robot operating system. In: ICRA Workshop on Open Source Software, vol. 3, p. 5 (2009). Kobe, Japan
Andersson, J.A., Gillis, J., Horn, G., Rawlings, J.B., Diehl, M.: Casadi: a software framework for nonlinear optimization and optimal control. Math. Program. Comput. 11, 1–36 (2019)
Bemporad, A., Morari, M., Dua, V., Pistikopoulos, E.N.: The explicit linear quadratic regulator for constrained systems. Automatica 38(1), 3–20 (2002). https://doi.org/10.1016/S0005-1098(01)00174-1
Tang, W., Daoutidis, P.: Distributed nonlinear model predictive control through accelerated parallel admm. 2019 Am. Control Conf. (ACC), 1406–1411 (2019). https://doi.org/10.23919/ACC.2019.8814732
Acknowledgements
This study was financed in part by the Coordination for the Improvement of Higher Education Personnel - Brazil (CAPES) through the Academic Excellence Program (PROEX) and by the Instituto Federal de Educação, Ciência e Tecnologia de Minas Gerais - Campus Ibirité. This work was also supported in part by the project INCT (National Institute of Science and Technology) under the grant CNPq (Brazilian National Research Council) 465755/2014-3 and FAPESP (São Paulo Research Foundation) 2014/50851-0, CNPq (grant numbers 407063/2021-8, 309925/2023-1, 317058/2023-1, and 422143/2023-5), and Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG), under grant number APQ-0063023.
Funding
Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG); Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); Coordenação de Aperfeiçoamento de Pessoal de NÍvel Superior (CAPES); Conselho Nacional de Desenvolvimento CientÍıfico e Tecnológico (CNPq).
Author information
Authors and Affiliations
Contributions
General work conduction: Arthur Vangasse and Luciano Pimenta; Conceptualization: Arthur Vangasse, Elias Freitas, Guilherme Raffo and Luciano Pimenta; Code Implementation: Arthur Vangasse and Elias Freitas; Simulation Methodology: Arthur Vangasse; Experimental Methodology: Arthur Vangasse; Conceived Images and Graphics: Arthur Vangasse and Elias Freitas; Work supervision: Luciano Pimenta and Guilherme Raffo; All authors wrote and reviewed the manuscript.
Corresponding author
Ethics declarations
Conflicts of Interest / Competing Interests
The authors declare no conflicts of interest or competing interests.
Ethical Approval
Not applicable
Consent to Participate
Not applicable
Consent for Publication
Not applicable
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
About this article
Cite this article
da C. Vangasse, A., J. R. Freitas, E., V. Raffo, G. et al. Safe Navigation on Path-Following Tasks: A Study of MPC-based Collision Avoidance Schemes in Distributed Robot Systems. J Intell Robot Syst 110, 166 (2024). https://doi.org/10.1007/s10846-024-02202-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10846-024-02202-3