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Cooperative Path Following with Collision Avoidance Guarantees Using Control Lyapunov and Barrier Functions

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CONTROLO 2022 (CONTROLO 2022)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 930))

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Abstract

In this paper, we address the problem of safety-critical, cooperative path following (CPF) control for a swarm of heterogeneous robotic vehicles following possibly intersecting paths. Control Lyapunov Functions (CLFs) and Control Barrier Functions (CBFs) are utilized on a Quadratic Program (QP) based controller to achieve the desired task, while also giving explicit collision avoidance guarantees. We propose a modified CLF-CBF based QP controller to overcome deadlock-like configurations by assigning specific priorities for each of the agents. Numerical simulation results for three agents shows the efficacy of the proposed methodology.

This work was financially supported by Fundação para a Ciência e Tecnologia (FCT), Portugal, Ph.D. Grant 2020.06795.BD, SYSTEC RD Unit Base Funding - UIDB/EEA/00147-2020 and Programmatic Funding - UIDB/EEA/00147-2020, ARISE Associated Lab - Advanced Production and Intelligent Systems - LA/P/0112/2020, Projects RELIABLE (PTDC/EEI-AUT/3522/2020), funded by national funds through FCT/MCTES and DynamiCITY (NORTE-01-0145-FEDER-000073), funded by CCDRN through P2020/N2020.

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Notes

  1. 1.

    An extended class \(\mathscr {K}_{\infty }\) function \(\beta _2: \mathbb {R} \rightarrow \mathbb {R}\) is strictly increasing with \(\beta _2(0) \!=\! 0\).

References

  1. Anderson, E.P., Beard, R.W., McLain, T.W.: Real-time dynamic trajectory smoothing for unmanned air vehicles. IEEE Trans. Control Syst. Technol. 13(3), 471–477 (2005)

    Article  Google Scholar 

  2. Prodan, I., et al.: Receding horizon flight control for trajectory tracking of autonomous aerial vehicles. Control Eng. Pract. 21(10), 1334–1349 (2013)

    Article  Google Scholar 

  3. Ren, W., Beard, R.W.: Trajectory tracking for unmanned air vehicles with velocity and heading rate constraints. IEEE Trans. Control Syst. Technol. 12(5), 706–716 (2004)

    Article  Google Scholar 

  4. Flores, G., Lugo-Cárdenas, I., Lozano, R.: A nonlinear path-following strategy for a fixed-wing Mav. In: 2013 International Conference on Unmanned Aircraft Systems (ICUAS), pp. 1014–1021. IEEE (2013)

    Google Scholar 

  5. Nelson, D.R., Blake Barber, D., McLain, T.W., Beard, R.W.: Vector field path following for miniature air vehicles. IEEE Trans. Robot. 23(3), 519–529 (2007)

    Article  Google Scholar 

  6. Sujit, P.B., Saripalli, S., Borges Sousa, J.: Unmanned aerial vehicle path following: a survey and analysis of algorithms for fixed-wing unmanned aerial vehicless. IEEE Control Syst. Mag. 34(1), 42–59 (2014)

    Article  MathSciNet  Google Scholar 

  7. Pedro Aguiar, A., Hespanha, J.P.: Trajectory-tracking and path-following of underactuated autonomous vehicles with parametric modeling uncertainty. IEEE Trans. Autom. Control. 52(8), 1362–1379 (2007)

    Article  MathSciNet  Google Scholar 

  8. Galloway, K., Sreenath, K., Ames, A.D., Grizzle, J.W.: Torque saturation in bipedal robotic walking through control Lyapunov function-based quadratic programs. IEEE Access 3, 323–332 (2015)

    Article  Google Scholar 

  9. Sontag, E.D.: A ‘universal’ construction of Artstein’s theorem on nonlinear stabilization. Syst. Control Lett. 13(2), 117–123 (1989)

    Article  MathSciNet  Google Scholar 

  10. Ames, A.D., Xu, X., Grizzle, J.W., Tabuada, P.: Control barrier function based quadratic programs for safety critical systems. IEEE Trans. Autom. Control. 62(8), 3861–3876 (2016)

    Article  MathSciNet  Google Scholar 

  11. Muhammad Zakiyullah Romdlony and Bayu Jayawardhana: Stabilization with guaranteed safety using control Lyapunov-barrier function. Automatica 66, 39–47 (2016)

    Article  MathSciNet  Google Scholar 

  12. Srinivasan, M., Coogan, S., Egerstedt, M.: Control of multi-agent systems with finite time control barrier certificates and temporal logic. In: 2018 IEEE Conference on Decision and Control (CDC), pp. 1991–1996. IEEE (2018)

    Google Scholar 

  13. Borrmann, U., Wang, L., Ames, A.D., Egerstedt, M.: Control barrier certificates for safe swarm behavior. IFAC-PapersOnLine. 48(27), 68–73 (2015)

    Article  Google Scholar 

  14. Khalil, H.K.: Nonlinear Systems. 3rd edn. Prentice-Hall, Upper Saddle River (2002)

    Google Scholar 

  15. Ames, A.D., et al.: Control barrier functions: theory and applications. In: 2019 18th European Control Conference (ECC), pp. 3420–3431. IEEE (2019)

    Google Scholar 

  16. 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. IEEE (2014)

    Google Scholar 

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Authors and Affiliations

  1. Research Center for Systems and Technologies, Department of Electrical and Computer Engineering, Faculty of Engineering, University of Porto, 4200-465, Porto, Portugal

    Matheus F. Reis, Pallov Anand & A. Pedro Aguiar

Authors
  1. Matheus F. Reis
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  2. Pallov Anand
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  3. A. Pedro Aguiar
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Corresponding author

Correspondence to Matheus F. Reis .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering Department, NOVA School of Science and Technology, NOVA University Lisbon, Caparica, Portugal

    Luís Brito Palma

  2. Electrical and Computer Engineering Department, NOVA School of Science and Technology, NOVA University Lisbon, Caparica, Portugal

    Rui Neves-Silva

  3. Electrical and Computer Engineering Department, NOVA School of Science and Technology, NOVA University Lisbon, Caparica, Portugal

    Luís Gomes

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Reis, M.F., Anand, P., Aguiar, A.P. (2022). Cooperative Path Following with Collision Avoidance Guarantees Using Control Lyapunov and Barrier Functions. In: Brito Palma, L., Neves-Silva, R., Gomes, L. (eds) CONTROLO 2022. CONTROLO 2022. Lecture Notes in Electrical Engineering, vol 930. Springer, Cham. https://doi.org/10.1007/978-3-031-10047-5_16

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