Skip to main content
Log in

Connectivity Preservation and Obstacle Avoidance in Small Multi-Spacecraft Formation with Distributed Adaptive Tracking Control

  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

This paper proposes an adaptive tracking control scheme for multi-spacecraft formation with inter-collision avoidance, obstacle dodging, and connectivity preservation. The proposed scheme is distributed, i.e., each spacecraft only needs to communicate with its neighbours. Both connectivity preservation and distributed networking are critical features for small spacecraft formation with limited computation and communication capacities. New artificial potential functions are defined to preserve the connectivity of neighbour spacecraft while avoiding their inter-collision as well as collision with obstacles. An adaptive sliding-mode controller is designed for reaching and maintaining the predetermined formation configuration while satisfying the safety assurance requirements, including inter-collision avoidance, obstacle dodging, and connectivity preservation. The stability of the controller is proven through the Lyapunov analysis, in the presence of gravitational, solar radiation pressure, and atmosphere drag perturbations and dynamic uncertainties. The performance of the control scheme is demonstrated through several comparative simulation studies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cao, H., Bai, Y.Q., Liu, H.G.: Distributed rigid formation control algorithm for multi-agent systems. Kybernetes. 41(10), 1650–1661 (2012). https://doi.org/10.1108/03684921211276819

    Article  Google Scholar 

  2. Ferreira-Vazquez, E.D., Hernandez-Martinez, E.G., Flores-Godoy, J.J., Fernandez-Anaya, G., Paniagua-Contro, P.: Distance-based formation control using angular information between robots. J. Intell. Robot. Syst. 83(3–4), 543–560 (2016). https://doi.org/10.1007/s10846-015-0312-1

    Article  Google Scholar 

  3. Kim, H.S., Park, J.K., Kuc, T.Y., Ko, N.Y., Moon, Y.S.: A formation and traction control design for multiple mobile robots. Int. J. Control. Autom. Syst. 15(3), 1287–1301 (2017). https://doi.org/10.1007/s12555-016-0025-7

    Article  Google Scholar 

  4. Xiang, X.B., Jouvencel, B., Parodi, O.: Coordinated formation control of multiple autonomous underwater vehicles for pipeline inspection. Int. J. Adv. Robot. Syst. 7(1), 75–84 (2010)

    Article  Google Scholar 

  5. Millan, P., Orihuela, L., Jurado, I., Rubio, F.R.: Formation control of autonomous underwater vehicles subject to communication delays. IEEE Trans. Control Syst. Technol. 22(2), 770–777 (2014). https://doi.org/10.1109/tcst.2013.2262768

    Article  Google Scholar 

  6. Liu, H., Lyu, Y.F., Lewis, F.L., Wan, Y.: Robust time-varying formation control for multiple underwater vehicles subject to nonlinearities and uncertainties. Int. J. Robust Nonlinear Control. 29(9), 2712–2724 (2019). https://doi.org/10.1002/rnc.4517

    Article  MathSciNet  MATH  Google Scholar 

  7. Liao, F., Teo, R., Wang, J.L., Dong, X.X., Lin, F., Peng, K.M.: Distributed formation and reconfiguration control of VTOL UAVs. IEEE Trans. Control Syst. Technol. 25(1), 270–277 (2017). https://doi.org/10.1109/tcst.2016.2547952

    Article  Google Scholar 

  8. Zhang, J.L., Yan, J.G., Zhang, P.: Fixed-wing UAV formation control design with collision avoidance based on an improved artificial potential field. IEEE. Access. 6, 78342–78351 (2018). https://doi.org/10.1109/access.2018.2885003

    Article  Google Scholar 

  9. Dentler, J., Kannan, S., Bezzaoucha, S., Olivares-Mendez, M.A., Voos, H.: Model predictive cooperative localization control of multiple UAVs using potential function sensor constraints: a workflow to create sensor constraint based potential functions for the control of cooperative localization scenarios with mobile robots. Auton. Robot. 43(1), 153–178 (2019). https://doi.org/10.1007/s10514-018-9711-z

    Article  Google Scholar 

  10. Lee, D., Sanyal, A.K., Butcher, E.A.: Asymptotic tracking control for spacecraft formation flying with decentralized collision avoidance. J. Guid. Control. Dyn. 38(4), 587–600 (2015). https://doi.org/10.2514/1.g000101

    Article  Google Scholar 

  11. Felicetti, L., Emami, M.R.: A multi-spacecraft formation approach to space debris surveillance. Acta. Astronaut. 127, 491–504 (2016). https://doi.org/10.1016/j.actaastro.2016.05.040

    Article  Google Scholar 

  12. Esfahani, N.R., Khorasani, K.: A distributed model predictive control (MPC) fault reconfiguration strategy for formation flying satellites. Int. J. Control. 89(5), 960–983 (2016). https://doi.org/10.1080/00207179.2015.1110753

    Article  MathSciNet  MATH  Google Scholar 

  13. Alfriend, K.T., Vadali, S.R., Gurfil, P., How, J.P., Breger, L.S.: Spacecraft Formation Flying: Dynamics, Control, and Navigation. Elsevier Science Bv, Amsterdam (2010)

  14. Zhao, L., Jia, Y.M.: Neural network-based distributed adaptive attitude synchronization control of spacecraft formation under modified fast terminal sliding mode. Neurocomputing. 171, 230–241 (2016). https://doi.org/10.1016/j.neucom.2015.06.063

    Article  Google Scholar 

  15. Huang, X., Yan, Y., Zhou, Y.: Neural network-based adaptive second order sliding mode control of Lorentz-augmented spacecraft formation. Neurocomputing. 222, 191–203 (2017). https://doi.org/10.1016/j.neucom.2016.10.021

    Article  Google Scholar 

  16. Esper, J., Panetta, P. V., Ryschkewitsch, M., Wiscombe, W., Neeck, S.: NASA-GSFC nanosatellite technology for earth science missions. Acta Astronautica. 46(2–6), 287–296 (2000). https://doi.org/10.1016/S0094-5765(99)00214-3

  17. Liu, G.P., Zhang, S.J.: A survey on formation control of small satellites. Proc. IEEE. 106(3), 440–457 (2018). https://doi.org/10.1109/jproc.2018.2794879

    Article  Google Scholar 

  18. Di Mauro, G., Lawn, M., Bevilacqua, R.: Survey on guidance navigation and control requirements for spacecraft formation-flying missions. J. Guid. Control. Dyn. 41(3), 581–602 (2018). https://doi.org/10.2514/1.g002868

    Article  Google Scholar 

  19. Scharf, D.P., Hadaegh, F.Y., Ploen, S.R., Aac, Aac: A survey of spacecraft formation flying guidance and control (Part I): Guidance. In: Proceedings of the 2003 American Control Conference, Vols 1–6. Proceedings of the American Control Conference, pp. 1733–1739. Ieee, New York (2003)

    Google Scholar 

  20. Scharf, D.P., Hadaegh, F.Y., Ploen, S.R., Acc: A survey of spacecraft formation flying guidance and control (Part II): Control. In: Proceedings of the 2004 American Control Conference, Vols 1–6. Proceedings of the American Control Conference, pp. 2976–2985. Ieee, New York (2004)

    Google Scholar 

  21. Krejci, D., Lozano, P.: Space propulsion technology for small spacecraft. Proc. IEEE. 106(3), 362–378 (2018)

    Article  Google Scholar 

  22. Seubert, C., Pernicka, H., Norgren, C.: Refrigerant-based propulsion system for small spacecraft. Proceedings of the 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Cincinnati, OH. 1–10 (2007). https://doi.org/10.2514/6.2007-5131

  23. Rossi, M., Lovera, M.: A predictive approach to formation keeping for constellations of small spacecraft in elliptic orbits. Proceedings of the 5th ESA International Conference on Spacecraft Guidance, Navigation and Control Systems, Frascati, Rome. 209–216 (2003)

  24. McCamish, S., Romano, M., Yun, X.: Autonomous Distributed LQR/APF Control Algorithm for Multiple Small Spacecraft during Simultaneous Close Proximity Operations. Proceedings of the 21st Annual AIAA/USU Conference on Small Satellites [CD-ROM], AIAA, Reston (2007)

  25. Chung, S.J., Bandyopadhyay, S., Foust, R., Subramanian, G.P., Hadaegh, F.Y.: Review of formation flying and constellation missions using Nanosatellites. J. Spacecr. Rocket. 53(3), 567–578 (2016). https://doi.org/10.2514/1.a33291

    Article  Google Scholar 

  26. Yan, Z., Jouandeau, N., Cherif, A.A.: A survey and analysis of multi-robot coordination. Int. J. Adv. Robot. Syst. 10, 18 (2013). https://doi.org/10.5772/57313

    Article  Google Scholar 

  27. Hu, Q.L., Dong, H.Y., Zhang, Y.M., Ma, G.F.: Tracking control of spacecraft formation flying with collision avoidance. Aerosp. Sci. Technol. 42, 353–364 (2015). https://doi.org/10.1016/j.ast.2014.12.031

    Article  Google Scholar 

  28. Sabattini, L., Secchi, C., Fantuzzi, C.: Arbitrarily shaped formations of mobile robots: artificial potential fields and coordinate transformation. Auton. Robot. 30(4), 385–397 (2011). https://doi.org/10.1007/s10514-011-9225-4

    Article  Google Scholar 

  29. 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

    Article  Google Scholar 

  30. Yu, J.L., Dong, X.W., Li, Q.D., Ren, Z.: Practical time-varying output formation tracking for high-order multi-agent systems with collision avoidance, obstacle dodging and connectivity maintenance. J. Frankl. Inst.-Eng. Appl. Math. 356(12), 5898–5926 (2019). https://doi.org/10.1016/j.jfranklin.2019.05.014

    Article  MathSciNet  MATH  Google Scholar 

  31. Wahl, T., HoweIl, K.C.: Autonomous guidance algorithm for multiple spacecraft and formation reconfiguration maneuvers. In: Zanetti, R., Russell, R.P., Ozimek, M.T., Bowes, A.L. (eds.) Spaceflight Mechanics 2016, Pts I-Iv, Vol. 158. Advances in the Astronautical Sciences, pp. 1939–1956. Univelt Inc, San Diego (2016)

    Google Scholar 

  32. Wang, Z.K., Xu, Y., Jiang, C., Zhang, Y.L.: Self-organizing control for satellite clusters using artificial potential function in terms of relative orbital elements. Aerosp. Sci. Technol. 84, 799–811 (2019). https://doi.org/10.1016/j.ast.2018.11.033

    Article  Google Scholar 

  33. Renevey, S., Spencer, D.A.: Establishment and control of spacecraft formations using artificial potential functions. Acta. Astronaut. 162, 314–326 (2019). https://doi.org/10.1016/j.actaastro.2019.06.024

    Article  Google Scholar 

  34. Ronchieri, E., Innocenti, M., Pollini, L.: Decentralized control of a swarm of unmanned air vehicles. Proceedings of the AIAA Guidance, Navigation, and Control Conference, pp. 1–11. Hilton Head (2007). https://doi.org/10.2514/6.2007-6457

  35. Kowalczyk, W., Kozlowski, K.: Artificial Potential Based Control for a Large Scale Formation of Mobile Robots. Climbing and Walking Robots. Springer, New York (2005)

    Google Scholar 

  36. Ge, S.S., Liu, X.M., Goh, C.H., Xu, L.G.: Formation tracking control of multiagents in constrained space. IEEE Trans. Control Syst. Technol. 24(3), 992–1003 (2016). https://doi.org/10.1109/tcst.2015.2472959

    Article  Google Scholar 

  37. Mondal, A., Bhowmick, C., Behera, L., Jamshidi, M.: Trajectory tracking by multiple agents in formation with collision avoidance and connectivity assurance. IEEE Syst. J. 12(3), 2449–2460 (2018). https://doi.org/10.1109/jsyst.2017.2778063

    Article  Google Scholar 

  38. Gazi, V.: Swarm aggregations using artificial potentials and sliding-mode control. IEEE Trans. Robot. 21(6), 1208–1214 (2005). https://doi.org/10.1109/tro.2005.853487

    Article  Google Scholar 

  39. Wang, M., Su, H., Zhao, M., Chen, M.Z., Wang, H.: Flocking of multiple autonomous agents with preserved network connectivity and heterogeneous nonlinear dynamics. Neurocomputing. 115, 169–177 (2013)

    Article  Google Scholar 

  40. Li, P., Xu, S., Chen, W., Wei, Y., Zhang, Z.: Adaptive finite-time flocking for uncertain nonlinear multi-agent systems with connectivity preservation. Neurocomputing. 275, 1903–1910 (2018)

    Article  Google Scholar 

  41. Nishida, S.-I., Kawamoto, S., Okawa, Y., Terui, F., Kitamura, S.: Space debris removal system using a small satellite. Acta. Astronaut. 65(1–2), 95–102 (2009)

    Article  Google Scholar 

  42. Bevilacqua, R., Lehmann, T., Romano, M.: Development and experimentation of LQR/APF guidance and control for autonomous proximity maneuvers of multiple spacecraft. Acta. Astronaut. 68(7), 1260–1275 (2011). https://doi.org/10.1016/j.actaastro.2010.08.012

    Article  Google Scholar 

  43. Cao, L., Qiao, D., Xu, J.W.: Suboptimal artificial potential function sliding mode control for spacecraft rendezvous with obstacle avoidance. Acta. Astronaut. 143, 133–146 (2018). https://doi.org/10.1016/j.actaastro.2017.11.022

    Article  Google Scholar 

  44. Chen, L.M., Sun, Z.Q., Li, C.J., Zhu, B.L., Wang, C.: Satellite affine formation flying with obstacle avoidance. Proc. Inst. Mech. Eng. Part G-J. Aerosp. Eng. 233(16), 5992–6004 (2019). https://doi.org/10.1177/0954410019861474

    Article  Google Scholar 

  45. Su, Y.F.: Leader-following rendezvous with connectivity preservation and disturbance rejection via internal model approach. Automatica. 57, 203–212 (2015). https://doi.org/10.1016/j.automatica.2015.04.015

    Article  MathSciNet  MATH  Google Scholar 

  46. Li, P., Zhang, B.Y., Ma, Q., Xu, S.Y., Chen, W.M., Zhang, Z.Q.: Flocking with connectivity preservation for disturbed nonlinear multi-agent systems by output feedback. Int. J. Control. 91(5), 1066–1075 (2018). https://doi.org/10.1080/00207179.2017.1305511

    Article  MathSciNet  MATH  Google Scholar 

  47. Dong, Y., Huang, J.: Flocking with connectivity preservation of multiple double integrator systems subject to external disturbances by a distributed control law. Automatica. 55, 197–203 (2015). https://doi.org/10.1016/j.automatica.2015.03.006

    Article  MathSciNet  MATH  Google Scholar 

  48. Poonawala, H.A., Satici, A.C., Eckert, H., Spong, M.W.: Collision-free formation control with decentralized connectivity preservation for Nonholonomic-wheeled Mobile robots. IEEE Trans. Control Netw. Syst. 2(2), 122–130 (2015). https://doi.org/10.1109/tcns.2014.2378876

    Article  MathSciNet  MATH  Google Scholar 

  49. Ji, M., Egerstedt, M.: Distributed coordination control of multiagent systems while preserving connectedness. IEEE Trans. Robot. 23(4), 693–703 (2007). https://doi.org/10.1109/tro.2007.900638

    Article  Google Scholar 

  50. Guo, Y.H., Zhou, J., Liu, Y.Y.: Distributed RISE control for spacecraft formation reconfiguration with collision avoidance. J. Frankl. Inst.-Eng. Appl. Math. 356(10), 5332–5352 (2019). https://doi.org/10.1016/j.jfranklin.2019.05.003

    Article  MathSciNet  MATH  Google Scholar 

  51. Nair, R.R., Behera, L., Kumar, V., Jamshidi, M.: Multisatellite formation control for remote sensing applications using artificial potential field and adaptive fuzzy sliding mode control. IEEE Syst. J. 9(2), 508–518 (2015). https://doi.org/10.1109/jsyst.2014.2335442

    Article  Google Scholar 

  52. Zhang, J.Q., Ye, D., Biggs, J.D., Sun, Z.W.: Finite-time relative orbit-attitude tracking control for multi-spacecraft with collision avoidance and changing network topologies. Adv. Space Res. 63(3), 1161–1175 (2019). https://doi.org/10.1016/j.asr.2018.10.037

    Article  Google Scholar 

  53. Lee, D., Kumar, K.D., Sinha, M.: Fault detection and recovery of spacecraft formation flying using nonlinear observer and reconfigurable controller. Acta. Astronaut. 97, 58–72 (2014). https://doi.org/10.1016/j.actaastro.2013.12.002

    Article  Google Scholar 

  54. Vaddi, S.S., Vadali, S.R., Alfriend, K.T.: Formation flying: accommodating nonlinearity and eccentricity perturbations. J. Guid. Control. Dyn. 26(2), 214–223 (2003). https://doi.org/10.2514/2.5054

    Article  Google Scholar 

  55. Schlanbusch, R., Kristiansen, R., Nicklasson, P.J.: Spacecraft formation reconfiguration with collision avoidance. Automatica. 47(7), 1443–1449 (2011)

    Article  MathSciNet  Google Scholar 

  56. Shi, Q., Li, T.S., Li, J.Q., Chen, C.L.P., Xiao, Y., Shan, Q.H.: Adaptive leader-following formation control with collision avoidance for a class of second-order nonlinear multi-agent systems. Neurocomputing. 350, 282–290 (2019). https://doi.org/10.1016/j.neucom.2019.03.045

    Article  Google Scholar 

  57. Hernández-Martínez, E.G., Aranda-Bricaire, E.: Convergence and collision avoidance in formation control: a survey of the artificial potential functions approach. InTech, London. (2011). https://doi.org/10.5772/14142

  58. Panagou, D.: A distributed feedback motion planning protocol for multiple unicycle agents of different classes. IEEE Trans. Autom. Control. 62(3), 1178–1193 (2017). https://doi.org/10.1109/tac.2016.2576020

    Article  MathSciNet  MATH  Google Scholar 

  59. Subramanian, G. P., Foust, R., Chan, S., Taleb, Y., Rogers, D., Kokkatk, J., Bandyopadhyay, S., Morgan, D., Chung, S.-J., Hadaegh, F. Y.: Information-driven systems engineering study of a formation flying demonstration mission using four cubesats. Proceedings of the 53rd AIAA Aerospace Sciences Meeting, AIAA, 2015–2043 (2015). https://doi.org/10.2514/6.2015-2043

  60. Rocketdyne, A.: https://www.rocket.com/sites/default/files/documents/In-Space%20Data%20Sheets%204.8.20.pdf. (2020). Accessed 0408 2020

  61. Godard, Kumar, K.D.: Fault Tolerant Reconfigurable Satellite Formations Using Adaptive Variable Structure Techniques. J. Guid. Control Dyn. 33(3), 969–984 (2010). https://doi.org/10.2514/1.38580

    Article  Google Scholar 

  62. Sun, K., Liu, L., Qiu, J. B., Feng, G.: Fuzzy adaptive finite-time fault-tolerant control for strict-feedback nonlinear systems. IEEE Trans. Fuzzy Syst. 1–11 (2020). https://doi.org/10.1109/TFUZZ.2020.2965890

  63. Sun, K., Jianbin, Q., Karimi, H.R., Fu, Y.: Event-triggered robust fuzzy adaptive finite-time control of nonlinear systems with prescribed performance. IEEE Trans. Fuzzy Syst. 1–12 (2020). https://doi.org/10.1109/TFUZZ.2020.2979129

  64. Sun, K., Qiu, J., Karimi, H.R., Gao, H.: A novel finite-time control for nonstrict feedback saturated nonlinear systems with tracking error constraint. IEEE Trans. Sys. Man Cybern. Sys. 1–12 (2019). https://doi.org/10.1109/TSMC.2019.2958072

Download references

Acknowledgements

The authors acknowledge the financial support of the China Scholarship Council [grant # 201906020129] as well as the provisions by the University of Toronto.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Reza Emami.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, Z., Emami, M.R. & Chen, W. Connectivity Preservation and Obstacle Avoidance in Small Multi-Spacecraft Formation with Distributed Adaptive Tracking Control. J Intell Robot Syst 101, 16 (2021). https://doi.org/10.1007/s10846-020-01269-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10846-020-01269-y

Keywords

Navigation