Spacecraft formation reconfiguration with multi-obstacle avoidance under navigation and control uncertainties using adaptive artificial potential function method

  • Yi Wang
  • Xiaoqian Chen
  • Dechao Ran
  • Yong Zhao
  • Yang Chen
  • Yuzhu BaiEmail author


In this paper, an adaptive artificial potential function (AAPF) method is developed for spacecraft formation reconfiguration with multi-obstacle avoidance under navigation and control uncertainties. Furthermore, an improved Linear Quadratic Regular (ILQR) is proposed to track the reference trajectory and a Lyapunov-based method is employed to demonstrate the stability of the overall closed-loop system. Compared with the traditional APF method and the equal-collision-probability surface (ECPS) method, the AAPF method not only retains the advantages of APF method and ECPS method, such as low computational complexity, simple analytical control law and easy analytical validation progress, but also proposes a new APF to solve multi-obstacle avoidance problem considering the influence of the uncertainties. Moreover, the ILQR controller obtains high control accuracy to enhance the safe performance of the spacecraft formation reconfiguration. Finally, the effectiveness of the proposed AAPF method and the ILQR controller are verified by numerical simulations.


spacecraft formation flying spacecraft formation reconfiguration collision avoidance artificial potential function uncertainties 



The work was supported by the Major Program of National Nature Science Foundation of China (Grant Nos. 61690210 and 61690213, the National Science Foundation of China (Grant Nos. 11725211, 61503414, 11302253, and 11702320), and the Scientific Research Project of National University of Defense Technology (ZK16-03-20).


  1. [1]
    Wang, J. H., Zhang, J. X., Cao, X. B., Wang, F. Optimal satellite formation reconfiguration strategy based on relative orbital elements. Acta Astronautica, 2012, 76: 114–114.Google Scholar
  2. [2]
    Cao, L., Chen, X. Q., Misra, A. K. Minimum sliding mode error feedback control for fault tolerant reconfigurable satellite formations with J2 perturbations. Acta Astronautica, 2014, 96: 216–216.CrossRefGoogle Scholar
  3. [3]
    Cao, L., Chen, X. Q., Misra, A. K. A novel unscented predictive filter for relative position and attitude estimation of satellite formation. Acta Astronautica, 2015, 112: 157–157.CrossRefGoogle Scholar
  4. [4]
    Zhang, B. Q., Song, S. M. Decentralized coordinated control for multiple spacecraft formation maneuvers. Acta Astronautica, 2012, 74: 97–97.CrossRefGoogle Scholar
  5. [5]
    Cai, W. W., Yang, L. P., Zhu, Y. W., Zhang, Y. W. Optimal satellite formation reconfiguration actuated by inter-satellite electromagnetic forces. Acta Astronautica, 2013, 89: 165–165.CrossRefGoogle Scholar
  6. [6]
    Garcia-Taberner, L., Masdemont, J. J. FEFF methodology for spacecraft formations reconfiguration in the vicinity of libration points. Acta Astronautica, 2010, 67(7–8): 817–817.Google Scholar
  7. [7]
    Godard, Dev Kumar, K., Zou, A. M. Robust stationkeeping and reconfiguration of underactuated spacecraft formations. Acta Astronautica, 2014, 105(2): 510–510.CrossRefGoogle Scholar
  8. [8]
    Huang, X., Yan, Y., Zhou, Y. Analytical solutions to optimal underactuated spacecraft formation reconfiguration. Advances in Space Research, 2015, 56(10): 2166–2166.CrossRefGoogle Scholar
  9. [9]
    Yoo, S. M., Lee, S., Park, C., Park, S. Y. Spacecraft fuel-optimal and balancing maneuvers for a class of formation reconfiguration problems. Advances in Space Research, 2013, 52(8): 1488–1488.CrossRefGoogle Scholar
  10. [10]
    Starek, J. A., Schmerling, E., Maher, G. D., Barbee, B. W., Pavone, M. Fast, safe, propellant-efficient spacecraft motion planning under Clohessy-Wiltshire-Hill dynamics. Journal of Guidance, Control, and Dynamics, 2017, 40(2): 438–438.CrossRefGoogle Scholar
  11. [11]
    Frey, G. R., Petersen, C. D., Leve, F. A., Kolmanovsky, I. V., Girard, A. R. Constrained spacecraft relative motion planning exploiting periodic natural motion trajectories and invariance. Journal of Guidance, Control, and Dynamics, 2017, 40(12): 3115–3115.CrossRefGoogle Scholar
  12. [12]
    Luo, Y. Z., Sun, Z. J. Safe rendezvous scenario design for geostationary satellites with collocation constraints. Astrodynamics, 2017, 1(1): 83–83.CrossRefGoogle Scholar
  13. [13]
    Chu, X. Y., Zhang, J. R., Lu, S., Zhang, Y., Sun, Y. Optimised collision avoidance for an ultra-close rendezvous with a failed satellite based on the Gauss pseudospectral method. Acta Astronautica, 2016, 128: 376–376.CrossRefGoogle Scholar
  14. [14]
    Cao, L., Qiao, D., Xu, J. W. Suboptimal artificial potential function sliding mode control for spacecraft rendezvous with obstacle avoidance. Acta Astronautica, 2018, 143: 146–146.CrossRefGoogle Scholar
  15. [15]
    Khatib, O. Real-time obstacle avoidance for manipulators and mobile robots. Autonomous Robot Vehicles, 1986, 396–404.Google Scholar
  16. [16]
    McInnes, C. R. Autonomous proximity maneuvering using artificial potential functions. ESA Journal, 1993, 17(2): 169–169.MathSciNetGoogle Scholar
  17. [17]
    Hu, Q. L., Dong, H. Y., Zhang, Y. M., Ma, G. F. Tracking control of spacecraft formation flying with collision avoidance. Aerospace Science and Technology, 2015, 42: 364–364.CrossRefGoogle Scholar
  18. [18]
    Ni, Q., Huang, Y. Y., Chen, X. Q. Nonlinear control of spacecraft formation flying with disturbance rejection and collision avoidance. Chinese Physics B, 2017, 26(1): 014502.Google Scholar
  19. [19]
    Badawy, A., McInnes, C. R. On-orbit assembly using superquadric potential fields. Journal of Guidance, Control, and Dynamics, 2008, 31(1): 43–43.CrossRefGoogle Scholar
  20. [20]
    Bevilacqua, R., Lehmann, T., Romano, M. Development and experimentation of LQR/APF guidance and control for autonomous proximity maneuvers of multiple spacecraft. Acta Astronautica, 2011, 68(7–8): 1275–1275.Google Scholar
  21. [21]
    Huang, X., Yan, Y., Zhou, Y. Underactuated spacecraft formation reconfiguration with collision avoidance. Acta Astronautica, 2017, 131: 181–181.CrossRefGoogle Scholar
  22. [22]
    Wang, Y., Bai, Y. Z., Ran, D. C., Zhao, Y., Zhang, X., Chen, X. Q. The equal-collision-probability-surface method for spacecraft collision avoidance. IAA-AAS-DyCoSS3-037, 2017, 761–776.Google Scholar
  23. [23]
    Wang, Y., Bai, Y. Z., Xing, J. J., Radice, G., Ni, Q., Chen, X. Q. Equal-collision-probability-curve method for safe spacecraft close-range proximity maneuvers. Advances in Space Research, 2018, 62(9): 2619–2619.CrossRefGoogle Scholar
  24. [24]
    Wang, Y., Chen, X. Q., Ran, D. C., Ou, Y. W., Ni, Q., Bai, Y. Z. Multi-equal-collision-probability-cure method for convex polygon-shape spacecraft safe proximity manoeuvres- corrigendum. The Journal of Navigation, 2019, 72(1): 255.CrossRefGoogle Scholar
  25. [25]
    Wang, Y., Bai, Y. Z., Ran, D. C., Chen, Q., Ni, Q., Chen, X. Q. Dual-Equal-Collision-Probability-Curve method for spacecraft safe proximity maneuvers in presence of complex shape. Acta Astronautica, 2019, 159: 76–76.Google Scholar
  26. [26]
    Fehse, W. Automated rendezvous and docking of spacecraft. Cambridge University Press, 2003.CrossRefGoogle Scholar
  27. [27]
    Cao, L., Qiao, D., Chen, X. Q. Laplace ℓ1 Huber based cubature Kalman filter for attitude estimation of small satellite. Acta Astronautica, 2018, 148: 56–56.CrossRefGoogle Scholar
  28. [28]
    Ou, Y. W., Zhang, H. B. Mars final approach navigation using ground beacons and orbiters: an information propagation perspective. Acta Astronautica, 2017, 138: 500–500.CrossRefGoogle Scholar
  29. [29]
    Rodriguez-Seda, E. J., Tang, C. P., Spong, M. W., Stipanovic, D. M. Trajectory tracking with collision avoidance for nonholonomic vehicles with acceleration constraints and limited sensing. The International Journal of Robotics Research, 2014, 33(12): 1592–1592.CrossRefGoogle Scholar
  30. [30]
    Kumar, V., Michael, N. Opportunities and challenges with autonomous micro aerial vehicles. The International Journal of Robotics Research, 2012, 31(11): 1291–1291.CrossRefGoogle Scholar
  31. [31]
    Yang, Z., Luo, Y. Z., Zhang, J., Tang, G. J. Uncertainty quantification for short rendezvous missions using a nonlinear covariance propagation method. Journal of Guidance, Control, and Dynamics, 2016, 39(9): 2178–2178.CrossRefGoogle Scholar
  32. [32]
    Luo, Y. Z., Liang, L. B., Wang, H., Tang, G. J. Quantitative performance for spacecraft rendezvous trajectory safety. Journal of Guidance, Control, and Dynamics, 2011, 34(4): 1269–1269.CrossRefGoogle Scholar
  33. [33]
    Ge, S. S., Cui, Y. J. Dynamic motion planning for mobile robots using potential field method. Autonomous Robots, 2002, 13(3): 222–222.CrossRefzbMATHGoogle Scholar
  34. [34]
    Lin, F. Robust control design: an optimal control approach. John Wiley & Sons, Ltd, 2007.CrossRefGoogle Scholar
  35. [35]
    Xing, J. J., Yu, Y., Wang, Y., Zheng, L. M., Chen, Z. A. Robust control of low earth orbit satellites formation based on improved linear quadratic regulator. Journal of National University of Defense Technology, 2016, 38(3): 106–106.Google Scholar
  36. [36]
    Xing, J. J., Tang, G. J., Xi, X. N., Li, H. Y. Satellite formation design and optimal stationkeeping considering nonlinearity and eccentricity. Journal of Guidance, Control, and Dynamics, 2007, 30(5): 1528–1528.CrossRefGoogle Scholar
  37. [37]
    Ou, Y. W., Zhang, H. B. Observability-based mars autonomous navigation using formation flying spacecraft. The Journal of Navigation, 2018, 71(1): 43–43.CrossRefGoogle Scholar
  38. [38]
    Psiaki, M. L. Absolute orbit and gravity determination using relative position measurements between two satellites. Journal of Guidance, Control, and Dynamics, 2011, 34(5): 1297–1297.CrossRefGoogle Scholar
  39. [39]
    Peynot, T., Lui, S. T., McAllister, R., Fitch, R., Sukkarieh, S. Learned stochastic mobility prediction for planning with control uncertainty on unstructured terrain. Journal of Field Robotics, 2014, 31(6): 995–995.CrossRefGoogle Scholar
  40. [40]
    Chen, Q., Wang, W. C., Yin, C., Jin, X. X., Zhou, J. Distributed cubature information filtering based on weighted average consensus. Neurocomputing, 2017, 243: 124–124.CrossRefGoogle Scholar
  41. [41]
    Chen, Q., Yin, C., Zhou, J., Wang, Y., Wang, X. Y., Chen, C. Y. Hybrid consensus-based cubature Kalman filtering for distributed state estimation in sensor networks. IEEE Sensors Journal, 2018, 18(11): 4569–4569.CrossRefGoogle Scholar

Copyright information

© Tsinghua University Press 2019

Authors and Affiliations

  • Yi Wang
    • 1
    • 2
  • Xiaoqian Chen
    • 2
  • Dechao Ran
    • 2
  • Yong Zhao
    • 1
  • Yang Chen
    • 1
  • Yuzhu Bai
    • 1
    Email author
  1. 1.College of Aerospace Science and EngineeringNational University of Defense TechnologyChangshaChina
  2. 2.National Innovation Institute of Defense TechnologyChinese Academy of Military SciencesBeijingChina

Personalised recommendations