Abstract
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.
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11 February 2022
A Correction to this paper has been published: https://doi.org/10.1007/s42064-022-0136-2
References
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.
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.
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.
Zhang, B. Q., Song, S. M. Decentralized coordinated control for multiple spacecraft formation maneuvers. Acta Astronautica, 2012, 74: 97–97.
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.
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.
Godard, Dev Kumar, K., Zou, A. M. Robust stationkeeping and reconfiguration of underactuated spacecraft formations. Acta Astronautica, 2014, 105(2): 510–510.
Huang, X., Yan, Y., Zhou, Y. Analytical solutions to optimal underactuated spacecraft formation reconfiguration. Advances in Space Research, 2015, 56(10): 2166–2166.
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.
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.
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.
Luo, Y. Z., Sun, Z. J. Safe rendezvous scenario design for geostationary satellites with collocation constraints. Astrodynamics, 2017, 1(1): 83–83.
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.
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.
Khatib, O. Real-time obstacle avoidance for manipulators and mobile robots. Autonomous Robot Vehicles, 1986, 396–404.
McInnes, C. R. Autonomous proximity maneuvering using artificial potential functions. ESA Journal, 1993, 17(2): 169–169.
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.
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.
Badawy, A., McInnes, C. R. On-orbit assembly using superquadric potential fields. Journal of Guidance, Control, and Dynamics, 2008, 31(1): 43–43.
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.
Huang, X., Yan, Y., Zhou, Y. Underactuated spacecraft formation reconfiguration with collision avoidance. Acta Astronautica, 2017, 131: 181–181.
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.
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.
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.
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.
Fehse, W. Automated rendezvous and docking of spacecraft. Cambridge University Press, 2003.
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.
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.
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.
Kumar, V., Michael, N. Opportunities and challenges with autonomous micro aerial vehicles. The International Journal of Robotics Research, 2012, 31(11): 1291–1291.
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.
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.
Ge, S. S., Cui, Y. J. Dynamic motion planning for mobile robots using potential field method. Autonomous Robots, 2002, 13(3): 222–222.
Lin, F. Robust control design: an optimal control approach. John Wiley & Sons, Ltd, 2007.
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.
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.
Ou, Y. W., Zhang, H. B. Observability-based mars autonomous navigation using formation flying spacecraft. The Journal of Navigation, 2018, 71(1): 43–43.
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.
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.
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.
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.
Acknowledgements
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).
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Yi Wang was born in Huaihua, Hunan Provice, China, in 1990. He received his B.S. degree in aerospace engineering from the Northwestern Polytechnical University, China, in 2012, and the M.S. degree in aerospace engineering from Central South University, China, in 2015. He is currently pursuing his Ph.D. degree in aerospace engineering with the National University of Defense Technology, China. His current research interests include spacecraft dynamics, navigation and control.
Xiaoqian Chen received his M.S. and Ph.D. degrees in aerospace engineering from National University of Defense Technology, China, in 1997 and 2001, respectively. He is currently a professor and the dean of National Institute of Defense Technology Innovation, Beijing, China. His current research interests include spacecraft systems engineering, advanced digital design methods of space systems, and multidisciplinary design optimization.
Dechao Ran received his M.S. and Ph.D. degrees in aerospace engineering from National University of Defense Technology, China, in 2013 and 2017, respectively. He is currently an assistant research fellow in National Institute of Defense Technology Innovation, China. He joined the McGill University as a visiting Ph.D. student from 2015 to 2016, and focused on the dynamics and control of spacecraft formation. His research interests include the areas of spacecraft formation dynamics and control, satellite control system design. Moreover, he has the interest of nano-satellite design and launch experiences.
Yong Zhao received his Ph.D. degree in aerospace engineering from National University of Defense Technology, China, in 2007. He is currently a professor in National University of Defense Technology, China. His current research interests include spacecraft systems engineering, advanced digital design methods of space systems, and multidisciplinary design optimization.
Yang Chen received his B.S. degree in aerospace engineering from the National University of Defense Technology, China, in 2017. He is currently pursuing his M.S. degree in aerospace engineering with the National University of Defense Technology, China. His current research interests include optimal theory, aerospace engineering and dynamics.
Yuzhu Bai received his Ph.D. degree in aerospace engineering from National University of Defense Technology, China, in 2010. He is currently an associate professor at National University of Defense Technology, China. His current research interests include micro-satellite design, spacecraft dynamics and control.
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Wang, Y., Chen, X., Ran, D. et al. Spacecraft formation reconfiguration with multi-obstacle avoidance under navigation and control uncertainties using adaptive artificial potential function method. Astrodyn 4, 41–56 (2020). https://doi.org/10.1007/s42064-019-0049-x
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DOI: https://doi.org/10.1007/s42064-019-0049-x