This paper studies the trajectory planning problem of spacecraft approaching non-cooperative targets and avoiding their field of view in space attack and defense. For the trajectory optimization problem with multiple constraints and strong nonlinearity, an efficient convexification and parameterization reconstruction method is proposed. First, the spacecraft approach trajectory planning is transformed into an optimal control problem containing non-convex constraints. A new convexification technology for field of view avoidance constraints is innovatively proposed. By introducing slack variables, a class of non-convex constraints are dimensionally expanded and softened, thereby realizing the overall transformation to a convex problem. In addition, the dynamic system is efficiently reconstructed based on differential flatness theory, and non-uniform rational b-spline curves are used to parameterize the state variables, control variables and the introduced slack variables, which greatly reduces the computational complexity. By designing multiple types of simulation scenarios for simulation analysis, it is verified that the algorithm can successfully plan an effective trajectory under strict compliance with various motion constraints, which can ensure that the spacecraft can safely avoid obstacles and avoid the detection field of view of non-cooperative targets. Through comparative simulation analysis, the proposed algorithm has comparable trajectory optimization quality and has advantages in solution speed compared with model predictive control and pseudo-spectral method.
[1] WILDE M, CLARK C, ROMANO M. Historical survey of kinematic and dynamic spacecraft simulators f-or laboratory experimentation of on-orbit proximity maneuvers[J].Progress in Aerospace Sciences, 2019, 110:100552.
[2] MOGHADDAM B M, CHHABRA R. On the guidance, navigation and control of in-orbit space robotic missions: A survey and prospective vision[J]. Acta Astronautica, 2021, 184: 70-100.
[3] WEISS A, BALDWIN M, ERWIN R S, et al. Model predictive control for spacecraft rendezvous and docking: Strategies for handling constraints and case studies[J]. IEEE Transactions on Control Systems and Technology, 2015, 23(4): 1638-1647.
[4] 于大腾, 王华, 孙福煜. 考虑潜在威胁区的航天器最优规避机动策略[J]. 航空学报, 2017, 38(01): 286-294.
YU D T, WANG H, SUN F Y. Optimal evasive maneuver strategy with potential threatening area being considered[J]. Acta Aeronautica et Astronautica Sinica (in Chinese), 2017, 38(01): 286-294.
[5] ZAPPULLA R, PARK H, VIRGILI-LLOP J, et al. Real-time autonomous spacecraft proximity maneuvers and docking using an adaptive artificial potential field approach[J]. IEEE Transactions on Control Systems and Technology, 2019, 27(6): 2598-2605.
[6] SHAO X D, HU Q L. Immersion and invariance adaptive pose control for spacecraft proximity operations under kinematic and dynamic constraints[J]. IEEE Transactions on Aerospace and Electronic Systems, 2021, 57(4): 2183-2200.
[7] ZAGARIS C, PARK H, VIRGILI J, et al. Model predictive control of spacecraft relative motion with convexified keep-out-zone constraints[J]. Journal of Guidance, Control and Dynamics, 2018, 41(9): 2051-2059.
[8] 董凯凯, 罗建军, 马卫华等. 非合作目标抵近的双层MPC全局轨迹规划控制[J]. 航空学报, 2021, 42(11): 224-235.
DONG K K, LUO J J, MA W H, et al. Global trajectory planning and control of rendezvous of non-cooperative targets based on double-layer MPC[J]. Acta Aeronautica et Astronautica Sinica (in Chinese), 2021, 42(11): 224-235.
[9] HOVELL K , ULRICH S. Deep reinforcement learning for spacecraft proximity operations guidance[J]. Journal of spacecraft and rockets, 2021, 58(2): 254-264.
[10] 岳承磊, 汪雪川, 岳晓奎等. 基于逆强化学习的航天器抵近对接方法[J]. 航空学报, 2023, 44(19): 257-268.
YUE C L, WANG X C, YUE X K, et al. A spacecraft rendezvous and docking method based on in-verse reinforcement learning[J]. Acta Aeronautica et Astronautica Sinica (in Chinese), 2023, 44(19): 257-268.
[11] MCINNES C R. Deep reinforcement learning for spacecraft proximity operations guidance[J]. European Space Agency Journal, 1993, 17(2): 159-169.
[12] LOPEZ I, MCINNES C R. Autonomous rendezvous using artificial potential function guidance[J]. Journal of Guidance, Control and Dynamics, 1995, 18(2): 237-241.
[13] JEWISON C, ERWIN R S, SAENZ-OTERO A. Model predictive control with ellipsoid obstacle constraints for spacecraft rendezvous[J]. IFAC-PapersOnLine, 2015, 48(9): 257-262.
[14] RICHARDS A, HOW J. Performance evaluation of rendezvous using model predictive control[J]. AIAA Guidance, Navigation and Control Conference and Exhibit, 2003.
[15] FEDERICI L, BENEDIKTER B, ZAVOLI A. Machine learning techniques for autonomous spacecraft guidance during proximity operations. Proceedings of the AIAA Scitech 2021 Forum, 2021.
[16] QU Q Y, LIU K X, WANG W, et al. Spacecraft proximity maneuvering and rendezvous with collision avoidance based on reinforcement learning[J]. IEEE Transactions on Aerospace and Electronic Systems, 2022, 58(6), 5823-5834.
[17] 耿远卓, 李传江, 郭延宁等. 单推力航天器交会对接轨迹规划及跟踪控制[J]. 航空学报, 2020, 41(9): 191-205.
GENG Y Z, LI C J, GUO Y N, et al. Rendezvous and docking of spacecraft with single thruster: Path planning and tracking control[J]. Acta Aeronautica et Astronautica Sinica (in Chinese), 2020, 41(9): 191-205.
[18] SHAO X and HU Q. Immersion and invariance adaptive pose control for spacecraft proximity operations under kinematic and dynamic constraints[J]. IEEE Transactions on Aerospace and Electronic Systems, 2021, 57(4): 2183-2200.
[19] 罗建军, 吕东升, 龚柏春等. 仅测角导航多约束抵近的闭环最优制导[J]. 宇航学报, 2017, 38(9): 956-963.
LUO J J, LV D S, GONG B C, et al. Closed-Loop Optimal Guidance for Multi Constrained Rendezvous with Angles-Only Navigation[J]. Journal of Astronautics, 2017, 38(9): 956-963.
[20] KIRK D E. Optimal Control Theory：An Introduction[M]. Dover Publications, 2004.
[21] FAULWASSER T, HAGENMEYER V, and FINDEISEN R. Constrained reachability and trajectory generation for flat systems[J]. Automatica, 2014, 50:1151-1159.
[22] THIEL M, SCHWARZMANN D, ANNASWAMY A M, et al. Computational methods for MIMO flat linear systems: Flat output characterization, test and tracking control[C]. In Proceedings of the 2015 American Control Conference, 3898-3904, Chicago, IL, USA, 2015.
[23] SINHA N K and ROZSA P. Some cannonical forms for linear multivariable systems[J]. International Journal of Control, 1976, 23(6):865-883.
[24] PRAUTZSCH H, BOEHM W, and PALUSZNY M. Be′zierand B-Spline Techniques[J]. Springer Science&Business Media, 2002.
[25] SURYAWAN F, DE DON′A J, and SERON M. Minimum-time trajectory generation for constrained linear systems using flatness and b-splines[J]. International Journal of Control, 2011, 84(9):1565–1585.
[26] FLIESS M, L′EVINE J, MARTIN P, et al. Flatness and defect of nonlinear systems: introductory theory and examples[J]. International Journal of Control, 1995, 61:1327-1361.
[27] BOYD S and VANDENBERGHE L. Convex optimization [J]. Cambridge University Press, 2004.
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