Adaptive prescribed performance attitude and orbit tracking control of spacecraft in irregular gravitational fields
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摘要:
深空探测是当今世界高新科技中极具挑战性的领域之一，小行星探测作为深空探测的重要方向，其具有重要的科学意义。研究了小行星引力场不规则项参数及航天器质量特性参数同时存在不确定性时刚体航天器的姿轨跟踪控制问题，基于不规则引力场下李群描述的航天器预设性能误差运动模型，提出一种复合自适应姿轨跟踪控制器。针对航天器质量特性参数的不确定性，基于浸入与不变（I&I）理论和动态回归扩展方法，设计了收敛性能良好的参数更新律对其进行估计。利用质量特性参数估计值设计了扩张状态观测器，对由引力场不规则项的不确定及外部干扰构成的系统总扰动进行估计。基于上述参数更新律和扰动估计补偿得到了复合自适应预设性能终端滑模控制器。通过Lyapunov理论证明了所提控制器保证姿轨跟踪误差、扰动估计误差及质量特性参数估计误差有界。仿真结果表明：动态回归扩展方法的引入提高了质量特性参数估计的收敛性能，在此基础上，扰动估计补偿的加入提高了姿轨跟踪控制精度。
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关键词:
- 航天器姿轨一体化控制 /
- 不规则引力场 /
- 参数不确定 /
- 扩张状态观测器 /
- 自适应预设性能控制
Abstract:This paper examines the attitude and orbit tracking control problem of rigid spacecraft when there are uncertainties in both the irregular terms of the asteroid’s gravitational field and the spacecraft’s mass characteristic parameters. Based on the spacecraft’s prescribed performance error motion model described by Lie groups under irregular gravitational fields, a composite adaptive attitude and orbit tracking controller is proposed. A parameter update rule with higher convergence performance is devised based on the dynamic regression extension method and the immersion and invariance (I&I) theory to estimate the mass characteristic parameters with the goal of minimizing their uncertainty. Utilizing the estimated values of the mass characteristic parameters, an extended state observer is devised to estimate the overall system disturbance, which stems from the irregularity of the gravitational field and external disturbances. Building upon this parameter update law and disturbance estimation compensation, a composite adaptive prescribed performance terminal sliding mode controller is formulated. By using Lyapunov theory, it is demonstrated that the suggested controller guarantees that the errors in mass characteristic parameter estimate, disturbance estimation, and attitude and orbit tracking stay within a certain bound. Simulation results demonstrate that the incorporation of the dynamic regression extension method enhances the convergence performance of mass characteristic parameter estimation, and further, the addition of disturbance estimation compensation improves the accuracy of attitude and orbit tracking control.
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图 5 扩张状态观测器观测误差$ {\boldsymbol{e}}_{1} $
Figure 5. Observation error $ {\boldsymbol{e}}_{1} $ of extended state observer
图 6 扩张状态观测器观测误差$ {\boldsymbol{e}}_{2} $
Figure 6. Observation error $ {\boldsymbol{e}}_{2} $ of extended state observer
图 9 对照组角速度与速度跟踪误差
Figure 9. Angular velocity and velocity tracking error of comparison group
表 1 Eros433相关参数
Table 1. Eros433 related parameters
万有引力常数$ /\left(\text{N}\cdot {\text{m}}^{2}\cdot \text{k}{\text{g}}^{-}{}^{2}\right) $ 质量$ /\text{kg} $ 密度$ /\left(\text{kg}\cdot {\text{m}}^{-}{}^{3}\right) $ 自转角速度$ /\left(\text{rad}\cdot {\text{s}}^{-1}\right) $ 自转周期$ /\text{h} $ 小行星引力场
相关参数${C}_{20}/\mathrm{k}{\mathrm{m}}^{2} $小行星引力场
相关参数${C}_{22}/\mathrm{k}{\mathrm{m}}^{2} $$ 6.673\;8\times {10}^{-11} $ $ 6.690\;4\times {10}^{15} $ 2670 $ 3.311\;7\times {10}^{-4} $ 5.57 −27.755 12.752 
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表 2 追踪航天器相关参数
Table 2. Tracking spacecraft related parameters
质量$ /\text{kg} $ 惯量$ /\left(\text{kg}\cdot {\text{m}}^{2}\right) $ 20 $ \left[\begin{matrix}5.5 & 0.03 & 0.05\\0.03 & 6.5 & 0.02\\0.05 & 0.02 & 5.8\end{matrix}\right] $
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表 3 目标初始位姿参数
Table 3. Target initial position and attitude parameters
目标轨道
初始位置$ \text{/m} $目标轨道初始
速度$ /\left(\text{m}\cdot {\text{s}}^{-1}\right) $目标姿态 目标姿态角
速度$ /\left(\text{rad}\cdot {\text{s}}^{-1}\right) $$ {\left[\begin{matrix}25\times {10}^{3}, & 0, & 0\end{matrix}\right]}^{\mathrm{T }} $ $ {\left[\begin{matrix}0, & 4.226\;1, & 0\end{matrix}\right]}^{\mathrm{T }} $ $ \left[\begin{matrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{matrix}\right] $ $ {\left[\begin{matrix}0, & 0, & 0\end{matrix}\right]}^{\mathrm{T }} $
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表 4 初始位姿参数
Table 4. Initial position and attitude parameters
初始位置$ \text{/m} $ 初始速度$ /\left(\text{m}\cdot {\text{s}}^{-1}\right) $ 初始姿态 初始姿态角速度$ /\left(\text{rad}\cdot {\text{s}}^{-1}\right) $ $ {\left[\begin{matrix}25\times {10}^{3}+15, & -10, & -15\end{matrix}\right]}^{\mathrm{T }} $ $ {\left[\begin{matrix}0.141 & 4.226\;1+0.27 & 0.27\end{matrix}\right]}^{\mathrm{T }} $ $ \left[\begin{matrix}0.852\;0 & 0.256\;5 & 0.454\;8\\-0.150\;4 & 0.954\;8 & -0.256\;5\\-0.5 & 0.150\;4 & 0.852\;9\end{matrix}\right] $ $ {\left[\begin{matrix}1.2\times {10}^{-2}, & -1.1\times {10}^{-2}, & 1.3\times {10}^{-2}\end{matrix}\right]}^{\mathrm{T }} $
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表 5 复合自适应预设性能控制器相关参数
Table 5. Composite adaptive prescribed performance controller related parameters
滑模面相关参数 线性滤波器相关参数 控制器相关参数 参数更新律相关参数 扩张状态观测器
相关参数$ \begin{aligned}{\boldsymbol{C}}_{1}&=\text{diag([}0.1{\boldsymbol{I}}_{3\times 1},0.05{\boldsymbol{I}}_{3\times 1}])\\{\boldsymbol{C}}_{2}&=\text{diag(0.001}{\boldsymbol{I}}_{6\times 1})\end{aligned} $ $ {\boldsymbol{\lambda }}_{\mathrm{f}}=\text{diag([}0.2{\boldsymbol{I}}_{3\times 1},0.02{\boldsymbol{I}}_{3\times 1}]) $ $ \boldsymbol{k}=\text{diag([1.5}{\boldsymbol{I}}_{3\times 1},1.2{\boldsymbol{I}}_{3\times 1}]) $ $ \begin{aligned}\boldsymbol{v}&=\text{diag(}10{\boldsymbol{I}}_{6\times 1})\\{\boldsymbol{k}}_{\mathrm{l}}&=\text{diag}([5{\boldsymbol{I}}_{3\times 1},0.01{\boldsymbol{I}}_{3\times 1},0.04]),\sigma =0.1\end{aligned} $ $ {b}_{1}={b}_{2}=10 $
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[1] 杨洪伟, 宝音贺西. 小行星附近制导与控制研究综述[J]. 深空探测学报, 2019, 6(2): 179-188.Yang H W, Baoyin H X. Review of guidance and control in the vicinity of asteroids[J]. Journal of Deep Space Exploration, 2019, 6(2): 179-188(in Chinese). [2] Feng J, Hou X, Armellin R. Survey on studies about model uncertainties in small body explorations[J]. Progress in Aerospace Sciences, 2019, 110: 100549. [3] 李俊峰, 曾祥远. 不规则小行星引力场内的飞行动力学[J]. 力学进展, 2017, 47(1): 429-451.Li J F, Zeng X Y. Flight dynamics in the gravitational fields of irregular asteroids[J]. Advances in Mechanics, 2017, 47(1): 429-451(in Chinese). [4] Wang Y, Xu S. Orbital dynamics and equilibrium points around an asteroid with gravitational orbit–attitude coupling perturbation[J]. Celestial Mechanics and Dynamical Astronomy, 2016, 125: 265-285. [5] Lee D, Sanyal A K, Butcher E A, et al. Almost global asymptotic tracking control for spacecraft body-fixed hovering over an asteroid[J]. Aerospace Science and Technology, 2014, 38: 105-115. [6] Lee D, Sanyal A K, Butcher E A, et al. Finite-time control for spacecraft body-fixed hovering over an asteroid[J]. IEEE Transactions on Aerospace and Electronic Systems, 2015, 51(1): 506-520. [7] Vukovich G, Gui H C. Robust adaptive tracking of rigid-body motion with applications to asteroid proximity operations[J]. IEEE Transactions on Aerospace and Electronic Systems, 2017, 53(1): 419-430. [8] 潘菲, 朱宏玉. 航天器非奇异自适应终端滑模姿轨联合控制[J]. 北京航空航天大学学报, 2020, 46(7): 1354-1362.Pan F, Zhu H Y. Spacecraft non-singular adaptive terminal sliding mode attitude-orbit coupling control[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(7): 1354-1362(in Chinese). [9] 夏冬冬, 岳晓奎. 基于浸入与不变理论的航天器姿态跟踪自适应控制[J]. 航空学报, 2020, 41(2): 307-318.Xia D D, Yue X K. Immersion and invariance based attitude adaptive tracking control for spacecraft[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(2): 307-318(in Chinese). [10] Seo D, Akella M R. High-performance spacecraft adaptive attitude-tracking control through attracting-manifold design[J]. Journal of Guidance, Control, and Dynamics, 2008, 31(4): 884-891. [11] Lee K W, Singh S N. Immersion-and invariance-based adaptive control of asteroid-orbiting and-hovering spacecraft[J]. The Journal of the Astronautical Sciences, 2019, 66(4): 537-553. [12] Xu Y Q, Hu Q L, Shao X D. Composite adaptive attitude control for combined spacecraft with inertia uncertainties[J]. Aerospace Science and Technology, 2022, 131: 107984. [13] Shao X D, Hu Q L, Shi Y, et al. Data-driven immersion and invariance adaptive attitude control for rigid bodies with double-level state constraints[J]. IEEE Transactions on Control Systems Technology, 2022, 30(2): 779-794. [14] Lee K W, Singh S N. Composite adaptive attitude control of asteroid-orbiting spacecraft with regressor integral excitation[J]. IEEE Transactions on Aerospace and Electronic Systems, 2022, 58(5): 4814-4823. [15] 张剑桥. 航天器姿轨一体化建模与控制方法研究[D]. 哈尔滨: 哈尔滨工业大学, 2020.Zhang J Q. Research on spacecraft integrated orbit-attitude modeling and control methods[D]. Harbin: Harbin Institute of Technology, 2020(in Chinese). [16] Scheeres D J. Orbit mechanics about asteroids and comets[J]. Journal of Guidance, Control, and Dynamics, 2012, 35(3): 987-997. [17] Jiang L, Wang Y, Xu S J. Integrated 6-DOF orbit-attitude dynamical modeling and control using geometric mechanics[J]. International Journal of Aerospace Engineering, 2017: 4034328. [18] Aranovskiy S, Bobtsov A, Ortega R, et al. Performance enhancement of parameter estimators via dynamic regressor extension and mixing[J]. IEEE Transactions on Automatic Control, 2017, 62(7): 3546-3550. -
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