多星姿态协同中的几何鲁棒控制

doi:10.12305/j.issn.1001-506X.2024.09.24

摘要/Abstract

摘要：

针对多星系统的姿态协同控制问题, 通过不变扩展卡尔曼滤波(invariant extended Kalman filter, InEKF)对航天器进行姿态估计, 将航天器的姿态估计与传递矩阵独立; 结合无向通信拓扑构建多星特殊正交群(special orthogonal group, SO(3))姿态模型, 推导SO(3)上姿态协同误差。然后，基于SO(3)提出基于一致性理论的姿态协同控制算法。其中，利用径向基函数神经网络对虚拟扰动进行拟合补偿, 所提出的算法考虑空间扰动, 以保证协同控制器适用于整个姿态空间，实现多星姿态协同、跟踪期望姿态和执行器能力约束下的协同。根据LaSalle不变集理论对系统进行分析, 证明系统具有全局渐近稳定性。最后, 利用六星航天器系统校验了所提姿态协同控制算法的有效性。

关键词: 多航天器, 特殊正交群, 协同控制, 径向基函数, 不变扩展卡尔曼滤波

Abstract:

Aiming at the attitude cooperative control problem of multi-spacecraft system, the attitude estimation of the spacecraft is estimated by invariant extended Kalman filter (InEKF), and the attitude estimation of the spacecraft is made independent of the transfer matrix. Then, the multi-spacecraft special orthogonal group (SO(3)) attitude model is constructed by combining the undirected communication topology, and the attitude coordination error on SO(3) is deduced. Among them, an attitude coordination control algorithm based on the consistency theory is proposed based on the special orthogonal group SO(3). The radial basis function neural network is used to fit and compensate virtual disturbances. The proposed algorithm considers spatial disturbances to ensure that the collaborative controller is applicable to the entire attitude space. Multi-satellite attitude collaboration, tracking desired attitude, and collaboration under the constraints of actuator capabilities are realized. The system is analyzed based on LaSalle invariant set theory, proving that the system has global asymptotic stability. Finally, the effectiveness of the proposed attitude collaborative control algorithm is verified by using a six-satellite spacecraft system.

Key words: multiple spacecraft, special orthogonal group (SO(3)), coordinated control, radial basis function (RBF), invariant extended Kalman filter (InEKF)

中图分类号:

V448.2

胡洋, 刘学超, 李化义, 曹芊. 多星姿态协同中的几何鲁棒控制[J]. 系统工程与电子技术, 2024, 46(9): 3118-3127.

Yang HU, Xuechao LIU, Huayi LI, Qian CAO. Geometrically robust control in multi-satellite attitude coordination[J]. Systems Engineering and Electronics, 2024, 46(9): 3118-3127.

图/表 15

图1

表1

图2

图3

图4

图5

图6

图7

图8

图9

图10

图11

图12

图13

图14

参考文献 32

1	FANL M,HUANGH,ZHOUK X.Robust fault-tolerant attitude control for satellite with multiple uncertainties and actuator faults[J].Chinese Journal of Aeronautics,2020,33(12):3380-3394. doi: 10.1016/j.cja.2020.06.026
2	CAPUANOV,HARVARDA,CHUNGS J.On-board cooperative spacecraft relative navigation fusing GNSS WITH vision[J].Progress in Aerospace Sciences,2022,128,100761. doi: 10.1016/j.paerosci.2021.100761
3	YED,ZOUA M,SUNZ W.Predefined-time predefined-bounded attitude tracking control for rigid spacecraft[J].IEEE Trans.on Aerospace Electronic Systems,2022,58(1):464-472. doi: 10.1109/TAES.2021.3103258
4	马鸣宇,董朝阳,马思迁,等.多航天器反步滑模SO(3)协同控制[J].宇航学报,2018,39(6):664-673.
	MAM Y,DONGC Y,MAS Q,et al.Coordinated attitude CONTROL of multiple spacecraft via backstepping sliding mode method on SO(3)[J].Journal of Astronautics,2018,39(6):664-673.
5	WANGW T,XIANGZ R.Distributed consensus tracking control for nonlinear multiagent systems with state delays and unknown control coefficients[J].International Journal of Robust and Nonlinear Control,2021,32(4):2050-2068.
6	NUNOE,ORTEGAR.Achieving consensus of Euler-Lagrange agents with interconnecting delays and without velocity measurements via passivity-based control[J].IEEE Trans.on Control Systems Technology,2018,26(1):222-232. doi: 10.1109/TCST.2017.2661822
7	GAOH,XIAY Q,ZHANGX P,et al.Distributed fixed-time attitude coordinated control for multiple spacecraft with actuator saturation[J].Chinese Journal of Aeronautics,2022,35(4):292-302. doi: 10.1016/j.cja.2021.05.022
8	RENY,WANGH M,XIED,et al.New terminal sliding mode consensus algorithm for disturbed second-order multi-agent systems[J].International Journal of Control, Automation, and Systems,2022,20(8):2534-2542. doi: 10.1007/s12555-021-0438-9
9	LIANGS,WANGF Y,LIUZ X,et al.Necessary and sufficient conditions for leader-follower consensus of discrete-time multiagent systems with smart leader[J].IEEE Trans.on Systems, Man, and Cybernetics: Systems,2021,52(5):2779-2788.
10	DUH B,ZHUW W,WENG H,et al.Finite-time formation control for a group of quadrotor aircraft[J].Aerospace Science and Technology,2017,69,609-616. doi: 10.1016/j.ast.2017.07.012
11	XIEX,SHENGT,HEL,et al.Distributed attitude consensus tracking control for spacecraft formation flying via adaptive nonsingular fast terminal sliding mode control[J].Journal of Aerospace Engineering,2022,236(8):1603-1616.
12	YEFYMENKON,KUDERMETOVR.Quaternion models of a rigid body rotation motion and their application for spacecraft attitude control[J].Acta Astronautica,2022,194,76-82. doi: 10.1016/j.actaastro.2022.01.029
13	ZHANGL,LIUQ Z,FANG W,et al.Parametric control for flexible spacecraft attitude maneuver based on disturbance observer[J].Aerospace Science and Technology,2022,130,107952. doi: 10.1016/j.ast.2022.107952
14	CHATURVEDI N A. Global dynamics and stabilization of rigid body attitude systems[D]. Ann Arbor: University of Michigan, 2007.
15	POSIELEKT,JOHANNR.Attitude reconstruction of a spacecraft from temperature measurements in solar eclipse analysis and observer design for a not globally observable nonlinear system[J].IEEE Trans.on Control Systems Technology,2023,31(2):631-645. doi: 10.1109/TCST.2022.3187916
16	HUD Y,ZHAOX T,ZHANGS J.Robust image-based coordinated control for spacecraft formation flying[J].Chinese Journal of Aeronautics,2022,35(9):268-281. doi: 10.1016/j.cja.2021.10.020
17	HASHEMIS H,PARIZN,HOSSEINIS S K.Observer-based hybrid control for global attitude tracking on SO(3) with input quantisation[J].International Journal of Control,2022,96(5):1352-1363.
18	MENGQ K,YANGH,JIANGB.Second-order sliding-mode on SO(3) and fault-tolerant spacecraft attitude control[J].Automatica,2023,149,110814. doi: 10.1016/j.automatica.2022.110814
19	SHIZ,XIEY E,DENGC C,et al.Disturbance observer based finite-time coordinated attitude tracking control for spacecraft on SO(3)[J].Journal of Systems Engineering and Electronics,2020,31(6):1274-1285. doi: 10.23919/JSEE.2020.000098
20	ZHENQ Z,WANL,LIY L,et al.Formation control of a multi-AUVs system based on virtual structure and artificial potential field on SE(3)[J].Ocean Engineering,2022,253,111148. doi: 10.1016/j.oceaneng.2022.111148
21	LEET.Global exponential attitude tracking controls on SO(3)[J].IEEE Trans.on Automatic Control,2015,60(10):2837-2842. doi: 10.1109/TAC.2015.2407452
22	邵海俊,缪玲娟,郭岩冰.一种用于SINS行进间对准的模糊抗野值滤波算法[J].宇航学报,2020,41(4):447-455.
	SHAOH J,MIAOL J,GUOY B.A robust filter based on fuzzy theory for SINS in-motion alignment[J].Journal of Astronautics,2020,41(4):447-455.
23	BARRAUA,BONNABELS.Invariant Kalman filtering[J].Annual Review of Control Robotics and Autonomous Systems,2018,1(1):237-257. doi: 10.1146/annurev-control-060117-105010
24	OLFATI-SABERR.Flocking for multi-agent dynamic systems: algorithms and theory[J].IEEE Trans.on Automatic Control,2006,51(3):401-420. doi: 10.1109/TAC.2005.864190
25	周健,龚春林,粟华,等.复杂约束下的编队姿态有限时间协同控制方法[J].宇航学报,2018,39(12):1340-1347. doi: 10.3873/j.issn.1000-1328.2018.12.004
	ZHOUJ,GONGC L,SUH,et al.Finite-time distributed synchronization of spacecraft formation attitude with complex constraints[J].Journal of Astronautics,2018,39(12):1340-1347. doi: 10.3873/j.issn.1000-1328.2018.12.004
26	ELAHIA,ALFIA,MODARESH.Distributed consensus control of vehicular platooning under delay, packet DROPOUT and noise: relative state and relative input-output control strategies[J].Transactions on Intelligent Transportation Systems,2022,23(11):20123-20133. doi: 10.1109/TITS.2022.3174060
27	HUO J H, MENG T, JIN Z H. Adaptive attitude control using neural network observer disturbance compensation technique[C]//Proc. of the IEEE 9th International Conference on Recent Advances in Space Technologies, 2019: 697-701.
28	WANGZ,WUZ.Nonlinear attitude control scheme with disturbance observer for flexible spacecrafts[J].Nonlinear Dynamics,2015,81(1/2):257-264.
29	YAN R D, WU Z. Nonlinear disturbance observer-based spacecraft attitude control subject to disturbances and actuator faults[C]// Proc. of the 5th International Conference on Computer-Aided Design, Manufacturing, Modeling and Simulation, 2017.
30	LEED.Nonlinear disturbance observer-based robust control for spacecraft formation flying[J].Aerospace Science and Technology,2018,76,82-90. doi: 10.1016/j.ast.2018.01.027
31	ALIPOURM,FANIS F,KABGANIANM.Inertia-free nonlinear attitude tracking with disturbance compensation using adaptive-sliding control based on quaternion algebra[J].Simulation,2020,96(1):43-54. doi: 10.1177/0037549719854178
32	AMIRKHANIA,BARSHOOIA H.Consensus in multi-agent systems: a review[J].Artificial Intelligence Review,2022,55(5):3897-3935. doi: 10.1007/s10462-021-10097-x

航天器序号	初始姿态/(°)(偏航, 俯仰, 滚转)	初始角速度/(rad/s)
1	(10, 6, 0)	(0.12, -0.08, -0.2)
2	(30, 20, 15)	(0.1, 0.08, 0.2)
3	(-8, 10, -5)	(-0.05, -0.09, -0.1)
4	(-10, 0, 4)	(-0.1, 0.08, 0.1)
5	(0, -3, 2)	(0.1, 0.09, 0.08)
6	(-10, 0, 4)	(-0.06, -0.07, 0.12)

[1]	齐兵, 程建华, 赵砚驰, 汪籽粒. 基于微形变分析的电容式MEMS加速度计温漂误差精密估计方法[J]. 系统工程与电子技术, 2024, 46(7): 2437-2445.
[2]	何通, 卢青, 周军, 郭宗易. 带有神经网络干扰观测器的视线角约束制导[J]. 系统工程与电子技术, 2024, 46(4): 1372-1382.
[3]	范大伟, 蔡伟伟, 杨乐平, 张润德. 基于多视线融合的高轨近场感知队形设计[J]. 系统工程与电子技术, 2023, 45(12): 3984-3994.
[4]	史浩然, 卢发兴, 祁江鑫, 杨光. 基于辅助信标的无人机协同目标跟踪[J]. 系统工程与电子技术, 2022, 44(7): 2302-2310.
[5]	张普, 薛惠锋, 高山, 左轩. 具有混合执行器故障的多智能体分布式有限时间自适应协同容错控制[J]. 系统工程与电子技术, 2022, 44(4): 1220-1229.
[6]	李纪强, 张国庆, 黄晨峰, 张卫东. 考虑执行器故障的无人帆船事件触发控制[J]. 系统工程与电子技术, 2022, 44(1): 242-249.
[7]	李桂英, 于志刚, 张扬. 带有角度约束的机动目标拦截协同制导律[J]. 系统工程与电子技术, 2019, 41(3): 626-635.
[8]	董朝阳, 马鸣宇, 王青, 周敏. 含有通信时滞的多航天器SO(3)姿态协同控制[J]. 系统工程与电子技术, 2018, 40(9): 2032-2039.
[9]	吕志峰, 张金生, 王仕成, 李婷. 基于RBF神经网络的磁屏蔽性能计算方法[J]. 系统工程与电子技术, 2018, 40(8): 1832-1838.
[10]	李飞, 胡剑波, 王坚浩, 汪涛. 一类输入受限的不确定非线性系统自适应Backstepping变结构控制[J]. 系统工程与电子技术, 2017, 39(8): 1823-1833.
[11]	周欢, 赵辉, 韩统, 黄汉桥. 基于规则的无人机集群飞行与规避协同控制[J]. 系统工程与电子技术, 2016, 38(6): 1374-1382.
[12]	张松, 侯明善. 轨迹优化的LASSO网格自适应加密方法[J]. 系统工程与电子技术, 2016, 38(5): 1195-.
[13]	李方伟, 张新跃, 朱江, 黄卿. 基于APDE-RBF神经网络的网络安全态势预测方法[J]. 系统工程与电子技术, 2016, 38(12): 2869-2875.
[14]	李响, 王晓鹏. 径向基代理模型中形状参数对精度的影响[J]. 系统工程与电子技术, 2015, 37(3): 688-692.
[15]	盖俊峰, 赵国荣, 宋超. 基于线性近似和神经网络逼近的模型预测控制[J]. 系统工程与电子技术, 2015, 37(2): 394-399.