Constrained State Estimation of Linear N-body Space Tethered System Based on the Pseudo Measurement Method
FANG Guotao1,2, ZHANG Yizhai1,2, HUANG Panfeng1,2
1. Research Center for Intelligent Robotics, School of Astronautics, Northwestern Polytechnical University, Xi'an 710072, China; 2. National Key Laboratory of Aerospace Flight Dynamics, Northwestern Polytechnical University, Xi'an 710072, China
Abstract：A constrained state estimation scheme based on the pseudo measurement method is proposed for the linear N-body space tethered system (STS), which takes the tether length as prior information and uses only two GPS (global positioning system) sensors. Firstly, a novel general dynamic model of linear N-body STS is established based on UdwadiaKalaba method. Then, an improved square root unscented Kalman filter (IUKF) is developed considering the low update frequency of GPS sensors and the high complexity of Jacobian matrix calculation in the linearization of the nonlinear system model. Furthermore, the rank criterion based on the local weak observability of Lie derivatives is utilized to prove that the proposed estimation scheme is observable. Finally, extensive simulation results are presented to verify the effectiveness of the proposed scheme. The simulation results show that the proposed scheme can guarantee the precise state estimation and real-time tracking.
 孟中杰, 黄攀峰, 鲁迎波, 等. 在轨服务中空间系绳的应用及发展[J]. 宇航学报, 2019, 40(10):1134-1145. Meng Z J, Huang P F, Lu Y B, et al. Application and development of space tether in on-orbit servicing[J]. Journal of Astronautics, 2019, 40(10):1134-1145.  Huang P F, Zhang F, Chen L, et al. A review of space tether in new applications[J]. Nonlinear Dynamics, 2018, 94:1-19.  Huang P F, Zhang F, Cai J, et al. Dexterous tethered space robot:Design, measurement, control, and experiment[J]. IEEE Transactions on Aerospace and Electronic Systems, 2017, 53(3):1452-1468.  Chung S J, Slotine J J E, Miller D W. Nonlinear model reduction and decentralized control of tethered formation flight[J]. Journal of Guidance, Control, and Dynamics, 2007, 30(2):390-400.  Yamagiwa Y, Nohmi M, Aoki Y, et al. Space experiments on basic technologies for a space elevator using microsatellites[J]. Acta Astronautica, 2017, 138:570-578.  Wang B H, Meng Z J, Jia C, et al. Reel-based tension control of tethered space robots[J]. IEEE Transactions on Aerospace and Electronic Systems, 2020, 56(4):3028-3043.  Yu B S, Jin D P, Wen H. Analytical deployment control law for a flexible tethered satellite system[J]. Aerospace Science and Technology, 2017, 66:294-303.  Ellis J R, Hall C D. Model development and code verification for simulation of electrodynamic tether system[J]. Journal of Guidance, Control, and Dynamics, 2009, 32(6):1713-1722.  徐秀栋, 黄攀峰, 孟中杰. 空间绳系机器人抓捕目标过程协同稳定控制[J]. 机器人, 2014, 36(1):100-110. Xu X D, Huang P F, Meng Z J. Coordinated stability control of tethered space robot for capturing the target[J]. Robot, 2014, 36(1):100-110.  Huang P F, Wang D K, Meng Z J, et al. Impact dynamic modeling and adaptive target capturing control for tethered space robots with uncertainties[J]. IEEE/ASME Transactions on Mechatronics, 2016, 21(5):2260-2271.  Zhang Y Z, Huang P F, Song K H, et al. An angles-only navigation and control scheme for noncooperative rendezvous operations[J]. IEEE Transactions on Industrial Electronics, 2019, 66 (11):8618-8627.  Ma Z Q, Huang P F. Nonlinear analysis of discrete-time sliding mode prediction deployment of tethered space robot[J]. IEEE Transactions on Industrial Electronics, 2021, 68(6):5166-5175.  Yousefian P, Salarieh H. Nonlinear control of sway in a tethered satellite system via attitude control of the main satellite[J]. Aerospace Science and Technology, 2017, 63:317-327.  Chung S J, Kong E, Miller D. Dynamics and control of tethered formation flight spacecraft using the SPHERES testbed[C]//AIAA Guidance, Navigation, and Control Conference and Exhibit. Reston, USA:AIAA, 2005. DOI:10.2514/6.2005-6089.  Misra A K, Amier Z, Modi V J. Attitude dynamics of three-body tethered systems[J]. Acta Astronautica, 1988, 17(10):1059-1068.  Li G Q, Zhu Z H. On libration suppression of partial space elevator with a moving climber[J]. Nonlinear Dynamics, 2019, 97(4):2107-2125.  Shi G F, Zhu Z X, Zhu Z H, et al. Parallel optimization of trajectory planning and tracking for three-body tethered space system[J]. IEEE/ASME Transactions on Mechatronics, 2019, 24(1):240-247.  Wang Z K, Cui N G, Fan Y H, et al. Modal and dynamic analysis of a tether for a nonequatorial space elevator[J]. IEEE Access, 2018, 6:74940-74952.  Netzer E, Kane T R. Estimation and control of tethered satellite systems[J]. Journal of Guidance, Control, and Dynamics, 1995, 18(4):851-858.  Fang G T, Zhang Y Z, Huang P F, et al. State estimation of double-pyramid tethered satellite formations using only two GPS sensors[J]. Acta Astronautica, 2021, 180:507-515.  Macdonald M, Badescu V. The international handbook of space technology[M]. Berlin, Germany:Springer, 2014.  Kojima H, Iwasaki M, Fujii H A. Nonlinear control of librational motion of tethered satellites in elliptic orbits[J]. Journal of Guidance, Control, and Dynamics, 2004, 27(2):229-239.  Kumar K D. Review on dynamics and control of nonelectrodynamic tethered satellite systems[J]. Journal of Spacecraft and Rockets, 2006, 43(4):705-720.  Zhou G J, Li K Y, Kirubarajan T, et al. State estimation with trajectory shape constraints using pseudomeasurements[J]. IEEE Transactions on Aerospace and Electronic Systems, 2019, 55(5):2395-2407.  Xu L F, Li X R, Duan Z S, et al. Modeling and state estimation for dynamic systems with linear equality constraints[J]. IEEE Transactions on Signal Processing, 2013, 61(11):2927-2939.  Simon D. Kalman filtering with state constraints:A survey of linear and nonlinear algorithms[J]. IET Control Theory & Applications, 2010, 4(8):1303-1318.  Xu L F, Li X R, Liang Y, et al. Constrained dynamic systems:Generalized modeling and state estimation[J]. IEEE Transactions on Aerospace and Electronic Systems, 2017, 53(5):2594-2609.  Liu C J, Li B B, Chen W H. Particle filtering with soft state constraints for target tracking[J]. IEEE Transactions on Aerospace and Electronic Systems, 2019, 55(6):3492-3504.  Cho H, Udwadia F E. Explicit control force and torque determination for satellite formation-keeping with attitude requirements[J]. Journal of Guidance, Control, and Dynamics, 2013, 36(2):589-605.  Liu Y, Zhang F, Huang P F, et al. Analysis, planning and control for cooperative transportation of tethered multi-rotor UAVs[J]. Aerospace Science and Technology, 2021, 113. DOI:10.1016/j.ast.2021.106673.  Udwadia F E, Kalaba R E. Analytical dynamics:A new approach[M]. Cambridge, UK:Cambridge University Press, 1996.  Qi J J, Sun K, Wang J H, et al. Dynamic state estimation for multi-machine power system by unscented Kalman filter with enhanced numerical stability[J]. IEEE Transactions on Smart Grid, 2018, 9(2):1184-1196.  Menegaz H M T, Ishihara J Y, Borges G A, et al. A systematization of the unscented Kalman filter theory[J]. IEEE Transactions on Automatic Control, 2015, 60(10):2583-2598.  Wolfe J D, Speyer J L, Lee E, et al. Estimation of relative satellite position using transformed differential carrier-phase GPS measurements[J]. Journal of Guidance, Control, and Dynamics, 2007, 30(5):1217-1227.  Gong B C, Wang S, Hao M R, et al. Range-based collaborative relative navigation for multiple unmanned aerial vehicles using consensus extended Kalman filter[J]. Aerospace Science and Technology, 2021, 112. DOI:10.1016/j.ast.2021.106647.  Zhang Y Z, Song K H, Yi J G, et al. Absolute attitude estimation of rigid body on moving platform using only two gyroscopes and relative measurements[J]. IEEE/ASME Transactions on Mechatronics, 2018, 23(3):1350-1361.