提出了一种无速度反馈的航天器姿轨耦合跟踪控制算法。首先建立起基于对偶四元数的带扰动和参数不确定性的航天器姿轨耦合动力学模型。然后基于浸入与不变流形理论设计了速度观测器，通过增益注入对非线性项抑制，从而同时估计角速度和线速度。利用李雅普诺夫函数分析了观测器状态量的收敛性以及注入增益的有界性，证明了该观测器的指数稳定性。最后设计了一个比例-微分（PD）位置与姿态跟踪控制器，该控制器可以实现航天器的任意姿态与位置跟踪，分析了这种观测-控制结构的闭环系统渐近稳定性。仿真验证了该速度观测器和控制器的有效性以及对于参数不确定性和测量噪声具有较好的鲁棒性。
An attitude and position coupled tracking control algorithm for spacecraft without velocity feedback is proposed in this paper. A coupling dynamics model for the spacecraft with perturbations and parameter uncertainties based on dual quaternions is established firstly. Then, based on the theory of immersion and invariance, a velocity observer is designed. The observer estimates the angular velocity and the linear velocity together, and suppresses the nonlinear terms by dynamic scaling injection. The convergence of the observer states and the boundedness of injection gain are analyzed theoretically by Lyapunov function, and the exponential stability of the observer is proved. The rate of convergence of the observer states can be changed by adjusting the gains. Finally, a PD position and attitude tracking controller is designed. The controller can realize tracking of any attitude and position of the spacecraft. The asymptotic stability of the closed-loop system of this observer-controller cascade structure is analyzed. Simulation verifies the effectiveness of the observer-controller system and its robustness to uncertain parameters and measurement noises.
[1] YEOMANS D K, ANTREASIAN P G, BARRIOT J P, et al. Radio science results during the NEAR-shoemaker spacecraft rendezvous with eros[J]. Science, 2000, 289(5487):2085-8.
[2] FUJIWARA A, KAWAGUCHI J, YEOMANS D K, et al. The rubble-Pile asteroid Itokawa as observed by hayabusa[J]. Science, 2006, 312(5778):1330-1334.
[3] FLORES-ABAD A, MA O, PHAM K, et al. A review of space robotics technologies for on-orbit servicing[J]. Progress in Aerospace Sciences, 2014, 68(8):1-26.
[4] AGHILI F. A prediction and motion-planning scheme for visually guided robotic capturing of free-floating tumbling objects with uncertain dynamics[J]. IEEE Transactions on Robotics, 2012, 28(3):634-49.
[5] YUANXIN W, XIAOPING H, DEWEN H, et al. Strapdown inertial navigation system algorithms based on dual quaternions[J]. IEEE Transactions on Aerospace and Electronic Systems, 2005, 41(1):110-32.
[6] CRASSIDIS J L, MARKLEY F L, CHENG Y. Survey of nonlinear attitude estimation methods[J]. Journal of Guidance, Control, and Dynamics, 2007, 30(1):12-28.
[7] FARHAD A, KOUROSH P. Adaptive motion estimation of a tumbling satellite using laser-vision data with unknown noise characteristics[C]//Proceedings of the 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, NJ:IEEE Press, 2007.
[8] AGHILI F, PARSA K. Motion and parameter estimation of space objects using laser-vision data[J]. Journal of Guidance, Control, and Dynamics, 2009, 32(2):538-50.
[9] GUI H, DE RUITER A H J. Quaternion invariant extended kalman filtering for spacecraft attitude estimation[J]. Journal of Guidance, Control, and Dynamics, 2018, 41(4):863-878.
[10] SCHLANBUSCH R, GRØTLI E I, LORIA A, et al. Hybrid attitude tracking of rigid bodies without angular velocity measurement[J]. Systems & Control Letters, 2012, 61(4):595-601.
[11] SCHLANBUSCH R, LORIA A, KRISTIANSEN R, et al. PD+ based output feedback attitude control of rigid bodies[J]. IEEE Transactions on Automatic Control, 2012, 57(8):2146-2152.
[12] HU J, ZHANG H. Bounded output feedback of rigid-body attitude via angular velocity observers[J]. Journal of Guidance, Control, and Dynamics, 2013, 36(4):1240-1248.
[13] ZOU A M. Finite-time output feedback attitude tracking control for rigid spacecraft[J]. IEEE Transactions on Control Systems Technology, 2014, 22(1):338-345.
[14] SCHLANBUSCH R, INGAR GROTLI E I. Hybrid certainty equivalence control of rigid bodies with quaternion measurements[J]. IEEE Transactions on Automatic Control, 2015, 60(9):2512-2517.
[15] YANG S, MAZENC F, AKELLA M R. Ultimate boundedness results for noise-corrupted quaternion output feedback attitude tracking controllers[J]. Journal of Guidance, Control, and Dynamics, 2017, 40(12):3265-3273.
[16] SUN D, CRASSIDIS J L. Observability analysis of six-degree-of-freedom configuration determination using vector observations[J]. Journal of Guidance, Control, and Dynamics, 2002, 25(6):1149-1157.
[17] SINGLA P, SUBBARAO K, JUNKINS J L. Adaptive output feedback control for spacecraft rendezvous and docking under measurement uncertainty[J]. Journal of Guidance, Control, and Dynamics, 2006, 29(4):892-902.
[18] VENKATRAMAN A, ORTEGA R, SARRAS I, et al. Speed observation and position feedback stabilization of partially linearizable mechanical systems[J]. IEEE Transactions on Automatic Control, 2010, 55(5):1059-1074.
[19] BRODSKY V, SHOHAM M. Dual numbers representation of rigid body dynamics[J]. Mechanism and Machine Theory, 1999, 34(5):693-718.
[20] ASTOLFI A, ORTEGA R. Immersion and invariance:A new tool for stabilization and adaptive control of nonlinear systems[J]. IEEE Transactions on Automatic Control, 2003, 48(4):590-606.
[21] ASTOLFI A, ORTEGA R, VENKATRAMAN A. A globally exponentially convergent immersion and invariance speed observer for mechanical systems with non-holonomic constraints[J]. Automatica, 2010, 46(1):182-189.
[22] STAMNES Ø N, AAMO O M, KAASA G O. A constructive speed observer design for general Euler-Lagrange systems[J]. Automatica, 2011, 47(10):2233-2238.
[23] GUI H, VUKOVICH G. Dual-quaternion-based adaptive motion tracking of spacecraft with reduced control effort[J]. Nonlinear Dynamics, 2015, 83(1-2):597-614.
CJA