Dual-quaternion-based modeling and control for motion tracking of a tumbling target

doi:10.21629/JSEE.2019.05.15

Journal of Systems Engineering and Electronics ›› 2019, Vol. 30 ›› Issue (5): 985-994.doi: 10.21629/JSEE.2019.05.15

• Control Theory and Application • Previous Articles Next Articles

Dual-quaternion-based modeling and control for motion tracking of a tumbling target

Xuan PENG^1,*(), Xiaoping SHI¹(), Yupeng GONG²()

¹ Control and Simulation Center, Harbin Institute of Technology, Harbin 150001, China
² Research Center of Satellite Technology, Harbin Institute of Technology, Harbin 150001, China

Received:2019-02-18 Online:2019-10-08 Published:2019-10-09
Contact: Xuan PENG E-mail:18745047873@163.com;sxp@hit.edu.cn;GTYPHIT@163.com
About author:PENG Xuan was born in 1993. She received her B.S. degree in automation from Harbin Institute of Technology in 2016. She is currently a Ph.D. candidate in Harbin Institute of Technology. Her research interests are dual quaternion, attitude and orbit coupled control of spacecraft. E-mail: 18745047873@163.com|SHI Xiaoping was born in 1965. He received his Ph.D. degree in spacecraft navigation guidance and control from Harbin Institute of Technology in 1994. He is currently a professor at the Control and Simulation Center, Harbin Institute of Technology. His research interests are aircraft control, nonlinear control, and complex system simulation. E-mail: sxp@hit.edu.cn|GONG Yupeng was born in 1993. He received his B.S. degree in spacecraft design and engineering from Harbin Institute of Technology in 2015. He is currently a Ph.D. candidate in Harbin Institute of Technology. His research interests are orbital dynamics of satellite swarms and design of satellite constellation. E-mail: GTYPHIT@163.com
Supported by:
the National Science Foundation of China(61427809);This work was supported by the National Science Foundation of China (61427809)

Abstract

Abstract:

This paper investigates the problem of controlling a chasing spacecraft (chaser) to track and rendezvous with an uncontrolled target. Based on the actual situation, the torque-free motion of an axisymmetric prolate rigid body is employed to represent the short-term attitude motion of the tumbling target. By taking advantage of the dual quaternion's compact and efficient description of the general rigid motion, the coupled and integrated model of the 6-degree-of-freedom (6-DOF) relative motion between the chaser and the tumbling target is derived in the chaser's body fixed frame after taking full consideration of coordinate transformation. Based on the logarithm of dual quaternion, a sliding mode control (SMC) law based on the exponential reaching law and the conti-nuous relay function is brought forward to address the problem of synchronization control of the 6-DOF relative motion. Simulation results illustrate the effectiveness of the proposed method.

Key words: tumbling target, dual-quaternion, coupled dynamics, relative motion

Xuan PENG, Xiaoping SHI, Yupeng GONG. Dual-quaternion-based modeling and control for motion tracking of a tumbling target[J]. Journal of Systems Engineering and Electronics, 2019, 30(5): 985-994.

Figures/Tables 11

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References 36

1	SHAN M H, GUO J, GILL E. Review and comparison of active space debris capturing and removal methods. Progress in Aerospace Sciences, 2016, 80, 18- 32. doi: 10.1016/j.paerosci.2015.11.001
2	ABAD A F, MA O, PHAM K, et al. A review of space robotics technologies for on-orbit servicing. Progress in Aerospace Sciences, 2014, 68, 1- 26. doi: 10.1016/j.paerosci.2014.03.002
3	GOMEZ N O, WALKER S J I. Earth's gravity gradient and eddy currents effects on the rotational dynamics of space debris objects:envisat case study. Advances in Space Research, 2015, 56 (3): 494- 508. doi: 10.1016/j.asr.2014.12.031
4	PRALY N, HILLION M, BONNAL J, et al. Study on the eddy current damping of the spin dynamics of space debris from the Ariane launcher upper stages. Acta Astronautica, 2012, 76 (4): 145- 153.
5	GURFIL P. Relative motion between elliptic orbits:generalized boundedness conditions and optimal formation keeping. Journal of Guidance, Control, and Dynamics, 2005, 28 (4): 761- 767. doi: 10.2514/1.9439
6	SABOL C, BURNS R, MCLAUGHLIN C A. Satellite formation flying design and evolution. Journal of Spacecraft and Rockets, 2001, 38 (2): 270- 278. doi: 10.2514/2.3681
7	MISHNE D. Formation control of satellites subject to drag variations and J2 perturbations. Journal of Guidance, Control, and Dynamics, 2004, 27 (4): 685- 692.
8	SEGAL S, GURFIL P. Effect of kinematic rotation-translation coupling on relative spacecraft translational dynamics. Journal of Guidance, Control, and Dynamics, 2009, 32 (3): 1045- 1050.
9	LI Q, YUAN J P, ZHANG B, et al. Model predictive control for autonomous rendezvous and docking with a tumbling target. Aerospace Science and Technology, 2017, 69, 700- 711. doi: 10.1016/j.ast.2017.07.022
10	JIANG B Y, HU Q L, FISHWELL M I. Fixed-time rendezvous control of spacecraft with a tumbling target under loss of actuator effectiveness. IEEE Trans. on Aerospace and Electronic Systems, 2016, 52 (4): 1576- 1586. doi: 10.1109/TAES.2016.140406
11	WANG X L, ZHOU Z C, HU G J. Global fast terminal sliding mode control of space manipulator for capturing a tumbling satellite. Proc. of the 2nd IEEE Advanced Information Technology Electronic and Automation Control Conference, 2017: 553-558.
12	CHEN B L, GENG Y H. Super twisting controller for on-orbit servicing to noncooperative target. Chinese Journal of Aeronautics, 2015, 28 (1): 285- 293. doi: 10.1016/j.cja.2014.12.030
13	ZHANG D Y, LUO J J, GAO D W, et al. A novel nonlinear control for tracking and rendezvous with a rotating noncooperative target with translational maneuver. Acta Astronautica, 2017, 138, 279- 289.
14	FUNDA J, RICHARD P P. A computational analysis of screw transformations in robotics. IEEE Trans. on Robotics and Automation, 1990, 6 (3): 348- 356. doi: 10.1109/70.56653
15	WU Y X, HU X P, HU D W, et al. Strapdown inertial navigation system algorithms based on dual quaternions. IEEE Trans. on Aerospace Electronic Systems, 2005, 41 (1): 110- 132. doi: 10.1109/TAES.2005.1413751
16	THOMAS F. Approaching dual quaternions from matrix algebra. IEEE Trans. on Robotics, 2014, 30 (5): 1037- 1048. doi: 10.1109/TRO.2014.2341312
17	SHARKAWY A N, ASRAGATHOS N. A comparative study of two methods for forward kinematics and Jacobian matrix determination. Proc. of the International Conference on Mechanical, System and Control Engineering, 2017: 179-183.
18	BRODSKY V, SHOHAM M. Dual numbers representation of rigid body dynamics. Mechanism and Machine Theory, 1999, 34 (5): 693- 718. doi: 10.1016/S0094-114X(98)00049-4
19	WANG J Y, LIANG H C, SUN Z W, et al. Finite-time control for spacecraft formation with dual-number-based description. Journal of Guidance, Control, and Dynamics, 2012, 35 (3): 950- 962. doi: 10.2514/1.54277
20	DONG H Y, HU Q L, MA G F. Dual-quaternion based faulttolerant control for spacecraft formation flying with finite-time convergence. ISA Transactions, 2016, 61 (99): 87- 94.
21	FILIPE N, TSIOTRAS P. Adaptive position and attitudetracking controller for satellite proximity operations using dual quaternions. Journal of Guidance, Control, and Dynamics, 2015, 38 (4): 566- 577. doi: 10.2514/1.G000054
22	GUI H C, VUKOVICH G. Dual quaternion based adaptive motion tracking of spacecraft with reduced control effort. Nonlinear Dynamics, 2016, 83 (1/2): 597- 614.
23	GAO W, ZHU X G, ZHOU M L, et al. ADRC law of spacecraft rendezvous and docking in final approach phase. Journal of Cybernetics, 2016, 47 (3): 236- 248.
24	KAZEMIPOUR A, NOVINZADEH A B. Adaptive position and attitude tracking control for satellite proximity operations using sliding mode and time delay estimation. Proc. of the 25th Iranian Conference on Electrical, 2017: 585-590.
25	DONG H Y, HU Q L, AKELLA M R. Dual-quaternion-based spacecraft autonomous rendezvous and docking under sixdegree-of-freedom motion constraints. Journal of Guidance, Control, and Dynamics, 2018, 41 (5): 1150- 1162. doi: 10.2514/1.G003094
26	LU W, GENG Y H, CHEN X Q, et al. Relative position and attitude coupled control for autonomous docking with a tumbling target. International Journal of Control and Automation, 2011, 4 (4): 1- 22.
27	CHEN B L, GENG Y H. Super twisting controller for on-orbit servicing to noncooperative target. Chinese Journal of Aeronautics, 2015, 28 (1): 285- 293. doi: 10.1016/j.cja.2014.12.030
28	BRODSKY V, SHOHAM M. Dual numbers representation of rigid body dynamics. Mechanism and Machine Theory, 1999, 34 (5): 693- 718. doi: 10.1016/S0094-114X(98)00049-4
29	WANG J Y, LIANG H C, SUN Z W, et al. Relative motion coupled control based on dual quaternion. Aerospace Science Technology, 2013, 25 (1): 102- 113. doi: 10.1016/j.ast.2011.12.013
30	COHEN A, SHOHAM M. Principle of transference-an extension to hyper-dual numbers. Mechanism and Machine Theory, 2018, 125 (1): 101- 110.
31	KUSSABA H T M, FIGUEREDO L F C, ISHIHARA J Y, et al. Hybrid kinematic control for rigid body pose stabilization using dual quaternions. Journal of the Franklin Institute, 2017, 354 (7): 2769- 2787. doi: 10.1016/j.jfranklin.2017.01.028
32	MARKLEY F L, CRASSIDIS J L. Fundamentals of spacecraft attitude determination and control. New York: Springer, 2014.
33	NAKAJIMA Y, MITANI S, TANI H, et al. Detumbling space debris via thruster plume impingement. Proc. of the AIAA/AAS Astrodynamics Dynamics Specialist Conference, 2016: 5660-5679.
34	YOUNGQUIST R C, NURGE M A, STARR S, et al. A slowly rotating hollow sphere in a magnetic field:first steps to despin a space object. American Journal of Physics, 2016, 84 (3): 181- 191. doi: 10.1119/1.4936633
35	GOMEZ N O, WALKER S J I. Eddy currents applied to detumbling of space debris:analysis and validation of approximate proposed methods. Acta Astronautica, 2015, 114, 34- 53. doi: 10.1016/j.actaastro.2015.04.012
36	PENG X, SHI X P, GONG Y P. Integrated modeling of spacecraft relative motion dynamics using dual quaternion. Journal of Systems Engineering and Electronics, 2018, 29 (2): 367- 377. doi: 10.21629/JSEE.2018.02.17

State variable	Value
Relative attitude/($^\circ$)	$10^{ - 2}\times [4.80\; \; \; 4.79\; \; \; 4.80]^{{{\rm{T}}}}$
Relative position/m	$10^{ - 4}\times [8.71\; \; \; 5.67\; \; \; 9.82]^{{{\rm{T}}}}$

Dual-quaternion-based modeling and control for motion tracking of a tumbling target

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