Integrated modeling of spacecraft relative motion dynamics using dual quaternion

doi:10.21629/JSEE.2018.02.17

Journal of Systems Engineering and Electronics ›› 2018, Vol. 29 ›› Issue (2): 367-377.doi: 10.21629/JSEE.2018.02.17

• Control Theory and Application • Previous Articles Next Articles

Integrated modeling of spacecraft relative motion dynamics using dual quaternion

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

¹ Control and Simulation Center, Harbin Institute of Technology, Harbin 150080, China
² Research Center of Satellite Technology, Harbin Institute of Technology, Harbin 150080, China

Received:2017-04-20 Online:2018-04-26 Published:2018-04-27
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 Instituter of Technology. She is a Ph.D in Harbin Institute of Technology. Her research interests are aircraft control and nonlinear control. 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. Now he is a professor at the Control and Simulation Center, Harbin Institute of Technology. His research interests are nonlinear control, aircraft 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 2011. Now he is a Ph.D in Harbin Institute of Technology. His research interests are spacecraft attitude dynamics and control. E-mail: GTYPHIT@163.com
Supported by:
the National Natural Science Foundation of China(61074127);the National Natural Science Foundation of China(61427809);This work was supported by the National Natural Science Foundation of China (61074127; 61427809)

Abstract

Abstract:

To realize high accurate control of relative position and attitude between two spacecrafts, the coupling between position and attitude must be fully considered and a more precise model should be established. This paper breaks the traditional divide and conquer idea, and uses a mathematical tool, namely dual quaternion to establish the integrated 6 degree-of-freedom (6-DOF) model of relative position and attitude, which describes the coupled relative motion in a compact and efficient form and needs less information of the target. Considering the complex operation rules and the unclarity of the current relative motion model in dual quaternion, necessary mathematical foundations are given at first, followed by clear and detailed modeling process and analysis. Finally a generalized proportion-derivative (PD) controller law is designed. The simulation results show that based on the integrated model established by dual quaternion, this control law can achieve a high control accuracy of relative motion.

Key words: relative motion, dual quaternion, position and attitude coupling, integrated modeling

Xuan PENG, Xiaoping SHI, Yupeng GONG. Integrated modeling of spacecraft relative motion dynamics using dual quaternion[J]. Journal of Systems Engineering and Electronics, 2018, 29(2): 367-377.

Figures/Tables 13

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References 26

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Item	Quaternion	Dual quaternion
Degree of	3	6
freedom	3	6
Coordinate	${{{\mathit{\boldsymbol{r}}}}}^b = {{{\mathit{\boldsymbol{q}}}}}^* \circ {{{\mathit{\boldsymbol{r}}}}}^a\circ{{{\mathit{\boldsymbol{q}}}}}$	$\widehat {{{{\mathit{\boldsymbol{a}}}}}}^b = \widehat {{{{\mathit{\boldsymbol{q}}}}}}^* \circ \widehat {{{{\mathit{\boldsymbol{a}}}}}}^a\circ \widehat {{{{\mathit{\boldsymbol{q}}}}}}$
transform	Euler theory	Charles theory
Geometric	$\left[\!\!\begin{array}{*{20}c} {\cos ({\it\Phi} /2)} \\ {{{{\mathit{\boldsymbol{e}}}}}\sin ({\it\Phi} /2)} \\ \end{array}\!\!\right]$	$\left[\!\!\begin{array}{*{20}c} {\cos (\widehat {{\it\Phi} }/2)} \\ {\widehat {{{{\mathit{\boldsymbol{L}}}}}}\sin (\widehat {{\it\Phi} }/2)} \\ \end{array}\!\!\right]$
meaning

Parameter	Value
$m_c $/kg	200
${{{\mathit{\boldsymbol{J}}}}}_c$/(kg·m2)	$diag(300, 200, 250)$
$r_t /\mbox{km}$	6 900
$\left[\!\!\begin{array}{*{20}c} {\varphi _x } & {\varphi _y } & {\varphi _z } \end{array}\!\!\right]/(^{\circ})$	$\left[\!\!\begin{array}{*{20}c} {-5.73} & {-2.86} & {6.86} \end{array}\!\!\right]$
${{{\mathit{\boldsymbol{r}}}}}_{e0}^c /\mbox{m}$	$\left[\!\!\begin{array}{*{20}c} {-120} & {-60} & {50} \end{array}\!\!\right]^{{{\rm{T}}}}$
$\bm\omega_{e0}^c /(\mbox{rad}/\mbox{s})$	$\left[\!\!\begin{array}{*{20}c} {0.008} & {-0.005} & {0.006}\end{array}\!\!\right]^{{{\rm{T}}}}$
$\dot {{{{\mathit{\boldsymbol{r}}}}}}_{e0}^c /(\mbox{m}/\mbox{s})$	$\left[\!\!\begin{array}{*{20}c} {0.255} & {{0.385}} & {{0.075}}\end{array}\!\!\right]^{{{\rm{T}}}}$
${{{\mathit{\boldsymbol{r}}}}}_{ew}^c /\mbox{m}$	$\left[\!\!\begin{array}{*{20}c} {-20} & 0 & 0 \end{array}\!\!\right]^{{{\rm{T}}}} $

Controlled variable	Order of magnitude
Attitude angle/(?)	10_?5
Relative position/m	10_?2
Angular velocity/(rad/s)	10_?6
Velocity/(m/s)	10_?3

Integrated modeling of spacecraft relative motion dynamics using dual quaternion

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