Contact detumbling toward a nutating target through deformable effectors and prescribed performance controller

doi:10.23919/JSEE.2023.000121

Journal of Systems Engineering and Electronics ›› 2024, Vol. 35 ›› Issue (3): 753-768.doi: 10.23919/JSEE.2023.000121

• CONTROL THEORY AND APPLICATION • Previous Articles

Contact detumbling toward a nutating target through deformable effectors and prescribed performance controller

Yue ZANG¹(), Yao ZHANG¹^,*(), Quan HU¹(), Mou LI²(), Yujun CHEN²()

¹ School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
² China Academy of Space Technology, Beijing 100029, China

Received:2022-01-04 Online:2024-06-18 Published:2024-06-19
Contact: Yao ZHANG E-mail:zangyue2016@bit.edu.cn;zhangyao@bit.edu.cn;huquan@bit.edu.cn;limou2333@163.com;chenyj1001@163.com
About author:
ZANG Yue was born in 1993. She received her Ph.D. degree in aeronautical and astronautical science and technology from the School of Aerospace Engineering, Beijing Institute of Technology in 2022. Her research interests are spacecraft attitude control and uncontrolled satellite detumbling. E-mail: zangyue2016@bit.edu.cn

ZHANG Yao was born in 1985. He received his Ph. D. degree in aeronautical and astronautical science and technology from School of Astronautics, Beihang Unicersity in 2012. He is an associate professor at the School of Aerospace Engineering, Beijing Institute of Technology. His research interests are spacecraft attitude control, spacecraft vibration isolation, spacecraft on-orbit service, and spacecraft cluster dynamics and control. E-mail: zhangyao@bit.edu.cn

HU Quan was born in 1987. He received his Ph.D. degree in aeronautical and astronautical science and technology from School of Astronautics, Beihang Unicersity in 2014. He is an associate professor at the School of Aerospace Engineering, Beijing Institute of Technology. His research interests are multibody dynamics, attitude control and vibration suppression of flexible spacecraft, and dynamics and control of space robot. E-mail: huquan@bit.edu.cn

LI Mou was born in 1992. He received his Ph. D. degree in aeronautical and astronautical science and technology from the School of Aerospace Engineering, Beijing Institute of Technology in 2021. He is an engineer in China Academy of Space Technology in 2021. His research interests are spacecraft dynamics and control and uncontrolled satellite detumbling. E-mail: limou2333@163.com

CHEN Yujun was born in 1981. He received his Ph. D. degree in aeronautical and astronautical science and technology from the School of Aerospace Engineering, Beijing Institute of Technology in 2011. He is is a senior engineer in China Academy of Space Technology. His research interests are spacecraft design and multidisciplinary optimization. E-mail: chenyj1001@163.com
Supported by:
This work was supported by the National Natural Science Foundation of China (11972077; 11672035).

Abstract

Abstract:

Detumbling operation toward a rotating target with nutation is meaningful for debris removal but challenging. In this study, a deformable end-effector is first designed based on the requirements for contacting the nutating target. A dual-arm robotic system installed with the deformable end-effectors is modeled and the movement of the end-tips is analyzed. The complex operation of the contact toward a nutating target places strict requirements on control accuracy and controller robustness. Thus, an improvement of the tracking error transformation is proposed and an adaptive sliding mode controller with prescribed performance is designed to guarantee the fast and precise motion of the effector during the contact detumbling. Finally, by employing the proposed effector and the controller, numerical simulations are carried out to verify the effectiveness and efficiency of the contact detumbling toward a nutating target.

Key words: nutating target, contact detumbling, dual-arm space robot, deformable end-effector, prescribed performance controller

Yue ZANG, Yao ZHANG, Quan HU, Mou LI, Yujun CHEN. Contact detumbling toward a nutating target through deformable effectors and prescribed performance controller[J]. Journal of Systems Engineering and Electronics, 2024, 35(3): 753-768.

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Parameter	Range
Parameter	Closed	Opened
x_c/m	0.350	0.050
θ_p/(°)	30.000	75.964
L_c/m	0.433	0.121
r_c/m	0.250	0.485

Item	Linear density/(kg/m)	Length/m	S_j/(kg·m²)	I_j/(kg·m²)
Value	5	l₁=0.8	S₁=[1.6;0;0]	I₁=diag([0.0012 0.853 0.853])
		l₂=2.5	S₂=[15.625;0;0]	I₂=diag([0.0038 26.042 26.042])
		l₃=2	S₃=[10;0;0]	I₃=diag([0.0031 13.33 13.33])
		l₄=1	S₄=[2.5;0;0]	I₄=diag([0.0015 1.667 1.667])

Item	Value
Initial position of the geometric center of the end tips/m	[6 1.5 0]
Final position of the geometric center of the end tips/m	[6 1.7 0]
Initial joints configuration/(°)	[16.95 2.28 −37.15 −12.24 −5.07 8.18 −64.26]
Initial x_c/m	0.3464 (θ_p0 = 30.29 °)
Demand deformation of x_c/m	$ - $0.241 (Δr_c =0.192 m)
Demand deformation of joints/(°)	[1.9 −0.02 0.06 0.07 −0.27 −0.32 −1.93]

Item	Value
SMC	$\begin{aligned} &{ {\lambda }_{\text{arm} } }={ {\lambda }_{\text{claw} } }=3 \\ &{ {k}_{\text{arm} } }={ {k}_{\text{claw} } }=120 \\ &{ {\varepsilon }_{\text{arm} } }={ {\varepsilon }_{\text{claw} } }=0.01 \\ \end{aligned}$
PPASMC	$\begin{array}{l}{\lambda _{ {\rm{arm} } } } = {\lambda _{ {\rm{claw} } } } = 3\\{{\boldsymbol{\varGamma }}_{\rm{1} } } = {\rm{diag} }([\begin{array}{{20}{c} }{20}&{20}&{20}&{20}&{20}&{20}&{20}&{0.05}\end{array}])\\{{\boldsymbol{\varGamma}} _2} = {\rm{diag} }([\begin{array}{{20}{c} }3&3&3&3&3&3&3&{0.5}\end{array}]){\kern 1pt} \\{{\boldsymbol{p}}_{ {\rm{arm} } } } = \left[ {\begin{array}{{20}{c} }{0.2}&{0.5}&5&{0.1}\end{array} } \right]\\{{\boldsymbol{p}}_{ {\rm{claw} } } } = \left[ {\begin{array}{{20}{c} }{0.2}&{0.2}&{20}&{0.1}\end{array} } \right]\\{k_{ {\rm{arm} } } } = 10{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {k_{ {\rm{claw} } } } = 5\\{\varepsilon _{ {\rm{arm} } } } = {\varepsilon _{ {\rm{claw} } } } = 0.001\end{array}$
Initial state of the target	$\begin{aligned}&{m_{\rm{T} } } = 500\;{\rm{kg,} }{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \\&{ { {V} }_{\rm{T} } }{\rm{ = 1} } \times {\rm{1} } \times {\rm{1} }{\kern 1pt}{ {\rm{m} }^3}\\&{ {\boldsymbol{\omega} } _{\rm{T} } } = \left[ {\begin{array}{{20}{c} }1&{20}&{ - 1}\end{array} } \right]^\circ /{\rm{s} }\\&{ {\boldsymbol{R} }_{\rm{T} } } = \left[ {\begin{array}{{20}{c} }6&0&0\end{array} } \right]{\rm{m} }\end{aligned}$
Initial state of the end-effector	x_c=0.1 m
Desired state of the end-effector	x_c=0.17 m
Impedance parameters of the deformable end-effectors	[10 15 10]

Parameter	Simulation 1	Simulation 2
Parameter	PPSMC	SMC
Angular accerleration of target/(°/s²)	−0.0177	−0.0101
Variation range of the target displacement/m	0.0083	0.0247
Average value of the normal contact force of one end-effector/N	${{\boldsymbol{F}}_1} = \left[ {\begin{array}{{20}{c} } {0.061} \\ {0.350} \\ {0.010} \end{array} } \right],{\kern 1pt} {\kern 1pt} {\kern 1pt} {{\boldsymbol{F}}_2} = \left[ {\begin{array}{{20}{c} } { - 0.063} \\ { - 0.351} \\ {0.031} \end{array} } \right]$	${{\boldsymbol{F}}_1} = \left[ {\begin{array}{{20}{c} } {0.027} \\ {0.177} \\ {0.012} \end{array} } \right],{\kern 1pt} {\kern 1pt} {\kern 1pt} {{\boldsymbol{F}}_2} = \left[ {\begin{array}{{20}{c} } { - 0.041} \\ { - 0.177} \\ {0.029} \end{array} } \right]$
Average value of the resultant force and torque acting on the target/(N/Nm)	${\boldsymbol{F}} = \left[ {\begin{array}{{20}{c} } {5 \times { {10}^{ - 4} } } \\ 0 \\ {6 \times { {10}^{ - 4} } } \end{array} } \right],{\kern 1pt} {\kern 1pt} {\kern 1pt} {\boldsymbol{T}} = \left[ {\begin{array}{{20}{c} } { - 0.038} \\ { - 0.070} \\ {0.052} \end{array} } \right]$	${\boldsymbol{F}} = \left[ {\begin{array}{{20}{c} } {7 \times { {10}^{ - 4} } } \\ 0 \\ {2 \times { {10}^{ - 3} } } \end{array} } \right],{\kern 1pt} {\kern 1pt} {\kern 1pt} {\boldsymbol{T}} = \left[ {\begin{array}{{20}{c} } { - 0.030} \\ { - 0.040} \\ {0.025} \end{array} } \right]$
Average tracking error of the arm joints/(°)	[0.026 0.022 0.014 0.007 0.003 0.093 0.093]	[0.183 0.038 0.090 0.009 0.006 0.109 0.109]
Variation range of the distance between the end tips and the surface center/m	0.062	0.075

Contact detumbling toward a nutating target through deformable effectors and prescribed performance controller

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