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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

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Front. Mech. Eng.    2022, Vol. 17 Issue (1) : 2    https://doi.org/10.1007/s11465-021-0658-y
RESEARCH ARTICLE
Trajectory planning and base attitude restoration of dual-arm free-floating space robot by enhanced bidirectional approach
Zongwu XIE1, Xiaoyu ZHAO1, Zainan JIANG1(), Haitao YANG2, Chongyang LI1
1. State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China
2. Robotic System Department, Jiangsu Jitri-Hust Intelligent Equipment Technology, Wuxi 214000, China
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Abstract

When free-floating space robots perform space tasks, the satellite base attitude is disturbed by the dynamic coupling. The disturbance of the base orientation may affect the communication between the space robot and the control center on earth. In this paper, the enhanced bidirectional approach is proposed to plan the manipulator trajectory and eliminate the final base attitude variation. A novel acceleration level state equation for the nonholonomic problem is proposed, and a new intermediate variable-based Lyapunov function is derived and solved for smooth joint trajectory and restorable base trajectories. In the method, the state equation is first proposed for dual-arm robots with and without end constraints, and the system stability is analyzed to obtain the system input. The input modification further increases the system stability and simplifies the calculation complexity. Simulations are carried out in the end, and the proposed method is validated in minimizing final base attitude change and trajectory smoothness. Moreover, the minute internal force during the coordinated operation and the considerable computing efficiency increases the feasibility of the method during space tasks.
Keywords free-floating space robot      dual arm      coordinated operation      base attitude restoration      bidirectional approach     
Corresponding Author(s): Zainan JIANG   
Just Accepted Date: 19 November 2021   Online First Date: 27 January 2022    Issue Date: 28 January 2022
 Cite this article:   
Zongwu XIE,Xiaoyu ZHAO,Zainan JIANG, et al. Trajectory planning and base attitude restoration of dual-arm free-floating space robot by enhanced bidirectional approach[J]. Front. Mech. Eng., 2022, 17(1): 2.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-021-0658-y
https://academic.hep.com.cn/fme/EN/Y2022/V17/I1/2
Fig.1  Task scenarios of free-floating space robot: (a) robot with free ends; (b) robot with end constraints.
Joint θi/(° ) αi/(° ) ai/m di/m
1 0 0 0 0.225
2 0 90 0 0.240
3 −90 −90 0 0.240
4 0 0 0.56 0.200
5 90 0 0.5 0.195
6 0 90 0 0.180
7 0 −90 0 0.476
Tab.1  D-H parameters of free-floating space robot system
Fig.2  D-H coordinate systems of dual-arm free-floating space robot.
Robot link Mass/kg Mass center coordinate Ixx/(kg?m2) Ixy/(kg?m2) Ixz/(kg?m2) Iyy/(kg?m2) Iyz/(kg?m2) Izz/(kg?m2)
X/m Y/m Z/m
Base 510.00 0 0 0 625.00 −4.95 6.58 452.50 −2.39 450.00
Body1 6.34 0 −0.07 −0.05 0.09 0 0 0.05 0.02 0.07
Body2 6.34 0 0.07 −0.05 0.09 0 0 0.05 0.02 0.07
Body3 7.93 0.23 0 −0.03 0.08 0 0.12 0.57 0 0.53
Body4 5.67 0.24 0 0 0.03 0 0.05 0.33 0 0.31
Body5 2.80 0 ?0.03 −0.03 0.01 0 0 0.01 0 0.01
Body6 2.70 −0.03 0.02 0 0.01 0 0 0.01 0 0.01
Body7 10.01 0 ?0.01 −0.20 0.15 0 0 0.20 0.01 0.10
Tab.2  Inertia parameters of free-floating space robot system
Fig.3  Structure of dual-arm free-floating space robot system.
Fig.4  Joint angular velocity of free-floating space robot without end constraints: (a) joint angular velocity in the enhanced bidirectional approach, (b) joint angular velocity in the bidirectional approach, (c) joint angular velocity in the 5-degree-polynomial planning method, and (d) joint angular velocity in the near-optimal control approach.
Fig.5  Joint angle of free-floating space robot without end constraints: (a) joint angle in the enhanced bidirectional approach, (b) joint angle in the bidirectional approach, (c) joint angle in the 5-degree-polynomial planning method, and (d) joint angle in the near-optimal control approach.
Fig.6  Satellite base attitude of free-floating space robot without end constraints: (a) RPY angle in the enhanced bidirectional approach, (b) RPY angle in the bidirectional approach, (c) RPY angle in the 5-degree-polynomial planning method, and (d) RPY angle in the near-optimal control approach.
Fig.7  Joint angular velocity of free-floating space robot with end constraints: (a) joint angular velocity of the enhanced bidirectional approach, (b) joint angular velocity of the leader–follower method, and (c) joint angular velocity of the near-optimal control approach.
Fig.8  Joint angle of free-floating space robot with end constraints: (a) joint angle of the enhanced bidirectional approach, (b) joint angle of the leader–follower method, and (c) joint angle of the near-optimal control approach.
Fig.9  Satellite base attitude of free-floating space robot with end constraints: (a) RPY angle in the enhanced bidirectional approach, (b) RPY angle in the leader–follower method, and (c) RPY angle in the near-optimal control approach.
Fig.10  Impedance force of slave arm in dual-arm system without end constraints: (a) impedance force in the enhanced bidirectional approach, (b) impedance force in the leader–follower method, and (c) impedance force in the near-optimal control approach.
Abbreviations
BA Bidirectional approach
DOF Degree of freedom
EBA Enhanced bidirectional approach
FFSR Free-floating space robot
RPY Roll-pitch-yaw
Variables
A, AL State matrices of the free-end system and constraint-end system in the EBA
A1, A2 State matrices of the real and virtual robots in the free-end system in the EBA
AL1, AL2 State matrices of the real and virtual robots in the constraint-end system in the EBA
B, BL Input matrices of the free-end system and constraint-end system in the EBA
B1, B2 Input matrices of the real and virtual robots in the free-end system in the EBA
BL1, BL2 Input matrices of the real and virtual robots in the constraint-end system in the EBA
h Number of the Fourier orthogonal basis
H Coefficient of the geometric constraints in coordinated operation
I Identity matrix
JGva, JGvb Velocity general-Jacobian matrix of arms A and B
JG ωa,J Gω b Angular velocity general-Jacobian matrix of arm i
Jsα, Jsω Analytical and geometric Base-Jacobian
k Arbitrary positive number
kij, kcij, ksij Coefficients of the near-optimal control approach
ki Coefficients of the 5-degree-polynomial
Kp Proportional parameter in the closed-loop PD inverse dynamic control method
Kd Differential parameter in the closed-loop PD inverse dynamic control method
L Null space of H
m Arbitrary positive number
N Joint number of space robot
Og Inertial coordinate system
P Undetermined intermediate matrix that unifies the dimensions of Δx and z
Q Arbitrary symmetric positive-definite matrix
ra, rb End vectors of arms A and B, respectively
  
rab Vector pointing from arm B end to arm A end
s Combined variable used for Lyapunov function
t0 Time when the joint velocities are desired to be zero
tm Meeting time
t* Initial time of trajectory planning
T Total planning time of the near-optimal method
u System input in the BA
u1, u2 Inputs of the real and virtual robots in the BA, respectively
u~ Augmented input composed by u1 and u2, and u~T = [ u1T, u2T]T
U System input in the EBA
U1, U2 Inputs of the real and virtual robots in the EBA, respectively
U~ Augmented input composed by U1 and U2, and U~T = [ U1T, U2T]T
va, vb End velocity of arms A and B, respectively
V Lyapunov function of the system
W Input matrix of the robot system in the BA
W1, W2 Input matrices of the real and virtual robot systems in the BA, respectively
W¯ Augmented input matrix of the robot system in BA, and W¯ = [W1, −W2]
WL Mapping matrix from variable z to variable x ˙ of the constraint-end robot system
W¯L Augmented mapping matrix in the constraint-end system
x State variable of robot in the BA
x1, x2 System state variables of the real and virtual robots in the BA, respectively
Δx System state error defined by Δx = x1 − x2
X State variable of robot in the EBA
X1, X2 System state variable of the real and virtual robots in the EBA, respectively
z Joint angular velocity in the EBA and is a component of the system state variable in the EBA
α Vector of satellite base roll-pitch-yaw (RPY) angle, rad
αx, αy, αz x, y, z terms of the satellite base RPY angle, respectively
Δα Base RPY angle error, rad
θ Vector of joint angle, rad
Δθ Joint angle error, rad
ω a, ω b End angular velocities of arms A and B, respectively
λ Damping factor
ξ Arbitrary vector
  
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