Trajectory planning and base attitude restoration of dual-arm free-floating space robot by enhanced bidirectional approach

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.

Graphical abstract

Keywords

free-floating space robot / dual arm / coordinated operation / base attitude restoration / bidirectional approach

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Nomenclature

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
{\mathit{J}}_{\mathrm{G}\omega \mathrm{a}},{\mathit{J}}_{\mathrm{G}\omega \mathrm{b}}	Angular velocity general-Jacobian matrix of arm i
Jsα, {\mathit{J}}_{\mathrm{s}\omega }	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
\tilde{\mathit{u}}	Augmented input composed by u1 and u2, and \tilde{\mathit{u}}T = [{\mathit{u}}_1^{\mathrm{T}},{\mathit{u}}_2^{\mathrm{T}}]T
U	System input in the EBA
U1, U2	Inputs of the real and virtual robots in the EBA, respectively
\tilde{\mathit{U}}	Augmented input composed by U1 and U2, and \tilde{\mathit{U}}T = [{\mathit{U}}_1^{\mathrm{T}},{\mathit{U}}_2^{\mathrm{T}}]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
\overline{\mathit{W}}	Augmented input matrix of the robot system in BA, and \overline{\mathit{W}} = [W1, −W2]
WL	Mapping matrix from variable z to variable \dot{\mathit{x}} of the constraint-end robot system
\overline{\mathit{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
{\text{ω}}_{\mathrm{a}}, {\text{ω}}_{\mathrm{b}}	End angular velocities of arms A and B, respectively
λ	Damping factor
ξ	Arbitrary vector

Acknowledgements

This study was funded by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 91848202), and the National Natural Science Foundation of China (Grant No. 51875114). No conflict of interest exists in the submission of this manuscript, and the manuscript is approved by all authors for publication.

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