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.
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Abbreviations
- BA:
-
Bidirectional approach
- DOF:
-
Degree of freedom
- EBA:
-
Enhanced bidirectional approach
- FFSR:
-
Free-floating space robot
- RPY:
-
Roll-pitch-yaw
- A, A L :
-
State matrices of the free-end system and constraint-end system in the EBA
- A 1, A 2 :
-
State matrices of the real and virtual robots in the free-end system in the EBA
- A l1, A l2 :
-
State matrices of the real and virtual robots in the constraint-end system in the EBA
- B, B L :
-
Input matrices of the free-end system and constraint-end system in the EBA
- B 1, B 2 :
-
Input matrices of the real and virtual robots in the free-end system in the EBA
- B L1, B L2 :
-
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
- J Gva, J Gvb :
-
Velocity general-Jacobian matrix of arms A and B
- J Gωa, J Gωb :
-
Angular velocity general-Jacobian matrix of arm i
- J sα J sω :
-
Analytical and geometric Base-Jacobian
- k :
-
Arbitrary positive number
- k ij, k cij, k sij :
-
Coefficients of the near-optimal control approach
- k i :
-
Coefficients of the 5-degree-polynomial
- K p :
-
Proportional parameter in the closed-loop PD inverse dynamic control method
- K d :
-
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
- O g :
-
Inertial coordinate system
- P :
-
Undetermined intermediate matrix that unifies the dimensions of Δx and z
- Q :
-
Arbitrary symmetric positive-definite matrix
- r a, r b :
-
End vectors of arms A and B, respectively
- r ab :
-
Vector pointing from arm B end to arm A end
- s :
-
Combined variable used for Lyapunov function
- t 0 :
-
Time when the joint velocities are desired to be zero
- t m :
-
Meeting time
- t* :
-
Initial time of trajectory planning
- T :
-
Total planning time of the near-optimal method
- u :
-
System input in the BA
- u 1, u 2 :
-
Inputs of the real and virtual robots in the BA, respectively
- ũ :
-
Augmented input composed by u1 and u2, and ũT = [u T1 , u T2 ]T
- U :
-
System input in the EBA
- U 1, U 2 :
-
Inputs of the real and virtual robots in the EBA, respectively
- Ũ :
-
Augmented input composed by U1 and U2, and ŨT = [U T1 , U T2 ]T
- v a, v b :
-
End velocity of arms A and B, respectively
- V :
-
Lyapunov function of the system
- W :
-
Input matrix of the robot system in the BA
- W 1, W 2 :
-
Input matrices of the real and virtual robot systems in the BA, respectively
- \({\boldsymbol{\bar W}}\) :
-
Augmented input matrix of the robot system in BA, and \({\boldsymbol{\bar W}} = [{{\boldsymbol{W}}_1}, - {{\boldsymbol{W}}_2}]\)
- W l :
-
Mapping matrix from variable z to variable ẋ of the constraint-end robot system
- \({{\boldsymbol{\bar W}}_L}\) :
-
Augmented mapping matrix in the constraint-end system
- x :
-
State variable of robot in the BA
- x 1, x 2 :
-
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
- X 1, X 2 :
-
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
- α x, α y, α z :
-
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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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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Xie, Z., Zhao, X., Jiang, Z. et al. Trajectory planning and base attitude restoration of dual-arm free-floating space robot by enhanced bidirectional approach. Front. Mech. Eng. 17, 2 (2022). https://doi.org/10.1007/s11465-021-0658-y
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DOI: https://doi.org/10.1007/s11465-021-0658-y