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Adaptive coordinated control of uncertain free-floating space manipulators with prescribed control performance

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Abstract

The paper proposes an adaptive coordinated control scheme on free-floating space manipulators at the dynamic level, with kinematic and dynamic uncertainties. The free-floating space manipulator can be controlled to realize the end-effector trajectory tracking task and the spacecraft attitude regulation task simultaneously, based on the carefully designed prescribed performance error transformations and the reaction null space. In face of nonlinearly parametric feature of the uncertain free-floating space manipulators, a novel attractive manifold control method is proposed by introducing the nonlinear filters on dynamics of the free-floating space manipulators. The parameter estimation error terms can converge to zero, independent of persistent excitation conditions. The proposed adaptive coordinated control scheme can guarantee that both the end-effector tracking error and the spacecraft attitude regulation error possess the prescribed control performances, in the presence of the nonlinearly parametric feature and the nonzero linear and angular momenta of the free-floating space manipulators. The simulation results show the effectiveness of the proposed control scheme.

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Abbreviations

\({\mathbf {E}}_{n}\) :

\((n \times n)\)-dimensional identity matrix

\({\mathcal {L}}_{\infty }\) :

Space on the essentially bounded functions

\({\mathcal {L}}_{p}\) :

Space on the p-order-integrable functions

\(\theta _{b}\) :

Parameters in the angular momentum conservation equation

\(\theta _{d}\) :

Parameters in the dynamic equation of the free-floating space manipulator

\(\theta _{z}\) :

Parameters in the kinematic equation of the free-floating space manipulator

\(A_{0}\) :

Nonzero angular momentum of the free-floating space manipulator

\(C_{bb}\) :

Centrifugal and Coriolis matrix of the base spacecraft

\(C_{bm}\) :

Centrifugal and Coriolis matrix of the base spacecraft and the manipulator

\(C_{mb}\) :

Centrifugal and Coriolis matrix of the manipulator and the base spacecraft

\(C_{mm}\) :

Centrifugal and Coriolis matrix of the manipulator

\(I_{i}\) :

Inertia of the ith link

\(J_{pb}\) :

Jacobian matrix between the spacecraft angular velocity and the end-effector linear velocity

\(J_{pm}\) :

Jacobian matrix between the manipulator joint angular velocity and the end-effector linear velocity

\(J_{qb}\) :

Jacobian matrix between the spacecraft angular velocity and the end-effector angular velocity

\(J_{qm}\) :

Jacobian matrix between the manipulator joint angular velocity and the end-effector angular velocity

\(l_{c,i}\) :

Distance between the ith link centroid and the \((i+1)\)th joint

\(l_{i}\) :

Length of the ith link

\(M_{bb}\) :

Spacecraft inertia matrix

\(M_{bm}\) :

Coupled inertia matrix between the base spacecraft and the mounted manipulator

\(m_{i}\) :

Mass of the ith link

\(M_{mm}\) :

Inertia matrix of the mounted manipulator

\(p_{e}\) :

End-effector position in the inertia frame

\(q_{b}\) :

Base spacecraft attitude in the inertia frame

\(q_{e}\) :

End-effector attitude in the inertia frame

\(q_{m}\) :

Joint angle

\(u_{m}\) :

Joint torque of the manipulator

\(v_{0}\) :

Nonzero linear velocity of the free-floating space manipulator in the inertia frame

\(w_{b}\) :

Base spacecraft angular velocity in the inertia frame

\(w_{m}\) :

Joint angular velocity

\(z_{e}\) :

Base spacecraft pose in the inertia frame

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Acknowledgements

This work was supported by the NSFC (61327807, 61521091, 61520106010, 61134005) and the National Basic Research Program of China (973 Program: 2012CB821200, 2012CB821201).

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  1. The Seventh Research Division and The Center for Information and Control, School of Automation Science and Electrical Engineering, Beihang University (BUAA), Beijing, 100191, China

    Xuhui Lu & Yingmin Jia

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Lu, X., Jia, Y. Adaptive coordinated control of uncertain free-floating space manipulators with prescribed control performance. Nonlinear Dyn 97, 1541–1566 (2019). https://doi.org/10.1007/s11071-019-05071-w

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