Rendezvous and Attitude Synchronization of a Space Manipulator
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Rendezvous and Attitude Synchronization of a Space Manipulator Vijay Muralidharan1 · M. Reza Emami1,2 Published online: 10 May 2019 © American Astronautical Society 2019
Abstract The control of a spacecraft equipped with a six-degree-of-freedom robot manipulator is studied in this paper. The objective is to rendezvous and synchronize with a satellite to facilitate inspection, servicing or de-orbiting. The space manipulator dynamics model with global parameterization on the configuration manifold is derived and used for designing asymptotically-stable control laws, so that they are valid globally in the configuration manifold. The control system consists of a sliding-mode rendezvous controller as well as a geometric attitude synchronization and a model-based servo control for the robot manipulator. The gains of the sliding-mode controller dictate a user-defined upper-bound on the thrust force. The attitude synchronization controller, concurrently with the rendezvous controller, is capable of micro-orbiting the space manipulator around spinning or tumbling satellites. It is observed through the simulations that the controller consumes limited amount of propellant, and it is feasible to use it for either a re-fueling (larger mass) or a de-orbiting (smaller mass) space manipulator. Keywords Space manipulator · Spacecraft rendezvous · Attitude synchronization · Spacecraft control
M. Reza Emami
[email protected]; [email protected] Vijay Muralidharan [email protected] 1
Department Computer Science, Electrical and Space Engineering, Lule˚a University of Technology, Lule˚a, Sweden
2
University of Toronto Institute for Aerospace Studies, North York, Canada
The Journal of the Astronautical Sciences (2019) 66:100–120
101
Nomenclature i, j, k : Indexing variables Rn : n-dimensional real numbers ei : Standard basis of Rn SO(3) : special orthogonal group in 3-dimensions (3D) so(3) : group of 3 × 3 skew-symmetric matrices Tn : n-dimensional torus iv : A vector vk measured with respect to the frame j and expressed k j in the frame i iJ : The Moment-of-inertia of the object with index k measured with k j respect to frame j and expressed in frame i i F ,i M : A force Fk or moment Mk applied on the origin of frame j , j k j k measured with respect to the inertial frame and expressed in the frame i i F ,i M : A force Fk or moment Mk applied on the point p, measured with p k p k respect to the inertial frame and expressed in the frame i ω : Skew-symmetric representation of a vector ω ∈ R3 A∨ : Vector representation of a matrix A ∈ so(3) jR : Rotation matrix for representing vectors in frame i into frame j i j R (0) : Rotation matrix between frames i and j at a default configuration i v : 2-norm of a vector v ∈ Rn v × w : Cross product of vectors v, w ∈ R3 θi , τi : Joint angles and torques pi , vi , ⎫ ωi : Linear positions, linear velocities and angular velocities Rx (·) ⎬ Ry (·) : Principal rotations in 3D ⎭ Rz (·) In : n × n identity matrix
Introduction The in-orbit inspection and servicing of satellites, a
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