  To avoid complex constraints of the traditional nonlinear method for tethered
space robot (TSR) deployment, this paper proposes a data-driven optimal control
framework with an improved deep learning based Koopman operator that could be
applied to complex environments. In consideration of TSR's nonlinearity, its
finite dimensional lifted representation is derived with the state-dependent
only embedding functions in the Koopman framework. A deep learning approach is
adopted to approximate the global linear representation of TSR. Deep neural
networks (DNN) are developed to parameterize Koopman operator and its embedding
functions. An auxiliary neural network is developed to encode the nonlinear
control term of finite dimensional lifted system. In addition, the state matrix
A and control matrix B of lifted linear system in the embedding space are also
estimated during training DNN. Then three loss functions that related to
reconstruction and prediction ability of network and controllability of lifted
linear system are designed for training the entire network. With the global
linear system produced from DNN, Linear Quadratic Regulator (LQR) is applied to
derive the optimal control policy for the TSR deployment. Finally, simulation
results verify the effectiveness of proposed framework and show that it could
deploy tethered space robot more quickly with less swing of in-plane angle.
