  The image-based visual servoing without models of system is challenging since
it is hard to fetch an accurate estimation of hand-eye relationship via merely
visual measurement. Whereas, the accuracy of estimated hand-eye relationship
expressed in local linear format with Jacobian matrix is important to whole
system's performance. In this article, we proposed a finite-time controller as
well as a Jacobian matrix estimator in a combination of online and offline way.
The local linear formulation is formulated first. Then, we use a combination of
online and offline method to boost the estimation of the highly coupled and
nonlinear hand-eye relationship with data collected via depth camera. A neural
network (NN) is pre-trained to give a relative reasonable initial estimation of
Jacobian matrix. Then, an online updating method is carried out to modify the
offline trained NN for a more accurate estimation. Moreover, sliding mode
control algorithm is introduced to realize a finite-time controller. Compared
with previous methods, our algorithm possesses better convergence speed. The
proposed estimator possesses excellent performance in the accuracy of initial
estimation and powerful tracking capabilities for time-varying estimation for
Jacobian matrix compared with other data-driven estimators. The proposed scheme
acquires the combination of neural network and finite-time control effect which
drives a faster convergence speed compared with the exponentially converge
ones. Another main feature of our algorithm is that the state signals in system
is proved to be semi-global practical finite-time stable. Several experiments
are carried out to validate proposed algorithm's performance.
