  In this paper, we open up new avenues for visual servoing systems built upon
the Path Integral (PI) optimal control theory, in which the non-linear partial
differential equation (PDE) can be transformed into an expectation over all
possible trajectories using the Feynman-Kac (FK) lemma. More precisely, we
propose an MPPI-VS control strategy, a real-time and inversion-free control
strategy on the basis of sampling-based model predictive control (namely, Model
Predictive Path Integral (MPPI) control) algorithm, for both image-based, 3D
point, and position-based visual servoing techniques, taking into account the
system constraints (such as visibility, 3D, and control constraints) and
parametric uncertainties associated with the robot and camera models as well as
measurement noise. Contrary to classical visual servoing control schemes, our
control strategy directly utilizes the approximation of the interaction matrix,
without the need for estimating the interaction matrix inversion or performing
the pseudo-inversion. We validate the MPPI-VS control strategy as well as the
classical control schemes on a 6-DoF Cartesian robot with an eye-in-hand camera
based on the utilization of four points in the image plane as visual features.
To better assess and demonstrate the robustness and potential advantages of our
proposed control strategy compared to classical schemes, intensive simulations
under various operating conditions are carried out and then discussed. The
obtained results demonstrate the effectiveness and capability of the proposed
scheme in coping easily with the system constraints, as well as its robustness
in the presence of large errors in camera parameters and measurements.
