A Voltage/Frequency Modeling for a Multi-DOFs Serial Nanorobotic System Based on Piezoelectric Inertial Actuators

Nanorobotic systems using piezoelectric stick-slip actuators are widely used in nanotechnology. They operate mainly in a coarse-positioning mode and a fine-positioning mode. In the first mode, the actuator performs large displacements with a maximal range of a dozen millimeters but with a low resolution. In the second mode, the displacements are of a few micrometers and below with a nanometer resolution. In order to achieve efficient automated tasks, it is often necessary to define closed-loop tracking strategies. To this end, an accurate multiscale model of the nanorobotic system is required. This paper deals with a new modeling approach to describe the dynamics of this class of systems in the time and the frequency domains for both coarse- and fine-positioning modes. We propose an augmented voltage/frequency modeling of the friction force based on a multistate elastoplastic formulation. Necessary conditions on the presliding modeling are studied to deal with the two operating modes and the motion direction. This model is combined with a nonlinear rate dependent hysteresis model. The main result and contribution of this paper is to demonstrate that a complete nanorobotic task involving closed-loop multiscale displacements can be precisely defined by simulations upstream of a real-time implementation with a mean error of 9.05%. The proposed model opens new perspectives for the definition of control strategies for complex nanorobotic tasks through simulation software tools.