Model predictive control with obstacle avoidance for inertia actuated AFM probes inside a scanning electron microscope

The Atomic Force Microscope (AFM) is a reliable tool for 3D imaging and manipulation at the micrometer and nanometer scales. When used inside a Scanning Electron Microscope (SEM), AFM probes can be localized and controlled with a nanometer resolution by visual feedback. However, achieving trajectory control and obstacles avoidance is still a major concern for manipulation tasks. We propose a Model Predictive Control (MPC) to address these two issues while AFM probes are actuated by Piezoelectric Inertia type Actuators (PIA). The novelty of this letter is that the model of our MPC-based approach relies on a velocity map of PIAs. It enables path following and obstacle avoidance while preserving safety margins. Control inputs are optimized by Quadratic Programming, referring to their increment and distance constraints. A cost function is defined to navigate the AFM probe with a specified velocity. Simulations and experiments are carried out to demonstrate that the proposed algorithm is suitable to perform path following with obstacle avoidance using map-based velocity references. This is the first time that MPC is implemented in micro/nano-robotic systems for autonomous control inside SEM.