Image-Guided Trajectory Tracking Control of the Nanopositioning Stages Using Regional Dense Photometic Information

For compliant nanopositioning stages, the closed-loop control can effectively reduce the trajectory tracking error caused by modeling uncertainties and unknown disturbances. However, pose sensing solutions with multiple degrees of freedom, high precision, and high sampling rate required for closed loops are difficult to find. In this article, rendering the closed-loop trajectory tracking as an image-guided problem, a visual servo scheme for trajectory tracking control of the CNPSs is presented. Specifically, by updating the planning trajectory parameters in the feedback image area, the closed-loop trajectory tracking problem is transformed into the problem of minimizing the errors of the regional dense photometric information. Subsequently, an image-guided trajectory tracking controller with submillisecond delay is designed based on iterative optimization technique, and its stability is analyzed using Lyapunov's first stability law. Simulation results show that when the size of the template is appropriate, the theoretical accuracy of translation-/rotation components can easily reach 0.1 pixel and 0.1 $^{\circ }$ , respectively, even under the interference of image noise. The experimental results show that the proposed method can successfully track complex trajectories, with the tracking error smaller than 50 nm. Comparison experiments demonstrate that the proposed method can effectively reduce the tracking error caused by model uncertainties.