Tracking Control for Optical Manipulation With Adaptation of Trapping Stiffness

In the optical manipulation problem of biological cells, the optical trap works only in a small neighborhood around the centroid of a focused light beam. Due to the Gaussian distribution of light intensity, the trapping stiffness is dependent on the distance between the cell and the centroid of the laser beam. In addition, the parameters of the stiffness vary with laser power and sizes of cells, and hence, it is difficult to obtain the exact model of the trapping stiffness. This paper considers the tracking control problem for the optical manipulation with unknown trapping stiffness. In the presence of unknown trapping stiffness, the tracking control tasks fail and the stability of the control system may not be guaranteed. We present parameter update laws to update the unknown trapping stiffness and dynamic parameters concurrently and separately. With online adaptation of the unknown trapping stiffness, a tracking control method is developed for optical tweezers such that the laser beam is able to automatically trap and manipulate the cell to follow a desired time-varying trajectory. The stability of the optical tweezers system is analyzed using the Lyapunov method, with consideration of the dynamic interaction between the cell and the manipulator of the laser source. The experimental results are presented to illustrate the performance of the proposed adaptive tracking controller with unknown trapping stiffness.