Tracking control for optical manipulation of biological cell with unknown trapping stiffness

In this paper, a tracking control scheme is proposed for optical manipulation of biological cell with unknown trapping stiffness. The requirement on the model of the trapping stiffness is eliminated in the proposed formulation and thus system identification and calibration are not needed. The unknown trapping stiffness and the uncertain dynamic parameters are estimated separately, with on-line update laws. By using the proposed control scheme, the laser beam is able to manipulate the trapped cell to track various time-varying trajectories, to suit different applications in cell manipulation. The proposed control scheme is based on the dynamic formulation where the position of laser beam is controlled by closed-loop robotic manipulation techniques. The stability of the overall system is analyzed by using Lyapunov-like method, with consideration of the dynamics of both the cell and the manipulator of laser source. Experimental results are presented to illustrate the performance of the proposed tracking controller with unknown trapping stiffness.