A Simple Trapping and Manipulation Method of Biological Cell Using Robot-Assisted Optical Tweezers: Singular Perturbation Approach

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Optical tweezers have been widely utilized in biological sciences and biomedical engineering because of the attractive feature of manipulating microobjects without physical contacts. The integration of optical tweezers and robotic technologies has also led to the emergence of many robot-assisted optical manipulation systems, and a variety of motion control schemes have been reported to automated the process and improve the efficiency. However, the performance of existing control methods for optical tweezers is commonly limited by several issues: 1) presence of spatially varying trapping stiffness, which is difficult to model and identify; 2) requirements of high-order state variables, which are not measurable; and 3) effectiveness of trapping is only valid locally around the center of laser beam. These issues lead to the constructions of controllers, which are computationally involved. This paper presents a simple tracking control method for optical manipulation, which enables the laser beam to automatically trap and then manipulate the cell to track a time-varying trajectory, without high-order derivatives or construction of observers. The development of the proposed controller is based on the singular perturbation approach, by treating the fast manipulator or stage dynamics as a perturbation of the slow cell dynamics, such that the lowest control complexity is achieved. The exponential stability of the overall system that consists of the fast and slow subsystems is proved by using Tikhonov's theorem. Experimental results are presented to illustrate the performance of the proposed controller.