Saturated PID Control for the Optical Manipulation of Biological Cells

Mingyang Xie ; Xiaojian Li ; Yong Wang ; Yunhui Liu ; Dong Sun

This brief presents a saturated PID control scheme for cell manipulation by using robot-aided optical tweezers, with consideration of both translational and rotational control of the cell. By incorporating saturation functions into a PID controller and utilizing a velocity observer, cell position and orientation can asymptotically converge to the desired values. The proposed control approach also guarantees that the trapped cell can always stay within a small neighborhood around the centroid of the optical trap, thereby preventing the cell from escaping by optical trapping. The controller does not require the use of accurate dynamic model parameters, and hence can be implemented easily. Utilizing a velocity observer, velocity measurement by directly differentiating the measured position of the cell is not needed, which benefits noise reduction and system stability. The asymptotic stability of the closed-loop system is analyzed using Lyapunov's direct method. Experimental results are presented to demonstrate the effectiveness of the proposed approach.

DOI

Cooperative Optical Trapping and Manipulation of Multiple Cells With Robot Tweezers

Xiang Li; Chien Chern Cheah; Quang Minh Ta

While several control schemes and automation techniques have been proposed for coordination and manipulation of multiple cells using optical tweezers, open-loop control methods are always utilized by treating the positions of lasers as the control inputs instead of feedback variables. As the positions of laser beams are not utilized in feedback control, it is, therefore, assumed in the literature that the multiple cells are always trapped by the laser beams throughout the manipulation task. However, the control techniques fail when the cells are not initially trapped by the laser beams, or when the laser beams move too fast, such that the cells escape from the traps during manipulation. This paper presents a closed-loop control formulation and strategy for optical manipulation of multiple cells, based on the cooperative movement of the motorized stage and the beam steering system. The closed-loop control method enables the trapping operation to be automatically activated whenever the cells are not inside the optical traps. The proposed controller does not require exact knowledge on the dynamic parameters and the varying trapping stiffness. Lyapunov methods are employed in the stability analysis of the optical tweezers system. Experimental results are presented to illustrate the performance of the proposed controller.

DOI

Tracking Control for Optical Manipulation With Adaptation of Trapping Stiffness

Xiang Li, Chien Chern Cheah

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.

DOI

Multilevel-Based Topology Design and Cell Patterning With Robotically Controlled Optical Tweezers

Xiao Yan; Dong Sun

This paper presents the use of robotically controlled optical tweezers to move a group of biological cells into a desired region for required patterning. A multilevel-based topology is designed to present different cell patterning in the desired region. A potential function-based controller is developed to control the cells in forming the required patterning as well as achieving rotation and scaling of the desired patterning. A pattern regulatory control force is additionally designed and added to the cell patterning controller for particularly addressing the local minima problem that causes the cells to stop at the undesired positions. The stability of the controlled system is analyzed using a direct Lyapunov approach. Experiments are performed with a cell manipulation system equipped with holographic optical tweezers to demonstrate the effectiveness of the proposed approach.

DOI