Stochastic control for optical manipulation of multiple microscopic objects

Quang Minh Ta, Chien Chern Cheah

While various control techniques have been developed for optical manipulation, the Brownian movement of microscopic objects in the medium is usually ignored for simplicity of analyzing the control systems. Nevertheless, due to the universality of the Brownian movement and its effect on optical manipulation of cells or micro-objects, it is required for the Brownian effect to be properly taken into consideration so as to ensure the stability and performance of the control systems. In this paper, we derive a stochastic control technique to achieve a theoretical framework for optical manipulation of multiple microscopic objects in the presence of the Brownian perturbations. In the proposed control methodology, a region control technique and a dynamic interaction approach are developed for collision-free manipulation of the target micro-objects with random perturbations. All the target micro-objects are trapped and manipulated simultaneously while being kept inside the desired dynamic region, and at the same time, preserving a minimum distance with each other to avoid collisions. While a bounded tracking or region error exists in current control techniques for optical manipulation due to the effect of the Brownian perturbations, this paper provides a new approach which guarantees that all the target micro-objects are kept inside the desired region during the course of manipulation. Rigorous mathematical formulation has been developed for automated manipulation of multiple microscopic objects in the presence of the Brownian perturbations, and experimental results are presented to demonstrate the feasibility and effectiveness of the proposed control technique.

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