## 1 Introduction  
The invention of optical tweezers has allowed scientists to develop an unprecedented manipulative ability at the single-cell level [1; 2; 3]. Focused laser beams, which can trap biological cells, cell organelles, and DNA bundles in a confined space [4; 5; 6], are opening up unexplored research areas that focus on single cells. In many biological and biomedical experiments, such as cell-to-cell interaction [7], cell sorting [8], and cell mechanical stiffness characterization [9], single-cell analysis has become feasible due to the customization of optical traps via light field waveform modulators [10; 11]. Cell transportation has attracted increased attention due to the fact that cell positioning is usually a basic and vital technique that is required in single-cell analysis [12; 13; 14; 15; 16; 17; 18; 19]. Techniques for cell transportation with optical tweezers can be classified into two, namely, direct and indirect manipulation. Direct optical manipulation techniques induce a trapping force by directly focusing the laser on the cell [20; 21; 22], in which laser beams act as special end-effectors. Using the direct technique, a large number of cells can be manipulated individually or simultaneously in a series or parallel manner with high precision and high efficiency [23; 24]. However, direct manipulation by the high focused laser beams may cause photobleaching and photodamage to the cells. The photobleaching makes it difficult to precisely visualize the spatio-temporal distribution of interesting proteins in the cells by combining fluorescent probes and optical tweezers. The photodamage may result in an impaired functionality or even the death of the cells [25; 26; 27; 28]. To address these problems, indirect optical manipulation approaches are proposed. Indirect techniques employ intermediate micro-objects as end-effectors of optical tweezers to manipulate cells. Instead of focusing on the cells, laser beams are focused on the non-biological and biocompatible micro-objects, thereby driving the micro-objects to interact with the biological cells [29; 30]. Cell manipulation is achieved under the reaction force of the micro-objects. Microbeads are ideal examples for optical trapping due to their spherical shape and manufacturing uniformity. [PERSON] et al. used two microbeads to push a yeast cell [31]; [PERSON] et al. proposed an optical gripper with an ensemble of optically trapped beads to reduce the laser exposure of gripped cells [32]. Although the use of microbeads for indirect manipulation in combination with automated control strategies is well-established [33; 34; 35], their transport with microbeads is frequently unstable, and laser fields remain close to trapped cells. With the advancement of the direct laser writing technique, designable microscale mechanisms with 3D nano features were printed using the two-photon photopolymerization (2 PP) method and trapped as microtools for indirect optical manipulation [36]. Various microhands, as the end-effector of optical tweezers, were proposed, and their manipulability by optical tweezers was verified [29; 37]. The optical manipulation of highly task-specific micromechanisms, such as an articulated microrobot and microsyringe, as fabricated by the 2 PP method, was further investigated [38; 39; 40]. [PERSON] et al. conducted a meaningful and innovative study to enable indirect optical cell manipulation [41]. In their study, however, meticulous functionalization of SU-8 microstructure and cells were needed to form a microstructure-cell attachment and prevent the cell from escaping from the structure during manipulation. These studies have contributed to the manipulation of the fabricated microtool. However, there are only a few examples of automated cell manipulation using microtools [42; 43]. Because often more than three spherical trap points in each microtool need to be manipulated simultaneously to transport a cell, manual manipulation is often difficult and tedious in its application.