3.1. Voltage Application Algorithm Based on Internal Division Ratio

Paramecium swims using approximately 5,000 cilia arranged helically over its surface. These cilia exhibit two beating modes: forward (normal) and backward (reversed), regulated by intracellular Ca\(^{2+}\) concentration linked to membrane potential. Under an external electric field, the Rudroff effect induces reversed beating on the negative side and normal beating on the positive side, resulting in cathode-directed swimming.

Paramecium does not show a proportional increase in swimming speed with electric field strength, but rather an on/off response to the field direction. Although the response threshold varies, most Paramecia swim in the intended direction at around 0.3 V/mm. A major difficulty in achieving control is the large variation in response time. At higher field strengths (above \({\sim}0.6\) V/mm), increased reversed beating of anterior cilia reduces swimming speed and enlarges the helical trajectory, degrading positioning accuracy.

Given these characteristics, the present study controls only swimming direction and not speed. Under conditions without pH variation, the Paramecium can be guided for over 100 cycles, indicating that the electric field has little effect on physiological activity.

To guide Paramecium smoothly along a prescribed path, an internal-division-based algorithm was employed instead of directly steering the organism toward each target point (Fig. 4). A temporary target point was defined by internally dividing the segment between the current target point and the perpendicular projection of the Paramecium position onto the path in a ratio of \(m:n\). A potential gradient was then applied toward this temporary target point.

The voltage applied to each electrode was calculated as

\(V_{\mathit{max}}\) is a coefficient representing the maximum applied voltage, which was set to 13.5 V in the present experiment.

Because Paramecium allows control of swimming direction but not speed, a nearly constant electric field was applied, and only its direction was varied. The field direction was adjusted using eight fixed electrodes according to Eq. (1).

The nominal field gradient was \(\pm 13.5\) V / 10 mm (2.7 V/mm), which is higher than the 0.3 V/mm used in previous small-pool experiments. However, due to field non-uniformity near the electrodes and attenuation caused by the membrane filter separating the electrode and experimental regions, this gradient produces behavior equivalent to that observed at 0.3 V/mm in the smaller system.

3.2. Target Point Switching Algorithm

When the target point is switched only after the Paramecium reaches it, the organism often overruns the apex of the path due to delays in both behavioral response and image processing.

To address this issue, a predictive switching method was introduced. In this method, the amount of overrun is predicted based on the overrun observed in the previous turn, and the target point is switched before the Paramecium reaches the apex (shown in Fig. 5).

The overrun distance is defined as the distance between the position at which the target point is switched and the position at which the Paramecium actually changes its swimming direction. To predict the overrun, instead of uniformly averaging past data, an exponentially weighted integral—referred to here as the integral value of equal-ratio damping—is employed, giving greater weight to more recent data.

The integral value is expressed as

For implementation in the control program, Eq. (2) can be simplified to the following recursive form:

This formulation allows the controller to adapt to gradual changes in the overrun caused by variations in swimming speed during the experiment. The switching position of the target point is defined on a circumference centered at the previous target point, with a radius equal to the current path length minus the integral value of the equal-ratio damping.

3.3. Automatic Control Experiments Along a Star-Shaped Path

Automatic control experiments were conducted along a star-shaped path with a side length of approximately 5 mm. The internal division ratio was set to \(m \mathbin{:} n = 1 \mathbin{:} 3\), and the damping coefficient was set to \(G = 0.25\). The smallest average control deviation obtained was 0.0947 mm at an average swimming speed of 0.911 mm/s, corresponding to less than half the body length of Paramecium (Fig. 6).

Experiments with varying internal division ratios revealed that control deviation generally increased with swimming speed. Among the tested ratios, values of approximately \(3 \mathbin{:} 7\) provided the most stable guidance with reduced oscillation, whereas larger ratios resulted in slower recovery to the path and increased deviation (Fig. 7).

4.1. Calculation of the Internal Division Ratio from Path Deviation and Swimming Speed

When a Paramecium deviates from the guidance path, it should be returned to that path as quickly as possible. Accordingly, the internal division ratio was modified in proportion to the deviation from the target path (Fig. 8, left).

In addition, to suppress residual deviation and prevent oscillatory motion when the Paramecium returns toward the path, the internal division ratio was adjusted based on the rate at which the Paramecium approaches the path, which is related to its swimming speed (Fig. 8, right). Using this concept, a method in which the application angle of the electric field is calculated indirectly via the internal division ratio was first examined.

The internal division ratio parameter \(m\) is calculated as

Figure 9 shows a representative swimming trajectory obtained with \(\mathit{Kp}_{\mathit{idr}} = -2.4\) and \(\mathit{Kd}_{\mathit{idr}} = -5.0\), and Fig. 10 shows the relationship between swimming speed and control deviation. Increasing the value of \(\mathit{Kp}_{\mathit{idr}}\) reduced the residual deviation, and stable swimming without oscillation relative to the path was achieved even at higher swimming speeds. Under these conditions, the average control deviation was reduced to 0.096 mm.

However, because this method determines the control action using the internal division ratio \(m\), the resulting electric field angle depends on the length of the path segment. This dependence complicates control when the path length varies, such as in star-shaped trajectories with short sides.

4.2. Direct Calculation of the Electric Field Angle from Deviation and Velocity

To eliminate the path-length dependence inherent in the internal-division-based approach, the control strategy was further refined by directly calculating the electric field angle from the deviation and the swimming velocity. The basic concept of this method is illustrated in Fig. 11.

The correction angle of the electric field, \(C_{\mathit{rad}}\), is calculated as

Figure 12 shows a swimming trajectory along a star-shaped path with a side length of 3 mm obtained using \(\mathit{Kp}_{\mathit{rad}} = 1.0\) and \(\mathit{Kd}_{\mathit{rad}} = 8.0\).

Figure 13 shows the relationship between swimming speed and control deviation. Even for short path lengths, stable guidance was achieved, and the average control deviation was reduced to 0.0997 mm.

5.1. Fabrication of the Transportation Object

To enable transportation using a single Paramecium, the payload was required to be sufficiently soft not to induce an avoidance response. Therefore, an artificial salmon-roe-shaped gel, which had been successfully transported by Paramecium in previous studies, was adopted as the transportation object.

The artificial salmon roe was fabricated by spraying a sodium alginate solution into a calcium lactate solution, where it solidified into spherical gel particles. For the experiments, particles with a diameter of approximately 300 μm were used, which is slightly smaller than the height of the control pool.

To facilitate image recognition, titanium dioxide was added to color the particles white.

An example of the fabricated minute gel is shown in Fig. 14 with four paramecia.

5.2. Image Recognition of Paramecium and Transportation Object

Automatic object transportation requires simultaneous detection of both the Paramecium and the transportation object. However, in binarized images, Paramecium could not be reliably distinguished from debris in the pool due to the lack of clear differences in size and brightness, making stable detection difficult.

To address this issue, a motion-based detection method was adopted to recognize Paramecium. Binarized images from the previous 10 frames were stored, and the current binarized image was compared with that from 10 frames earlier. An image highlighting only regions with temporal changes was generated, in which changing regions were represented in white and static regions in black. Objects satisfying predefined area conditions were identified as Paramecium.

Each detected Paramecium was assigned a unique ID. By comparing consecutive frames, the ID was continuously assigned to the nearest detected Paramecium, enabling stable tracking and control of a single individual throughout the experiment.

5.3. Generation of Swimming Paths for Object Transportation

Observation of manual control experiments revealed that maintaining continuous contact between Paramecium and the object was difficult. Instead, transportation was achieved through repeated collisions, resulting in the gradual displacement of the object.

Based on this observation, the swimming path for automatic object transportation was designed such that the Paramecium repeatedly circulates around the object. The control method applied to Paramecium was identical to that used in the star-shaped swimming experiments described earlier; only the coordinates of the target points were modified.

As shown in Fig. 15, a three-point path consisting of target points 0, 1, and 2 was defined, along which the Paramecium swims sequentially in the order 0 \(\to\) 1 \(\to\) 2. Targets 0 and 2 were positioned on a straight line connecting the transportation object and the destination point. Target 0 was generated on the side toward the destination, whereas target 2 was generated on the opposite side.

Target 1 was placed off this straight line and served as an avoidance point. Its purpose was to prevent the Paramecium from pushing the object away from the destination while moving toward target 2 for the subsequent collision after reaching target 0.

The geometry of the three-point path was determined prior to the experiment by specifying the distance \(d_3\) from target 2 to the object, the distance \(d_0\) from the object to target 0, and the interior angles \(\theta_1\) and \(\theta_2\) at targets 2 and 0, respectively.

To suppress pH bias caused by electrolysis, the direction in which target 1 was generated was alternated between left and right after each complete revolution of the Paramecium around the path.

5.4. Setting of the Transportation Path

The global transportation path for the object is defined as a star-shaped trajectory with a side length of 3.24 mm.

The internal-division-based control algorithm used for guiding the Paramecium was also applied during object transportation to prevent the object from deviating from the prescribed path. The target point is switched when the object approaches the current target point or when it exits a circular region centered at the previous target point with a radius equal to the current path length.

7.1. System Concept

This study demonstrated automatic object transportation driven by a single living Paramecium. Although the transportation speed was relatively slow, these results clarify the fundamental conditions required for autonomous bio-hybrid transport systems.

The transportation process relied on repeated collisions between the Paramecium and the payload rather than continuous mechanical contact. Consequently, transportation efficiency was limited by the small propulsive force of the organism and by the stochastic nature of collision-based transport. In addition, avoidance reactions during contact constrained the payload to soft, deformable materials such as gel. These characteristics reflect intrinsic limitations of tool-less transport.

A key finding of this study is that autonomous object transportation becomes feasible when the control deviation of Paramecium is reduced to less than approximately half its body length. This indicates that behavioral control precision is a dominant factor governing transport success at the microscale. From an engineering perspective, this result provides a practical guideline: sufficient control accuracy must be achieved before mechanical interaction can be effectively introduced. The scheme is shown in Fig. 18.

The limitations observed here are expected to be alleviated by the use of transport tools. However, in the case of Paramecium, fabricating and attaching such tools while maintaining stable physiological activity remains a major technical challenge. This study establishes a quantitative baseline for transport performance achievable through behavioral control alone, against which future tool-assisted systems can be evaluated and integrated.

7.2. Cause of the Large Improvement in Behavioral Control Accuracy

In the present study, behavioral control accuracy was significantly improved, reducing the positioning error from 0.3 mm to 0.1 mm, which enabled automatic object transportation.

The adopted control strategy applies a nearly constant electric field and adjusts only its direction, without incorporating a motion-dynamics model. This is based on the biological characteristics of Paramecium, whose galvanotactic response is essentially on/off and whose swimming speed cannot be controlled. The control therefore regulates position only, without considering time or speed.

Biological variability, particularly in response delay, is much greater than that of artificial systems, making conventional time-dependent control difficult. By ignoring time, the proposed method effectively accommodates this variability.

However, positioning accuracy still depended on swimming speed and deteriorated for faster individuals. This was improved by correcting the field direction using recent swimming velocity and direction. For large directional changes, where variability in response delay becomes dominant, EMA filtering of past delay data was additionally introduced.

Although simple, this control approach effectively compensates for biological variability, resulting in high positioning accuracy.