Injection algorithm using ΔT and X
The method for improving the efficiency of the injecting task is shown in the previous study [19]. Figure 1 shows the injecting task performed by a robot in this study. The angle of the injection bottle changed from 45° to 70° to reduce the culture media left in the injection bottle. The robot performs the injecting task only by rotating around the tool center point (TCP), the injecting spout of the injection bottle. To reduce the risk of liquid dripping, a protruding inspiration port on the lid of the injection bottle is changed to a non-protruding inspiration hole.
Figure 2 shows the transition of the injection volume after the start of the injection end motion. The injection algorithm predicts the injection volume (X%) to be injected in a fixed period (ΔT). If the injection is continued without stopping, the injection volume during ΔT is assumed to be 100%. The injection end motion is triggered when the injection algorithm predicts that X will reach the target volume. ΔT and X depend on the injecting angle and the angular velocity of the injecting task, the structure of the lid of the injection bottle, and the control cycle of the robot. Therefore, it is necessary to determine ΔT and X in advance by analyzing data obtained when the robot performs the injecting task.
In the previous study [19], a slope from 40 to 60 g was adopted, considering that the injection volume was fixed at 75 g and that the volume closer to the injection end motion could be more accurately predicted. However, the injection volume should be changed. The range slope, excluding 20 g at the start and end of the injection volume, was to be used since the flow rate is stable within the range, excluding the start and end of the injection.
Correction by the y-intercept
Although the conventional algorithm can achieve the same accuracy as the operator, it was found that the injection volume varied depending on the number of injections. The injection volume when the injection is repeated multiple times is shown in Fig. 3. Specifically, the remaining volume in the injection bottle decreases as the number of injections, and the following phenomenon occurs.
- The y-intercept decreases (the x-intercept increases) because of the decrease in the volume injected during the injection start motion.
- The final volume decreases because of the decrease in the volume injected during the injection end motion.
Therefore, the difference in (a) is used to compensate for the effect of (b). Figure 4 shows the system overview. First, ΔT and X are calculated using load cell data when the injection experiment is repeated. The maximum volume of the culture media in the injection bottle is 500 g. Because the injection bottle is tilted 70° for injection, it is assumed that the remaining approximately 50 g cannot be injected. If the injection end motion is started when the injection volume exceeds 68 g, approximately 75 g is injected. Thus, it is possible to inject six times in a row. The six times of this experiment was repeated six sets. The average value was adopted; ΔT was determined to be 1.28 s, and X was determined to be 75.0%.
Afterward, the injection algorithm using the obtained ΔT and X was applied to the original data. Because the data were obtained when the injection end motion was started after the injection volume exceeded 68 g, it was possible to calculate a theoretical value for how much of a target volume should be set. An additional experiment with a target volume of 75 g can be conducted using the obtained ΔT and X to determine the difference between the theoretical and measured values; however, this was not conducted in this study. Figure 5 shows the correlation between the y-intercept of the injection volume and the difference between the theoretical and measured values. The smaller the y-intercept, the smaller the measured value, whereas the theoretical value remains constant. A linear approximation equation can be obtained because there is a linear correlation between the y-intercept and injection error. By calculating the volume of increase or decrease from the y-intercept and shifting the stop timing, it is possible to approach the theoretical value. The equation for calculating the correction volume C1 using the y-intercept by is as follows.
A correction using the x-intercept is also possible. Figure 6 shows the correlation between the x-intercept of the injection volume and the difference between the theoretical and measured values. Each correction was applied to the original data to calculate the root mean square (RMS) of the difference between the theoretical and measured values. The result was 0.261 when the y-intercept was used and 0.262 when the x-intercept was used. Although both can be used, this study uses the y-intercept. By employing the correction by the y-intercept, it is possible to respond to changes in the injection volume caused by the number of injections.
Correction by the target volume
In Fig. 3, if the target volume is different, even if the y-intercept is the same, the effect of (b) is different because the remaining volume at the start of the injection end motion is different. The correction by the y-intercept is for a target volume of 75 g. It includes the correction for the effect of (b). However, if the target volume is not 75 g, the remaining volume at the start of the injection end motion increases or decreases compared to the case where the target volume is 75 g. In other words, the effect of (b) changes and the correction of only (a) is insufficient. Therefore, the correction method for the case where the target volume is not 75 g is considered.
Figure 7 shows the correlation between the remaining volume at the start of the injection end motion and the injection volume after the injection end motion. The smaller the remaining volume, the smaller the injection volume. A linear approximation equation can be obtained because there is a linear correlation between the remaining volume and injection volume. Then, the change in injection volume per unit remaining volume can be calculated. Because the difference between 75g and the target volume is the difference in the remaining volume, the equation for calculating the correction volume C2 using the target volume Vt is as follows.
Using the correction by the target volume, the injection algorithm using ΔT and X can be applied to target volumes other than 75 g.
Flowchart of the injection algorithm
A flowchart of the injection algorithm using ΔT and X with two types of corrections is shown in Fig. 8. In the conventional method, the injection end motion is started when the injection volume exceeds the stopping volume Ve. However, it turned out that an injection error occurred depending on the number of injections and target volume. Therefore, the correction volumes C1 and C2 are added to Ve. Although not employed in this study, another method for adding correction volumes C1 and C2 to the target volume Vt is shown in Figure 9.
Injection algorithm using machine learning
As an alternative to the injection algorithm using ΔT and X with two types of corrections (called Algorithm A), the injection algorithm using ML (called Algorithm B) is considered.
Algorithm B uses multiple linear regression to predict the time to stop injecting based on the flow rate, the y-intercept of the injection volume, and the target value. When two features are fixed, there is a linear relationship between the remaining and predicted values. Therefore, linear regression is considered to be effective. Because the features include the y-intercept and target value, the correction of Algorithm A is included. The prediction equation by the linear regression model is shown in Eq. (3), and each feature value of the linear regression model is shown in Fig. 10. The slope x1, y-intercept x2, and target value x3 are feature values; the weights w1, w2, w3, and the offset b are parameters of the learned model; and the stopping volume Vea is a predicted value from the model. The model is developed using scikit-learn [22], a Python ML library.
First, preliminary experiments were repeated to collect training data, and a linear regression model was developed from the collected training data. For each target volume, six sets of injection experiments were conducted. The target volume was set between 50 and 150 g at 10-g intervals. The injection end motion began at 7 g less than the target volume to keep the final injection volume close to the target volume. 500 g of culture media was repeatedly injected. However, the remaining volume should not be less than 50 g. Each parameter of Algorithm B was calculated using the training data. Algorithm A can also be expressed in Eq. (3). The values of each parameter for both algorithms are shown in Table 1. Vea in Fig. 8 can also be calculated using Algorithm B.