**4. Control Method of Undamaged Picking**

Due to the complex growing environment, size, and different postures, the values of piking force cannot be determined in the actual picking process. The movement distance and speed of the constrain part cannot be set as the only condition for picking control. If the clamping force is too small, the finger and the fruit will slide [30–34], and the picking will fail. Too much clamping force will damage the fruit. Thus, the feedback signals should be added. It is the best choice to make the manipulator and fruit synchronous rotation with the smallest clamping force. It is a critical state where no slip just happens. This strategy can be used as the control target of undamaged picking.

Therefore, the experiment designed the two-stage "Holding-Rotating" picking strategy. The clamping stage is the key to realizing undamaged picking, and the clamping force directly affects the degree of fruit damage. The rotation stage is another key to achieving the separation of the fruit handle, and it is the stage where the fruit slides relative to the manipulator. It is an effective way to design the undamaged picking algorithm to explore the minimum clamping force and slip criterion through the clamping experiment.

#### *4.1. Experiment and Analysis of Clamping Fruit*

The pressure on the sensor's surfaces changes as the gripper grasps and rotates the fruits. Its output signals will also vary according to working principle. Therefore, this experiment mainly collected the corresponding time signal changes of sensor outputs to explore the undamaged grab strategy in the picking process. The precise mathematical relationship between the grasping force and the output of the sensor's electrical signal had not been established.

Figure 11 is the experiment of grasping and slipping. Fixing cherry tomato, constrain part at 0.08m/s advanced to close fingers and clamped fruit. Then, the gripper was rotated through the DC motor, producing a slide between it and the fruit. Three pressure sensors were calibrated first, and their output values were collected in real-time. The sampling frequency of sensors was set to 0.2 kHz. The aim was to explore the law of grasping and find the basis for relative slip. The Dragon Skin 10 with 3 mm was covered between the finger ends and the sensors.

**Figure 11.** Experiment of grabbing fruit.

Figure 12 shows the output values of sensors during the experiment. The changes in sensor outputs had the following five stages according to the results. (I) The fingers closed with the constrain part motivation. However, the finger ends did not touch the fruit. The output values were zero. (II) The constraint part moved, and the ends grasped the fruit. The output values increased with the increase in the clamping force. (III) When the constraint part stopped moving, the output values were maintained at a relatively stable value. (IV) The slip happened when the gripper was rotated. The output values fluctuated greatly. (V) When the gripper stopped, the slip disappeared. The output values were maintained at a relatively stable value.

**Figure 12.** The output values of three pressure sensors.

The output values of the three sensors were inconsistent according to the above results. The reason is the asymmetry on the cherry tomato surface. In addition, fingers clamped the fruit in different positions. However, the trends of output values were the same during

the picking process. Obviously, in combination with the above picking strategy, it was a key that minimum gripping force was set during III, and it was another key that slip was judged during IV. The other three stages need not be judged. Therefore, the above two keys were studied to be critical for achieving undamaged and stable picking based on the sensor output values.

The greater the pressure on the sensor surface, the smaller its resistance, and the greater its output values. Therefore, the output values were set during III. In addition, the output values of the three sensors were different under stable clamping. Therefore, when the output of any sensor is greater than the minimum clamping force, it is judged to have reached the minimum clamping force condition. During IV, the values of the three sensors did not have the specific change rule, which cannot judge slip directly. Still, their fluctuation was obvious, and the numerical discreteness degree became higher. Therefore, this work introduced five statistical statistics to find the judgment basis of slip. They were adjacent difference (*AD*), average (*A*), average deviation (*AD*), variance (*DX*), and standard deviation (*SD*), respectively. They are shown in Equations (14)–(18).

$$AD = \mathfrak{x}(i+1) - \mathfrak{x}(i) \tag{14}$$

$$A = \frac{\sum\_{i=1}^{n} \mathfrak{x}(i)}{i} \tag{15}$$

$$AD = \frac{\sum\_{i=1}^{n} |\mathbf{x}(i) - A|}{i} \tag{16}$$

$$DX = \frac{\sum\_{i=1}^{n} \left(\mathbf{x}(i) - A\right)^2}{i} \tag{17}$$

$$SD = \sqrt{DX} \tag{18}$$

where *i* represents the sampling frequency; *x(i)* represents the output value; *n* represents the total amount of data collected since III. The sensor output values were analyzed according to the above formulas in stages III and IV. The results are shown in Figure 13.

**Figure 13.** Statistical analysis of pressure sensor output: (**a**) Adjacent difference; (**b**) Average; (**c**) Average deviation; (**d**) Variance; (**e**) Standard deviation; (**f**) Variance-to-mean ratio.

It can be seen from Figure 13a that the difference in adjacent data fluctuates greatly. When a little external interference is encountered in the picking, the adjacent data difference will increase, resulting in wrong judgments. Compared with the smooth trend of the average in Figure 13b, the average deviation, the variance, and the standard deviation had upward inflection points, as shown in Figure 13c–e. However, these three statistics occurred in small fluctuations before the 30th sampling. The reason is that the original output values of the sensor fluctuated instantly during the III to IV. The trend of these three statistics was first up, then down in the 30th–210th sampling of sensor three. The reason is that the pressure sensor three output values appeared to float in the early stage. These three statistics happened small range rise at the 290th–310th sampling of pressure sensor one, corresponding to the frequency of the original value that appeared a small hill. The reasons might be due to the irregular shape of cherry tomatoes or the small gripping force. The inevitable slight fluctuation affected the mean deviation, variance, and standard deviation, and it also affected the correct judgment of slip.

To reduce the influence of unavoidable slight fluctuations of data and realize more reliable slip detection, this study proposed the "Variance-to-Mean Ratio (*VMR*)" as the slip criterion, and it is shown in Formula (19). Figure 13f is the result of the variance-to-mean ratio.

$$VMR = \frac{SD}{A} \tag{19}$$

The variance-to-mean ratio remained near 0 and did not fluctuate significantly during phase III. It eliminates the judgment that values fluctuate due to fluctuations in the raw data. In addition, it also had significant inflection points to judge slide during V. The reason is that averages simply flattened out small data fluctuations but did not change the trend of the standard deviation. Therefore, the variance-to-mean ratio can be used as the sliding criterion. However, the corresponding samplings of the three sensors were different when the rising inflection points occurred. For example, sensor one changed first, followed by the other two. It shows that the three fingers slide for the cherry tomato at different times during rotation. The first appeared inflection point should be used as the judgment of the slip criterion.
