Evaluation of Cutting Stability of a Natural-Rubber-Tapping Robot

Abstract

Natural rubber is a crucial raw material in modern society. However, the process of latex acquisition has long depended on manual cutting operations. The mechanization and automation of rubber-tapping activities is a promising field. Rubber-tapping operations rely on the horizontal cutting of the leading edge and vertical stripping of the secondary edge. Nevertheless, variations in the impact acceleration of the blade can lead to changes in the continuity of the chip, affecting the stability of the cut. In this study, an inertial measurement unit (IMU) and a robotic arm were combined to achieve the real-time sensing of the blade’s posture and position. The accelerations of the blade were measured at 21 interpolated points in the optimized cutting trajectory based on the principle of temporal synchronization. A multiple regression model was used to establish a link between impact acceleration and chip characteristics to evaluate cutting stability. The R-squared value for the regression equation was 0.976, while the correlation analysis for the R-squared and root mean square error (RMSE) values yielded 0.977 and 0.0766 mm, respectively. The correlation coefficient for the Z-axis was the highest among the three axes, at 0.22937. Strict control of blade chatter in the radial direction is necessary to improve the stability of the cut. This study provides theoretical support and operational reference for subsequent work on end-effector improvement and motion control. The optimized robotic system for rubber tapping can contribute to accelerating the mechanization of latex harvesting.

1. Introduction

Artificial rubber tree cultivation has a long history, in which cutting tasks have traditionally relied on manual labor. Early in the morning, workers dressed in overalls set out with sharp latex knives. Rubber-tapping operation requires a high level of hand–eye–feet coordination. Experienced workers move around the trunk, cutting off the bark to ensure a good yield without damaging the trees or risking injury. Speed is also essential, as a local worker in Hainan Province, China, for instance, is expected to cut around 500 trees between 2 a.m. and 7 a.m. Rubber tapping is indeed a laborious physical task.

Furthermore, the unstructured environment of the rubber forest also poses limitations on the efficiency of cutting operations. The ground covered with dead branches and leaves presents difficulties in cutting and walking, while the precision required is at a sub-millimeter level. The workers must focus intently on the blades in their hands. Given these challenges, there is a need to revolutionize traditional rubber-tapping operations with modern technologies.

In addition, the emergence of advanced technologies, such as the Digital Revolution and the Information Age has brought about significant transformations in the agricultural field. Robotics, for instance, has been demonstrated to enhance efficiency and reduce workloads in various agricultural activities, such as fruit harvesting and yield measurement [1,2,3]. Similar potential applications can be found in the field of rubber tapping. However, research on automated rubber-tapping operations is still in its nascent stages. Ref. [4] employed the OTSU method to separate secant and latex, allowing for the exact secant and latex binary image to be obtained and removing interference factors from the background. More recent research has focused on improving the cutting equipment, especially for worker assistance. For instance, [5] developed a semi-automatic rubber-tapping machine (SART) to assist unskilled laborers. The device features a mechanical guiding mechanism and a sensory-based electronic system for proper orientation during operation, while an IMU is used to provide real-time orientation data. Users can orient the device within the required range. Ref. [6] created a hand glove based on force sensitive resistor (FSR) technology to measure the effort required when using the SART and traditional tapping knives, with the results indicating that using the SART involves less effort. Meanwhile, [7] designed the cordless brushless tapping knife 4GXJ-I, which features a position limitation protection device that can be adjusted to different bark consumption and cutting depth requirements. Damage to the tree is also reduced.

Previous research has primarily focused on improving cutting equipment or developing semi-automated devices to assist in manual labor. However, a more promising solution is to develop fully automated tree-hanging cutting equipment. For example, [8] established a mathematical model of rubber tapping based on the simplified manual tapping trajectory and developed a suspension-typed mechanized rubber-tapping device that effectively controls the cutting depth and bark consumption. Still, the device requires manual operation and lacks a power unit. Alternatively, [9] designed a semi-automated rubber-tapping machine that moves the blade on a gear-rack mechanism driven by a wiper motor. The device’s level of automation remains limited. Other researchers have explored navigation systems for rubber forests based on 2D LiDAR and a gyroscope [10], but without incorporating cutting operations.

Our team developed an innovative rubber-tapping robot prototype that integrates automated operations and equipment flexibility [11,12]. The prototype features a railcar that moves on a track in front of the rows of rubber trees, equipped with an industrial personal computer (IPC) and batteries. The central part of the operation is a six-joint series robotic arm, which incorporates a binocular stereo vision system and integrated sensors on the end effector. This enables the perception of the trunk and cutting line structural parameters, culminating in the blade on the end effector completing the cutting operation using a vision servo control strategy. While the robot prototype marks an initial exploration of automation for rubber tapping, further research is still necessary to improve the system’s overall performance, including its cutting stability.

Determining the cutting principle is a crucial prerequisite to address the problem. From a mechanics perspective, cutting involves controlled force damage, where the cutting force comprises deformation resistance, separation resistance, and friction resistance. During the cutting process, the wood and blade tip experience significant impact loads or regenerative chatter [13]. The impact force depends on factors such as relative speed, material properties of the blade, physical and mechanical properties of the wood, cutting position and angle, among others [14]. The change in impact force during the collision is complex, and negative vibrations occur when the blade tip’s acceleration reaches a certain level. This may result in chip breakage and unevenness, ultimately affecting cutting stability. Cutting stability refers to the blade’s ability to cut uniformly without excessive chatter or wobbling, leading to continuous and uniform chips [15,16]. In woodcutting, it is usually necessary to control impact acceleration within reasonable limits.

The industrial-grade robotic arm can provide real-time feedback on the position and speed information of the end effector [17]. However, these parameters alone are not sufficient to improve the cutting performance. With the increasing popularity of wearable devices, a new approach to monitoring cutting stability has emerged. Wearable devices with integrated perceptual components, such as IMUs and thermometers, have been shown to be effective in measuring hand motion [18,19,20]. In particular, IMUs are increasingly used due to their rich perception information and high accuracy [2,21]. Like the human hand, the end effector of the robotic arm needs to perform trajectory planning to accomplish precise cutting operations [22]. Motivated by these considerations, a Bluetooth IMU was integrated into the robot to evaluate the cutting stability in this study.

Algorithms integrating IMU and other sensor data have been widely applied in robotics. For instance, [23] simulated human movement on a tandem robotic arm and systematically quantified the accuracy under static conditions and typical human dynamics. Multiple IMUs were used to assess the accuracy of orientation measurements based on data fusion algorithms. IMU-based human movement measurements are proving to be a valuable alternative to standard tools, such as stereo photogrammetry, due to their portability and flexibility. Ref. [24] proposed a framework for mobile robot localization using a 2D laser scanner and an IMU, where laser and inertial data are fused for pose estimation. The proposed method performs more robustly than traditional geometry-based methods in challenging situations, such as moving with a large angular velocity. Hence, integrating an IMU with the robotic arm allows for accurate real-time sensing of posture and position.

This paper proposes a set of criteria for evaluating the cutting stability of rubber tapping based on an investigation of the cutting mechanism. Changes in impact acceleration during rubber tapping can cause variations in the cutting state, including changes in the continuity or physical properties of the chips. As a result, the characteristics of the chips can serve as indicators of the cutting stability. By establishing a correlation between impact acceleration and the physical properties of the chip, the cutting stability can be effectively evaluated.

This study has made two main contributions. Firstly, a system for measuring acceleration on the six-joint robotic arm is developed, which allows for real-time measurement of acceleration values at 21 interpolation points in the cutting trajectory. Secondly, the impact of acceleration variations in different axes on cutting stability is investigated, and a relationship between acceleration and chip thickness—a key indicator of cutting stability—is established.

The remainder of this paper is organized as follows. Section 2 details the experimental conditions and research methodology, including the robotic platform used and the evaluation algorithm’s running process. Section 3 presents the experimental results evaluating the cutting stability, while Section 4 offers a discussion and analysis of these results. Finally, Section 5 provides a summary of the entire paper, including conclusions and plans for future research.

2. Materials and Methods

2.1. Optimization of the Cutting Trajectory

After conducting field investigations and preliminary research, it was found that the rubber-tapping operation follows a complex spatial semicircular spiral trajectory. To replicate this intricate cutting path, a six-joint series robotic arm was employed, drawing inspiration from the rapid advancements in intelligent fruit harvesting robots. Tandem robotic arms offer three primary types of motion control: axial motion, rectilinear motion, and trajectory motion. These three types can be combined to generate a wide variety of motions. The trajectory motion type provides support for four distinct trajectory types, which include arc, circle, MoveP, and B-sample curves, with MoveP facilitating smooth transitions between linear trajectories (see Figure 1). To ensure a continuous motion trajectory, a circular arc is implemented to smooth the transition at the junction of two adjacent straight lines $\overline{AB}$ and $\overline{BC}$, resulting in a seamless trajectory $\widehat{AMNC}$ without any halts. The radius of the arc $\widehat{MN}$ is defined as the blend radius R. Notably, reducing the value of R leads to more significant turning angles in the trajectory, indicating a sharper change in the direction of the robotic arm.

The cutting trajectory is a crucial factor for achieving efficient rubber-tapping with a robotic arm. To optimize the trajectory for the six-joint series robotic arm, a mathematical model of the trunk was constructed, as shown in Figure 2a. In this model, the trunk coordinate system is defined as $\left\{O_{\mathrm{T}}-X_{\mathrm{T}}{Y}_{\mathrm{T}}{Z}_T\right\}$, and the starting and end points of the trajectory are denoted as $P_{\mathrm{s}}\left(X_{\mathrm{s}},Y_{\mathrm{s}},Z_{\mathrm{s}}\right)$ and $P_{\mathrm{e}}\left(X_{\mathrm{e}},Y_{\mathrm{e}},Z_{\mathrm{e}}\right)$, respectively. The thickness of the bark for each cut is denoted as $\delta$. To achieve a standardized cutting trajectory that is compatible with the robotic arm, the slope of the cutting line, denoted as $\gamma$, was set to 30°, and the radius of the trunk was denoted as R. By utilizing the geometric relationships, the endpoint position can be calculated from the starting point using Equation (1):

$$\left\{\begin{array}{c}{X}_{\mathrm{e}}=X_{\mathrm{s}}\\ Y_{\mathrm{e}}=Y_{\mathrm{s}}+2R\\ Z_{\mathrm{e}}=Z_{\mathrm{s}}-\pi R\tan \gamma \end{array}\right.$$

(1)

The process of optimizing the cutting trajectory is depicted in detail in Figure 2b. First, the cutting line separates the smooth tapped surface and the rough uncut surface. Then the cutting line is decomposed into multiple rectilinear trajectories, indicated by red line segments. The green circles indicate the interpolation points between the rectilinear segments, 21 in total. At these points, the robotic arm performs MoveP, which is a circular transition motion. By stitching multiple rectilinear and circular transition motions, the spiral trajectory is eventually reproduced. Driven by the robotic arm, one blade moves parallel to the cutting line, passing through all 21 interpolation points. To ensure that the cutting trajectory is standardized and suitable for a robotic arm, it was adapted from manual experience. The number of interpolation points, which was determined based on the kinematic characteristics of the tandem robotic arm and the results of pre-experimental exploration, is critical for accurate cutting.

After evaluating performance and cost factors, the AUBO i5 (AUBO, Beijing, China) was identified as the most suitable series six-joint robotic arm for the study.

Table 1. Main parameters of the AUBO i5.

Parameter	Performance Specification
Reach (mm)	924
Linear Velocity (m/s)	2.8 adjustable
Payload (kg)	5
Repeatability (mm)	±0.05
Communication	CAN bus
Motor Type	Harmonic drive 48 Volt

presents the key parameters of the chosen robotic arm. In the mobile platform, an industrial personal computer (IPC) serves as the host. The development and compilation environment utilized for this project was Visual Studio 2013 (Microsoft, Redmond, WA, USA), running on the Windows 7 operating system (Microsoft, Redmond, WA, USA). Additionally, a locally established MySQL 8.0 database (Oracle, Redwood City, CA, USA) was employed to store the cutting data, including operating time and cutting line parameters.

Figure 3a depicts the rubber-tapping robotic system, which was deployed in a natural rubber plantation. In order to facilitate the operation, parallel tracks were installed in front of the rubber tree rows, and a railcar was used to carry the six-joint robotic arm along the track. To ensure precise detection of the cutting line, a binocular stereo vision system, composed of two cameras and light sources, was mounted on the robotic arm. Moreover, a highly integrated end effector was designed to assist the arm, as shown in Figure 3b. This end effector incorporated laser distance sensors and a hand–eye camera to accurately locate the cutting line’s starting point. Laser sensors were also utilized to control the feed during the cutting process. Furthermore, Figure 3c illustrates some detailed features of the cutter, which included a horizontal leading edge and a secondary edge to effectively remove the bark. The tool was made of durable tool steel, while the base was constructed from lightweight aluminum alloy. Our previous work [11] provides a more detailed description.

The field trials were carried out in January 2020 at a natural rubber plantation located in Danzhou City, Hainan Province, China. The geographic coordinates of the plantation are 109°29′25″ E and 19°32′2″ N. The cultivar of these trees is Reyan 73397, which was bred by the Chinese Academy of Tropical Agricultural Sciences (CATAS) [25]. The rubber trees in the grove are grown in rows according to a standard specification of 6 m × 3 m. The trees, which are approximately 11 years old, attain a lofty average height of 10–20 m. At 1.0 m above the ground, the tree circumference exceeds 50 cm, meeting the rigorous local tapping standard. This criterion facilitates the pruning of rubber trees at a favorable height for human labor.

In order to realize the automation of rubber tapping, the robot must be programmed with appropriate parameter settings. A series of pre-cutting trials were conducted, both manually and with the robot, to determine the optimal parameters. The quantity of bark consumption was identified as a crucial factor in evaluating the stability of the cutting process. If the bark consumption is set too high, the blade will encounter greater resistance, and may even sink into the trunk, necessitating a halt in robot movement. Conversely, the blade may merely skim the bark surface, resulting in incomplete chips and an overall reduction in the stability of the cut. By contrast, the adjustment of parameters related to cutting depth primarily influences the area of the final latex yield. Thus, for the purposes of this study, the setting of the bark consumption parameter is of paramount importance in influencing the degree of cutting stability. Specifically, the cutting depth was established at 5.0 mm, while the bark consumption was varied in groups of 1.0 mm, 1.5 mm, 2.0 mm and 2.5 mm, with ten trials conducted for each group.

To ensure precision and accuracy throughout the cutting process, every interpolation point was meticulously recorded and timestamped with Universal Time Coordinated (UTC) to the millisecond (ms). The time interval between adjacent interpolation points was approximately 0.481 s, thus allowing for detailed and comprehensive analysis of the robotic performance. Notably, all cutting operations were carried out within the same day, with no cross-day operation taking place. At the completion of each cutting process, the robot automatically generated a data log file in the xml format, meticulously capturing and storing all relevant information for later analysis. The complete collection of these data log files is denoted by the set $\left\{Arm\right\}$, constituting a comprehensive and valuable record of the robot’s cutting performance.

2.2. Acceleration Measurement

To obtain a precise and comprehensive understanding of the cutting process, a wireless IMU WT901BLE5.0C (WitMotion, Shenzhen, China) was introduced. The sensor is compatible with an Android smartphone, Honor 20 Pro (Honor, Shenzhen, China), based on the low consumption Bluetooth 5.0. The accompanying client software, WitMotion v3.0, allows for the simultaneous connection of up to 4 sensors, while the Android 10 operating system (Google, Mountain View, CA, USA) ensures optimal functionality and ease of use. Employing kinetic calculations and Kalman dynamic filtering algorithms, this advanced sensor is capable of solving real-time poses, even in complex and challenging environments. The key parameters of the IMU are presented in

Table 2. Main parameters of the IMU.

No.	Parameter	Specification
1	Voltage (V)	3.3∼5.0
2	Dimensions ($L\times W\times H$, mm)	$51.3\times 36.0\times 15.0$
3	Measurement Dimension	(1) Acceleration	3
		(2) Angle	3
4	Measurement Range	(1) Acceleration (g)	±16
		(2) Angle of $\mathit{X}$/$\mathit{Z}$ (°)	±180
		(3) Angle of $\mathit{Y}$ (°)	±90
5	Repeatability	(1) Acceleration (g)	0.01
		(2) Angle (°)	0.05
6	Output Frequency (Hz)	0.2∼50
7	Transmission Distance (m)	50 (Without obstacles)

, with the output frequency set to a precise and reliable 50 Hz. The wireless communication method employed by the sensor offers unparalleled installation flexibility and significantly reduces interference from the wiring harness, ultimately contributing to more accurate and reliable data. No communication delays or issues were observed throughout the course of the trials.

Initially, the IMU needs to be calibrated to eliminate the zero-bias error. The calibration process involved both horizontal and lateral calibration in two directions, namely Left and Right. Once the calibration was complete, the IMU was firmly affixed to the motor cover at the robotic arm’s end, as illustrated in Figure 4. The sensor allowed for simultaneous measurement of acceleration on the three orthogonal axes, namely the X, Y, and Z axes. Specifically, the X axis was aligned with the central axis of the trunk and oriented vertically upwards, whereas the Y axis was directed opposite to the blade’s advance. Additionally, the Z axis was oriented radially away from the trunk and perpendicular to the central axis of the trunk at all times. These parameters allowed for precise recording and analysis of the accelerations during the rubber-tapping process.

In this study, the chatter of the end-effector was monitored in close proximity to the cutting actions. The blade is rigidly connected to the end flange and joint six, which directly conduct force. Changes in the acceleration of joint six were used to characterize the blade’s vibration, providing valuable insights into the stability of the cutting process. In addition, the wireless IMU was equipped with a 260 mAh lithium battery, eliminating the need for a power supply through the robotic arm and enhancing the flexibility of the experimental setup. Importantly, the wireless IMU was thoroughly tested and found to have no discernible electromagnetic interference with the robotic arm and end-effector, ensuring the reliability of the data obtained.

Prior to each cutting operation, the Bluetooth IMU was activated via the smartphone, enabling the system to initialize and synchronize the hardware components. Upon the mobile platform stopping in front of the target trunk, the cutting operation commenced, and the entire process took approximately 80 seconds to complete. This duration included the initial locating stage, the cutting movements, and the additional actions of the robotic arm during the two-step detection–cutting operation, as outlined in [11]. The cutting process involved seven distinct stages, namely, initial locating, arm additional action I, start point detection, compensation testing, arm additional action II, tapping, and arm additional action III. As described in Section 2.1, the cutting trajectory is optimized as a continuous curve with multiple interpolations. Figure 5 illustrates the percentage of time spent in each stage. The actual cutting action occurs in the sixth stage, tapping, which occupied 16.25% of the total time, while the IMU recording covered all stages of the cutting process. In particular, varying the cutting parameters does not result in a change in time consumption.

Following each cutting operation, a data logging file was generated in txt format. Within these log files, the recorded values of each measurement point were annotated with their corresponding timestamp, which was determined using the time zone of the smartphone device (i.e., Chinese Standard Time, UTC+08:00). The temporal accuracy of the recorded values was also at the millisecond level. The entirety of these data files was subsequently compiled and referred to as the $\left\{gyroscope\right\}$ dataset. Notably, the $\left\{gyroscope\right\}$ dataset contained a substantially greater number of time points than the $\left\{arm\right\}$ dataset.

During the cutting process, the blade applies pressure on the wood, inducing shear stress at the contact zone. As the blade advances, the wood fibers experience repeated deformation, leading to a progressive accumulation of shear-induced damage. This damage manifests as fractures, cracks, and de-laminations, which further weaken the material and facilitate the propagation of the cutting front. The combined effects of stress concentration, triaxial deformation, and anisotropic material properties contribute to the formation of spiral chips, which are characteristic of wood cutting.

After each cutting process, all chips were collected and numbered in chronological order. Vernier calipers (WD, Wenzhou, China) were employed to measure their width and thickness, and an electronic balance (MEIJIANING, Ruijin, China) was used for the weight. All measurements’ total mean and standard deviation (SD) were used.

2.3. Alignment Based on Absolute Time Synchronization

After the completion of all cutting operations, two groups of digital data were recorded from the robotic arm and the acceleration sensor, respectively. The assessment of acceleration variations at each interpolation point was executed with precision, drawing upon the principle of absolute time synchronization. The processing tools are Anaconda3 (Continuum Analytics, Austin, TX, USA) and Origin 2021b Learning Edition (OriginLab, Northampton, MA, USA). The flow block diagram in Figure 6 presents a detailed outline of the processing procedure for the two data files, underscoring the systematic approach utilized in this study.

First, the two sets of log files were processed with a similar methodology. Since there were no cross-day operations, the recorded points were kept to seconds and milliseconds. In addition, the acceleration parameters in $\left\{Gyroscope\right\}$ were retained to provide a comprehensive analysis. To establish a common ground for time synchronization processing, the first time points of the two groups were designated as ${\mathrm{T}}_1$ and ${\mathrm{S}}_1$, respectively. ${\mathrm{S}}_1$ was utilized as the reference point for time synchronization processing. With respect to $\left\{Arm\right\}$, a comparative analysis was conducted by comparing the other points ${\mathrm{T}}_n$ with ${\mathrm{T}}_1$. If ${\mathrm{T}}_n$ was greater, the time consumption at that point was calculated by subtracting ${\mathrm{S}}_1$ from ${\mathrm{T}}_n$, and the results were stored in matrix $\left\{A\right\}$. Conversely, the cutting process was observed to extend into the next minute with ${\mathrm{T}}_n$ plus 60 s. The same treatment was applied for the other data ${\mathrm{S}}_n$ in $\left\{Gyroscope\right\}$. The processing outcomes were meticulously documented and recorded in matrix $\left\{B\right\}$. By adopting this approach, a comprehensive and reliable analysis of the recorded data was conducted, which facilitates the accurate assessment of the cutting process.

Subsequently, a crucial step in the analysis involved the merging of the data present in matrices $\left\{A\right\}$ and $\left\{B\right\}$. The 21 rows in $\left\{A\right\}$ corresponded to the 21 interpolation points, which played a pivotal role in accurately assessing the cutting process. Furthermore, the value $B_j$ in $\left\{B\right\}$ was meticulously examined, and it was observed that the minimum value of j exceeded 130, indicating that there were ample time points from $\left\{Gyroscope\right\}$ to execute the proposed algorithm. The assessment of the square of the difference between $A_i$ and $B_j$ was conducted, and the outcomes were subsequently compared with a predetermined threshold p. The threshold value p was manually adjusted to ensure that all $i^{\prime }s$ were appropriately matched, while minimizing the number of $j^{\prime }s$ required for the matching. Given the high frequency of Bluetooth sensor sampling, it was found that almost no time points in $\left\{Gyroscope\right\}$ could correspond precisely to the interpolated point records in $\left\{Arm\right\}$. To address this issue and ensure the accuracy of the measurements, a meticulous approach was employed. Specifically, the average acceleration data within the neighborhood was meticulously examined to provide more nuanced insights into the cutting process. To this end, the neighborhood radius was set to 2, and the average was obtained from Equation (2), which allowed for the systematic and precise assessment of the data while minimizing any potential inaccuracies:

$$d_j^{\prime }=\frac{d_{j-2}+d_{j-1}+d_j+d_{j+1}+d_{j+2}}{5}$$

(2)

where j represents the number of the eligible time point. $d_{j-2}$, $d_{j-1}$, $d_j$, $d_{j+1}$ and $d_{j+2}$ denote all values in the neighborhood. $d_j^{\prime }$ represents the mean value, i.e., the final result given to the time point j. Still, there might be cases where i is not unique during the processing. Their averages were calculated and stored in the matrix $\left\{C\right\}$ as the final results.

2.4. Correlation Analysis of Chip Thickness

Further investigation into the factors affecting cutting stability.Many factors are taken into account, including chip thickness, chip width and smoothness of the cutting surface. Under the influence of shock loads or impact vibrations, chips may break off and compromise cutting stability. A critical factor in determining chip continuity is thickness. On the one hand, thinner chips may break off and cause jamming of the insert, which can damage the cutting line. On the other hand, thicker chips can increase cutting resistance and make the cut unstable.

The chip width, or cutting depth, however, is more influenced by the amount of feed control and the density of bark stratification. With a reasonable setting of bark consumption, a complete chip will always be generated. Chip width, on the other hand, characterizes the area of bark cut off and measures the yield of the latex. The width is not suitable to assess cutting stability. As for the smoothness of the cutting surface, it reflects the denseness of the bark itself, the sharpness of the blade and the flatness of the cutter body. Chip thickness is more reflective of the variation in the inherent flatness of the chip, not just the surface. In contrast, the chip thickness is a more appropriate indicator of cutting stability.

To unravel the complex and interdependent relationships among the influencing factors that affect chip thickness in the latex harvesting process, a multivariate regression analysis was performed. The objective of this analysis was to develop a predictive model that can capture the underlying mechanisms of chip formation and provide insights into the factors that contribute to the stability of the cutting process.

The multivariate model was constructed in Equation (3), investigating the relationship between chip thickness and the influencing factors:

$$T={\beta }_0+{\beta }_1\ast \delta +{\beta }_2\ast X+{\beta }_3\ast Y+{\beta }_4\ast Z$$

(3)

where T represents the thickness of the chip at one particular interpolation point. ${\beta }_0$, ${\beta }_1$, ${\beta }_2$ and ${\beta }_3$, ${\beta }_4$ stand for coefficients. $\delta$ indicates the setting value of chip thickness. X, Y, and Z represent the acceleration measurements in the three axes at the same interpolation point, respectively. $\delta$ and the acceleration values in all three axes are normalized.

Moreover, correlation analysis was conducted to further investigate the relationship between chip thickness and the influencing factors. The objective was to identify the factors that have the most significant impact on the stability of the cutting process and to assess the strength and direction of their influence. The Pearson correlation coefficient was used to calculate the correlation in Equation (4):

$$r=\frac{N\sum x_i{y}_i-\sum x_i\sum y_i}{\sqrt{N\sum x_i^2-{\left(\sum x_i\right)}^2}\sqrt{N\sum y_i^2-{\left(\sum y_i\right)}^2}}$$

(4)

where r indicates the calculated correlation coefficient and N denotes the number of elements in the sample. $x_i$ and $y_i$ represent the values of the corresponding elements in the two samples, respectively. Finally, all correlation calculation results are presented in a heat-map.

3. Results

3.1. Acceleration Measurement Results

In order to accurately measure the real-time variation of acceleration on each axis and the corresponding acceleration to which the blade is subjected at the interpolation points, a rigorous process of data collection and alignment was employed. This process is based on the fundamental principle of time synchronization and involves collecting acceleration measurements and aligning them with the values at the 21 interpolation points. As shown in Figure 7, the resulting data clearly demonstrate the intricate and complex patterns of acceleration variation that occur during the cutting process. The time axis was adjusted to relative time consumption, providing a detailed and accurate representation of the acceleration values at each point in time. The three black fluctuation curves indicate the real-time variation of acceleration on each axis.

To further facilitate the analysis and interpretation of the data, the three vertical lines (red, green and blue) were added to mark the temporal positions of the 21 interpolation points on the X, Y and Z axes, respectively. The intersection of these lines with the fluctuation curves represents the acceleration, to which the blade is subjected on that axis at the current interpolation point. It is worth noting that the acceleration values at the interpolation points are generally different from the rest. For example, in Figure 7b, the interpolation point acceleration is mainly found at the crest of the curve or a higher position, indicating that the blade is subjected to a higher acceleration at these points. In addition, the irregular roundness of the trunk poses a challenge to the accurate and even distribution of the interpolation points, which can be seen in the uneven spacing of the vertical lines in Figure 7.

The acceleration measurements of the X, Y, and Z axes were comprehensively analyzed and are presented through three distinct figures. Figure 8 illustrates the acceleration curve on the X axis, which exhibits significant fluctuations around the horizontal line. The magnitude of these fluctuations tends to increase with the number of interpolation points used for data analysis. Moreover, the fluctuation situation is exacerbated with an increase in bark consumption. In Figure 9, the acceleration variation curve on the Y axis depicts a subtle upward trend. The fluctuations on this axis are more pronounced and tend to intensify with increasing bark consumption. On the other hand, the Z axis shows a discernible upward trend (as shown in Figure 10). The fluctuations on this axis are more prominent in the initial phase, gradually stabilizing over time.

Furthermore, to gain deeper insights into the patterns of acceleration variation, a linear fit was made to the variation of accelerations over the three measurement axes (see Figure 11). The changes in acceleration values at 21 interpolated points on the same axis were fitted to a straight line. The resulting slope changes of the fitted lines were then compared to identify any discernible patterns. On the X axis, all four fitted straight lines were observed to be almost horizontal (see Figure 11a), consistent with the trend depicted in Figure 8. The fourth line (2.5 mm) showed a slight deviation from the other lines, exhibiting a negative slope. For the Y axis, the first three lines showed a clear upward trend, with the last straight line (2.5 mm) exhibiting a minor upward trend (see Figure 11b). These trends were more pronounced than those in Figure 9, making the comparison clear. Finally, on the Z axis, all lines showed a clear upward trend and were close to parallel (see Figure 11c), which was consistent with the trend depicted in Figure 10. However, the fourth line (2.5 mm) was significantly higher than the other lines due to a more significant intercept. This difference cannot be easily seen in Figure 10, and additional data support is needed to explore the reasons for the fitted results.

Table 3. Statistical results of the acceleration values (g).

$\mathit{\delta }$ (mm)	X-Axis	Y-Axis	Z-Axis
1.0	0.9990 ± 0.0015	−0.0367 ± 0.0036	−0.0020 ± 0.0009
1.5	1.0012 ± 0.0012	−0.0309 ± 0.0033	−0.0015 ± 0.0012
2.0	1.0013 ± 0.0017	−0.0302 ± 0.0046	−0.0030 ± 0.0011
2.5	0.9950 ± 0.0033	−0.0535 ± 0.0043	0.0044 ± 0.0018

presents comprehensive statistics for the acceleration values on the three axes. To ensure the accuracy, the mean values of acceleration at the 21 interpolation points were calculated for the four bark consumption settings in each trial. The experiment was repeated ten times to derive the overall averages and standard deviations, thereby minimizing accidental errors. The comparison between the groups was then carried out based on both the mean values and standard deviations of the acceleration measurements. The results show that, on both the X and Y axes, the acceleration values at the chip thickness of 2.5 mm setting are smaller compared to the other groups, consistent with the fit results depicted in Figure 11a,b. Additionally, for the Z axis, the mean values of the first three groups are negative, while the fourth group (2.5 mm) exhibits a positive mean value (0.0044 g). This observation is also confirmed by Figure 11c. Moreover, on both the X and Z axes, the standard deviation of the fourth group (2.5 mm) is larger compared to the other three groups, which have relatively smaller values. These comparison results are generally consistent with the fluctuations of the curves depicted in Figure 8 and Figure 10.

Moreover, the range of acceleration values on the three axes was counted and compared (see Figure 12). On the X axis, the acceleration values exhibited a gradual increase and then a sudden decrease as the bark consumption amount increased (see Figure 12a). However, the data in the last group deviated from the trend observed in the first three groups. On the Y axis, the $\delta =2.5$ mm group had significantly larger maximum and minimum values compared to the other groups (see Figure 12b). Nonetheless, the ranges of data were similar across all groups. Regarding the Z axis, the differences are particularly conspicuous. As illustrated in Figure 12c, the acceleration values of all groups oscillate around 0, with no significant differences among their minimum values. However, the maximum value of the fourth group is higher than that of the other groups, indicating a substantial discrepancy.

3.2. Results of Chip Measurements

Figure 13 shows the chips collected. The measurements of the width, thickness, and weight of each chip are depicted in Figure 14. Specifically, in Figure 14a, the chip width displays a non-monotonic trend with bark consumption, initially increasing and then decreasing. The widest chips are observed when the bark consumption is set to 2.0 mm, with the fluctuations being most pronounced at the 1.5 mm and 2.5 mm settings. Additionally, Figure 14b highlights a tendency for the chip thickness to increase with the amount of bark consumption, with the curve of chip thickness gradually flattening as $\delta$ increases. The fluctuations of the curves with smaller $\delta$ are more pronounced. The trend for the weight of the chips (see Figure 14c) is similar to that of the chip thickness, with the weights increasing as the amount of bark consumption grows. The chip weights in the groups with a $\delta$ of 2.5 mm are consistently the largest, aligning with the observed trends for chip thickness. While these findings provide insightful initial observations, more detailed data are needed for further rigorous comparisons.

3.3. Results of Correlation Analysis

This study utilized a multiple regression analysis to investigate the relationship between chip thickness and relevant factors, including bark consumption settings and acceleration values on the three axes. The mean of ten group results at each interpolation point was used to determine the chip thickness and acceleration values. A total of 84 sets of data were obtained from four bark consumption settings for regression analysis. The results of the analysis are presented in

Table 4. Results of multiple regression analysis calculations.

	Value	Standard Error	t-Value	Prob > |t|
Intercept	0.91148	0.05123	17.79303	$2.311\times {10}^{-29}$
${\beta }_1$	1.27003	0.02652	47.88689	$3.95328\times {10}^{-60}$
${\beta }_2$	0.08308	0.08563	0.97019	0.33492
${\beta }_3$	−0.26037	0.06940	−3.75167	$3.3352\times {10}^{-4}$
${\beta }_4$	0.23798	0.05779	4.11817	$9.32684\times {10}^{-5}$
RSS	0.4927 mm2
${\mathit{R}}^2$	0.976

, with the residual sum of squares (RSS) calculated to be 0.4927 mm² and the coefficient of determination (${\mathit{R}}^2$) estimated to be 0.976. The best multivariate model was constructed in Equation (5), providing insights into the factors that contribute to the variation in chip thickness:

$$T=0.91148+1.27003\ast \delta +0.08308\ast X-0.26037\ast Y+0.23798\ast Z$$

(5)

Significance tests were performed on the resulting regression equation.

Table 5. Calculated results of ANOVA.

	DF	Sum of Squares	Mean Square	F Value	Prob > F
Model	4	21.065	5.26625	844.4232	0
Error	79	0.49268	0.00624
Total	83	21.55769

displays the results of the analysis of variance (ANOVA). The F-test was performed in this study, and an F-value of 844.4232 was derived. At the $\alpha =0.05$ level, the critical value ${\mathrm{F}}_{\alpha }\left(4,79\right)$ is 2.487. The F-value is larger.

Subsequently, the measured $\delta$ and acceleration values in the three axes were used to calculate the predicted chip thickness values using Equation (5). To assess the accuracy of the predictions, the resulting values were compared with the ground truth data. The comparison results are presented in Figure 15. Specifically, the coefficient of determination (${\mathit{R}}^2$) was estimated to be 0.977, and the root mean square error (RMSE) of the predicted values was 0.0766 mm.

Further, the influence degrees of each factor on the chip thickness were compared. Figure 16 shows the results of the correlation analysis. The correlation coefficient of the bark consumption setting is the highest, reaching 0.98443. This is followed by the accelerations on the Z axis with 0.22937. Meanwhile, correlations of the acceleration values on the X and Y axes are negative. Their correlation coefficients are −0.34863 and −0.39573, respectively.

4. Discussions

Cutting the bark of a rubber tree is an inherently complex process. In particular, the interaction between the blade and the bark is a critical aspect that must be carefully analyzed and optimized, especially when using a six-joint robotic arm that must balance a flexible workspace with high precision. This study established a logical relationship between the blade accelerations and the resulting chip parameters, providing a valuable framework for understanding the underlying mechanisms that contribute to the observed outcomes. Building on the results of the field trials presented in Section 3, there are several key findings and implications that warrant further discussion and analysis. Concretely, data fusion based on the principle of temporal synchronization, chip characteristics, and influencing factors of chip thickness is discussed separately. By integrating these disparate sources of information, we can gain a more comprehensive understanding of the complex interplay between the various factors that affect the final chip thickness, and ultimately develop more effective strategies for enhancing the cutting stability in real-world applications.

4.1. Data Fusion Based on the Principle of Temporal Synchronization

Data fusion is a widely used technology in the field of automation, thanks to its ability to reduce errors and improve filtering accuracy, making it an attractive option for a variety of measurement applications [26,27]. IMU is also often utilized in data fusion systems due to its flexibility and richness of sensory information [28]. This paper introduced a Bluetooth-based wireless IMU to provide real-time evaluations of cutting stability. As shown in Figure 7, the positions of the 21 interpolation points are clearly delineated on the acceleration variation curves. Moreover, the use of absolute time synchronization down to the millisecond level ensures that the resulting measurements are highly accurate and reliable. These features make the proposed measuring system a valuable tool for evaluating cutting stability in real-world applications and offer numerous opportunities for further research and development in this important area.

In this study, use of the built-in gyroscope enables simultaneous measurements of the X, Y and Z axes without any interference, providing rich sensory information for data fusion. As illustrated in Figure 8, Figure 10 and Table 3, the acceleration variations on the three axes exhibit independent behavior. It is notable that all three groups of accelerations show different trends, but a more significant effect on the blade vibration is observed when the bark consumption is set to 2.5 mm. This is confirmed by the SDs, which are the largest for almost all the fourth group, with only a 6.52% decrease in the Y axis, indicating that blade vibration increases in all three directions when the amount of $\delta$ exceeds a certain threshold. In other words, the stability of the cutting would be damaged.

This study reveals that the absolute value of the change in acceleration varies depending on the bark thickness. Figure 11a displays that the acceleration in the group of 2.5 mm is lower overall compared to the other groups. This can be attributed to the thicker bark which hinders the change of acceleration in the X direction, leading to greater compression on the blade. However, the moment of cut induces more significant elastic deformation to the blade, resulting in lower absolute values but higher instability. This observation is supported by the large difference in most values for the 2.5 mm group in Figure 12a. On the other hand, the thicker bark increases the resistance of the blade to advance, resulting in a smaller overall acceleration that changes more slowly in the Y direction, as seen in Figure 11b. Consequently, the 2.5 mm group in Figure 12b displays the lowest maximum and minimum values. In the Z direction, the acceleration values are more sensitive to changes in chip thickness due to the secondary edge (see Figure 3c). Specifically, the secondary edge needs to make contact with the tapped surface and tear away the uncut bark, leading to greater pressure on the secondary edge and more drastic changes at the kerf. Therefore, the acceleration values are significantly higher and change dramatically. However, the elastic deformation caused by increasing thickness still cannot be ignored, as shown by the variation in the maximum and minimum values for the 2.5 mm group in Figure 12c. These observations are also consistent with the differences in the average results reported in Table 3.

Furthermore, it is noteworthy that a significant surge in the acceleration along the Z axis is evident during the latter section of the cutting process, as convincingly depicted in both Figure 10 and Figure 11c. This phenomenon could plausibly be attributed to the augmented blade-to-trunk distance, which is a direct consequence of the intricate and convoluted configuration of the trunk. It is also worth emphasizing that the radial acceleration fluctuations are considerably more responsive to the nuances of the trunk profile.

In Section 2.3, the selection of the appropriate time point $B_j$ was performed by manually adjusting the threshold P. While the eventual P successfully addressed the majority of the data in the $\left\{gyroscope\right\}$ dataset, the introduction of an algorithmic approach to automatically fine tune P would undoubtedly be an advantageous improvement. It is noteworthy that, in addition to the acceleration measurements, the sensor can contemporaneously capture information pertaining to angular velocity and angular displacement. Leveraging these additional parameters, future investigations will be able to enhance the cutting results with increased precision and accuracy.

4.2. Chip Characteristics

Similar to other cutting operations, such as bush trimming [29] and butchering [30], the characteristics of the produced chips can serve as a noteworthy indicator of the cutting stability. As illustrated in Figure 13, the chips derived from natural rubber trees exhibit a curved flake shape, with occasional instances of fracturing. Notably, setting $\delta$ to 2.5 mm results in the production of a pile of debris. In a sense, the continuity of the chip shapes can provide insight into the stability of the cutting process. As blade chatter increases, the chips undergo stress deformation, leading to fracturing. In conventional rubber-tapping practices, the generation of excessively fragmented chips can impede the latex output and flow. Regarding the measured chip parameters, no significant variation in width was observed as $\delta$ increased, as evidenced in Figure 14. However, the thickness and weight of the chips exhibited distinct behaviors. Specifically, both thickness and weight were observed to increase with an increase in $\delta$. Another noteworthy finding is that the variations in chip thickness and weight were more pronounced when $\delta$ was smaller. This phenomenon could be attributed to the limited cutting space available in the blade. This observation emphasizes the importance of establishing a suitable range for the $\delta$ value. Additionally, it is worth mentioning that, in local rubber plantations, there are strict limits on the total bark thickness that can be removed each year. The total number of cuts is typically restricted to approximately 80. If the chips are too thin, breakage occurs, leading to a reduced latex output. Conversely, an insufficient number of cuts may also result in reduced latex yield.

Moreover, it is worth noting that natural rubber trees exhibit anisotropic ingredients, and the composition of their bark is remarkably complex. The bark’s density, hardness, and other physical properties vary at different depths, further complicating the mechanized rubber-tapping process. In this study, the trunk was assumed to be a homogeneous cylinder to facilitate initial mechanized tapping operations. However, the complex nature of the bark necessitates further investigation. It is crucial to consider the varying characteristics of the bark at different depths, as they are expected to significantly impact the cutting results. Therefore, future research should aim to explore and quantify the heterogeneous nature of the bark more comprehensively to facilitate more accurate and efficient tapping operations.

4.3. Influencing Factors of Chip Thickness

The primary challenge associated with performing the cutting operation lies in effectively controlling the thickness of the chips produced. Thin chips can pose a significant risk as they are more prone to fracturing, which can lead to blade stuttering and ultimately, compromise the cutting line’s integrity. On the other hand, thicker chips can exacerbate cutting resistance, negatively impacting the overall stability of the process. It is imperative to strike a balance to achieve optimal cutting performance. Furthermore, in the context of rubber tree tapping, the amount of bark consumed during a given year is closely regulated and directly correlates with the tree’s cutting life. As such, excessively thick chips must be avoided to ensure that the bark’s consumption remains within the stipulated limit. This underscores the need for a meticulous approach to cutting operations.

In summary, the characterization of cutting stability via chip thickness constitutes a fundamental aspect of the study for cutting processes, and thus, an appropriate modeling approach is essential in this field [31]. To this end, an in-depth analysis of the factors that influence chip thickness was undertaken via a rigorous multiple-regression model. In a similar vein, prior research efforts have leveraged analogous methodologies toward the design and development of a novel end-effector prototype for pruning applications [32]. Herein, a thin force sensor was utilized to accurately measure the force required for branch-cutting, while the relationship between the required torque and the diameter of the branches was established. The performance of the end-effector was thoroughly verified via comprehensive field tests.

The statistical analysis results, as shown in Table 4 and Table 5, highlight the validity of the regression model presented in Equation (5) in predicting the chip thickness. The high correlation coefficient of 0.977 and the well-fitted linear equation $y=0.977x+0.036$, as observed in Figure 15, provide further evidence for the effectiveness of the model. Moreover, the investigation of the influence degree of different factors on the chip thickness, as illustrated in Figure 16, provides significant insights into the critical parameters in the cutting process. The results show that the bark consumption parameter, denoted by $\delta$, is the most critical factor in achieving a stable cutting process, with a correlation coefficient of 0.98443. After selecting an appropriate value for $\delta$, the acceleration variations on the three axes become the key to ensuring cutting stability. Interestingly, the Z axis acceleration exhibits a positive correlation coefficient of 0.22937, while the X and Y axis accelerations have negative correlation coefficients of −0.34863 and −0.39573, respectively. The study reveals that the radial acceleration of the blade plays a crucial role in determining the chip thickness. The chip thickness is more sensitive to changes in the radial acceleration of the blade than to other acceleration variations. This finding can be attributed to the secondary edge squeezing the bark as the blade vibrates in the radial direction, causing the fibrous tissue to tear more easily. Therefore, carefully controlling the radial acceleration is crucial to achieving the desired chip thickness.

Excessive Z-directional acceleration, that is, an excessively rapid radial movement of the blade, has the potential to interfere with normal cutting processes. Although a positive correlation coefficient is expected, it should be limited. Negative values along the X and Y axes are also understandable in this context. During the upward movement of the blade, the bark is peeled off, and the chip thickness is reduced. However, as the blade chatters along the Y axis, it deviates from the cutting contact point. Inadequate tangential force hinders the production of a new cut, leading to the rapid detachment of the secondary edge and bark. Finally, the positive correlation coefficients of Y-X (0.70569) and Y-Z (0.33654) indicate that resistance in the tangential direction affects blade vibration in the remaining two directions, with a greater impact on the vertical dimension. It can be inferred that forces acting on the X and Y axes play a more significant role in peeling off bark at the cutting contact point. Further study is necessary to support this conclusion with force measurement data.

By analyzing the relationship between the dependent variable (i.e., chip thickness) and the independent variables (i.e., the influencing factors), the multivariate model enables us to quantitatively assess the contribution of each factor to the overall variation in chip thickness. This information is invaluable for identifying the critical factors that affect cutting stability and for designing strategies to optimize the cutting process. Overall, the application of multivariate regression analysis to investigate the relationship between chip thickness and the influencing factors represents a significant advancement in our understanding of the complex and dynamic nature of the latex harvesting process. The resulting multivariate model provides a powerful tool for predicting and controlling the chip thickness, which is essential for achieving a stable and efficient cutting process.

5. Conclusions and Outlook

This study aimed to evaluate the cutting stability of an innovative rubber-tapping robot. Data fusion technology was employed to integrate a Bluetooth-based IMU with the six-joint robotic arm, which enabled real-time measurements of the cutter. In general, rubber tapping is achieved by relying on the horizontal cutting of the leading edge and the vertical stripping of the secondary edge. To assess cutting stability, blade accelerations and end-effector position information were simultaneously measured and aligned. The thickness of the produced chips was used as an indicator of cutting stability. The evaluation of the cutting stability was performed by investigating the correlation between chip thickness and various influencing factors. The results showed that the acceleration values on the X, Y, and Z axes fluctuated differently, with a particular similarity observed when the bark consumption reached 2.5 mm, leading to intensified fluctuations of each acceleration value. A similar trend was observed for the characteristic change curves of the chips. The bark consumption should, therefore, be controlled to no more than 2.0 mm. Multiple regression analysis revealed an ${\mathit{R}}^2$ value of 0.976, while the ${\mathit{R}}^2$ of the correlation analysis was 0.977, with a RMSE of 0.0766 mm. Among the three axes, the correlation of the Z axis acceleration was the strongest, with a correlation coefficient of 0.22937. Conversely, the correlations for accelerations on the remaining two axes were negative. The results of the multiple linear regression were consistent with the particular configuration of the blades used. To improve cutting stability, blade vibration in the radial direction should be attenuated. Additionally, a more flexible trajectory that more closely follows the cutting line is necessary to offset the negative effects on both the X and Y axes.

The study results improved the safe and efficient automated rubber-tapping robot system, thus speeding up the process of latex harvesting mechanization. However, it is systematic work to determine the factors that affect the cutting stability and improve its performance. First, the bark density and hardness vary at different depths. The effect of differences in bark characteristics at various depths on cutting results remains to be explored. Next, although the robot we developed solved or alleviated many of the problems faced in actual operations, it still cannot fully achieve the superior refinement level of workers. The robot needs to be optimized and upgraded in the production practice to complement manual work. For example, a cheaper tracked mobile chassis might replace the tracks, making the robot more scalable. In the future, specific causes of the unstable cutting will be explored. A force transducer will be installed on the end effector to measure the force upon the blade during the cutting accurately. Other parts of the robotic arm will be measured similarly to this study. Additionally, the influence of other platform components needs to be considered comprehensively. Addressing areas of weakness in stiffness will help improve the stability of the end effector and the whole system.