Stability Control of the Agricultural Tractor-Trailer System in Saline Alkali Land: A Collaborative Trajectory Planning Approach

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Q1: The stability control you proposed in this paper was suitable for saline alkali land. But I could not find any details about the information which is relative with saline alkali land. As we known, the soils of the saline alkali land should be different from the loam soils. Please make it clearly.

Q2: 4. Experimental Results and Discussion. The comparison should be added. The conclusion you proposed should be compared with the others. The comparison could support your discussion.

Q3: One dynamic yaw plane model was established in this paper. If you can conduct a simulation verification, the entire article structure would be more complete.

Q4: In Figure 5, The cyan curve and the green curve could not be easily distinguished. Please make it modified.

Q5: line255-267, The control system described in this paragraph is a closed loop, but the control block diagram is an open loop control. Please make it clearly. The steering wheel angle measurement and vehicle speed detection devices should be described.

Author Response

Q1: The stability control you proposed in this paper was suitable for saline alkali land. But I could not find any details about the information which is relative with saline alkali land. As we known, the soils of the saline alkali land should be different from the loam soils. Please make it clearly.

Response 1: We gratefully thank you for your time and effort in reviewing our manuscript! And we greatly appreciate your valuable suggestions. The design and innovation of intelligent agricultural machinery and equipment is an important guarantee for the comprehensive management of saline alkali land and the improvement of production capacity. In this study, the content related to saline alkali land is mainly reflected in the following three aspects:

The main direction of this study is the development of intelligent agricultural equipment for saline alkali land, aiming to provide solutions for trajectory planning and tracking control of Tractor-Trailer Systems (TTS).

More details about saline alkali land are reflected in the interaction between TTS and saline alkali land pavement. Specifically, this is reflected in the friction coefficient and resistance coefficient parameters and relationships between TTS’s tires and saline alkali road surfaces. The following table shows the sliding friction coefficient and rolling resistance coefficient between the tire and different ground surfaces (Reference [40] in the new manuscript). We mainly examine the impact of the road surface properties of saline alkali farmland on the vehicle system. During the experiment, we found that the experimental road in saline alkali soil is essentially a typical, compacted soil road. Combining the dryness of the road surface and tire style (rubber off-road tires) at our experimental site，we chose a sliding friction coefficient of 0.6. The numerical range of rolling resistance coefficient is [0.025-0.035]. Considering that the tire is new, the upper limit of the rolling friction coefficient is taken as 0.035.

Table 1 Sliding Friction Coefficient (Table 6-1 in “Automotive Tire Science”)

Road surface	Maximum sliding friction coefficient	Coefficient of sliding friction
Asphalt or concrete road (dry)	0.8-0.9	0.75
Asphalt road (wet)	0.5-0.7	0.45-0.6
Concrete road (wet)	0.8	0.7
Gravel road	0.6	0.55
Dirt road (dry)	0.68	0.65
Dirt road (wet)	0.55	0.4-0.5
Snow covered road (compressed)	0.2	0.15
Frozen road	0.1	0.07

Table 2 Rolling Resistance Coefficient Values (Table 5-3 in “Automotive Tire Science”)

Road surface	Rolling Resistance Coefficient
Good asphalt or concrete road	0.010-0.018
Ordinary asphalt or concrete pavement	0.018-0.020
Macadam road	0.020-0.025
Good pebble road	0.025-0.030
Bumpy cobblestone road	0.035-0.050
Compacted dirt road：dry	0.025-0.035
Compacted dirt road：after the rain	0.050-0.150
Wet sand	0.060-0.150
Frozen road	0.015-0.030
Tightened snow road	0.030-0.050
Muddy dirt road	0.100-0.250
Dry sand road	0.100-0.300

Specifically, it refers to the selection of correlation coefficients such as C₁, C₂, C₃, and C₄ in the model.

3.The TTS system in this study is mainly aimed at farm management and agricultural product transportation in saline alkali land scenarios. In fact, the trailer part can be replaced by an unpowered shovel throwing machine, a mouse plough and a trailer mounted spray device, etc. Therefore, the trajectory planning and tracking control of the underactuated nonlinear system in this study are quite referential to the promotion and application of the above scenarios. We hope to provide technical support for the intelligent production and management equipment in saline alkali land scenarios.

According to your suggestion, we have made the following corrections in the new version of the manuscript:

Lines 174-176：Where C_i (i=1,2,3,4) is the rolling resistance coefficient between the tire and the ground, the driver's perspective is used as the benchmark to unify the vehicle coordinate system. According to the tool manual, C_i = 0.035 [40].

Lines 383-388: The roads in the saline alkali land are all dry and compacted, and the vehicles used are equipped with cross-country tread pattern tires, which provide excellent friction and traction between the road and the tires. Consequently, based on the rolling resistance coefficient table [insert citation], a value of C_i = 0.035 was selected for equations (15), (16), (17), and (18). As illustrated in Figure 8, six experimental roads were chosen within the saline alkali land farm.

Lines 593: 40. Zhuang, J., Automotive Tire Science, 1rd ed.; Beijing Institute of Technology Press: Beijing, China, 1995; pp. 186–229.

Q2: 4. Experimental Results and Discussion. The comparison should be added. The conclusion you proposed should be compared with the others. The comparison could support your discussion.

Response 2: Thank you for your valuable suggestions, which has greatly improved the quality of the manuscript. Based on your suggestion, we have adopted multiple control schemes and conducted multiple experiments to compare the results of TTS tracking control. The most classic method for tracking control of TTS systems is PID control. In addition, we also chose the LQR (Linaer Quadratic Regulator) and Kalman control method with stable performance. A comprehensive comparison and analysis were conducted with the dual trajectory collaborative control method proposed in this study. As mentioned in our research, in traditional studies, TTS control strategies are mostly based on single trajectory tracking. The default motion trajectory of the unpowered trailer should be the same as that of the tractor. However, according to the research in this research, the unpowered trailer actually has its own independent motion patterns. This is also one of the innovative points and focuses of this research. Based on your suggestion, we selected 5 control strategies, including the control method proposed in this study, for longitudinal comparison in the experiment. At the same time, 6 roads from different saline alkali land farms were selected for horizontal comparison based on 6 parameters (Max e_off, Mean e_off, Standard Deviation e_off, Max e_θ, Mean e_θ, and Standard Deviation e_θ) to comprehensively evaluate the tracking and control effect of the system.

According to your suggestion, we have made the following corrections in the new version of the manuscript:

Lines 391-418：To ensure the rigor of the experiment and the practicality of the algorithm, three conventional algorithms (PID, LQR, and Kalman), the proposed TTS-KM and the TTS-DM were selected for comparison. As listed in Table 2, six indicators used to systematically evaluate the tracking and control effects of the TTS. Max e_off represents the maximum deviation, Mean e_off is the average deviation, and the Standard Deviation e_off represents the discrete deviation of the trailer during driving. Max e_θ represents the maximum heading angle deviation; Mean e_θ represents the average heading angle deviation; and Standard Deviation e_θ represents the heading angle fluctuation of the tractor during driving. These two standard deviations (Standard Deviation e_off and Standard Deviation e_θ) can effectively measure the stability of TTS.

Lines 412-429：Compared to the PID controller, the lateral offset was controlled to a certain extent; however, the heading angle between the tractor and trailer exhibited significant fluctuations. This indicates that the tractor has made considerable compromises in control stability to ensure effective trailer tracking. While large positional deviations can be corrected through adjustments, frequent modifications to the heading angle may introduce unknown risks. Therefore, this type of operation should be avoided under high-speed conditions.

In this study, due to the intrinsic properties of the TTS, the tractor and trailer do not overlap during turns. However, the trailer's trajectory can be reasonably predicted and planned under certain conditions. The two algorithms, (TTS-KM and TTS-DM) consider both the tractor and trailer. The results indicate that the tracking and control outcomes have been significantly optimized and improved. In six road experiments, the Max e_off of the system did not exceed 0.2 meters, and the Max e_θ did not exceed 0.28 radians. The Mean e_off and the Mean e_θ decreased by at least 1/3. Notably, the two standard deviation metrics decreased by more than 2/3 compared to conventional control methods. Furthermore, the proposed TTS-DM slightly outperformed the kinematic model at high-speeds in terms of the two standard deviations. This suggests that the lateral control stability of the kinematic model was enhanced, which is crucial for the high-speed.

Q3: One dynamic yaw plane model was established in this paper. If you can conduct a simulation verification, the entire article structure would be more complete.

Response 3: Thank you for your valuable suggestion. In the previous version of the manuscript, our expression regarding this part was not clear and explicit enough. Please allow us to provide further clarification here. In this study, two models were proposed for high-speed and low-speed conditions, namely TTS-KM (TTS kinematic model) and TTS-DM (TTS dynamic model). Among them, in section 2.2, we established a kinematic model. In section 2.3, we have established a dynamic model control equation. In fact, the kinematic model is applicable to low-speed conditions. The dynamic model is applicable under both low-speed and high-speed conditions, and the results obtained are very similar to those obtained from the kinematic model. The difference is that the computational complexity of the dynamic model is higher. Because the dynamic model has a wider coverage range, we chose the naming convention “dynamic yaw plane model”, which has a wider coverage range. This has indeed caused difficulties in understanding. Two models are integrated in parallel into the control algorithm and switched in an orderly manner based on speed conditions. Essentially, both the TTS-KM and TTS-DM are yaw plane model which are also two branches of our proposed model. In order to make the expression of the manuscript more logical and coherent, we have made modifications and supplements to the relevant statements, replacing the “dynamic yaw plane model” with the “yaw plane model”. I hope we have understood your meaning correctly.

According to your suggestion, we have made the following corrections in the new version of the manuscript:

Lines114-115: To achieve the closed-loop feedback performance for the TTS, a yaw plane model is established.

Q4: In Figure 5, The cyan curve and the green curve could not be easily distinguished. Please make it modified.

Response 4: Thank you very much for your kind advice and reminder. We have regenerated and modified Figure 5. The original blue curve has been replaced with a more prominent bright yellow curve. At the same time, corresponding modifications and adjustments have been made to the wording in the paper.

At the same time, the relevant statements regarding Figure 5 in the manuscript have also been modified and adjusted accordingly.

The specific modifications are as follows:

Lines 276-281: The green curve is generated by the TTS-KM at low-speed. The fine yellow curve illustrates the trajectory predicted using the dynamic model proposed in this study. It is important to note that, for the sake of clarity and calculation, both the green and thick yellow curves are fitted based on the motion trajectory of the left rear wheel of the trailer, rather than the midpoint of the rear axle or the center of gravity.

Lines 284-294: As illustrated in Figure 5, the fine yellow curve does not precisely align with the green curve and is generally situated between the green and black curves. The system exhibits improved longitudinal stability and maintenance performance when the TTS operates at high-speeds. However, the fine yellow and green curves are relatively close to each other. This proximity occurs because a larger turning angle amplifies the influence of the hinge point on the lateral traction of the trailer, resulting in a more pronounced lateral offset motion. It is evident that, regardless of whether the system is operating at high or low-speeds, the lateral offset of the trailer remains constrained within a specific range, defined by upper and lower limits. Additionally, a comparison of the predicted trajectories from both methods mutually confirms the objectivity and predictability of the IWD phenomenon in the TTS.

Q5: line255-267, The control system described in this paragraph is a closed loop, but the control block diagram is an open loop control. Please make it clearly. The steering wheel angle measurement and vehicle speed detection devices should be described.

Response 5: Thank you for your meticulous inspection. As you said, the system is closed-loop controlled. The description of the closed loop is not very prominent in the Figure 3, Because our intention was to highlight the innovation of the algorithm proposed in this study-Double trajectory cooperative planning and tracking control algorithm. So the part of closed loop control and iteration is briefly represented by the two red arrows in the upper right corner of Figure 3.

In addition, the steering wheel Angle measurement is realized by the steering gear and the Angle encoder, and the speed feedback is realized by the BDS box and the IMU. Each sensor has established the corresponding topic transceiver node and channel in the ROS system. As you said, we also did a lot of trial and optimization work. For example, we have also added digital encoders to the wheel motor. However, due to road reasons, the wheels may slip, and simply obtaining the vehicle speed from the wheel motor may not be accurate, so we use BDS and IMU to compensate the measurement results. In fact, some of us thought that this part was more of an engineering problem during the experiment, so in the last version, this part was only briefly explained. Of course, in the new version, we have added related descriptions on steering wheel angle measurement and vehicle speed detection devices according to your suggestions. The introduction and supplementary explanation of the vehicle computer and control system are also given.

According to your suggestion, we have made the following corrections in the new version of the manuscript:

Lines 249-264: Its configuration is as follows: The size of the tractor is 970 mm*680mm*400mm. The size of the trailer is the same as the tractor. Traction arm (the distance between the tractor and the trailer) is 0.4m. The configuration of the TTS industrial control computer is as follows: The system is con-figured with Linux 20.04 and ROS-noetic. The motherboard is equipped with an Intel i7-13700K CPU and 256GB of RAM.

In order to ensure accurate observation of the position and orientation of the TTS system, the system integrates the "Beidou Navigation Satellite System (BDS) + Inertial Measurement Units (IMU)" module. The IMU model used is the RION TL-740D. The architecture for signal acquisition, storage, and sharing is integrated into the software system. Channels and nodes for signal publication and subscription are established for each sensor. Specifically, the measurement of the steering wheel angle is achieved through the collaboration of the steering gear and the angle encoder, while speed feedback is obtained from both the BDS unit and the IMU.

Thank you again for taking the time and effort to review our manuscript!

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper proposed a dual-trajectory collaborative control model based on the nonlinear under actuation characteristics of the tractor-trailer system and the law of passive trailer steering. The work of the paper is relatively complete, and it can be accepted for publication after making the following modifications:

(1) In the paper, only the kinematic constraints of the tractor trailer system are considered, but the impact of hinge angle constraints on the stability of the tractor trailer system is not taken into account.

(2) According to the control block diagram of two-trajectory collaborative strategy shown in Figure 3, the author adopts different lateral stability control strategies for high-speed and low-speed operating conditions? If so, will this approach lead to weak applicability of the control strategy in practical applications? And how are high and low speeds distinguished?

(3) There are still many formatting or writing errors in the paper, such as: 1)The first letter of ‘combining’ in line 24 of the text should be capitalized. 2) The black curve in Figure 7 represents a low-speed trajectory, but the legend indicates a high-speed trajectory.

(4) The application scenario of the research object in this paper is saline alkali land. Therefore, the author’s research should pay more attention to the special characteristics of saline alkali land and its impact on tractor control systems.

(5) Regarding the literature survey, the reviewer recommends to add a few more papers related to this study. Such as:  En Lu, Xin Zhao, Zheng Ma, et al. Robust Leader-Follower Control for Cooperative Harvesting Operation of a Tractor-Trailer and a Combine Harvester Considering Confined Space [J]. IEEE Transactions on Intelligent Transportation Systems, 2024, 25(11): 17689-17701.

(6) Several English grammar errors must be carefully checked and corrected.

Comments on the Quality of English Language

The English could be improved to more clearly express the research.

Author Response

This paper proposed a dual-trajectory collaborative control model based on the nonlinear under actuation characteristics of the tractor-trailer system and the law of passive trailer steering. The work of the paper is relatively complete, and it can be accepted for publication after making the following modifications:

Q1: In the paper, only the kinematic constraints of the tractor trailer system are considered, but the impact of hinge angle constraints on the stability of the tractor trailer system is not taken into account.

Response 1: We gratefully thank you for your time and effort in reviewing our manuscript! And we greatly appreciate your valuable suggestions. In previous versions of the manuscript, the interaction between hinges and tractors and trailers was not clear enough. As for the force relationship between the hinge and the tractor-trailer system (TTS), we have made relevant supplements according to Figure 2. As can be seen from the Figure 2, the hinge point of the TTS system is located in the center of the rear axle of the tractor. The traction is transmitted through the hinge point. As can be seen, the forces of the tractor and the trailer are broken down respectively. For tractors, the pulling forces are orthogonally decomposed to F_TX and F_TY. For trailers, the pulling forces are orthogonally decomposed to F_AX和F_AY. This is also reflected in equations (11)-(14).

Meanwhile, based on your suggestion, we have provided additional explanations in the new manuscript.

Lines 163-171:In the equation (11)-(14), m_i is the total mass of the tractor or the trailer; I_zi represent moment of inertia; v_i is the lateral velocity; u_i is the longitudinal velocity;  is the angular velocity at which the tractor or the trailer rotates around the center of mass. F_Y1, F_Y2, F_Y3 and F_Y4 are the lateral forces of the ground against the tire. F_AX, F_AY, F_TY and F_TX are the action and reaction force (through orthogonal decomposition) caused by the tow arm. a_i and b_i are the length from the front-axle center and the rear-axle center to the center of gravity of the tractor or the trailer.  is the steering angles of the TTS. Among them, i = 1,2.

Q2: According to the control block diagram of two-trajectory collaborative strategy shown in Figure 3, the author adopts different lateral stability control strategies for high-speed and low-speed operating conditions? If so, will this approach lead to weak applicability of the control strategy in practical applications? And how are high and low speeds distinguished?

Response 2: Thank you very much for your careful examination of the manuscript. In this study, two models were proposed for high-speed and low-speed conditions, namely TTS-KM (TTS kinematic model) and TTS-DM (TTS dynamic model). Among them, in section 2.2, we established a kinematic model. In section 2.3, we have established a dynamic model control equation. In fact, this study has found that the kinematic characteristics of the tractor-trailer system impose more significant constraints on the system at low speeds. However, as the speed increased, the dynamic characteristics became the main factor affecting the trajectory planning and tracking control of the tractor-trailer system. The kinematic model is applicable to low-speed conditions. The dynamic model is applicable under both low-speed and high-speed conditions, and the results obtained are very similar to those obtained from the kinematic model. The difference is that the computational complexity of the dynamic model is higher. Two models are integrated in parallel into the control algorithm and switched in an orderly manner based on speed conditions. The reason is that in engineering applications, we often integrate a variety of sensors in vehicle systems, such as vision cameras, Lidar, BDS, IMU, etc. This requires sufficient computing power support. Therefore, we have integrated two parallel branches, TTS-KM and TTS-DM, into the system for both the system and researchers to choose. The selection of two modules provides the system with more selectivity and adaptability.

In addition, according to urban traffic regulations, the speed for distinguishing between high and low speeds is usually 40 km/h or 60 km/h. In this study, based on the research conventions related to TTS control methods, scholars usually set the boundary between high-speed and low-speed at 30 km/h-36 km/h. Based on the above situation, this study followed the convention of using a speed of 30 km/h as the boundary between high and low speeds.

According to your suggestion, we have made the following corrections in the new version of the manuscript:

Lines 241-243：In this study, a speed of 30 km/h is used as the threshold between high speed and low speed. When the system exceeds 30 km/h, it is classified as high speed, and when it falls below 30 km/h, it is classified as low speed

Q3: There are still many formatting or writing errors in the paper, such as: 1)The first letter of ‘combining’ in line 24 of the text should be capitalized. 2) The black curve in Figure 7 represents a low-speed trajectory, but the legend indicates a high-speed trajectory.

Response 3: Thank you very much for your careful inspection. Based on your valuable suggestions, we have carefully corrected the questions you raised. At the same time, we have invited experts who are native English speakers to comprehensively and carefully revise and polish the manuscript, including spelling, grammar, terminology, etc. All modifications have been highlighted in the manuscript.

Lines 25-27: Combining the dual trajectory independent offset and lateral acceleration indicators of the tractor-trailer system, an energy function optimization control parameter is constructed to balance the system trajectory tracking performance and lateral control stability.

Q4: The application scenario of the research object in this paper is saline alkali land. Therefore, the author’s research should pay more attention to the special characteristics of saline alkali land and its impact on tractor control systems.

Response 4: We greatly appreciate your valuable suggestions. The design and innovation of intelligent agricultural machinery and equipment is an important guarantee for the comprehensive management of saline alkali land and the improvement of production capacity. In this study, the content related to saline alkali land is mainly reflected in the following three aspects:

The main direction of this study is the development of intelligent agricultural equipment for saline alkali land, aiming to provide solutions for trajectory planning and tracking control of Tractor-Trailer Systems (TTS).

More details about saline alkali land are reflected in the interaction between TTS and saline alkali land pavement. Specifically, this is reflected in the friction coefficient and resistance coefficient parameters and relationships between TTS’s tires and saline alkali road surfaces. The following table shows the sliding friction coefficient and rolling resistance coefficient between the tire and different ground surfaces (Reference [40] in the new manuscript). We mainly examine the impact of the road surface properties of saline alkali farmland on the vehicle system. During the experiment, we found that the experimental road in saline alkali soil is essentially a typical, compacted soil road. Combining the dryness of the road surface and tire style (rubber off-road tires) at our experimental site，we chose a sliding friction coefficient of 0.6. The numerical range of rolling resistance coefficient is [0.025-0.035]. Considering that the tire is new, the upper limit of the rolling friction coefficient is taken as 0.035.

Table 1 Sliding Friction Coefficient (Table 6-1 in “Automotive Tire Science”)

Road surface	Maximum sliding friction coefficient	Coefficient of sliding friction
Asphalt or concrete road (dry)	0.8-0.9	0.75
Asphalt road (wet)	0.5-0.7	0.45-0.6
Concrete road (wet)	0.8	0.7
Gravel road	0.6	0.55
Dirt road (dry)	0.68	0.65
Dirt road (wet)	0.55	0.4-0.5
Snow covered road (compressed)	0.2	0.15
Frozen road	0.1	0.07

Table 2 Rolling Resistance Coefficient Values (Table 5-3 in “Automotive Tire Science”)

Road surface	Rolling Resistance Coefficient
Good asphalt or concrete road	0.010-0.018
Ordinary asphalt or concrete pavement	0.018-0.020
Macadam road	0.020-0.025
Good pebble road	0.025-0.030
Bumpy cobblestone road	0.035-0.050
Compacted dirt road：dry	0.025-0.035
Compacted dirt road：after the rain	0.050-0.150
Wet sand	0.060-0.150
Frozen road	0.015-0.030
Tightened snow road	0.030-0.050
Muddy dirt road	0.100-0.250
Dry sand road	0.100-0.300

Specifically, it refers to the selection of correlation coefficients such as C₁, C₂, C₃, and C₄ in the model.

3.The TTS system in this study is mainly aimed at farm management and agricultural product transportation in saline alkali land scenarios. In fact, the trailer part can be replaced by an unpowered shovel throwing machine, a mouse plough and a trailer mounted spray device, etc. Therefore, the trajectory planning and tracking control of the underactuated nonlinear system in this study are quite referential to the promotion and application of the above scenarios. We hope to provide technical support for the intelligent production and management equipment in saline alkali land scenarios.

According to your suggestion, we have made the following corrections in the new version of the manuscript:

Lines 174-176：Where C_i (i=1,2,3,4) is the rolling resistance coefficient between the tire and the ground, the driver's perspective is used as the benchmark to unify the vehicle coordinate system. According to the tool manual, C_i = 0.035 [40].

Lines 383-388: The roads in the saline alkali land are all dry and compacted, and the vehicles used are equipped with cross-country tread pattern tires, which provide excellent friction and traction between the road and the tires. Consequently, based on the rolling resistance coefficient table [insert citation], a value of C_i = 0.035 was selected for equations (15), (16), (17), and (18). As illustrated in Figure 8, six experimental roads were chosen within the saline alkali land farm.

Lines 593: 40. Zhuang, J., Automotive Tire Science, 1rd ed.; Beijing Institute of Technology Press: Beijing, China, 1995; pp. 186–229.

Q5: Regarding the literature survey, the reviewer recommends to add a few more papers related to this study. Such as:  En Lu, Xin Zhao, Zheng Ma, et al. Robust Leader-Follower Control for Cooperative Harvesting Operation of a Tractor-Trailer and a Combine Harvester Considering Confined Space [J]. IEEE Transactions on Intelligent Transportation Systems, 2024, 25(11): 17689-17701.

Response 5: Thank you for your valuable suggestions and recommendations. The document you provided does have considerable inspiration and reference significance for this research. We have added it to the section of Reference, and we cite it in section 2.

According to your suggestion, we have made the following corrections in the new version of the manuscript:

Lines 572-574: 30. Lu, E.; Zhao, X.; Ma, Z.; Xu, L.; Liu, Y.; Robust leader-follower control for cooperative harvesting operation of a tractor-trailer and a combine harvester considering confined space. IEEE Transactions on Intelligent Transportation Systems. 2024, 25, 17689-17701.

Q6: Several English grammar errors must be carefully checked and corrected. Comments on the Quality of English Language. The English could be improved to more clearly express the research.

Response 6: Thank you for your kind reminder and valuable suggestions. Your suggestions are of great significance to improve the quality of the article. Based on your valuable suggestions, we have invited experts who are native English speakers to comprehensively and carefully revise and polish the manuscript, including spelling, grammar, terminology, etc. All modifications have been highlighted in the manuscript (Please refer to the new version of the manuscript attachment for details).

Thank you again for taking the time and effort to review our manuscript!

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Tractor-trailer system research is relevant to improve the operation and stability of these systems. However, there are flaws and shortcomings in the article

Abstract.  Why does the article emphasize "salina alcadi land"? Does the tractor equipment research not apply to any soil? Do the results not depend on soil density, slipperiness or relief? What are the soil indicators in the study?

Key words. Keywords are words, not long phrases and sentences

2. State Space of the Tractor-Trailer System

"Owing to the small high-order error term and the fact that the calculation results were dynamically updated and covered, the high-order term can be ignored".(156-158)-So what is this error?

In the formula...(184)-Give specific formulas

3. Lateral Stabilizer Based on Dual-Trajectory Prediction

Under what conditions did you choose the distance parameter 0.03 m? (224)

Under what conditions are low-speed and high-speed separated? (268)

Fig. 5 should indicate the line designations (315)

Hard to perceive Fig. 6. Maybe reduce the number of R. (331)

It is unclear under what road conditions Table 2 was obtained. Describe the road surface/soil. What is the distance between the tractor and the trailer? How will this distance affect the study?

 

Author Response

Q1: Abstract.  Why does the article emphasize "salina alcadi land"? Does the tractor equipment research not apply to any soil? Do the results not depend on soil density, slipperiness or relief? What are the soil indicators in the study?

Response 1: We gratefully thank you for your time and effort in reviewing our manuscript! Anderson we greatly appreciate your valuable suggestions. The design and innovation of intelligent agricultural machinery and equipment is an important guarantee for the comprehensive management of saline alkali land and the improvement of production capacity. In this study, the content related to saline alkali land is mainly reflected in the following three aspects:

The main direction of this study is the development of intelligent agricultural equipment for saline alkali land, aiming to provide solutions for trajectory planning and tracking control of Tractor-Trailer Systems (TTS).

More details about saline alkali land are reflected in the interaction between TTS and saline alkali land pavement. Specifically, this is reflected in the friction coefficient and resistance coefficient parameters and relationships between TTS’s tires and saline alkali road surfaces. The following table shows the sliding friction coefficient and rolling resistance coefficient between the tire and different ground surfaces (Reference [40] in the new manuscript). We mainly examine the impact of the road surface properties of saline alkali farmland on the vehicle system.During the experiment, we found that the experimental road in saline alkali soil is essentially a typical, compacted soil road. Combining the dryness of the road surface and tire style (rubber off-road tires) at our experimental site，we chose a sliding friction coefficient of 0.6. The numerical range of rolling resistance coefficient is [0.025-0.035]. Considering that the tire is new, the upper limit of the rolling friction coefficient is taken as 0.035.

Table 1 Sliding Friction Coefficient (Table 6-1 in “Automotive Tire Science”)

Road surface	Maximum sliding friction coefficient	Coefficient of sliding friction
Asphalt or concrete road (dry)	0.8-0.9	0.75
Asphalt road (wet)	0.5-0.7	0.45-0.6
Concrete road (wet)	0.8	0.7
Gravel road	0.6	0.55
Dirt road (dry)	0.68	0.65
Dirt road (wet)	0.55	0.4-0.5
Snow covered road (compressed)	0.2	0.15
Frozen road	0.1	0.07

Table 2 Rolling Resistance Coefficient Values (Table 5-3 in “Automotive Tire Science”)

Road surface	Rolling Resistance Coefficient
Good asphalt or concrete road	0.010-0.018
Ordinary asphalt or concrete pavement	0.018-0.020
Macadam road	0.020-0.025
Good pebble road	0.025-0.030
Bumpy cobblestone road	0.035-0.050
Compacted dirt road：dry	0.025-0.035
Compacted dirt road：after the rain	0.050-0.150
Wet sand	0.060-0.150
Frozen road	0.015-0.030
Tightened snow road	0.030-0.050
Muddy dirt road	0.100-0.250
Dry sand road	0.100-0.300

Specifically, it refers to the selection of correlation coefficients such as C₁, C₂, C₃, and C₄ in the model.

3.The TTS system in this study is mainly aimed at farm management and agricultural product transportation in saline alkali land scenarios. In fact, the trailer part can be replaced by an unpowered shovel throwing machine, a mouse plough and a trailer mounted spray device, etc. Therefore, the trajectory planning and tracking control of the underactuated nonlinear system in this study are quite referential to the promotion and application of the above scenarios. We hope to provide technical support for the intelligent production and management equipment in saline alkali land scenarios.

According to your suggestion, we have made the following corrections in the new version of the manuscript:

Lines 174-176：Where C_i (i=1,2,3,4) is the rolling resistance coefficient between the tire and the ground, the driver's perspective is used as the benchmark to unify the vehicle coordinate system. According to the tool manual, C_i = 0.035 [40].

Lines 383-388: The roads in the saline alkali land are all dry and compacted, and the vehicles used are equipped with cross-country tread pattern tires, which provide excellent friction and traction between the road and the tires. Consequently, based on the rolling resistance coefficient table [insert citation], a value of C_i = 0.035 was selected for equations (15), (16), (17), and (18). As illustrated in Figure 8, six experimental roads were chosen within the saline alkali land farm.

Lines 593: 40. Zhuang, J., Automotive Tire Science, 1rd ed.; Beijing Institute of Technology Press: Beijing, China, 1995; pp. 186–229.

Q2: Key words. Keywords are words, not long phrases and sentences.

Response 2: We greatly appreciate your valuable suggestions. We have refined and revised the keywords in the manuscript.

The details are as follows：

Lines 33-34: Keywords: dual-trajectory collaborative planning; intelligent agricultural machinery; lateral stability control; saline alkali land; tractor-trailer system.

Q3: 2. State Space of the Tractor-Trailer System

"Owing to the small high-order error term and the fact that the calculation results were dynamically updated and covered, the high-order term can be ignored". (156-158)-So what is this error?

Response 3: Thank you for your careful inspection. Here, “the higher order term” is the higher order expansion term of the Taylor series of this equation (5):  .In order to construct a linear function and reduce the amount of computation in the iterative process, we ignore the higher order terms with smaller errors. Errors due to the environment and system may be more significant than this higher order term error, and in order to compensate for this error, we added “BDS + IMU” to monitor and feedback the system position and attitude in real time. Generally speaking， this is a common technique in engineering.

Q4: In the formula...(184)-Give specific formulas

Response 4: Thank you for your valuable advice. According to your suggestions, we have made relevant supplementary explanations in the new version manuscript.

Lines 163-171: In the equation (11)-(14), m_i is the total mass of the tractor or the trailer; I_zi represent the inertia of the tractor or the trailer, respectively; v_i is the lateral velocity; u_i is the longitudinal velocity;  is the angular velocity at which the tractor or the trailer rotates around the center of mass. F_Y1, F_Y2, F_Y3 and F_Y4 are the lateral forces of the ground against the tire. F_AX, F_AY, F_TY and F_TX are the action and reaction force (through orthogonal decomposition) caused by the tow arm. a_i and b_i are the length from the front-axle center and the rear-axle center to the center of gravity of the tractor or the trailer.  is the steering angles of the front-axle wheels. Among them, i = 1,2.

Q5: 3. Lateral Stabilizer Based on Dual-Trajectory Prediction

Under what conditions did you choose the distance parameter 0.03 m? (224)

Response 5: Thank you very much for your careful examination. In fact, 0.03m is the condition for judging whether the vehicle has traveled to the end point. Because in the actual working conditions, the saline-alkali land scene and road conditions are worse than the urban structured road conditions. Therefore, the decision conditions of terminal arrival are set relatively loosely. That is, the distance between the vehicle and the end point is less than 0.03m, and the system determines that the end point has been reached.

Q6: Under what conditions are low-speed and high-speed separated? (268)

Response 6: Thank you very much for your careful examination. according to urban traffic regulations, the speed for distinguishing between high and low speeds is usually 40 km/h or 60 km/h. In this study, based on the research conventions related to TTS control methods, scholars usually set the boundary between high-speed and low-speed at 30 km/h-36 km/h. Based on the above situation, this study followed the convention of using a speed of 30 km/h as the boundary between high and low speeds.

According to your suggestion, we have made the following corrections in the new version of the manuscript:

Lines 241-243：In this study, a speed of 30 km/h is used as the threshold between high speed and low speed. When the system exceeds 30 km/h, it is classified as high speed, and when it falls below 30 km/h, it is classified as low speed.

Q7: Fig. 5 should indicate the line designations (315)

Response 7: Thank you very much for your kind advice and reminder. We have regenerated and modified Figure 5. The original blue curve has been replaced with a more prominent bright yellow curve. At the same time, corresponding modifications and adjustments have been made to the wording in the paper.

At the same time, the relevant statements regarding Figure 5 in the manuscript have also been modified and adjusted accordingly.

The specific modifications are as follows:

Lines 276-281: The green curve is generated by the TTS-KM at low-speed. The fine yellow curve illustrates the trajectory predicted using the dynamic model proposed in this study. It is important to note that, for the sake of clarity and calculation, both the green and thick yellow curves are fitted based on the motion trajectory of the left rear wheel of the trailer, rather than the midpoint of the rear axle or the center of gravity.

Lines 284-294: As illustrated in Figure 5, the fine yellow curve does not precisely align with the green curve and is generally situated between the green and black curves. The system exhibits improved longitudinal stability and maintenance performance when the TTS operates at high-speeds. However, the fine yellow and green curves are relatively close to each other. This proximity occurs because a larger turning angle amplifies the influence of the hinge point on the lateral traction of the trailer, resulting in a more pronounced lateral offset motion. It is evident that, regardless of whether the system is operating at high or low-speeds, the lateral offset of the trailer remains constrained within a specific range, defined by upper and lower limits. Additionally, a comparison of the predicted trajectories from both methods mutually confirms the objectivity and predictability of the IWD phenomenon in the TTS.

Q8: Hard to perceive Fig. 6. Maybe reduce the number of R. (331)

Response 8: Thank you for your valuable advice. Based on your suggestion, We further refined Figure 6 to make it clearer. In the new version, we have redrawn Figure 6 based on your comments. As you said, in fact, we have tried to reduce the number of R in the previous work to make the image more ornamental. However, as R decreases in the graph, the number of curves decreases. In order to reflect the regularity and distribution consistency of the trailer's motion trajectory well, we retain a certain amount of R at the end of the new version.

Q9: It is unclear under what road conditions Table 2 was obtained. Describe the road surface/soil. What is the distance between the tractor and the trailer? How will this distance affect the study?

Response 9: Thank you for your valuable comments. To validate the control method proposed in this study, we conducted further tracking and control experiments in saline-alkali farmland. The test sites are the Guanxian saline alkali land test field in Shandong Province and the Wudi saline alkali land test base of Shandong Agricultural University. As shown in Figure 8, six experimental roads were selected in saline-alkali land farms. The experimental roads are all dry dirt roads. The tires are rubber off-road tires. They ensure good friction and restraint on roads and tire. Therefore, according to the Table 2 of Q1，the C_i is 0.035. In addition, about the parameters of TTS experimental platform, The length of a single vehicle body was 970 mm. The width was 680 mm. Traction arm (the distance between the tractor and the trailer) is 0.4m.

During the turning process, the longer the distance of the traction arm, the greater the maximum lateral offset of the trailer. In the follow-up experiment, we will further investigate the influence of the length of the traction arm and the position of the hinge point on the motion. That is exactly what we are doing.

According to your valuable suggestion, we have made a supplementary explanation about the tractor and the trailer parameters in section 4.1.:

Lines 174-167: Where C_i (i=1,2,3,4) is the rolling resistance coefficient between the tire and the ground, the driver's perspective is used as the benchmark to unify the vehicle coordinate system. According to the tool manual, C_i = 0.035 [40].

Lines 251-255: Its configuration is as follows: The size of the tractor is 970 mm*680mm*400mm. The size of the trailer is the same as the tractor. Traction arm (the distance between the tractor and the trailer) is 0.4m. The configuration of the TTS industrial control computer is as follows: The system is con-figured with Linux 20.04 and ROS-noetic. The motherboard is equipped with an Intel i7-13700K CPU and 256GB of RAM.

Thank you again for taking the time and effort to review our manuscript!

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

none