Correction: Ren et al. Research on an Intelligent Agricultural Machinery Unmanned Driving System. Agriculture 2023, 13, 1907

1. Figure Legend

In the original publication [1], there was a mistake in the legend for “Figure 2. Schematic diagram of farmland boundary.” This graph was generated by calling the Fields2Cover library, but no reference to the library was added. The correct legend appears below. The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

Figure 2. Schematic diagram of farmland boundary [30].

In the original publication, there was a mistake in the legend for “Figure 3. Schematic diagram of agricultural machinery operation area.” This graph was generated by calling the Fields2Cover library, but no reference to the library was added. The correct legend appears below. The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

Figure 3. Schematic diagram of agricultural machinery operation area [30].

In the original publication, there was a mistake in the legend for “Figure 4. Parallel path sorting method.” This graph was generated by calling the Fields2Cover library, but no reference to the library was added. The correct legend appears below. The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

Figure 4. Parallel path sorting method [30].

In the original publication, there was a mistake in the legend for “Figure 9. Simulation experiment full-coverage path generation rendering.” This graph was generated by calling the Fields2Cover library, but no reference to the library was added. The correct legend appears below. The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

Figure 9. Simulation experiment full-coverage path generation rendering [30].

In the original publication, there was a mistake in the legend for “Figure 16. full-coverage path generation rendering for actual vehicle testing.” This graph was generated by calling the Fields2Cover library, but no reference to the library was added. The correct legend appears below. The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

Figure 16. Full-coverage path generation rendering for actual vehicle testing [30].

2. Missing Citation

In the original publication, “[29] Mier, G.; Valente, J.; de Bruin, S. Fields2Cover: An open-source coverage path planning library for unmanned agricultural vehicles. IEEE Robot. Autom. Lett. 2023, 8, 2166–2172. https://doi.org/10.1109/LRA.2023.3248439.” was not cited. The citation has now been inserted in “3. A Fully Covered Path Planning Algorithm with Multi-Objective Function Coupling”, “3.1. Agricultural Machinery Operation Area and Parallel Path Generation”, “Paragraph 3” and should read:

“Firstly, the objective function for generating the number of parallel paths within the work area is to minimize the number of parallel paths generated while ensuring job coverage, in order to improve the walking and working efficiency of agricultural machinery. The number of parallel paths generated is related to the area and shape of the agricultural machinery operation area, as well as the width of the agricultural machinery itself. Moreover, since the minimum number of parallel paths corresponding to square farmland is the largest when the area of the agricultural machinery operation area is fixed, the objective function satisfies the following relationship [29]:”

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

3. Text Correction

There was an error in the original publication. “We use an open-source full-coverage path planning algorithm, but the original description of proposing a full-coverage path planning algorithm is inaccurate”.

A correction has been made to “Abstract”, “Paragraph 1”:

“Abstract: Intelligent agricultural machinery refers to machinery that can independently complete tasks in the field, which has great significance for the transformation of agricultural modernization. However, most of the existing research on intelligent agricultural machinery is limited to unilateral research on positioning, planning, and control, and has not organically combined the three to form a fully functional intelligent agricultural machinery system. Based on this, this article has developed an intelligent agricultural machinery system that integrates positioning, planning, and control. In response to the problem of large positioning errors in the large range of plane anchoring longitude and latitude, this article integrates geographic factors such as ellipsoid ratio, long and short axis radius, and altitude into coordinate transformation, and combines RTK/INS integrated inertial navigation to achieve precise positioning of the entire vehicle over a large range. In response to the problem that existing full-coverage path planning algorithms only focus on job coverage as the optimization objective and cannot achieve path optimization, this paper adopted a multi-objectivefunction-coupled full-coverage path planning algorithm that integrates three optimization objectives: job coverage, job path length, and job path quantity. This algorithm achieves optimal path planning while ensuring job coverage. As the existing pure pursuit algorithm is not suitable for the motion control of tracked mobile machinery, this paper reconstructs the existing pure pursuit algorithm based on the kinematics characteristics of tracked mobile machinery, and adds a linear interpolation module, so that the actual tracking path points of motion control are always ideal tracking path points, effectively improving the motion control accuracy and control stability. Finally, the feasibility of the intelligent agricultural machinery system was demonstrated through corresponding simulation and actual vehicle experiments. This intelligent agricultural machinery system can cooperate with various operating tools and independently complete the vast majority of agricultural production activities.”

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

There was an error in the original publication. “We use an open-source full-coverage path planning algorithm, but the original description of proposing a full-coverage path planning algorithm is inaccurate. At the same time, we further demonstrate that the full coverage path planning algorithm in this article adopts the algorithm proposed by Mier et al., and the path planning part of the intelligent agricultural machinery system calls the Fields2Cover library, with relevant references added.”

A correction has been made to “1. Introduction”, “Paragraph 6”:

“In summary, there are two main methods for positioning agricultural machinery vehicles: machine vision positioning and satellite positioning. Machine vision positioning is susceptible to environmental factors such as light and weather, and is unstable. However, satellite positioning frequency is too low and single GPS antenna positioning can only achieve sub-meter-level positioning. Based on this, this article adopts RTK/INS integrated inertial navigation fusion positioning, supplemented by a high-precision coordinate transformation algorithm, to achieve high-frequency centimeter-level positioning of the entire vehicle in the local Cartesian coordinate system. In response to the problem of existing full-coverage path algorithms only considering job coverage or job repetition rate, this paper adopted a multi-objective function-coupled full-coverage path planning algorithm [29] that integrates three optimization objectives: job coverage, job path length, and job path quantity. Mier et al. proposed this algorithm after fully analyzing the shortcomings of existing full coverage path planning. Considering the excellent performance of the path planning algorithm, this article adopts this algorithm as the path planning algorithm. This algorithm achieves the optimal path planning while ensuring job coverage. Therefore, the intelligent agricultural machinery system in this article adopts the Fields2Cover library developed by Mier et al. [30] to achieve full coverage path planning. In response to the difficulties in tuning existing PID control parameters and the poor real-time performance of model predictive control, this paper reconstructs the existing pure pursuit algorithm based on the kinematic model of tracked agricultural machinery, supplemented by a linear interpolation module, so that the path points tracked by the entire vehicle are all ideal path points, effectively improving the accuracy and stability of vehicle motion control. Based on the three major technologies, namely, fusion positioning, full-coverage path planning, and motion control, an intelligent unmanned driving system for agricultural machinery is constructed. The simulation and real vehicle test platforms are built using tracked agricultural machinery as a prototype for relevant experiments. The simulation and actual vehicle experiment results prove that the intelligent agricultural machinery unmanned driving system constructed in this paper has precise positioning, high control accuracy, and can effectively complete field full-coverage path tracking, laying a certain foundation for the development of intelligent agricultural machinery unmanned-driving-related technologies in the future.”

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

There was an error in the original publication. “The title of our third section is not particularly appropriate and does not reflect the details of using the Fields2Cover library for full coverage path planning.”

A correction has been made to “3. A Fully Covered Path Planning Algorithm with Multi-Objective Function Coupling”, “Name of Section”:

“3. A Fully Covered Path Planning Algorithm with Multi-Objective Function Coupling Using the Fields2Cover Library”

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

There was an error in the original publication. “We use an open-source full-coverage path planning algorithm, but the original description of proposing a full-coverage path planning algorithm is inaccurate. At the same time, we further demonstrate that the full coverage path planning algorithm in this article adopts the algorithm proposed by Mier et al., and the path planning part of the intelligent agricultural machinery system calls the Fields2Cover library, with relevant references added.”

A correction has been made to “3. A Fully Covered Path Planning Algorithm with Multi-Objective Function Coupling”, “Paragraph 1”:

“In response to the problems of existing full-coverage path planning algorithms that only consider job coverage or job repetition rate as optimization objectives, i.e., they have a single optimization objective and a non-optimal path generation, this paper adopted a multi-objective function-coupled full-coverage path planning algorithm [29], which takes parameters such as job coverage, global path length, and number of paths as coupling optimization objectives to generate the global optimal path while meeting job coverage, effectively improving operational efficiency and saving energy costs for agricultural machinery. This algorithm was proposed by Mier et al. and is currently an advanced full-coverage path planning algorithm. The full-coverage path planning part of the intelligent agricultural machinery system in this article adopts the Fields2Cover library developed by Mier et al. [30], which can meet the full-coverage path planning needs of most existing farmland and has strong practicality. The core principles of this algorithm will be explained below.”

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

There was an error in the original publication. “We use an open-source full-coverage path planning algorithm, but the original description of proposing a full-coverage path planning algorithm is inaccurate”.

A correction has been made to “3. A Fully Covered Path Planning Algorithm with Multi-Objective Function Coupling”, “3.1. Agricultural Machinery Operation Area and Parallel Path Generation”, “Paragraph 1”:

“The technical route of the multi-objective function-coupled full-coverage path planning algorithm adopted in this article is as follows. Firstly, the RTK/INS integrated inertial navigation is used to dot the actual farmland boundary, obtain the longitude and latitude altitude coordinates corresponding to each vertex of the actual farmland boundary, and generate the corresponding farmland boundary in the ENU coordinate system, as shown in Figure 2. On the basis of the corresponding farmland boundary, a certain width is shrunk inward to generate the agricultural machinery operation area, as shown in Figure 3. The contraction width is generally set as the turning radius of the agricultural machinery.”

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

There was an error in the original publication. “We use an open-source full-coverage path planning algorithm, but the original description that this article sets three optimization objective functions is inaccurate”.

A correction has been made to “3. A Fully Covered Path Planning Algorithm with Multi-Objective Function Coupling”, “3.1. Agricultural Machinery Operation Area and Parallel Path Generation”, “Paragraph 2”:

“Several parallel paths are planned within the generated agricultural machinery operation area to achieve full-coverage path planning and the operation of agricultural machinery within the operation area. To ensure the optimal coverage and operation path of agricultural machinery in the operation area, this algorithm sets three optimization objective functions.”

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

There was an error in the original publication. “We use an open-source full-coverage path planning algorithm, but the original description that the second optimization objective function set in this article is the job coverage objective function is inaccurate. We have changed the article in the problem description to this algorithm and added relevant reference.”

A correction has been made to “3. A Fully Covered Path Planning Algorithm with Multi-Objective Function Coupling”, “3.1. Agricultural Machinery Operation Area and Parallel Path Generation”, “Paragraph 4”:

“The second optimization objective function set in this algorithm is the job coverage objective function, which aims to maximize the job coverage of agricultural machinery traveling along the planned path, as shown in Equation (10) [29].

$$S_{\mathrm{cov}}=\frac{S_w\cap \left\{{\cup }_i{S}^i\right\}}{S_w}$$

(10)

where $S_{\mathrm{cov}}$ is the coverage rate of agricultural machinery operation, $S_w$ is the area of agricultural machinery operation area, and $S^i$ is the area of agricultural machinery operation along the $i$-th parallel path. The third optimization objective function set in this algorithm is the total length of the operation path. The function is to minimize the total length of the generated fully covered path while ensuring the coverage rate of agricultural machinery operations, as shown in Equation (11) [29].”

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

There was an error in the original publication. “We use an open-source full-coverage path planning algorithm, but the original description that this article sets up four parallel path-sorting methods, namely boustrophedon sorting, snake sorting, spiral sorting, and custom sorting, as shown in Figure 4 is inaccurate”.

A correction has been made to “3. A Fully Covered Path Planning Algorithm with Multi-Objective Function Coupling”, “ 3.2. Parallel Path Sorting and Curve Generation”, “Paragraph 1”:

“In order to adapt agricultural machinery to different scenarios, this algorithm sets up four parallel path-sorting methods, namely, boustrophedon sorting, snake sorting, spiral sorting, and custom sorting, as shown in Figure 4. The boustrophedon sorting method is widely used in full-coverage path planning. It adopts a reciprocating and circuitous covering method. After driving along the first parallel path, it immediately follows the second parallel path, and so on, until the entire vehicle runs along all parallel paths. The disadvantage of this method is that the distance between adjacent driving paths is too short, resulting in sharp curves that affect the control effect of the entire vehicle. Unlike the sequential traversal of boustrophedon sorting, snake sorting skips one parallel path each time, travels to the last parallel path, and then returns to driving along other parallel paths that have not been driven. The advantage of this method is that the distance between adjacent driving paths is large, and the generated curves are relatively smooth.”

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

There was an error in the original publication. “We use an open-source full-coverage path planning algorithm, but the original description in this article is inaccurate”.

A correction has been made to “3. A Fully Covered Path Planning Algorithm with Multi-Objective Function Coupling”, “ 3.2. Parallel Path Sorting and Curve Generation”, “Paragraph 3”:

“After arranging the parallel paths in order, corresponding curves can be generated between adjacent parallel paths with sequence numbers. In this algorithm, there are three methods for generating curves: the straight line method, the Dubins curve [31], and the Reeds–Shepp curve [32]. The straight line method directly connects the endpoint of the current parallel path with the starting point of the adjacent parallel path with a straight line. The Dubins curve method and the Reeds–Shepp curve method use the Dubins curve and the Reeds–Shepp curve to connect the endpoint of the current parallel path with the starting point of the adjacent parallel path with the next ordinal, respectively. It is worth noting that the curves generated by the Dubins curve method only require the vehicle to have forward function to complete tracking, while the curves generated by the Reeds–Shepp curve method require the vehicle to have both forward and backward functions to complete the corresponding curve tracking.”

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

There was an error in the original publication. “We use an open-source full-coverage path planning algorithm, but the original description of proposing a full-coverage path planning algorithm is inaccurate”.

A correction has been made to “5. Building and Related Experiments Based on Gazebo Simulation Platform”, “Paragraph 1”:

“To verify the performance of the positioning, planning, motion control, and other algorithms in this article, a tracked intelligent agricultural machinery simulation platform was built based on Gazebo, as shown in Figure 7.”

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

There was an error in the original publication. “We use an open-source full-coverage path planning algorithm, but the original description of proposing a full-coverage path planning algorithm is inaccurate”.

A correction has been made to “5. Building and Related Experiments Based on Gazebo Simulation Platform”, “Paragraph 3”:

“To conduct a prior verification of the performance of the positioning, planning, and motion control algorithms in this article, corresponding simulation scenarios were constructed for simulation experiments, as shown in Figure 8.”

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

There was an error in the original publication. “We use an open-source full-coverage path planning algorithm, but the original descrip-tion of proposing a full-coverage path planning algorithm is inaccurate”.

A correction has been made to “5. Building and Related Experiments Based on Gazebo Simulation Platform”, “5.1. Simulation Performance Verification of RTK/INS Fusion Positioning Coordinate Transformation Algorithm”, “Paragraph 1”:

“Firstly, the vehicle GPS is used to dot the testing area to obtain the longitude and latitude altitude coordinates of each vertex at the boundary of the testing area. The coordinate transformation algorithm proposed in this article converts the longitude and latitude altitude coordinates of each vertex into the corresponding Cartesian coordinates in the ENU coordinate system. Then, the multi-target function-coupled full-coverage path planning algorithm adopted in this article is used for the full-coverage path planning of the testing area, as shown in Figure 9.”

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

There was an error in the original publication. “We use an open-source full-coverage path planning algorithm, but the original description of proposing a full-coverage path planning algorithm is inaccurate”.

A correction has been made to “6. Construction and Testing of Intelligent Agricultural Machinery Real Vehicle Test Platform”, “Paragraph 1”:

“To further validate the performance of the positioning, planning, and motion control algorithms in this article, an intelligent agricultural machinery real vehicle test platform was built based on an electric tracked chassis, as shown in Figure 14. This real vehicle testing platform is equipped with sensors such as binocular cameras, LiDAR, RTK/INS integrated navigation, etc. The perception information of each sensor is received through the onboard computing platform, which can be used for the real vehicle verification of various algorithms in the field of intelligent agricultural machinery. The main equipment parameters of the actual vehicle test platform are shown in Table 1.”

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

There was an error in the original publication. “We use an open-source full-coverage path planning algorithm, but the original description of proposing a full-coverage path planning algorithm is inaccurate”.

A correction has been made to “6. Construction and Testing of Intelligent Agricultural Machinery Real Vehicle Test Platform”, “Paragraph 3”:

“Firstly, the RTK/INS integrated inertial navigation system is used to plot points at the four corners of the test site edge, obtaining the corresponding latitude and longitude altitude coordinates. The coordinates are converted into the corresponding ENU coordinates through coordinate transformation algorithms. Finally, the full-coverage path planning algorithm adopted in this article is used to generate the full-coverage path within the test area, as shown in Figure 16.”

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

There was an error in the original publication. “We use an open-source full-coverage path planning algorithm, but the original description of establishing multiple objective functions and coupling mechanisms is inaccurate”.

A correction has been made to “ 7. Conclusions”, “Paragraph 1”:

“This article creates an intelligent agricultural machinery system that integrates positioning, planning, and motion control. Based on RTK/INS integrated inertial navigation and self-designed coordinate transformation algorithm, high-precision vehicle positioning is achieved. The vehicle positioning error is within 10 cm, which can effectively meet the requirements of agricultural machinery intelligent systems for vehicle positioning accuracy. By utilizing multiple objective functions and coupling mechanisms, high coverage and full-coverage path planning are achieved, effectively improving the efficiency of agricultural machinery operations.”

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

There was an error in the original publication. “We use an open-source full-coverage path planning algorithm, but the original description of proposing a full-coverage path planning algorithm is inaccurate”.

A correction has been made to “7. Conclusions”, “Paragraph 4”:

“Based on the existing foundation of this article, subsequent research can focus on the following aspects. Firstly, the full-coverage path planning adopted in this article is only applicable to relatively regular land. In the future, we can consider combining the cell segmentation method to achieve full-coverage path planning for irregular farmland. Secondly, the improved pure pursuit algorithm proposed in this article is only applicable to the motion control of medium- and low-speed agricultural machinery. In the future, we can consider introducing dynamic motion control methods to make this algorithm suitable for high-speed agricultural machinery motion control. Thirdly, this article only achieves single-machine intelligence, and can be combined with intelligent interconnected systems such as drones and 5G communication to achieve multi-machine collaborative work in the future.”

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

4. References

Due to the addition of two references, the reference index has undergone some changes, but the serial number before [29] remains unchanged.

We updated the original references [29,30]. The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

29. Mier, G.; Valente, J.; de Bruin, S. Fields2Cover: An open-source coverage path planning library for unmanned agricultural vehicles. IEEE Robot. Autom. Lett. 2023, 8, 2166–2172. https://doi.org/10.1109/LRA.2023.3248439.

30. Mier, G.; Valente, J.; de Bruin, S. Fields2Cover/Fields2Cover Github. Available online: https://github.com/Fields2Cover/Fields2Cover (accessed on 30 October 2023).

We changed the original references [29,30] to [31,32]. The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

31. Dubins, L.E. On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents. Am. J. Math. 1957, 79, 497–516. https://doi.org/10.2307/2372560.

32. Reeds, J.; Shepp, L. Optimal paths for a car that goes both forwards and backwards. Pac. J. Math. 1990, 145, 367–393. https://doi.org/10.2140/pjm.1990.145.367.