Optimal Path Generation with Obstacle Avoidance and Subfield Connection for an Autonomous Tractor

Abstract

As autonomous tractors become more common crop harvesting applications, the need to optimize the global servicing path becomes crucial for maximizing efficiency and crop yield. In recent years, several methods of path generation have been researched, but very few have studied their applications on complex field shapes. In this study, a method of creating the optimal servicing path for simple and complex field shapes is proposed. The proposed algorithm creates subfields for a target land, optimizes the track direction for several subfields individually, merges subfields that result in overall increased efficiency, and finds the minimum non-operating paths to travel from subfield to subfield while selecting the respective optimal subfield starting locations. Additionally, it is required that this process must be done within 3 seconds to meet performance requirements. Results from 3 separate field shapes show that the field traversal efficiency can range from 68.0% to 94.4%, and the coverage ratio can range from 98.8% to 99.9% for several different conditions. In comparison with previous studies using the same field shape, the proposed methods demonstrate an increase of 5.5% in field traversal efficiency.

1. Introduction

Research in crop-harvesting techniques has seen an increase in recent years because it is a process that can benefit from advanced path planning for autonomous applications. Traditionally speaking, crop harvesting is done by an operator who is driving a tractor that will service a large field of crops. This can be modeled as the coverage path planning (CPP) problem [1]. With the operator driving the tractor, the generated path is dependent on human decisions, and as a result, cannot be guaranteed as the optimal path in this case. Additionally, as the field shape becomes more complex, so do the decisions of the operator, which can in turn lead to less optimal solutions. To compare the optimality of different generated paths, a quantitative metric should be chosen as an index. Zhou et al. [2] developed the field traversing efficiency (FTE) index which describes the ratio of the effective versus non-effective traveled distances. Zhou et al. generated complete operation paths for multiple obstacle-free fields and observed their respective FTE values. Another important index is the coverage ratio, which describes the percentage of the farm area which is covered by the attachment of the tractor.

There are several variations of this problem have been researched. Vahdanjoo et al. [3] studied the path optimality of farms with more than one depot location and reported the total travelled distances for each scenario. Han et al. [4] compared the path efficiency for different headland turning patterns. Santos et al. [5] compared the previous studies on path planning in agriculture fields. According to their research, the path-planning method aiming to optimize field coverage is a more developed method than the point-to-point method since field coverage is a requirement in most agricultural scenarios.

The problem-solving approach of the reviewed paper varies from genetic algorithm (GA) optimization, A* search algorithms, Hamiltonian graphs, etc. Spekken et al. [6] optimized the servicing route by minimizing the non-productive tractor movements, such as turning. They optimized the route by adjusting the direction angle of tracks, sequence of tracks, and turning patterns to go from one track to the next. Chakraborty et al. [7] made a comprehensive comparison of the different path-planning optimization approaches for ground robots in agriculture. The path optimization in a farm with obstacles was studied by Jin et al. [8]. They designed a geometric approach to divide the farm with obstacles into sub-regions and developed a path planning method to find the optimal path for each sub-region individually. Ali et al. [9] provided a technique to generate the minimum cost paths that can be used by one, or several, combine harvesters on a large field that is made up of several smaller ones. The problem solved by Ali et al. is made up of 2 parts, the optimal covering path generation for the combine harvesters plowing the fields, and the position allocation for grain transfer between harvesters and tractors. Blanco at al. [10] solved a similar problem as Ali et al., one that involves the cooperation of harvesters and transportation tractors to return the harvested crop with the objective of minimizing the operating time. He et al. [11,12] proposed methods to reduce non-working distances in intra and inter field logistics for harvesters. This is under the assumption that there are multiple harvesters in a large field that is made up of several smaller ones.

The problem faced in our study revolves around creating the optimal coverage path for a single field for only one autonomous harvester. However, the idea of the previously mentioned studies is still significant in the sense that multiple fields can be serviced by one harvester. Looking at research done by Han et al. [13], a method of creating a single continuous path servicing a crop field with headlands, and headland turning, was discussed. Their method also finds the optimal travel direction that maximizes the efficiency of servicing. However, their results show that sometimes a field needs to be split into multiple subfields that can have different traveling directions to produce the best efficiency. Han et al. did not automate the connection path between subfields. Jeon et al. [14] introduced the concept of an entry-exit path planning technique. Their method focuses on generating a continuous coverage path, the path from the entrance to the starting point, and the path from the end to the exit location of a field. Shen et al. [15] proposed a solution to solving the coverage path planning problem in hilly farmlands. Like Jeon et al., Shen et al. also introduced the idea that a field can have a starting and ending location. Expanding on this, each subfield can have its own entrance and exit locations, so the traversal sequence can be optimized. They used a genetic algorithm (GA) to solve the total minimum cost path that is needed to connect (and service) all subfields. For their approach, they assume that each subfield has a single entrance with a corresponding exit location. In comparison with previous studies in the same area, our study has the following novelty.

The proposed method can find the optimal direction angle for each subfield. If possible, the neighboring subfields are then merged to reduce the amount of headland area and improve the route's efficiency. Additionally, the proposed method uses the X-type pattern as a turning method to minimize the length of turning tracks, thus, optimizing the generated path. With regard to having multiple subfields, the proposed method can also find the optimal subfield traversal sequence, with the respective subfield starting locations, such that the total non-operating distance is minimized between subfields. The subfield connecting paths have been carefully designed to eliminate the possibility of overlapping with subfields, which will degrade soil quality, and colliding with obstacles (if any exist). The proposed methods are used to generate the global path only, future research will include simulation results and physical experiments to validate this approach.

2. Materials and Methods

2.1. Metrics and Considered Parameters

Upon discovering that large fields can be split into several smaller subfields, the optimal travel direction should be found for each subfield independently. The FTE and coverage ratio will be used as metrics to quantify the improvements found during optimization.

The FTE defines the efficiency of the planned tracks based on the length of the distances traveled [2]. The FTE is calculated based on the effective length of the headland and infield tracks over the total length of the continuously designed path, as described in Equation (1):

$$FTE=\frac{{\sum }_{i=1}^{h}d\left(H_i\right)+{\sum }_{i=1}^{n}d\left(T_i\right)}{d\left(p\right)}$$

(1)

where ${\sum }_{i=1}^{h}d\left(H_i\right)$ is the total effective length of headland tracks, ${\sum }_{i=1}^{n}d\left(T_i\right)$ is the total effective length of the infield tracks, and $d\left(p\right)$ is the total length of the continuous path. Therefore, the high FTE shows that the number of ineffective paths is low.

The coverage ratio index shows the percentage of the area of the farm which is covered by the attachment of the tractor. To evaluate this index, the covered area of all headland and infield tracks are merged to shape the covered area. Then, the covered area is divided by the total area of the subfield to calculate the coverage ratio. The high value of the coverage ratio shows that most of the arable land is covered to maximize the production of the farm.

In this study, both rotary and plowing attachments were considered. The dimensions related to each attachment type are listed in

Table 1. The dimensions considered for each attachment type.

Parameter	Rotary Attachment	Plowing Attachment
Attachment width	2020 mm	1800 mm
Overlap width	200 mm	200 mm
Tractor’s turning radius	4135 mm	4135 mm

.

To ensure that there is no gap between the two infield tracks, a portion of the previous track will be covered again by the next infield track. So, the overlap width defines the width of this overlap area.

2.2. Creation of Subfields

If there are obstacles or vertices (Figure 1) in a land requiring path planning, it is difficult to generate optimal paths for a tractor within a land, and subdividing it is critical. This is because the number and orientation of split sub-fields affect the redundancy and direction of turns.

The first step in splitting the land is to identify a splitting angle between zero and 180 degrees, which is illustrated in Figure 1b to split the land in Figure 1a into two subfields. In this case, 45 degrees relative to the horizon is selected as a splitting angle.

This selection uses the index defined in Equation (2), where the angle is incrementally increased by 15 degrees and the maximum score of the index determines the splitting angle.

The score in Equation (2) was defined by the authors to evaluate the usability of the generated subfields. It aims to maximize the ratio of the length of the subfield's MBR to its width while simultaneously maximizing its area. In addition, the inland area for each subfield is considered not too small for the autonomous tractor to perform the required tasks. Therefore, the maximum score in Equation (2) represents the maximization area of both subfields and their inlands with longer and narrower subfields.

$$Score={\displaystyle \sum }_{i=1}^n\left(\frac{\mathrm{Inland}\_{\mathrm{Area}}_{\mathrm{i}}}{{\mathrm{Area}}_{\mathrm{i}}}\right)\times {\mathrm{Area}}_{\mathrm{i}}^2\times \left(\frac{{\mathrm{MBR}}_{\mathrm{i}}^{\mathrm{Max}}}{{\mathrm{MBR}}_{\mathrm{i}}^{\mathrm{Min}}}\right)$$

(2)

where n is the number of subfields, ${\mathrm{Area}}_{\mathrm{i}}$ is the ith subfield’s area, $\mathrm{Inland}\_{\mathrm{Area}}_{\mathrm{i}}$ is the inland area of the ith subfield’s area, and ${\mathrm{MBR}}_{\mathrm{i}}^{\mathrm{Max}}$ and ${\mathrm{MBR}}_{\mathrm{i}}^{\mathrm{Min}}$ are the maximum and minimum lengths of the minimum bounding rectangle (MBR) in Figure 2.

As GPS data contain considerable noise, it is necessary to reduce the number of vertices in the target land shape (contour line or polygon) outlined based on GPS measurements to simplify it. For this purpose, the Ramer-Douglas-Peucker algorithm [16] was used, in which a reduction factor of 8 was chosen after trial and error to control the reduction degree. The Ramer-Douglas-Peucker algorithm can reduce the original polyline to fewer points while maintaining its shape. Using the simplified polygon and the selected vertices with an internal angle greater than 180 degrees, the land is split to have its subfields. Upon successfully creating the shape of the subfield(s) within a field, the process of creating the continuous global path can begin.

Figure 3a,b show the target land for a split and the result of subfield generation by applying the aforementioned method. In Figure 3b, the target land’s shape is simplified first (yellow polygon) and then vertices with internal angles greater than 180 degrees are chosen. By using these vertices and the lines with 35 degrees relative to the horizon, splitting is achieved (green areas). The angle is incremented by 5 degrees, and 35 degrees is selected as the angle having the highest score in Equation (2). As a result, the produced sub-lands can have fewer vertices with internal angles greater than 180 degrees. Finally, if there is a subfield with an extremely narrow width (less than 6*width of the attachment+2*turning radius of the tractor; see Figure 4), it will be merged into a neighbor subfield (Figure 3c). The principle of merging subfields is explained in Section 2.3.6.

2.3. Continuous Service Paths within Subfields

2.3.1. Design of the Headland Tracks

The headland area will be used for turning tracks going from one infield track to another. The input of this step is the boundary of each subfield. The first headland tack is placed at a distance equal to half the width of the attachment inwards from the outermost boundary of the subfield. The rest of the headland tracks are generated by increasing the offset by one width of the attachment inwards until the number of desired headland tracks is created. It must be noted that the tractor cannot follow the sharp corners of the headland path. Therefore, the corners must be rounded by the turning radius of the tractor. Figure 5 shows a side-by-side of the 3 headland passes before and after applying the tractor turning radius. The number of headland passes depends on the tractor’s turning radius and the attachment’s width. Specifically, the number of headland passes must be greater than the ratio of the turning radius to the attachment width to provide enough space in the boundary of the farm (i.e., headland area) for turning and traveling from one infield track to another one. In this study, the turning radius is 4135 mm and the attachment widths are 2020 mm and 1800 mm for rotary and plowing, respectively. Therefore, the required minimum number of headland passes is 3 for both rotary and plowing tasks, and thus this number was chosen.

Finally, the inner boundary of each subfield is defined by offsetting the outer boundary by the number of headland passes multiplied by the width of the attachment. This creates the area where the infield servicing tracks will need to be placed. This can be seen in Figure 6 as the red line. Since the geometry of each subsection affects the shape of the headland and infield area, the proportion of the processed headland and infield area is dependent on the subfield's geometry (shape) as well as the turning radius and the attachment width.

2.3.2. Design of the Infield Tracks

The infield tracks are a series of parallel straight tracks which cover the area in the inner boundary of each subfield. To add them, a series of parallel tracks are generated to cover all the inner areas of the subfield. The perpendicular distance between two tracks is equal to the attachment width minus the overlap distance (if any).

For each subfield, the angle of track directions will vary over the span of 0 to 180 degrees with a default 15-degree resolution that was chosen to satisfy the computation time requirement of 3 seconds.

However, if none of the angles yield a valid infield track, the resolution will be reduced to 5 degrees. If it cannot find a valid angle yet in this case, the resolution will be further reduced to 1 degree as the final step size. If still, no valid angle is found, it means that designing infield tracks for that respective subfield is not possible. Therefore, the program will stop. An example of several different infield track angles for the rectangular field can be seen in Figure 7, which were generated by the aforementioned technique.

2.3.3. Design of the Turning Tracks

The turning tracks will connect the infield tracks to each other to form a continuous path that goes through all the infield tracks exactly once. There are two types of turning tracks that can be applied to each subfield, namely X pattern and C pattern. The X pattern connects two adjacent tracks together via a forward curve-backward straight-forward curve motion. The C pattern omits the backward motion and replaces that with a forward straight motion. Figure 8 depicts the C-type and X-type patterns.

However, the C-type patterns cannot connect two adjacent tracks anymore. Therefore, it divides the subfield into the bottom and upper areas. It starts with covering the first tracks on the bottom side and then goes to the first track on the upper side. Then, back to the second track on the bottom side and back to the second track on the upper side, and so on.

This process repeats until all the tracks are covered. If the number of infield tracks is even, there would be no issues as all the tracks will be covered. However, if the number of tracks is odd, the last remaining track will be connected using the X-type pattern as there is no other possibility. Examples of the X-type pattern used with different track directions can be seen in Figure 9.

2.3.4. Optimizing the Direction of the Infield Tracks

After designing the infield and turning tracks for each angle, the next step is to choose the best direction angle among the valid angles. To do so, the FTE index is calculated for all the valid angles and the one with the highest FTE is selected as the optimal angle. The results for the rectangular field seen in Figure 9 can be found in

Table 2. FTE values for different infield track orientations.

	0°	15°	30°	45°	60°	75°	90°	105°	120°	135°	150°	165°
FTE (%)	86.6	78.6	74.4	71.6	70.5	71.2	73.6	71.2	70.5	71.6	74.3	78.6

. From the results shown, the optimal infield track angle is 0 degrees since it has the maximum FTE.

2.3.5. Connecting the Continuous Path

The last step is to connect all the headland, infield, and turning tracks into a single continuous path that will cover the whole subfield. However, there are four possible entry points for each subfield. Specifically, these 4 cases depend on whether the tractor enters from the first or last infield track, as well as whether it enters from the right or left point.

Therefore, there will be 4 possible entry points for each subfield. Based on the selected entry point, the continuous path is different. The four possible entry points for a subfield of an irregular farm can be seen in Figure 10.

The next step is to include the turning tracks into the continuous path as well. To do so, a point on each headland track must be defined as a starting point for that respective headland track. To define the starting point, a straight line from the entry point is drawn which is perpendicular to the infield track. The intersection of that line and the headland tracks determine the starting point of each headland track. An example of the headland track starting points can be found in Figure 11.

The headland tracks start at the intersection point of the first headland pass. After completing the first headland pass, the tractor moves from the intersection point of the first headland pass to that of the second headland pass. The same pattern is repeated until all the headland passes are covered. The tractor then travels from the intersection point of the last headland pass to the entry point of the first infield track.

Figure 11a,b show the entry points and connection paths between each headland pass.

2.3.6. Merging Subfields

After designing the continuous path for each subfield, the proposed method tries to merge neighboring subfields if possible. The first criteria are that the two subfields must be next to each other. Then, if both subfields have a common valid angle, the subfields merge into a bigger one and then, the method tries to design the headland, infield, and turning tracks for them. If it was possible and the FTE value of the merged subfields was higher than the weighted sum of the individual subfields, those two subfields were replaced with the merged one and the process of merging subfields starts over again.

2.4. Subfield Connecting Paths

2.4.1. A* Path Generation

As explained by Hart et al. [17], the A* algorithm can be used to compute the minimum cost path between any 2 points in a graph. The graph can be represented as a 2D binary occupancy grid with a cell size of 1.25 m × 1.25 m. This mesh size was selected because smaller cell sizes would result in computation time larger than the required 3 seconds for discretizing larger fields.

Since traveling over the soil will degrade the soil quality, the subfields need to be treated as obstacles for the subfield-to-subfield connection. This means that the only free space for traveling from subfield-to-subfield exists in the headlands of the subfields. In the binary occupancy grid, the obstacles and subfields will be represented as 0, and the empty headland space will be represented as 1.

An additional safety buffer is added around all boundaries in the field that is equal to 0.75 times the tractor width. This is used to further reduce the possibility of the path generated by the A* algorithm to collide with obstacles or travel over subfields. Additionally, since the connecting paths will need to go from the end of one subfield to the start of another subfield, the starting point of the A* path will always be inside (or on the edge of) a subfield because the tractor ends its infield tracks at the border of the respective subfield. For this study, subfields are treated as obstacles so as not to degrade the soil quality. Because of this, the algorithm will not be able to execute. To ensure this error does not occur, an arbitrary cut out of any overlapping subfields is made at the start/end points. An example of the safety buffer and starting/ending point cut-outs can be seen in Figure 12, where the headland travel space is seen as blue, and the safety buffer and starting/ending point cut-outs can be seen as traced in red.

Additionally, the first subfields starting location will be used as the total path ending location. This is used to mimic the gate location since this is arbitrary for this study. Since A* is used to generate the shortest connecting path, it may not take the physical properties of the tractor into consideration, such as the turning radius. For this, the Reeds-Shepp path will be used to refine the path generated by the A* algorithm.

2.4.2. Reeds-Shepp Path Improvement

Reeds-Shepp paths are applied to the ends of each connecting path created by the A* algorithm. This ensures that the generated path can accommodate the turning radius of the tractor and ensures that a maneuver from the A* path to the subfields with respect to the starting location and travel direction is achievable. Based on the concept of the Dubins curve [18], the Reeds-Shepp curve can create an optimal path that can go forwards and backwards given starting and ending locations and orientations, as explained by Reeds et al. [19]. The created path also considers the fixed turning radius of the tractor.

For this study, the path generated by the A* algorithm is assumed to be feasible between the start and end points. The Reeds-Shepp curve is only used at the beginning and end of each A* path to improve the entrance/exit path in/out of the respective subfield to the A* path. From trial and error with several field shapes, it was found that the first and last 6 points of the A* path should be replaced with the Reeds-Shepp curve for every A* path connecting the subfields. A side-by-side comparison of the A* path and the refined Reeds-Shepp path can be seen in Figure 13.

2.4.3. Genetic Algorithm for the Subfield Traversal Order

For complex field shapes, the field may be split into several subfields to maximize efficiency. To minimize the non-servicing distance between the subfields, a GA can be used to select the order of subfields and the corresponding starting/ending locations of the subfields. As explained by Holland et al. [20], GAs are ideal for optimizing discrete problems through evolving solutions via selection, crossover, and mutation.

The subfield number and starting node need to be encoded into the chromosome for proper interpretation. The chromosome length can be calculated by multiplying the number of subfields by 2. Every odd gene in the chromosome represents the subfield number, and every even gene will be the corresponding subfield’s entrance point. An example of the chromosome structure can be seen in Figure 14.

As explained in Section 2.3.6, each subfield has 4 possible starting points on the outermost headland path, each with their own pre-determined end points along the border of the subfield. Shen et al. [14] explored something like this, except they assumed that each field only had a single entrance/exit, and their connecting paths were defined as the straight-line distance between the subfield’s entrance/exit. Our study aims to expand on this concept by finding the best subfield traversal order and corresponding subfield starting/ending points.

Additionally, the distance calculation between subfields has been improved by taking a rough estimation of the distance needed while avoiding obstacles. In other words, an estimated feasible path. This is done by drawing the straight-line connecting path and finding the shortest distance around any obstacles/subfields that may exist in the straight-line path. The fitness of each chromosome is defined as the total non-servicing distance needed to connect the subfields in the order that they occur in the chromosome sequence. For example, referencing Figure 14, the distance from subfield 1’s ending point is calculated to subfield 2’s starting point, and so on.

A roulette-style selection technique is used to select the parents used to create the next generation of solutions. This method favors solutions with better fitness (lower total distance) over others. The crossover operator is only done on even genes to preserve the connection between subfields and their corresponding starting point. The mutation operator is only done on even genes to randomly change the corresponding subfield’s starting point. Additionally, the best 2 solutions from each generation will be copied to the new generation to preserve them. Over several generations, the solutions will gradually improve due to simulated natural selection. The proposed GA has been verified with a full enumeration to yield globally optimal results for up to 3 subfields. Specifically, the fields in Figure 15 (Cases A and B) were used to verify the GA. A global optimum of 412.74 m and 171.39 m was identified by the full enumeration for Case A and B, respectively. The proposed GA was capable of finding these results within the 3s timeframe. There are no test cases containing more than 3 subfields, concluding that this approach is appropriate for this application. The general procedure of the applied GA can be outlined in Figure 16.

3. Results

To evaluate the performance of the proposed methods, a series of farms were selected as the test cases. The farms are divided into simple and complex farms. The simple farm only consists of one subfield, while the complex ones will be divided into multiple subfields due to obstacles or irregular shapes. The selected farm fields can be seen in Figure 15.

Since Case A and B are irregular shapes, these are needed to be split into multiple subfields by following the methods discussed in Section 2.2. So, the subfield connecting path optimization is only needed for these 2 cases. The parameters used in the GA for optimization can be found in

Table 3. Genetic algorithm variables.

Variable	Value
Population Size	30
Number of Generations	30
Number of Runs	4
Crossover Probability	0.9
Mutation Probability	0.07

, and the optimized connecting paths can be seen in Figure 17. In Figure 17a,b, the total path starts at the outermost headland track of the first subfield, services all headland tracks in order, services the infield of the first subfield, travels the A* path from the ending of the first subfield’s infield tracks to the outermost headland track of the second subfield, services all headland tracks in order, then to the second subfield’s infield tracks, and so on. This process repeats until all subfields have been serviced. Once the last subfield has been serviced, the tractor will follow the A* path connecting the ending point of the last subfield’s infield tracks to the outermost headland track of the first subfield (starting location), thus completing the cycle. The total connecting path lengths needed for Case A and Case B are 412.74 m and 171.39 m, respectively.

The results of the path generation for Cases A, B, and C can be found in

Table 4. Results from X-type turning pattern.

Field Shape	Rotary			Plowing
	FTE (%)	Coverage Ratio (%)	Computation Time (s)	FTE (%)	Coverage Ratio (%)	Computation Time (s)
Case A (Irregular)	76.9	99.1	2.73	75.2	99.1	2.77
Case B (Irregular)	73.6	98.8	0.84	73.9	98.8	0.99
Case C (Regular)	94.4	99.9	0.81	94.3	99.9	0.93

and

Table 5. Results from C-type turning pattern.

Field Shape	Rotary			Plowing
	FTE (%)	Coverage Ratio (%)	Computation Time (s)	FTE (%)	Coverage Ratio (%)	Computation Time (s)
Case A (Irregular)	N/A	N/A	N/A	N/A	N/A	N/A
Case B (Irregular)	N/A	N/A	N/A	N/A	N/A	N/A
Case C (Regular)	68.0	99.9	0.09	67.8	99.9	0.11

for the X-type and C-type turning patterns, respectively. It is worth mentioning that due to the irregular shapes of Cases A and B, the C-type turning pattern was not able to execute. Table 4 and Table 5 contain metrics such as the FTE, coverage ratio, and computation time for both rotary and plowing operations after applying the proposed path generation methods. These 2 service operations need to be analyzed separately since the attachment width was different; 1.8 m for plowing, and 2.02 m for rotary.

4. Discussion

As highlighted in Table 4 and Table 5, the following methods show promising results, all of which are computed in less than 3s. In a previous study done by Zhou et al. [2], the same Case C fields the AB and BL turning patterns were evaluated to have an FTE of 88.9%, whereas this study shows an FTE of 94.4%, an increase of 5.5% by using X-type turns that can shorten the length of the turning tracks, directly contributing to higher FTE values (30% reduction under the same scenario). Additionally, the coverage ratio is over 99% in a majority of the cases discussed in this report, meaning that all the land within the subfields can be serviced without a noticeable loss of area.

Additionally, the subfield connection path optimization shows satisfactory results as well. Compared to the previous study by Shen et al. [15], our method improves on the existing straight-line connection optimization by introducing obstacle avoidance using the A* algorithm to give a more realistic path and distance calculation. Additionally, our proposed GA methods are more dynamic since the algorithm can pick not only the traversal order of the subfields but the starting locations for each subfield as well, which may yield potentially more improved results compared to the case of having only one designated starting location for each subfield. The A* path has not been verified with simulations or physical experiments; however, appropriate measures have been taken to improve the feasibility of the generated path, such as the Reeds-Shepp curve at the entrance/exit of subfields, and safety buffer around the boundaries of obstacles and subfields to reduce cut-corners. Research by Chakraborty et al. [7] also states that there are several applications in agricultural path planning that utilize the A* algorithm in conjunction with other methods to generate point-to-point navigation, which leads to the conclusion that the A* path can be used to generate the global path for an autonomous tractor. In future research, a local path planning algorithm will be used to follow the A* path, which will smoothen any sharp turns caused by the resolution of the occupancy grid.

Future research includes physical tests with an autonomous tractor using the proposed path-generation techniques. All the results presented in this report are theoretical and have yet to be tested in the field.

5. Conclusions

In this study, a method of generating a continuous global servicing path for an autonomous tractor was proposed. The path has been optimized with respect to the FTE by experimenting with creating subfields of the target land, optimizing infield track directions, and combining adjacent subfields (if possible). The traversal order of the subfields and their respective starting locations have been optimized to yield the least total distance through a GA. For all three case studies, the computation time was less than the required 3 seconds, and the overall quality of the solutions was satisfactory. When compared to previous studies, Case C saw a 5.5% improvement in efficiency, thus verifying the proposed methodology.

Limitations of this study include failing to generate valid infield tracks when the field shape is concave, and the occasional occurrence of overlapping small portions of subfields when using the Reeds-Shepp path. As future work, we can consider optimizing the traversal sequence of the infield tracks by combining C-type turning and X-type turning based on the shape of the field, as well as developing an obstacle-avoiding Reeds-Shepp algorithm to eliminate the subfield overlap that may exist.