Predictive Spray Switching for an Efficient Path Planning Pattern for Area Coverage

Abstract

This paper presents, within an arable farming context, a predictive logic for the on- and off-switching of a set of nozzles. The predictive logic is tailored to a specific path planning pattern. The nozzles are assumed to be attached to a boom aligned along a working width and carried by a piece of machinery with the purpose of applying spray along the working width. The machinery is assumed to be travelling along the specific path planning pattern. The concatenation of multiple path patterns and the corresponding concatenation of the proposed switching logics enable nominal lossless spray application for area coverage tasks. The proposed predictive switching logic is compared to the common and state-of-the-art reactive switching logic for Boustrophedon-based path planning for area coverage. The trade-off between a reduction in pathlength and increase in the number of required on- and off-switchings for the proposed method is discussed.

1. Introduction

Within an agricultural open-space arable farming context focusing on the cereal crop cultivation of grains like wheat, rapeseed, barley and the like, area coverage applications can in general be manifold. They can include spraying, mowing, fertilising, seeding, harvesting and so forth.

In this paper, area coverage only relates to spraying applications. This includes (i) the spraying of herbicides, pesticides and the like for plant protection but can alternatively (ii) also refer to the spraying of fertilising means or in general (iii) to applications where input means are sprayed onto a work area through one nozzle or a set of nozzles.

Thus, the methods presented in this paper do not relate to mowing, seeding and harvesting applications, or in general to applications where a piece of machinery does not apply spray to a work area, but instead operates in direct physical contact with a work area.

For this setup of area coverage planning for spraying applications, there are two fundamental building blocks, (i) path planning and (ii) a switching logic for control of the nozzles, where these two steps follow after each other in sequence. First, a path is planned before a switching logic is applied on top; see Figure 1 and Figure 2.

The simplest possible switching logic is to switch on at the start of the path plan and to switch off after the completion of the path plan. However, within an agricultural area coverage context, this may be inefficient since it typically generates spray overlap where some areas would be sprayed multiple times. Therefore, more efficient switching logics and efficient path plans are desired.

A literature review is provided for the two building blocks, path planning for area coverage and switching logics for the control of nozzles for spray application.

First, for area coverage, Boustrophedon paths, whose name is derived from Ancient Greek for “like the ox turns”, are mentioned. They describe a meandering or ‘zig-zag’ path pattern. Its usage is widespread, e.g., from search and scan applications to early robotic applications in [1]. It is by far the predominant path pattern employed in practice throughout agricultural applications. The reason is that it is convenient to use by driving with agricultural machinery alternately one lane after another to achieve area coverage.

Nevertheless, it is important to point out that this pattern is not pathlength optimal in combination with a headland path that is typical for area coverage in arable farming applications [2].

The topic of optimising path planning for area coverage has been addressed by a large number of different techniques, typically tailored to the different structures of work areas. See [3] for a 2013 survey and [4] for a more recent 2021 survey.

Within the arable farming context, the inclusion of a headland path is a characteristic constraint that has to be taken into account for area coverage path planning (see, e.g., [5,6,7,8,9,10,11]). For illustration, compare Figure 3 and Figure 4 for area coverage paths with and without headland paths, respectively. Headland paths are required for full area coverage when operating nonholonomic vehicles such as tractors with a limited turning radius within the work area.

In [12], optimal in-field routing was discussed for arbitrary non-convex fields and multiple obstacle areas. In general, in such a setup, the optimal solution can result in a route that would be unintuitive to drive in contrast to a Boustrophedon path. Nevertheless, it was found that there exists a specific path planning pattern that often can form part of an optimal solution. This path pattern was further analysed in [2]. This pattern shall also represent the pattern based on which a predictive spray switching logic is presented in this paper.

The second building block is discussed. Spraying is typically applied to the work area via a set of nozzles aligned along a boom for broadcast spraying [13,14]. This implies that spray is applied over the entire width of the boom. For broadcast spraying, nozzles are spaced along the boom such that individual nozzle sprays overlap such that uniform spray coverage along the entire boom width can be achieved. Spraying is a highly dynamic process and affected by a plethora of parameters. These include nozzle type, spray fan angle, spray pressure, boom height, nozzle spray overlap, nozzle spacing, nozzle clogging, machinery travelling speed, cross wind for spray drift, terrain undulations and more [15,16,17,18,19,20,21,22,23]. For unmanned aerial spraying [24], in contrast to traditional spraying with tractors carrying or trailing spraying machinery and sprayers operating close to the ground, dynamic effects are further amplified.

The aforementioned effects are listed to emphasise the high real-world complexity of the spraying process. For the remainder of this paper, however, (i) nominal instant switching and (ii) the absence of any of the abovementioned spray dynamics and spray transients are assumed. This is justified for two reasons: First, spray effects hold simultaneously for both the Boustrophedon-based path pattern and the suggested alternative path pattern. Second, for a deterministic planning problem, this paper presents a novel deterministic solution technique, i.e., a predictive deterministic switching logic that exploits the structure of a specific path planning pattern. For this presentation, spray transients are omitted in the following since these do not alter the general switching logic. Therefore, in the following, the two objective evaluation metrics (i) pathlength and (ii) the number of on-/off-switches are used to compare the proposed predictive method to an alternative reactive Boustrophedon-based and state-of-the-art baseline under nominal conditions. Analytical formulas are derived that underline the potential of the proposed method for pathlength savings that scale linearly with the number of mainfield lanes and the working width.

The research gap and motivation for this paper is discussed. There is a research gap in linking spray switching logics to path planning patterns that are different to the Boustrophedon pattern. Moreover and in particular, individual nozzle control is typically applied reactively, varying laterally along the boom within the framework of variable rate automatic section (boom section or nozzle) control [25,26]. The reactive aspect implies that nozzles are switched on during path traversal when an area has not yet been sprayed and switched off (i) when an area is traversed a second or more times such that no overlap occurs with already sprayed areas and (ii) when an area is traversed that is not meant to be sprayed according to a map [25].

In contrast, to the best of the author’s knowledge, this is the first paper that proposes (i) a predictive switching logic that (ii) exploits the structure of an efficient path planning pattern for area coverage that is different to the Boustrophedon pattern.

The remaining paper is organised as follows: problem formulation, problem solution, numerical results and the conclusion are described in Section 2, Section 3, Section 4 and Section 5.

2. Materials and Methods

The problem addressed in this paper is as follows:

Problem 1. 

Given a convexly shaped two-dimensional work area, determine a path plan for area coverage based on the concatenation of a recurring path pattern and determine a corresponding logic for the on- and off-switching of a set of nozzles attached to a boom aligned along the working width. The boom with nozzles shall be carried by a machinery or trailed by a piece of machinery as an implement with the purpose of applying spray along the working width while the machinery is travelling along the path plan, subject to the constraint that the path plan for area coverage shall include a headland path.

Three comments are made. First, the constraint of the inclusion of a headland path is a typical setup for outdoor agricultural applications. It is warranted (i) for nonholonomic vehicles such as tractors that typically operate in agricultural fields with a limited turning radius and (ii) in order to ensure field contours shall not be exceeded or violated while still enabling full area coverage. Note that the benefits of the inclusion of a headland path can also apply to drone applications [27]. Second, the assumption of a convexly shaped work area enables that Problem 1 can be fully solved by the concatenation of a recurring path pattern. Third, the treatment of non-convexly shaped work areas and work areas that further include obstacle areas such as tree islands, ponds, power pole masts and so forth is more complex and not the subject of this short paper, where the focus is on the presentation of a switching logic for a specific alternative path planning pattern. However, short comments and an outlook for the non-convex setup are provided at the end of this section.

The following discusses two solution approaches for Problem 1. First, the state-of-the-art and widespread method applied in agricultural practice that is based on Boustrophedon path planning and a corresponding reactive switching logic is discussed. Second, an alternative proposition that is based on an alternative path pattern and a predictive switching logic is presented. The high-level approach is illustrated in Figure 2.

2.1. Boustrophedon-Based Reactive Switching Method

The switching logic for Boustrophedon-based path planning for area coverage is visualised in Figure 5. It is switched on along the initial full headland path traversal beginning at the field entrance; see Figure 5a. Then, it is reactively switched on along traversals of mainfield lanes as soon as a work area has not yet been sprayed. This occurs along the mainfield lanes at closest projection distances of half the operating width, $W/2$, away from the headland path. Likewise, it is reactively switched off towards the end of traversal of a mainfield lane at the closest projection distances of half the operating width, $W/2$, away from the headland path such that no overlap occurs with the already sprayed area. See Figure 5b for an illustration. This procedure is repeated while the machinery is traversing the mainfield lanes in the typical Boustrophedon pattern; see Figure 5c. After the traversal of the last mainfield lane, the machinery travels along the shortest path along the headland path to the field exit with spray nozzles switched off such as to avoid spray overlap. The final result of this reactive spraying method implies full area coverage; see Figure 5d.

2.2. Alternative Predictive Switching Method

The second method to address Problem 1 differs from the previous Boustrophedon-based reactive method in two ways: (i) a different path pattern is employed, and (ii) the switching method includes a predictive logic.

The path pattern and its waypoints of interest are highlighted in Figure 6. Several comments are made. First, the path traversal begins a start point, A, and follows the letters in order A, B, C, ... until end point M. Second, path segments B–C, F–G, H–I and L–A indicate turn manoeuvres for transitions between the headland path and mainfield lanes. A turning radius $R>0$ for nonholonomic vehicle dynamics is assumed. Third, waypoints D, E, J and K indicate locations along mainfield lanes that have the closest projection distance of half the working width, $W/2$, away from the headland path. Fourth, the headland path segments that are part of the path pattern are segments A–B, G–H and A–M. Note that the initial segment A–B is also a sub-segment of segment A–M.

For the path pattern in Figure 6, the proposed switching logic is visualised in Figure 7 and is as follows:

(a)

Along transition A–D, it is switched off.

(b)

Along transition D–E, it is switched on.

(c)

Along transition E–J, it is switched off.

(d)

Along transition J–K, it is switched on.

(e)

Along transition K–A, it is switched off.

(f)

Along transition A–M, it is switched on.

Multiple comments are made. First, according to the logic, it is never switched on along turn manoeuvres for the transition between the headland path and mainfield lanes; see Steps (a), (c) and (e). This is beneficial in that during such turn manoeuvres, nozzles located at different locations along the boom exhibit different travelling velocities. In order to maintain uniform spray application along the entire working width in such scenarios, individual nozzle control [25] would be required. This is avoided here.

Second, according to Step (b) and (d), it is switched on only along segments of mainfield lanes that are at the closest projection distance at least half the operating width away from the headland path. This is because the area around segments of the mainfield lanes that are close to the headland path are more efficiently sprayed during the traversal of the headland path segments. This avoids spraying during turn manoeuvres for transitions between the headland path and mainfield lanes.

Third, assuming nominal instant switching and spray application without a transient phase, there is zero overlap in the total sprayed area, as shown in Figure 7f indicated by the gray area. This is the result of the three switching-on phases illustrated in Figure 7.

Finally, the two predictive characteristics of the switching pattern are discussed. The first predictive aspect of the method involves the headland path segment A–B in Figure 6. The first transition A–D according to Figure 7a is traversed with the switching-off state. This transition includes the traversal of the path segment A–B along the headland path. According to the above switching logic, it is explicitly switched off along this transition. This is because, by knowledge of the path pattern, it is predictively known that the path segment A–B will be traversed a second time as part of the sixth and final transition A–M of the path pattern. Importantly, the entire transition A–M, which includes the path segment A–B, is along the headland path. In contrast, the first transition A–D, which also includes the path segment A–B, is only partly along the headland path and also partly along a turn manoeuvre for the transition from the headland path to the mainfield lane. Note that such a predictive switching logic is absent from the state-of-the-art reactive switching logic for Boustrophedon-based area coverage path planning described in Section 2.1.

The second predictive aspect of the method involves the concatenation of multiple path patterns and their switching logics. As the sprayed area in Figure 7f illustrates, after the traversal of the path pattern and according to the switching logic outlined in Figure 7a–f, not all segments along the path pattern are sprayed during their traversal. In particular, this relates to transition E–J in Figure 7c and transition K–A in Figure 7e. However, being aware of the embedding of the path pattern within an overall area coverage path plan, the coverage of these missing segments can be achieved by

(i)

Concatenating multiple path patterns.

(ii)

Introducing a switching logic for the initial transition from a field entrance to the first occurrence of the path pattern according to the overall area coverage path plan.

(iii)

Introducing a switching logic for the path after the completion of the last path pattern according to the overall area coverage path plan.

These three aspects are elaborated on next.

Regarding (i), Figure 8 illustrates the concatenation of two path patterns, illustrating how a concatenation enables the spraying of a larger area.

Regarding (ii), the initial switching logic for the initial transition from a field entrance to the first occurrence of the path pattern shall be reactive. Thus, during this phase, it shall be switched on during path traversal when an area has not yet been sprayed and switched off when an area is traversed a second or more times.

Regarding (iii), the switching logic for the path after the completion of the last path pattern according to the overall area coverage path plan shall likewise be reactive. Thus, it shall be switched on during path traversal when an area has not yet been sprayed and switched off when an area is traversed a second or more times.

Finally, Figure 9 illustrates two special cases of the path pattern in Figure 6, where a headland path segment is prolonged. Two comments are made.

First, if an area coverage path plan consists entirely of a concatenation of path patterns of Figure 6, then one of these special cases marks the last path pattern according to the overall area coverage path plan. Then, waypoint M in Figure 9 marks the field exit point, whereby, in general, the final headland path segment A–M can span multiple path patterns.

Second, it is noted that Figure 9a,b represent boundary cases. In general, any intermediate case is also possible. In such scenarios, spray overlap occurs, resulting from spraying along the prolonged headland path segment and one mainfield lane. However, this can be mitigated by boom section control [25,26] and does not affect the general switching logic. The effect of spray overlap for the area between the first or last mainfield lane and the headland path is a well-known phenomenon in agriculture and does also occur for the Boustrophedon-based path planning and switching logic.

For a full area coverage example illustrating the above rules (i)–(iii), see Figure 10.

2.3. Non-Convexly Shaped Work Areas

As outlined in Problem 1, the scope of this paper includes convexly shaped work areas. The objective of this paper is to present an efficient predictive switching logic for a specific path planning pattern.

Not subject of this paper is the application of the method to non-convexly shaped work areas. Here, optimised area coverage path planning (e.g., [12]) is more complex and area coverage paths often consist of concatenations of the path pattern in Figure 6 but also often consist of freely optimised and less intuitive routing paths. The above switching logics, and in particular listings (i)–(iii), are still maintained. Likewise, for the case of field contours described by polygons and freeform mainfield lanes (see e.g., [28] and Figure 11), the switching logics according to Section 2.2 are still maintained.

The evaluation of the method for (i) non-convexly shaped real-world work areas, (ii) the inclusion of turn compensation for individual boom section control, and (iii) the effect of spray transients during switching is the subject of ongoing work.

3. Results

For the experimental setup displayed in Figure 12, analytical formulas can be derived for the pathlength and for the number of required switching-on and switching-off states. For this calculation, an odd and an even number of mainfield lanes N have to be distinguished.

For an odd number of mainfield lanes, the following formulas can be derived analytically:

$$\begin{array}{cc}\hfill L_{\mathrm{path}}^{\mathrm{Boustrophedon}}\left(N\right)& =N(H-4R+2{\displaystyle \frac{2R\pi }{4}}+4W)+c_1,\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill N_{\mathrm{ON}}^{\mathrm{Boustrophedon}}\left(N\right)& =N+1,\hfill \end{array}$$

(2)

$$\begin{array}{cc}\hfill L_{\mathrm{path}}^{\mathrm{Alternative}}\left(N\right)& =N(H-4R+2{\displaystyle \frac{2R\pi }{4}}+3W)+c_2,\hfill \end{array}$$

(3)

$$\begin{array}{cc}\hfill N_{\mathrm{ON}}^{\mathrm{Alternative}}\left(N\right)& ={\displaystyle \frac{3}{2}}(N+1),\hfill \end{array}$$

(4)

with offset constants $c_1=(3H-14R+6{\displaystyle \frac{2R\pi }{4}}+2W)$ and $c_2=(3H-12R+6{\displaystyle \frac{2R\pi }{4}}+3W)$.

For an even number of mainfield lanes, the following formulas can be derived analytically:

$$\begin{array}{cc}\hfill L_{\mathrm{path}}^{\mathrm{Boustrophedon}}\left(N\right)& =N(H-4R+2{\displaystyle \frac{2R\pi }{4}}+4W)+c_3,\hfill \end{array}$$

(5)

$$\begin{array}{cc}\hfill N_{\mathrm{ON}}^{\mathrm{Boustrophedon}}\left(N\right)& =N+1,\hfill \end{array}$$

(6)

$$\begin{array}{cc}\hfill L_{\mathrm{path}}^{\mathrm{Alternative}}\left(N\right)& =N(H-4R+2{\displaystyle \frac{2R\pi }{4}}+3W)+c_4,\hfill \end{array}$$

(7)

$$\begin{array}{cc}\hfill N_{\mathrm{ON}}^{\mathrm{Alternative}}\left(N\right)& ={\displaystyle \frac{3}{2}}N+1,\hfill \end{array}$$

(8)

with offset constants $c_3=(3H-12R+6{\displaystyle \frac{2R\pi }{4}}+2W)$ and $c_4=(2H-8R+4{\displaystyle \frac{2R\pi }{4}}+2W)$.

For visualisation, the calculations in Formulas (1)–(4) are evaluated and displayed in Figure 13 and

Table 1. Experiments: The results for an odd number of mainfield lanes $N>0$. A turning radius of $R=5$ m is assumed throughout. For the formulas and qualitative evaluation, see (1)–(4) and Figure 13, respectively.

Example Setup	Boustrophedon	Alternative
$W,H,\mathrm{Area}$	$L_{\mathrm{path}},N_{\mathrm{ON}}$	$L_{\mathrm{path}},N_{\mathrm{ON}}$
N		$\Delta L_{\mathrm{path}}^{\mathrm{m}},\Delta N_{\mathrm{ON}}$
12 m, 100 m, 0.7 ha	1020 m, 6	982 m, 9
5		−38 m, 3
12 m, 100 m, 6.2 ha	7630 m, 52	7040 m, 78
51		−590 m, 26
12 m, 500 m, 3.6 ha	4220 m, 6	4182 m, 9
5		−38 m, 3
12 m, 500 m, 31.2 ha	29,230 m, 52	28,640 m, 78
51		−590 m, 26
36 m, 100 m, 2.2 ha	1548 m, 6	1414 m, 9
5		−134 m, 3
36 m, 100 m, 18.7 ha	12,574 m, 52	10,784 m, 78
51		−1790 m, 26
36 m, 500 m, 10.8 ha	4748 m, 6	4614 m, 9
5		−134 m, 3
36 m, 500 m, 93.6 ha	34,174 m, 52	32,384 m, 78
51		−1790 m, 26

. Similarly, those in Formulas (5)–(8) are visualised in Figure 14 and

Table 2. Experiments: The results for an even number of mainfield lanes $N>0$. A turning radius of $R=5$ m is assumed throughout. For the formulas and qualitative evaluation, see (5)–(8) and Figure 14, respectively.

Example Setup	Boustrophedon	Alternative
$W,H,\mathrm{Area}$	$L_{\mathrm{path}},N_{\mathrm{ON}}$	$L_{\mathrm{path}},N_{\mathrm{ON}}$
N		$\Delta L_{\mathrm{path}}^{\mathrm{m}},\Delta N_{\mathrm{ON}}$
12 m, 100 m, 0.6 ha	886 m, 5	742 m, 7
4		−144 m, 2
12 m, 100 m, 6.1 ha	7497 m, 51	6801 m, 76
50		−696 m, 25
12 m, 500 m, 3.0 ha	3686 m, 5	3142 m, 7
4		−544 m, 2
12 m, 500 m, 30.6 ha	28,697 m, 51	27,601 m, 76
50		−1096 m, 25
36 m, 100 m, 1.8 ha	1318 m, 5	1078 m, 7
4		−240 m, 2
36 m, 100 m, 18.4 ha	12,345 m, 51	10,449 m, 76
50		−1896 m, 25
36 m, 500 m, 9.0 ha	4118 m, 5	3478 m, 7
4		−640 m, 2
36 m, 500 m, 91.8 ha	33,545 m, 51	31,249 m, 76
50		−2296 m, 25

.

4. Discussion

Several comments can be made. First, the key insight is that in both cases, the difference in pathlengths, and thus the pathlength savings that can be achieved by the Alternative method, scales linearly with the number of mainfield lanes and the working width:

$$L_{\mathrm{path}}^{\mathrm{Alternative}}\left(N\right)-L_{\mathrm{path}}^{\mathrm{Boustrophedon}}\left(N\right)=\left\{\begin{array}{cc}-NW+\widetilde{c_{21}},\hfill & \mathrm{if}N\mathrm{odd},\hfill \\ -NW+\widetilde{c_{43}},\hfill & \mathrm{if}N\mathrm{even},\hfill \end{array}\right.$$

(9)

where the constants are $\widetilde{c_{21}}=c_2-c_1$ and $\widetilde{c_{43}}=c_4-c_3$. Thus, the more mainfield lanes are needed to cover an agricultural field or work area, the more pathlength savings can be achieved in absolute values by the alternative method.

Second, while the alternative method offers pathlength savings as a benefit, the Boustrophedon-based method offers savings in the required number of switchings:

$$N_{\mathrm{ON}}^{\mathrm{Alternative}}\left(N\right)-N_{\mathrm{ON}}^{\mathrm{Boustrophedon}}\left(N\right)=\left\{\begin{array}{cc}{\displaystyle \frac{1}{2}}(N+1),\hfill & \mathrm{if}N\mathrm{odd},\hfill \\ {\displaystyle \frac{1}{2}}N,\hfill & \mathrm{if}N\mathrm{even}.\hfill \end{array}\right.$$

(10)

Note that while (9) and (10) were derived for the experimental setup in Figure 12, similar analytical formulas can be derived for alternative starting positions (field entrance) located at a different location along the headland path. This changes the offset constants in (9) and (10); however, importantly, the linear relationships remain the same.

Thus, both the Boustrophedon-based and alternative method have one advantage and one disadvantage with respect to each other.

What remains to be evaluated is whether pathlength savings or savings in the number of switches are of greater importance. Therefore, in order to better obtain a sense of orders of magnitudes and savings potential, formulas are evaluated for a range of typical parameters. The results are summarised in Table 1 and Table 2.

For example, for an agricultural field of size 18.4 ha with an even number of lanes $N=50$, a working width $W=36$ m and $H=100$ m, the pathlength savings for the alternative method would be −1896 m and 25 more switching-on states in comparison to the Boustrophedon method. Here, several comments can be made.

First, the larger number of required switching-on states is undesired. This is because each switching generates real-world transient behaviour (without the aforementioned nominal assumption of instant spray application), during which only partial spray is applied while the nozzle switching occurs. Thus, spray uniformity is lost during transient distances. To put this in perspective, suppose this switching transient occurs for 2 m (e.g., a travelling speed of 7.2 km/h and a switching transient duration of 1 s) for each switching while the machinery is travelling in the agricultural field. Then, 25 more switching-on states and their corresponding switching-off states collectively imply a 100 m pathlength of the total pathlength where transient switching behaviour occurs. Note that these 100 m stand in contrast to −1896 m pathlength savings that can be achieved through the alternative method. This discussion is given to underline different orders of magnitude.

Pathlength savings imply (i) time savings and (ii) fuel savings for the machinery. For example, pathlength savings of −1896 m at a travelling speed of 5 km/h imply 22.8 min time savings. This is significant. At a travelling speed of 10 km/h, the time savings are still 11.4 min.

Whether to more highly value pathlength savings or instead to prefer fewer nozzle switchings is a decision any practitioner has to decide for themselves. On the one hand, there are time savings and fuel savings, and on the other hand, there is the avoidance of switching transients where spray is applied only partially. From an economic point of view, time and fuel savings are arguably more important.

Finally, a detail about the effect of an odd or even number of mainfield lanes on pathlength savings is discussed. As Figure 13a illustrates that, for a small odd number of mainfield lanes, $N=5$, the pathlength savings of the alternative method with respect to the Boustrophedon-based method are between $-0.9\%$ and $-8.7\%$. In contrast, as Figure 14a illustrates, for a small even number of mainfield lanes, $N=4$, the pathlength savings are between $-14.8\%$ and $-18.2\%$. The reason for this large discrepancy in pathlength savings depends on which one of the two cases in Figure 9 applies. For the given examples, Figure 9a applies for an even number for N, whereas Figure 9b applies for an odd number for N. Thus, for an odd number N the right-most headland path segment is traversed twice according to Figure 9b. This is unavoidable and necessary to cover the penultimate mainfield lane but results in smaller pathlength savings with respect to the Boustrophedon-based method. The smaller the N and the larger the mainfield length H, the more profound this loss of pathlength savings potential is. In contrast, for an even number of mainfield lanes, maximal pathlength savings potential is achieved by the alternative method with respect to the Boustrophedon-based method.

5. Conclusions

This paper presented a predictive logic for the on- and off-switching of a set of nozzles attached to a boom aligned along a working width for a specific path pattern for area coverage. The path pattern is efficient for area coverage in that its concatenation yields shorter area coverage pathlengths than an alternative Boustrophedon-based area coverage path. The proposed switching logic for the path pattern is efficient in that it avoids switching-on states during turn manoeuvres by exploiting the special structure of the path pattern.

Two predictive aspects of the proposed switching logic were highlighted, first within its framework for one path pattern and then within the framework of concatenating multiple path patterns.

The method was compared to a state-of-the-art reactive switching logic for Boustrophedon-based area coverage path planning.

Assuming a convexly shaped work area, one advantage and one disadvantage of the proposed method were highlighted. The advantage is pathlength savings that scale linearly with the number of mainfield lanes and the working width. The disadvantage is that the number of required switching-on states is larger than that for the Boustrophedon-based method and scales linearly with 50% times the closest rounded up even number of mainfield lanes.

The implications of pathlength savings for time and fuel savings were hinted at and numerical examples for illustration were given. The implications of short transients during switching changes, in which only partial spray is applied, was discussed.

Future work will analyse the effect of the proposed switching logic for non-convexly shaped work areas.