Agricultural Field Models

The agricultural fields were modeled in two steps. To represent "go" and "no go" areas (obstacles), binary occupancy maps (BOM) [26] were used and to find non-collision paths within the "go" areas, probability roadmaps (PRM) [27] were used.

In this research, to investigate the possible effects of field complexity, two different fields were studied. Field 1 (see Figure 2) is a rectangular field without any obstacle areas imitating a quite typical environment for bale collection operations. Field 2 (see Figure 3) on the other hand, is a representation of an irregular more complex agricultural field with obstacle or intrusion areas. For both fields, bales were positioned by calculating the distance, going in straight lines from one end to the other until the whole field was covered, and the harvesting vehicle had collected enough material to form a bale based on the average yield, etc. given in Table 1.

Figure 2a shows the BOM of field 1 where black dots indicates bales occupancy and Figure 2b shows the inflated BOM of field 1. To reduce the calculation intensity for simulations, only 10 discrete points on each bale collection radius were used, which are represented as black dots surrounding the inflated bales in Figure 2b.

**Figure 2.** (**a**) Binary occupancy map of the bale position in field 1. (**b**) Inflated binary occupancy map of the bale position in field 1.

**Figure 3.** (**a**) Binary occupancy map (BOM) of the bale position in field 2. (**b**) Inflated binary occupancy map (BOM) of the bales and bale collection positions in field 2.

**Table 1.** Bale distribution parameters.


Figure 3a shows the BOM of field 2 where black dots indicates bales occupancy and Figure 3b shows the inflated BOM of field 2 including the discretized collection points at AVN's reach radius.

The distance traveled to release a bale can then be calculated through

$$d \times HW \times \check{Y}\_{\text{grass}} = \check{W}\_{HB} \tag{2}$$

where *d* is the distance required to make one bale by harvester; *HW* is the harvester width; *<sup>W</sup> HB* is the average weight of one bale; and *<sup>Y</sup>*<sup>ˇ</sup> *grass* is the average grass yield in a typical season. '×' represents multiplication operator. Based on the parameters in Table 1 and Equation (2), bales were released after a travelled distance of around 330 m (some minor adjustments were made if the release position coincided with the boundary of the field).
