Experimental Analysis of an Autonomous Driving Strategy for a Four-Wheel Differential Drive Agricultural Rover ^†

Abstract

Currently, the entire agricultural sector is under significant pressure. The causes that may explain this are different, such as climate change, market instability, and the decline in the population of agricultural workers. As a result, the agricultural tractor and machinery field is at the center of an intense technological revolution. One of the possible solutions to the aforementioned problems can be represented by agricultural vehicles equipped with autonomous driving systems. The key pillar of an autonomous driven vehicle is its autonomous driving algorithm which represents the link between the information coming from the vehicle’s sensor systems and the success of the vehicle’s operative mission. In this paper, an experimental assessment of the motion strategy for a four-wheel differential drive agricultural rover was conducted. This work is structured in three parts. First, the description of the working principles of the autonomous driving algorithm is proposed. Then, the case study and the scaled prototype designed for this purpose are described. In the end, the result obtained by the virtual model, which acts as reference case, is compared with the results that came out of the field test campaign. The outcomes show the overlap between the virtual and real results.

1. Introduction

In recent years, the agricultural machinery sector has been involved in an authentic technological revolution. There are several reasons linked to this phenomenon. One of the main causes is represented by climate change [1,2], since agriculture represents 11% of the total anthropogenic greenhouse gas (GHG) emissions [3]. Climate change, in its turn, is responsible for the increase in unexpected and intense weather events with unavoidable consequences for crop quality and quantity [4,5]. Also needing to be considered is the necessity of increasing food production, despite the population of agricultural workers declining [6,7], due to the actual growth trend of the world’s population [8]. In this challenging context, both the academic and industrial sectors are exploring several ways to achieve cleaner and more efficient operations in agriculture [9,10]. The consequences of these attempts are the design of agricultural vehicles equipped with innovative powertrains such as hybrid electric tractors [11,12,13], experimentation with alternative propellants [14,15], and the increasing implementation of IoT systems onboard agricultural vehicles [16,17]. In this context, agricultural robots can represent the best compromise, because they include all the aforementioned features [18,19,20]. Agricultural robots are intelligent and autonomous vehicles with a very large field of application. Indeed, they can be used in modern precision farming applications [21,22], such as monitoring field health status [23,24], or they can also perform traditional agricultural tasks like spraying or harvesting [25,26,27]. One of the most important features of these kinds of vehicles lies in their motion strategy [28,29,30].

To the authors’ knowledge, there is still a lack of understanding with respect to agricultural rovers equipped with four-wheel differential drive systems. Indeed, most of the work currently presented in the literature focuses on autonomous agricultural vehicles, operating in orchards, equipped with traditional steering systems. For example, some works focus on the optimization of steering maneuvers for front-wheel steering agricultural tractors [31,32,33,34] or on the fleet movement synchronization of tractors [35,36]. Other works focus on certain specific aspects that the autonomous tractor must consider during its mission such as fuel consumption optimization [37] or soil condition [38,39].

The aim of this work is to prove the applicability and the reliability of an autonomous driving strategy, developed in a virtual environment, for an agricultural rover equipped with a four-wheel differential drive system and operating in a vineyard/orchard environment. This paper must be considered in continuity with the work presented in [40], where the algorithm principles, developed by the same authors of this study, are described. Consequently, the proposed model would represent a powerful tool for developing control strategies for this kind of vehicle. After a description of the working principles of the autonomous driving algorithm, the case study and a scale prototype, specifically designed and assembled for this study, are described. Then, the results obtained from the virtual model are discussed and compared with the ones obtained during the field tests.

2. Materials and Methods

In this section, the autonomous driving algorithm and the case study under investigation are described. The flow chart of the conceptualization of this study is shown in Figure 1.

In particular, the autonomous driving algorithm and its execution in a virtual environment, which is taken as a reference case, represents the starting point. Then, a scale prototype, in which the algorithm can be implemented, was designed and built for this study, through a multidisciplinary approach. Then, a series of field tests were conducted in order to compare the experimental results with the modeled ones in order to eventually validate the autonomous driving model itself.

2.1. Autonomous Driving Algorithm

The autonomous driving algorithm is essentially made up of two main parts, as it is possible to observe in Figure 2: path planning and path following.

The path-planning phase aims to define a succession of points, namely waypoints (WPs), that represent the path that the vehicle must follow in order to accomplish its mission. The motion planning process is performed in offline mode, i.e., before the vehicle’s mission starts. Once the rover’s ideal trajectory has been generated, it will be implemented in the rover control unit and used to perform the vehicle mission. The first step of the path-planning process is the reconstruction of the environment in which the rover will operate. The map consists of a matrix where only two possible values are permitted for each cell:

• 1 in the case of the presence of an obstacle;
• 0 in the case of a free path.

The generation of the map is managed automatically by the algorithm after the user defines several input parameters (Figure 3):

• The number of fruit plant rows n;
• The width Rw and length Rl of fruit plant row;
• The width L1 and length L2 of the orchard field;
• The fruit plant row’s start position Ys;
• The mesh refinement m, which consists of the number of cells contained in each square meter;
• The number of free rows N = n + 1;
• The fruit plant row recurring step P = L1/N.

The next step, necessary for solving the motion planning process, is the definition of the input parameters related to the vehicle features. The developed algorithm is based on a 2D model; thus, the state of the vehicle is fully defined through three degrees of freedom, two translational (longitudinal X and lateral Y movements), and one rotational (yaw ϴ) around the axis perpendicular to the movement plane (Figure 4).

In this regard, there are four vehicle parameters:

• Rover width w;
• Rover wheelbase l;
• Tire radius r;
• Minimum vehicle turning radius.

As can be seen, among the vehicle’s input parameters there is no information about the vehicle’s steering system. Indeed, the trajectory planned is independent of the steering system equipped on the rover, which is implemented in the path-following phase instead.

At this point, the ideal trajectory of the rover can be traced. The motion planning process is based on Dubins theory [41,42]. It consists of a geometrical planner according to which the trajectory of an object can be traced with a combination of segments and circular arcs, given a start and an arrival point and their relative orientation on the map. This kind of theory is particularly appropriate in the case of vineyards/orchards since there are mainly two kinds of trajectory executed by the rover:

• A straight line along the fruit plant row;
• Hairpin turns to go out from a free row and enter the next one.

The input variables that must be set in order to generate the planned trajectory are:

• Start and goal points and their respective orientations on the map.
• The number of checkpoints that are some known reference points through which the vehicle must pass.
• Waypoints pitch distribution (WPP), which consists of the distance between two consecutive waypoints.

In particular, the checkpoints are inserted manually by the user. In Figure 5, an example of the results of the path-planning phase is shown.

The output of the path-planning phase represents the input of the path-following phase. The scope is to follow a predetermined trajectory (waypoints) adequately. The working principle of the path-following process, which is based on a pure-pursuit controller [43], is shown in Figure 6.

The input parameters of the path-following phase are:

• Cycle time t, which defines the time range in which the rover takes action.
• Distance threshold Dth, which represents the maximum distance below which the reference waypoint is considered reached.
• Look-ahead distance LD, which represents the radius of the circumference centered on the rover’s center of mass.

The path-following algorithm is structured in four steps. First, the algorithm identifies a local goal point (LGP), given by the intersection between the LD circumference and the ideal path (Figure 7). The LGP represents the provisional arrival point that the rover tries to reach in the cycle time considered.

Then, the rover is able to define the LGP direction φ with respect to its position. Hence, given the rover’s orientation γ with respect to the map reference system, the algorithm calculates the yaw angle/steering angle ϴ (Figure 8) according to the following equation:

$$\mathrm{ϴ} = \mathrm{\phi } - \mathrm{\gamma }$$

(1)

At this point, it is possible to determine the yaw speed:

$$\dot{\theta }={\displaystyle \frac{\theta }{t}}$$

(2)

The longitudinal speed v is calculated according to the following equation:

$$v=v_t \cdot \left(1-{\displaystyle \frac{\theta }{{\theta }_{max}}}\right)$$

(3)

where

• v_t represents the maximum rover speed;
• ϴ_max is the maximum steering angle of the rover which, in this case, has been set to 360° because according to the kinematic model used the pivot maneuver is admissible.

Given the vehicle’s longitudinal and yaw speeds, the algorithm calculates the angular speeds that must be imposed on the left and right wheels, according to the differential drive kinematic model [44]:

$${\omega }_{r/l}={\displaystyle \frac{v}{r}} \pm \dot{\theta } \cdot {\displaystyle \frac{l}{r}}$$

(4)

where

• ω_r/l represents the angular speeds of the right and left tires, respectively;
• v is the rover’s actual longitudinal speed;
• r is the tire radius;
• l is the rover’s wheelbase;
• $\dot{\theta }$ represents the yaw speed.

In this way, the rover can reach the local goal point in the specific time cycle considered.

2.2. Case Study and Prototype

As stated previously, the scope of this study is the empirical assessment of an autonomous motion strategy for a four-wheel differential agricultural rover. The input parameters used in the algorithm are shown in

Table 1. Algorithm input parameters.

Algorithm Input Parameters
Vehicle Parameters	Vehicle Wheelbase	0.240 m
	Vehicle Width	0.375 m
	Tire Radius	0.067 m
	Rover Minimum Turning Radius (ϴmax)	0 m (360°)
	Rover Max Speed	0.9 m/s
Map Parameters	Field Width–Field Length	5 m–8 m
	Number of Fruit Plant Rows n	2
	Number of Check Points	8
	Waypoint Distance Threshold	0.2 m

:

There are just two parameters that remain to be defined: the look-ahead distance LD and the waypoint pitch distribution WPP. Indeed, the aim of the virtual model is to find the best combination of these two parameters so that the rover is able to pursue the ideal trajectory in the best way possible. Both the virtual model and the simulations were carried out on MATLAB R2021b (Mathworks Inc., Natick, MA, USA). With respect to the input parameters, a scaled orchard was reconstructed (Figure 9) and a scaled prototype was designed and developed.

Focusing on the scale prototype, its functioning block diagram is represented in Figure 10.

The rover is equipped with a 12 V lead-acid battery as an electric storage system (ESS). This provides electric energy both for traction and control. All the vehicle functionalities are managed by the vehicle control unit (VCU). There are several sensors connected to the VCU:

• A gyroscope sensor which is used to manage the steering angle and the vehicle’s direction on the map;
• A positioning system which is based on GPS-RTK technology that is composed of a GPS module and a radio module;
• A datalogger integrated into the VCU in order to collect all the information related to the actual status of the vehicle such as its position, direction, speed, etc.;
• A display making it possible to directly read information about the current status of the vehicle;
• LiDAR, ultrasonic, and vision sensors, which in this study are used as an emergency stop system.

The real aspect of the rover, highlighting its main components, is reported in Figure 11.

3. Results and Discussion

In this section, the results obtained by the virtual model are compared with the experimental ones.

3.1. Virtual Model Results

As stated previously, once the input parameters linked to the field and vehicle characteristics have been defined, there are only two parameters that must be defined:

• Waypoint pitch distribution WPP;
• Look-ahead distance LD.

Indeed, the aim of the virtual model is to identify the best combination of these two parameters that, having fixed all the remaining variables, makes it possible to accomplish the mission of the vehicle in the best way possible. Hence, the opportunity to calibrate the algorithm virtually is a great advantage in terms of saving time and also security, because the user does not need to perform all the tuning phases in the real tests.

Several simulations with different values of LD and WPP were run. In particular, the LD range was varied from 0.25 to 1.2 m, whereas the WPP range was varied from 0.1 to 1 m. The aim was to avoid the rover following the planned trajectory as represented in Figure 12. All the simulations were performed using MATLAB R2021 according to the parameters defined in Table 1. Furthermore, since the simulations were run using a 2D virtual model, the following considerations were included:

• The rover is completely defined with three degrees of freedom: lateral and longitudinal movements, and yaw rotation.
• The vehicle is represented as a rigid body and its wheels are in a condition of pure rolling with respect to the ground.
• The rover’s low operating speed implies that lateral slip can be ignored.

To evaluate the best possible combination of factors, the methodology defined in [40] was adopted. According to this method, the evaluation occurs through two parameters:

• The average trajectory deviation (ATD), which corresponds to the mean value of the trajectory deviation (expressed in meters) of the rover calculated for every occupied position with respect to the ideal path.
• The oscillating factor (OF), which takes into account the number of steering corrections performed by the rover to keep itself near to the ideal trajectory.

These two performance parameters are condensed into one single performance indicator, namely relative accuracy (RA), and are defined according to the following equation:

$$RA={\displaystyle \frac{1}{OF\cdot ATD}}$$

(5)

Hence, the simulation with the highest value of RA will correspond with the best combination of WPP and LD, because this means that the trajectory deviation and steering corrections are lower.

The RA trend as a function of WPP and LD is reported in Figure 13.

Observing the chart, it can be noted that the best results in terms of RA occur when LD and WPP are equal to 1 m and to 0.5 m, respectively (Figure 14).

Once the best combination was identified, the accuracy error of the rover’s position was implemented to bring the simulations closer to the real-world case. The accuracy error consists of a random location error, added to the rover’s current position, before the calculation of the steering direction. The accuracy error varies at every time cycle and can range from 0 to the maximum settable accuracy error.

For this study, a maximum accuracy error of 2 cm was implemented, which is the maximum admissible accuracy value for a GPS-RTK positioning system [45,46,47], thus placing it in a worst-case condition. Furthermore, to improve the performance of the rover, a threshold value of 2.5° on the possible minimum steering angle was implemented. In this way, it is possible to avoid steering micro-corrections, which decrease the RA value without an actual decline in the vehicle performance. In

Table 2. Virtual model simulation results.

Case	ATD [m]	OF	RA [m−1]	∆ RA %
Ideal Case	0.0756	11	1.202	0%
0.02 m Accuracy Error Case	0.1133	13	0.679	−43.54%
0.02 m Accuracy Error + 2.5° minimum steering angle threshold	0.1162	10	0.861	−28.4%

, the results of three cases, the ideal one, the one with the accuracy error, and the one with the accuracy error and the steering angle threshold, are displayed.

The third case represents the reference case, and it will be compared with the results obtained by the experimental field test.

3.2. Field Test Reuslts

The field tests were performed according to the input parameters defined in Table 1 on the field visible in Figure 9. The first step of the field tests consists of the acquisition of the eight checkpoints (Figure 15).

Then, the checkpoints and the values of LD and WPP, determined by the virtual model, were implemented in the algorithm. Hence, the field tests could be carried out correctly. Three field tests (Figure 16) were run to compare the experimental performance with the modeled tests. The parameters used for the field tests were the ones shown in Table 1 and they were the same as those used for the virtual analyses (WPP was set to 0.5 m and LD was set to 1 m) in order to compare them under the same conditions.

It must be noted that the algorithm works with a cartesian coordinate system, whereas the positioning system provides the rover’s position in terms of geodetic coordinates (latitude and longitude). Hence, the algorithm converts the geographical coordinates according to the following equation:

$$X=r_{earth}\cdot \cos \left(latitude\right)\cdot \cos \left(longitude\right)$$

(6)

$$Y=r_{earth}\cdot \cos \left(latitude\right)\cdot \sin \left(longitude\right)$$

(7)

where

• X and Y are the projections of the geodetic coordinates in a cartesian reference system.
• Latitude and longitude are the geodetic coordinates provided by the positioning system.
• r_earth is the mean value of the Earth’s radius and is equal to 6.371 × 10⁶ m.

Equations (6) and (7) are the projections of a sphere on a cartesian plane. This approximation of the geoid shape with a sphere surface can be considered valid when the considered surface is quite small like in this study. The trajectory of the three field tests obtained and referred to a cartesian coordinate system are shown in Figure 17.

The comparison between the field tests and the reference virtual case was made by evaluating the average trajectory deviations ATDs of each performance. Indeed, for real cases, it is quite impossible to evaluate the oscillating factor OF. In particular, during the simulation phase, the actual current position is always known, and the accuracy of the locating error operates only to determine the steering direction of the vehicle. Instead, during the real tests the current position of the vehicles is also affected by an accuracy error provided by the positioning system. The results of the field tests are shown in

Table 3. Field test results and comparison with the reference case.

Case	ATD [m]	∆ ATD %
Reference Case	0.1162	0%
Test 1	0.1063	−8.52%
Test 2	0.1207	3.87%
Test 3	0.1613	38.8%

.

The obtained results highlight that, in the majority of the performances carried out, the trajectory deviation is neglectable with respect to the virtual reference case. Actually, during Test 1, the performance was better than the virtual one. On average, the ATD percentage variation is around 10%. Speaking in absolute terms, the difference between the ATD of the real cases and the modeled one is just above 1 cm. Hence, the importance of the developed virtual model and its applicability in terms of developing the control logic for this kind of vehicle and applications emerged from the field tests campaign.

4. Conclusions

In this study, an autonomous driving strategy for an agricultural rover, equipped with a four-wheel differential drive system and operating in a vineyard/orchard environment was proposed. Then, a scale prototype was designed and assembled in order to verify the reliability of the developed autonomous driving algorithm. In this way, the virtual model developed could represent a powerful tool for the development of control logic for this kind of vehicle and these kinds of operative environments. The autonomous driving strategy is structured into two main parts: path planning and path following. The first step consists of the definition of the ideal trajectory that allows the rover to accomplish its mission. The second one allows the vehicle to follow the ideal trajectory in order to reach its specific goals. Two fundamental parameters must be tuned in order to enable the vehicle to follow the ideal trajectory properly, namely the look-ahead distance and the waypoint pitch distribution. Indeed, the aim of the virtual model is to find the best combination of these two parameters, on the basis of some performance indicators: average trajectory deviation, oscillating factor, and relative accuracy. Once the best combination was defined, an accuracy locating error and a minimum steering angle threshold were set. In this way, the behavior of the rover could be closer to the real case. At this point, a scale prototype was designed and assembled, and a vineyard/orchard replica was built in order to carry out some field tests and verify the applicability and reliability of the described motion strategy. From the campaign, it emerged that, in the majority of the performed tests, the differences with respect to the reference case were neglectable. So, the validity of the virtual model proposed can be considered verified and reliable. However, the results obtained from this study can be viewed as a starting point for further analysis and development. In particular, the virtual model can be improved especially during the execution of corners in order to reach higher values of relative accuracy. Another further improvement of the proposed strategy is the implementation of an obstacle avoidance strategy in order to avoid unexpected obstacles. In the end, the design of a 1:1 scale prototype is also necessary, so that several tests can be performed in a real vineyard/orchard environment.