A Predictive Control Strategy to Offset-Point Tracking for Agricultural Mobile Robots

Stephane Ngnepiepaye Wembe; Vincent Rousseau; Johann Laconte; Roland Lenain

cs.ROMar 30, 2026

A Predictive Control Strategy to Offset-Point Tracking for Agricultural Mobile Robots

Authors: Stephane Ngnepiepaye Wembe, Vincent Rousseau, Johann Laconte, Roland Lenain

Organizations: Université Clermont Auvergne, INRAE, UR TSCF, 63000, Clermont-Ferrand, France · SABI AGRI, 63360, Saint-Beauzire, France

Abstract

Robots are increasingly being deployed in agriculture to support sustainable practices and improve productivity. They offer strong potential to enable precise, efficient, and environmentally friendly operations. However, most existing path-following controllers focus solely on the robot's center of motion and neglect the spatial footprint and dynamics of attached implements. In practice, implements such as mechanical weeders or spring-tine cultivators are often large, rigidly mounted, and directly interacting with crops and soil; ignoring their position can degrade tracking performance and increase the risk of crop damage. To address this limitation, we propose a closed-form predictive control strategy extending the approach introduced in [1]. The method is developed specifically for Ackermann-type agricultural vehicles and explicitly models the implement as a rigid offset point, while accounting for lateral slip and lever-arm effects. The approach is benchmarked against state-of-the-art baseline controllers, including a reactive geometric method, a reactive backstepping method, and a model-based predictive scheme. Real-world agricultural experiments with two different implements show that the proposed method reduces the median tracking error by 24% to 56%, and decreases peak errors during curvature transitions by up to 70%. These improvements translate into enhanced operational safety, particularly in scenarios where the implement operates in close proximity to crop rows.

Figures & tables

Figure 1: An autonomous agricultural system, consisting of a robot linked to a mounted implement. In this configuration, the control accuracy is required at the implement-soil interaction point rather than at the center of the robot, which renders center-based control laws inadequate.

Figure 2: Notations used in this paper. Unlike standard robotics control problems, the objective is not to steer the robot’s center

O

to converge to the reference path

\Pi_{\text{ref}}

but rather to an offset point

I

that represents the agricultural implement in this context. The lateral perturbation

\dot{Y}_{P}

arises from the rear sideslip angle

\beta^{R}

, while the front sideslip angle

\beta^{F}

is observed at the front wheel. The tracking errors are computed in the Frenet frame

(\vec{\tau},\vec{n})

. The robot frame is such that

I_{y}

is positive when the implement point

I

is at the left, and

I_{s}

is positive when the point

I

is at the front. The theoretical velocity of the robot is denoted by

\vec{v}

, and the green arrow represents the actual velocity due to the sideslip angles.

Figure 3: Representation of the offset of the point O when the point

I

follows the reference path

\Pi_{\text{ref}}

. The desired tracking error of the point

O

is set to

y_{d}

, enabling the implement

I

to remain on the reference path. Tracking errors are computed in the Frenet base

(\vec{\tau},\vec{n})

Figure 4: Representation of the convergence process of an agricultural implement toward its reference path: Left: the implement is at the front, and is able to follow a pure exponential convergence. Right: the implement is located at the rear. To converge toward the reference path, it must first deviate from it, since the lever arm effect requires a vehicle rotation before convergence.

Figure 5: Illustration of the proposed approach: the predictive control input is defined as the one that minimizes the tracking error between the reference path

\Pi_{\text{ref}}

and the chosen convergence trajectory profile

h(s)

over a given prediction horizon

s_{h}

Figure 6: Evolution of the RMSE of the implement tracking error with respect to the prediction horizon

s_{h}

for different velocities with their associated optimal values (vertical dashed lines).

Figure 7: Bottom: Evolution of the median tracking error and interquartile range of the implement point as a function of speed. Each point corresponds to the median tracking error values throughout all the simulated trajectories. The shaded area represents the interquartile range at the

25\text{\,}\%

and

75\text{\,}\%

percentiles. Top: optimal prediction horizon

s_{h}

used for each speed.

Figure 8: Left: Median tracking error as a function of its longitudinal and lateral offsets of the implement control point. Right: Associated interquartile range at $25\text{\,}\%$ and at $75\text{\,}\%$ . $I_{s}$ denotes front ( $>0$ ) or rear ( $<0$ ) placement, $I_{y}$ left ( $>0$ ) or right ( $<0$ ); the origin $(0,0)$ marks the midpoint of the rear axle (red cross) and corresponds to a classical control framework.

Figure 9: Robotic platform used in this paper. It is equipped with two GNSS antennas to accurately estimate the position and orientation of the vehicle. A weeder is rigidly attached at the rear of the robot.

Figure 10: Pipeline of the system. Using onboard sensors, the positions of both the robot and the implement are known. A path-matching algorithm, based on the reference path and the current position of the robot, computes the tracking errors. These errors are then used to estimate the sideslip angles, which are subsequently incorporated into the control law to compute the required steering angle for the robot.

Figure 11: Reference path used in the first part of the experiments. It consists of three straight segments $(L1,L2,L3)$ and three circular arcs $(C1,C2,C3)$ with different curvatures. It starts with the straight line $L1$ and ends with $L3$ . This path features all transition types, which are straight-to-arc, arc-to-straight, and arc-to-arc.

	Implement position	Parameters
Front-Left (FL)	$I_{s}=$ 2.0\text{,}\mathrm{m}$$	$\lambda=0.15$ , $k_{\theta}=0.4$
Front-Left (FL)	$I_{y}=$ 0.5\text{,}\mathrm{m}$$	$s_{h}=$ 0.5\text{,}\mathrm{m}$$
Front-Right (FR)	$I_{s}=$ 2.0\text{,}\mathrm{m}$$	$\lambda=0.15$ , $k_{\theta}=0.4$
Front-Right (FR)	$I_{y}=$ -0.5\text{,}\mathrm{m}$$	$s_{h}=$ 0.5\text{,}\mathrm{m}$$
Rear-Left (RL)	$I_{s}=$ -2.0\text{,}\mathrm{m}$$	$\lambda=0.2$ , $k_{\theta}=0.8$
Rear-Left (RL)	$I_{y}=$ 0.5\text{,}\mathrm{m}$$	$s_{h}=$ 2.0\text{,}\mathrm{m}$$

Table 1: Parameters used in the validation of the control law experiment

Figure 12: Control Law Validation with Various Implement Positions: Front-Left, and Front-Right, Rear-Left and Rear-Right. Each plot shows both the reference path in dashed black and the trajectory followed by the implement. Two zoom-in views are presented: The first highlights the peak tracking error of the implement point during the first transition phase, which corresponds to a straight-line to circular-arc segment. The second one highlights the peak tracking error of the implement during the fourth transition phase, which corresponds to a circular-arc to circular-arc segment. Note that, because of the lever arm effect of the implement, the reference path is physically infeasible in some parts and the tracking error cannot be reduced to zero.

Method	Parameters
Lateral Servoing [ 25 ]	$k_{d}=0.7$ , $k_{p}=0.13$
Backstepping [ 25 ]	$k_{y}=0.15$ , $k_{\theta}=0.6$
MPC [ 23 ]	$Q=[1,5,1]$ , $R=[0.15,1]$ , $h=$ 1.0\text{,}\mathrm{s}$$
Predictive (Ours)	$\lambda=0.15$ , $k_{\theta}=0.4$ , $s_{h}=$ 0.5\text{,}\mathrm{m}$$

Table 2: Parameters used in the comparison experiment. All parameters have been hand-tuned to reach the best possible results on the given trajectory.

Figure 13: Comparison of the proposed approach with the three state-of-the-art methods in [ 25 , 23 ] . The straight segments (L1, L2, L3) and circular sections (C1, C2, C3) correspond to the areas highlighted in Figure 11 . In the graph, the right-hand plot shows the overall distribution of tracking errors for each method, with the median and the

1^{st}

and

3^{rd}

quartiles represented as box plots.

Implement tracking error	Lateral Servoing [ 25 ]	Back stepping [ 25 ]	MPC [ 23 ]	Predictive (Ours)
Median	0.06	0.06	0.09	0.04
IQR	0.18	0.11	0.11	0.06
$1^{st}$ t.p. max	0.34	0.33	0.24	0.17
$2^{nd}$ t.p. max	0.35	0.29	0.23	0.12
$3^{rd}$ t.p. max	0.46	0.34	0.12	0.17
$4^{th}$ t.p. max	0.78	0.65	0.27	0.31

Table 3: Quantitative comparison of each method, including the median and interquartile range of the implement tracking error, as well as the maximum tracking error observed in each transient phase. The unit in meters (

\text{\,}\mathrm{m}

). “t.p.” stands for transient phase.

Implement tracking error	Predictive (Ours) with S.O.	Predictive (Ours) without S.O.
Median during $C1$	0.03	0.06
Median during $C2$	0.05	0.14
Median during $C3$	0.04	0.11

Table 4: Sliding observer ablation analysis. The median tracking error of the implement point during the circular sections

C1

C2

, and

C3

is reported for the proposed predictive controller with and without the sliding observer (

\beta^{F}=0

and

\beta^{R}=0

). All values are expressed in meters. “S.O.” stands for Sliding Observer.

Figure 14: Reference path used in the agricultural scenario experiments. The trajectory begins with a straight line (L1), followed by a U-turn (C1). The second segment (L2) is modified to bypass a large natural obstacle, represented by the black box. It consists of three straight lines (L2-1, L2-2, L2-3) connected by two deviations (D1, D2), and ends with a U-turn (C2) returning the robot to its initial direction.

Figure 15: Agricultural implements used in the experiments: a weeder (top) and a spring tine cultivator (bottom). The spring tine cultivator works more deeply than the weeder and is subjected to greater forces.

Figure 16: Path-following results for the agricultural scenario using the methods from [ 25 ] and our proposed approach. The zoomed-in areas highlight the worst tracking errors of the methods in the deviations

D1

and

D2

, showing that the reactive methods from [ 25 ] lead to a tracking error over

1\text{\,}\mathrm{m}

, while our method halves these errors. Note that the trajectory is physically infeasible due to the lever-arm effect of the implement and considerable changes in curvatures, making zero-error tracking unattainable.

Implement tracking error	Lateral servoing [ 25 ]	Back stepping [ 25 ]	Predictive (Ours)
Weeder
Median	0.22	0.17	0.13
IQR	0.49	0.40	0.16
Max during $D1$	0.92	1.03	0.27
Max during $D2$	1.21	1.26	0.38
Spring Tine Cultivator

Table 5: Quantitative analysis of our method and the approaches of [ 25 ] , including nominal cases on the whole trajectory with median and interquartile range, and edge cases during the deviation segments

D1

and

D2

. The units are in meter (

\text{\,}\mathrm{m}

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