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

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 (16)

• 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 $s_h$.