## 3 Mathematical Models and Control Design  
To visualize the simulation scenario in the MATLAB/Simulink environment, the mathematical model of the wheeled mobile robot (WMR) is first defined in the code compiler. Next, the system checks for the presence of an obstacle. If an obstacle is identified, the distance to the obstacle is calculated. If no obstacle is detected, the system proceeds to monitor the WMR's status (Figure 1). If the distance to the obstacle is calculated, the system proceeds to compute the objective function. Following this, the algorithm settings are configured, collision detection is performed, and the data are stored in the memory cell. Subsequently, the system calculates possible collision avoidance strategies and maps the solution for the collision avoidance operation. This process yields an optimal path for the WMR. If the terminal criteria are not met, the system recalculates the objective function. If the terminal criteria are satisfied, the optimal strategy is evaluated, and the WMR continues its motion. After this, the system checks the WMR's monitoring status. If the WMR is not  
Figure 1: Simulation scenario of the current work. being monitored, the system verifies the continuation of the motion. If the WMR is being monitored, the process restarts from the beginning and repeats. The current work is motivated by the growing interest in autonomous wheeled mobile robots, a topic that holds significant promise for both scientific research and practical applications in agriculture. Research into the control of autonomous wheeled mobile robotic platforms in unstructured, obstacle-filled environments is particularly relevant and feasible [20]. For safe navigation in such challenging conditions, wheeled mobile robots must be equipped with robust collision avoidance systems. These systems rely on sensors, cameras, and advanced algorithms to detect obstacles and generate safe paths. Ensuring reliable and consistent performance of these collision avoidance mechanisms is critical for the safe operation of wheeled mobile robots. In Figure 2, the wheeled mobile robot's planned path to its goal is represented by a solid red line. A potential collision with an obstacle is indicated by a dotted red line, while the robot's mobility and maneuvering area are depicted by a dotted rectangle. This visualization highlights the importance of effective path planning and collision avoidance in dynamic and complex environments. * Wheeled Robots: Typically used in relatively flat and even terrains such as orchards, vineyards, or open fields. They are ideal for environments where the ground is stable and free from large obstacles. * Other Environments: In uneven, rocky, or muddy terrains (e.g., hilly areas or dense forests), wheeled robots may struggle. In such cases, tracked robots or legged robots might be more suitable due to their better stability and traction. * Wheeled Robots: Generally, they offer high speed and efficiency on flat surfaces. They are easier to control and require less energy compared to other types of robots. Figure 2: A wheeled mobile robot platform’s trajectory for avoiding obstacles [3]. The solid red line indicates the path traveled by the wheeled mobile robot. The red dashed line indicates the possibility of a collision-sion. The black dashed rectangle represents the robot’s past positions, and the black dotted rectangle outlines the entire agricultural-al field. Other Environments: In environments with dense vegetation or narrow pathways, robots with higher maneuverability (e.g., drones or legged robots) might be preferred. Drones can fly over obstacles, while legged robots can navigate through rough terrain. * Wheeled Robots: Often used for tasks like planting, spraying, harvesting, and soil analysis in open fields. They can carry heavy payloads and are suitable for repetitive tasks over large areas. * Other Environments: In environments requiring precise navigation or access to hard-to-reach areas (e.g., treetops or steep slopes), drones or specialized robots might be more effective.