## 4 Key Enabling Technologies
### Multi-Machine Cooperative Scheduling Based on IHHO
\[min\ J_{2}=w_{1}\Delta x^{2}+w_{2}\Delta y^{2}+w_{3}\Delta\phi^{2} \tag{9}\]  
where \(w_{1}\), \(w_{2}\), and \(w_{3}\) are weight parameters. \(\Delta x\) and \(\Delta y\) represent the variation in current position coordinates, while \(\Delta\phi\) denotes the change in heading angle. The Pareto optimal solution is obtained using the \(\varepsilon\)-constraint method. The algorithm's flowchart is shown in Figure 7.0 To reduce MPC optimization time and improve real-time performance, this paper introduces an event-triggered warm-start mechanism. By initializing the MPC solver with historical data, redundant computations are avoided, enhancing computational efficiency [50]. An error evaluation criterion is established, where warm start is applied when the error remains below a predefined threshold, while a full recalculation is performed otherwise to ensure optimization effectiveness. Additionally, the prediction horizon is dynamically adjusted based on path complexity, shortening it in challenging scenarios such as sharp turns to improve system responsiveness. This approach significantly enhances MPC solving efficiency while maintaining computational accuracy, making it more suitable for large-scale agricultural machinery scheduling. To validate the superiority of the proposed algorithm, a Jiangsu Mode WF1404-2 tractor (Manufacturer: Jiangsu Mode Machinery, Jiangsu Province, China, wheelbase: 2.8 m, maximum front wheel steering angle: \(\pm\)0.44 rad) was selected as the simulation model. A deviated path was generated using a path planning algorithm, with noise introduced to simulate real farmland conditions. The experiments were conducted using Matlab R2022b software on a computer equipped with an Intel(r) Core(tm) i5-9400H CPU, 8 GB RAM, and the Windows 10 operating system. The simulation speed was set to 2.5 m/s. Through a series of step-by-step comparative experiments, the feasibility of conventional MPC, DD-MPC, F-SMC, and the proposed control scheme was evaluated. As shown in Figure 12, the Mean Absolute Error relative to y = 0 for each control method was 0.128025 for conventional MPC, 0.107817 for DD-MPC, 0.054832 for F-SMC, and 0.019409 for the proposed method. The results clearly demonstrate that the proposed method achieves the lowest tracking error, highlighting its effectiveness and superiority in enhancing control precision. After completing the agricultural machinery experimental platform, the test field at Xihua University was chosen as the test site for path planning and tracking experiments. The agricultural machinery's initial parameters were set as: a speed of 1 m/s, a heading angle of 0\({}^{\circ}\), and a starting point located at coordinates (31.118721, 104.480488). The proposed Multi-Objective Optimization algorithm was applied to plan the agricultural machinery's path within the experimental area, with the resulting coordinates provided in latitude and longitude format. Data were extracted using the ROS toolbox to plot the planned and actual trajectories of the agricultural machinery. As shown in Figure 13, the X and Y axes represent longitude and latitude, respectively, with the red solid line indicating the desired path and the black solid line representing the actual trajectory. The results demonstrate that the agricultural machinery can accurately follow the target path. At a travel speed of 1 m/s, the maximum tracking error is only 0.2 m, with an average error of 0.092 m. The proposed approach has proven to be accurate and stable in real-world environments, offering reliable support for the precise navigation of intelligent agricultural machinery. Figure 7.1 Chart of the MPC algorithm. Figure 7.2 Tracking Error Comparison Chart.