## 5 Conclusions  
(1) This study established an ideal model based on the seven-degree-of-freedom model of the high-clearance self-propelled electric sprayer. The stability of the sprayer's body was assessed using an instability judgment module. An upper-layer stability controller and a lower-layer torque distribution controller were designed to control the centroid sideslip angle, yaw rate, and wheel slip ratio during operation, achieving stability control of the sprayer.  
(2) A hierarchical stability control framework was adopted, and simulation experiments were conducted under four operating conditions: transit transport and field operations. The control strategies of \"SMC + optimal distribution\" and \"PID + average distribution\" control were compared with no control to analyze the stability characteristics under different control strategies. The simulation results demonstrate that the designed control algorithms optimized the stability parameters of the sprayer to varying degrees, improving the stability control of the high-clearance self-propelled electric sprayer with a four-wheel independent drive.  
(3) This paper advances the theoretical understanding of stability control for self-propelled sprayers, specifically in the areas of nonlinear model development, control strategy design, and simulation validation. By introducing fuzzy PID theory, SMC theory, and optimal torque distribution algorithms, it offers innovative technical approaches to stabilizing sprayers. These advancements hold significant technological value in the current trend toward the intelligentization and automation of agricultural machinery. In terms of practical application, the results of simulation trials substantiate the efficacy of the control strategies, providing a basis for the optimization and enhancement of self-propelled sprayer design and performance. This contributes to improved efficiency and safety in agricultural operations.  
Conceptualization, L.Z., C.H., Y.C. ([PERSON]), and P.G.; methodology, L.Z., C.H., and Y.C. ([PERSON]); software, L.Z. and C.H.; validation, L.Z., C.H., Y.C. ([PERSON]), P.G., J.L., and Y.C. ([PERSON]); formal analysis, L.Z., C.H., Y.C. ([PERSON]), P.G., J.L., and Y.C. ([PERSON]); investigation, Y.C. ([PERSON]), C.H., Y.C. ([PERSON]), and P.G.; resources, J.L., L.Z., and Y.C. ([PERSON]); data curation, L.Z., C.H., Y.C. ([PERSON]), P.G., J.L., and Y.C. ([PERSON]); writing--original draft preparation, L.Z., C.H., Y.C. ([PERSON]), J.L., and J.C.; writing--review and editing, L.Z., C.H., Y.C. ([PERSON]), P.G., J.L., Y.C. ([PERSON]), and J.C.; visualization, Y.C. ([PERSON]), P.G., and J.L.; supervision, C.H. and Y.C. ([PERSON]); project administration, Y.C. ([PERSON]); funding acquisition, Y.C. ([PERSON]) and J.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Key R&D projects in Shaanxi Province (2024 NC-YBXM-202, 2024 NC-YBXM-244, 2023-YBNY-241) and the innovational fund for scientific and technological personnel of Hainan Province (KJRC2023D38).  
Not applicable.  
The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.