Prescription-Map-Guided Bi-Level Multi-Objective Path Planning for UAV–UGV Collaborative Spraying and Fertilization in Smart Agriculture

Variable-rate pesticide spraying and fertilizer application require coordinated operation of heterogeneous agricultural machines, particularly in irregular fields where task demands, vehicle mobility, payload capacity, energy consumption, and resupply requirements vary spatially. However, most existing studies optimize aerial spraying or ground fertilization separately and do not jointly consider prescription-map demands, air–ground synchronization, pesticide-drift risk, and agricultural vehicle constraints. This study formulates collaborative UAV spraying and UGV fertilization as a multi-objective mixed-integer nonlinear programming problem with three objectives: minimizing system makespan, weighted energy consumption, and pesticide-drift penalty. A prescription-map-guided bi-level planning framework is proposed. At the upper level, the problem-specific TNSAOO solver determines UAV and UGV task sequences and collaborative resupply-point activation. At the lower level, adaptive Theta* and row-constrained Hybrid A* generate UAV spraying and UGV fertilization trajectories, respectively, while prescription-dependent application commands are assigned along active operation segments and a time-window mechanism detects and corrects residual air–ground conflicts. The framework was evaluated using 30 real farmland boundaries and 90 randomized prescription scenarios. Mean geometric coverage rates reached 98.82% for UAV spraying and 98.95% for UGV fertilization, while the mean prescription-compliance errors were 6.21% and 2.13%, respectively. In addition, 96.7% of the batch runs contained no more than one detected air–ground conflict, with a mean corrective waiting time of 1.07 s. Compared with traditional independent operation, collaborative planning reduced mean system makespan by 9.32%, weighted energy consumption by 7.21%, modeled drift penalty by 3.62%, and total path length by 5.79%. In the multi-objective comparison, TNSAOO obtained a mean hypervolume of 0.597 and a mean inverted generational distance of 0.375, showing competitive Pareto-search performance relative to established comparison algorithms, particularly NSGA-II. Additional terrain and drift sensitivity analyses produced systematic changes in energy, completion time, and modeled drift risk under controlled parameter perturbations. These findings demonstrate the simulation-based feasibility of jointly planning heterogeneous variable-rate spraying and fertilization under a shared prescription map. Physical field experiments remain necessary to validate spray deposition, fertilizer-distribution uniformity, terrain effects, and model calibration under environmental uncertainty.