Coupling artificial hummingbird algorithm with energy balancing model for multi-UAV path planning in mountainous orchards

Multi-unmanned aerial vehicle (UAV) cooperative operations in mountainous orchards face four critical challenges: prohibitively high computational complexity due to large-scale 3D path planning, slow algorithmic convergence in rugged terrain, geometrically unstable flight path generation, and uneven energy consumption leading to premature battery depletion among heterogeneous drone fleets. To address these interconnected issues, this study proposes an integrated computational framework synergistically combining an Improved Artificial Hummingbird Algorithm (IAHA) with a recursive energy-balancing model. Empirical validation was conducted in a lychee orchard (23°9' N, 113°22' E), where centimeter-resolution digital elevation models (DEMs) were constructed via UAV photogrammetry at a spatial resolution of 5.41 cm/pixel. These DEMs enabled precise georeferencing of 57 mission-critical waypoints, comprising one depot at 25 m elevation and 56 operational points dynamically maintained at 10 m above heterogeneous tree canopies to accommodate variable crown heights. The core innovation lies in the IAHA, which significantly enhances the foundational artificial hummingbird algorithm through three algorithmic advancements: (1) Hybrid population initialization strategically injects one high-quality solution generated via nearest-neighbor greedy heuristic into a Monte Carlo-sampled population at a 1:99 ratio, simultaneously seeding solution quality while preserving population diversity. (2) Adaptive parameter control employs cosine annealing for dynamic step size modulation across iterations and exponential decay for directional perturbation coefficients, enabling nuanced exploration-exploitation tradeoffs. (3) Periodic local optimization automatically triggers a 2-opt refinement every 10 generations to eliminate topological path crossings, ensuring physically flyable trajectories. To counteract search stagnation, a visit-table-driven guidance system implements inverse probability selection to prioritize visitation of underexplored spatial regions, complemented by a tournament-based migration strategy that replaces 10% of the poorest-performing individuals per generation to maintain evolutionary pressure. For multi-UAV energy equilibrium, physics-based rotor power consumption models were extended through hierarchical recursive segmentation with bidirectional boundary adjustment. This technique recursively partitions waypoint clusters while co-optimizing segment boundaries to balance cumulative energy demands, subsequently employing weight-aware path aggregation that explicitly accounts for UAV payload differentials (e.g., spraying modules vs. sensors). The model enforces a strict upper bound of 5% total energy variance across the fleet—critical for operations in mountainous terrain where elevation changes exponentially impact power draw. Validation experiments demonstrated IAHA's superiority in single-UAV path optimization. Compared to five benchmark algorithms (AHA, ACO, GA, SA, PSO), IAHA achieved path length reductions of 25.7%, 2.0%, 20.6%, 12.74%, and 19.19%, respectively, in real-world orchard flights. Significantly, it maintained a path length standard deviation ratio of merely 1.24%, highlighting exceptional solution stability across trials. In multi-UAV deployment scenarios using a heterogeneous fleet (2×DJI Mavic 3 + 1×DJI Phantom 4 varying in thrust-to-weight ratios), the integrated IAHA-energy framework achieved an unprecedented energy consumption Coefficient of Variation (CV) of 1.16%. Concurrently, task completion time decreased by 56.52% compared to sequential single-UAV operations. The framework's efficacy stems from synergistic algorithmic innovations: dynamic parameter adaptation prevents premature convergence while maintaining exploration capability; visit-table guidance sustains population diversity; and recursive energy segmentation enables near-equitable workload distribution—the latter proving particularly critical for operations in mountainous topography where altitude variances induce nonlinear power demands. Statistical analysis confirms these components interact multiplicatively rather than additively. Theoretical contributions include establishing convergence guarantees for the modified hummingbird dynamics and proving recursive segmentation's computational tractability under constrained energy variance bounds. This study validated the feasibility of the algorithm framework through simulation. In future field flight tests, we will focus on verifying the engineering applicability of path planning and energy consumption optimization, including: three-dimensional trajectory tracking accuracy in complex mountainous environments, consistency between actual battery consumption and model predictions, and balance in flight duration among heterogeneous fleets.