The study focuses on agricultural landscapes with irregular fields and pronounced elevation changes, where a UAV may need to travel between monitoring locations scattered across orchards, maize, wheat, rice and natural vegetation. The modeled terrain covered an elevation range of 60 metres, with a mean slope of 10 degrees and a maximum of 25 degrees. Fifty-two candidate monitoring sites were positioned in three-dimensional space around a fixed operating base. Each mission had to leave the base, visit every selected site once, collect data and return, making the planning problem a three-dimensional traveling-salesman problem with directed energy costs.

To calculate the cost of each candidate flight segment, the researchers divided movement into four stages: vertical climb to a common 80-metre cruise altitude, horizontal cruise, descent to the destination and a 10-second hover for data acquisition. Their model used a vertical speed of 3 metres per second, a horizontal speed of 12 metres per second, climb power of 2.5 kilowatts, descent power of 0.3 kilowatts, cruise power of 1.0 kilowatt and hover power of 0.5 kilowatt. Because climb and descent power differs, traveling between two sites can have different costs in opposite directions, making the resulting energy matrix asymmetric. A route was penalized for the sum of the energies of all directed segments, including the final return to base but excluding hover energy on that return.

EADGWO adapts an optimization method normally used for continuous search to the discrete problem of ordering monitoring sites. Each candidate wolf carries one random key for every site, and sorting those keys produces a visitation sequence. That sequence is decoded into a complete route and evaluated with the stage-based energy matrix. The same matrix guides an energy-aware nearest-neighbor initialization, fitness comparisons and local-search decisions. The method also uses opposition-based initialization, a nonlinear convergence schedule, changing weights for the three leading wolves and local operations that swap sites, relocate one site or reverse a section of a route. Only a candidate with lower energy is accepted, so these local refinements cannot increase modeled energy.

In an ablation experiment on all 52 sites, the complete method produced a mean energy use of 3,161.01 ± 56.37 kilojoules across 30 runs. Standard Grey Wolf Optimization averaged 3,947.77 ± 220.28 kilojoules, 24.89% more than EADGWO, with a paired effect size of 3.34 and a Holm-adjusted significance value of 7.30 × 10⁻⁶. Removing energy-aware initialization increased mean energy by 4.58%, while removing multi-neighborhood local search increased it by 2.87%. Disabling nonlinear convergence control and dynamic leader weights together produced a smaller 0.54% increase. The full method recorded paired win rates of 93.3%, 81.7% and 93.3% against those three ablated variants, and all comparisons remained statistically significant after correction for multiple testing.

Performance was also evaluated as the number of monitoring sites increased from 10 to 52. EADGWO achieved the lowest mean energy at every tested size, with reductions relative to standard Grey Wolf Optimization widening from 1.5% for 10 sites to 5.5% for 20, 10.8% for 30, 16.7% for 40 and 21.3% for 52. At 52 sites, EADGWO averaged 2,945.8 ± 4.1 kilojoules, compared with 2,995.8 kilojoules for nearest-neighbor routing, 3,291.9 kilojoules for a genetic algorithm, 3,559.3 kilojoules for particle swarm optimization and 3,583.5 kilojoules for differential evolution. The nearest-neighbor margin was only 1.7%, showing that a simple directed-energy heuristic captured much of the useful structure in that particular instance, whereas further search delivered larger gains against the other algorithms.

Search stability and computation time also changed with task size. The energy coefficient of variation for the 52-site task was approximately 0.1% for EADGWO and 7.8% for standard Grey Wolf Optimization. Mean runtime rose from 137.0 milliseconds for 10 sites to 158.1 milliseconds for 52 sites, an increase of about 15.4%. At the largest task size, EADGWO ran faster than all four evolutionary-comparison baselines, although the single-pass nearest-neighbor heuristic remained the fastest because it performed no iterative search. Repeated experiments with dispersed, random and clustered sets of 30 sites also produced the lowest mean energies for EADGWO: 1,916.2, 1,850.1 and 1,809.8 kilojoules, respectively. Its savings over standard Grey Wolf Optimization across these layouts ranged from 9.8% to 11.2%.

The researchers then transferred the 52-site layout into a six-degree-of-freedom closed-loop simulation built around a reconstructed scene near the Longji rice terraces. The simulated multirotor weighed 4 kilograms, with horizontal and vertical speed limits of 12 and 3 metres per second. Calm, steady-wind and gust conditions were tested using identical aircraft dynamics, controllers and random seeds for the two planners. EADGWO generated a planned trajectory of 10,570.84 metres and estimated energy of 3,551.96 kilojoules, compared with 29,040.26 metres and 9,456.76 kilojouts for standard Grey Wolf Optimization. During execution, EADGWO’s actual travel remained within 0.43% of its planned distance under every wind condition.

Wind disturbances raised the energy consumed by the EADGWO aircraft from 3,562.94 kilojoules in calm conditions to 3,588.69 kilojoules under steady wind and 3,768.02 kilojoules in gusts, which the researchers attributed to attitude adjustments and velocity compensation needed to reject disturbances. Mission duration rose from 3,167.82 seconds in calm air to 3,517.74 seconds under gusts, yet remained 57.31% shorter than the corresponding standard-GWO simulation. Trajectory-tracking root mean square error was 0.44 metres in steady wind and 0.67 metres in gusts, respectively 8.33% and 53.79% lower than for standard Grey Wolf Optimization. These execution results apply only to the simulated aircraft, terrain, controller and wind disturbances; no real-flight validation was performed.

Several limitations constrain how broadly the findings can be applied. The framework assumes fixed task sets and predefined flight parameters, and its closest evaluation was in simulated hilly terrain rather than a field campaign. It does not yet incorporate dynamic tasks, explicit endurance constraints, other terrain types or different aircraft platforms, and the offline sequence planner remains separated from low-level motion control. Under the fixed cruise altitude and task sets tested, most energy savings arose from shorter horizontal cruise distances; the contributions of climb and descent energy would require a different parameter setup in which operating altitudes also vary. The authors propose calibrating the energy model with field measurements, matching algorithms under equal computational budgets, generating continuous terrain-aware trajectories and eventually enabling replanning based on remaining battery energy. Until those steps are completed, the results support EADGWO as a promising computational method for the modeled conditions rather than as a demonstrated real-world endurance solution.

Subject of Research: Energy-aware optimization of multirotor UAV monitoring routes in hilly agricultural terrain

Article Title: Mission planning for multi-site UAV monitoring in hilly terrain by coupling a stage-based energy model with an improved Grey Wolf optimizer

Article References: Qian, S., Li, P., Yiming, G., Yang, L., & Chang, Y. (2026). Mission planning for multi-site UAV monitoring in hilly terrain by coupling a stage-based energy model with an improved Grey Wolf optimizer. Results in Engineering, 32, Article 113631. https://doi.org/10.1016/j.rineng.2026.113631

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113631

Keywords: UAV route planning, hilly agriculture, multirotor energy model, Grey Wolf Optimizer, task sequencing, flight endurance, closed-loop simulation, terrain-aware monitoring, Mission, planning, multi-site, monitoring