1. Introduction
The operational reliability and economic viability of wind farms hinge critically on efficient maintenance strategies. Unmanned Aerial Vehicle (UAV) based inspection offers a promising solution for monitoring wind turbine blades, detecting defects like cracks, erosion, and icing that arise from prolonged operation in harsh environments. Compared to traditional manual or ground-based methods, UAV inspections provide superior accessibility, reduced downtime, and enhanced safety. However, the widespread adoption of autonomous Unmanned Aerial Vehicle inspection in complex environments, particularly mountainous onshore wind farms, remains limited. Current practices often rely heavily on manual remote piloting, constrained by factors such as intricate geography, limited Unmanned Aerial Vehicle endurance, and crucially, the hazardous aerodynamic conditions created by operational wind turbines.
The primary challenge stems from the complex, dynamic environment within an active wind farm. Mountainous terrain introduces significant 3D obstacles requiring frequent Unmanned Aerial Vehicle altitude and heading adjustments. More critically, operational turbines generate powerful wakes characterized by strong turbulence and velocity deficits downstream. These wakes significantly impact Unmanned Aerial Vehicle stability, flight precision, and energy consumption. Flying through these turbulent zones poses substantial risks to the Unmanned Aerial Vehicle and compromises inspection quality. Existing research predominantly focuses on 2D path planning for offshore wind farms during turbine shutdowns or overlooks the critical influence of aerodynamic effects on UAV flight dynamics in 3D space. Planning safe, efficient, and feasible inspection paths for UAVs that actively avoid wake-induced turbulence zones while navigating complex 3D terrain under stringent flight constraints is a significant and unresolved problem.
To address these critical gaps, we propose a novel intelligent path planning methodology specifically designed for Unmanned Aerial Vehicle inspection of operational wind farms, explicitly accounting for turbine wake effects and complex 3D terrain. Our core contributions are:
- Problem Formulation: We establish a comprehensive multi-objective, multi-constrained global inspection optimization model. The objectives are minimizing total inspection path cost (distance) and minimizing the mission time relative to the Unmanned Aerial Vehicle’s endurance limit. Constraints rigorously incorporate Unmanned Aerial Vehicle flight dynamics (e.g., turning limits, pitch/yaw angles, minimum flight distances, maximum altitude) and environmental threats (terrain obstacles, turbine structures, and defined wake exclusion zones).
- Wake and Terrain Modeling: We develop a virtual wind farm scenario based on real-world topographic data and integrate high-fidelity wake modeling using the FLORIS framework. Wake exclusion zones are defined based on turbulence intensity thresholds and Unmanned Aerial Vehicle operational limits.
- PITB-RRT Algorithm: We introduce the Policy Interactive Target Bias Rapidly-exploring Random Tree (PITB-RRT) algorithm. This novel path planner significantly enhances both path quality (efficiency) and computational efficiency (solution time) by intelligently integrating obstacle-aware sampling bias with tree expansion policies.
- Global Optimization with NSGA-II: We employ the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to optimize the visitation sequence of turbine inspection points, utilizing the feasible paths generated by PITB-RRT between all point pairs. This solves the Traveling Salesman Problem (TSP) variant under endurance constraints to find the global shortest inspection tour.
- Validation: We rigorously validate the proposed methodology using a realistic virtual scenario featuring 12 turbines in complex mountainous terrain. Results demonstrate substantial improvements in path length, computational speed, and robustness compared to baseline methods.
2. Problem Formulation: Unmanned Aerial Vehicle Inspection in Wind Farms
The core objective is to enable a single Unmanned Aerial Vehicle to autonomously inspect the blade surfaces of all wind turbines within a farm, minimizing operational costs primarily driven by time and energy consumption. This necessitates solving two interconnected problems: 1) Finding feasible, low-cost 3D flight paths between every pair of turbine inspection points that avoid all obstacles (terrain, turbines, wake zones) and respect UAV flight dynamics; 2) Determining the optimal sequence to visit all turbines such that the total path length (and thus flight time) is minimized and falls within the Unmanned Aerial Vehicle’s battery endurance limit.
2.1 Global Inspection Optimization Model
The problem is formulated as a constrained multi-objective optimization problem (MOP):
Objectives:
- Minimize Total Path Cost:
$$\min \sum_{i=1}^{n} \sum_{j=1}^{n} d_{ij}x_{ij}$$
Where:\(n\): Total number of turbine inspection points.\(d_{ij}\): Distance cost (path length) from inspection point\(i\)to point\(j\), obtained by solving the path planning problem between\(i\)and\(j\)considering obstacles and UAV constraints.\(d_{ij} \neq d_{ji}\)in general 3D terrain.\(x_{ij}\): Binary decision variable.\(x_{ij} = 1\)if the path from\(i\)to\(j\)is used in the tour, otherwise\(x_{ij} = 0\).
- Minimize Mission Time Penalty / Ensure Endurance:
$$\min \left( \sum_{i=1}^{n} \sum_{j=1}^{n} d_{ij}x_{ij} + n T_0 - T_m \right)^2$$
Where:\(T_0\): Time required to inspect one turbine (includes approach, hover, scan, and potentially repositioning time).\(T_m\): Unmanned Aerial Vehicle’s maximum rated flight endurance (battery life).\(n T_0\): Total time spent inspecting all\(n\)turbines.\(\sum_{i=1}^{n} \sum_{j=1}^{n} d_{ij}x_{ij}\): Total distance of the flight path between inspection points.- The term
\(\sum_{i=1}^{n} \sum_{j=1}^{n} d_{ij}x_{ij} / v_m\)represents the total flight time between points, where\(v_m\)is the Unmanned Aerial Vehicle’s rated cruise speed. For simplicity in the optimization objective, the penalty function squares the difference between the total mission time estimate\((\sum_{i=1}^{n} \sum_{j=1}^{n} d_{ij}x_{ij} / v_m + n T_0)\)and\(T_m\), heavily penalizing solutions exceeding endurance. Minimizing this penalty ensures solutions respect the\(T_m\)constraint.
Constraints:
- Flow Conservation (Each point visited once):
$$\sum_{j=1,j\neq i}^{n} x_{ij}=1,\quad \forall i\in\{1,2,...,n\}$$(Enter each point once)$$\sum_{i=1,i\neq j}^{n} x_{ij}=1,\quad \forall j\in\{1,2,...,n\}$$(Exit each point once) - UAV Flight Dynamics Constraints (Applied during PITB-RRT path planning between points):
- Maximum Range: Total flight distance cannot exceed Unmanned Aerial Vehicle range
\(L_{max}\).$$\sum_{k=0}^{N} ||p_{k+1} - p_k|| \leq L_{\text{max}}$$
Where\(p_k = (x_k, y_k, z_k)\)is the\(k^{th}\)waypoint on a path segment,\(N\)is the total number of segments. - Minimum Segment Length: Avoids overly sharp turns by ensuring minimum distance
\(L_{\text{min}}\)between consecutive waypoints.$$||p_{k+1} - p_k|| \geq L_{\text{min}}$$ - Yaw and Pitch Angle Limits: Constrain the Unmanned Aerial Vehicle’s turning agility for stability and energy efficiency. Define vector
\(\alpha_k = (x_k - x_{k-1}, y_k - y_{k-1})^T\)representing the horizontal movement between waypoints\(k-1\)and\(k\).
Yaw Angle Constraint (\(\psi_k \leq \psi_{\text{max}}\)):$$\psi_k = \arccos\left( \frac{\alpha_k^T \alpha_{k+1}}{||\alpha_k|| \cdot ||\alpha_{k+1}||} \right) \leq \psi_{\text{max}}$$
Pitch Angle Constraint (\(-\phi_{\text{max}} \leq \phi_k \leq \phi_{\text{max}}}\)):$$\phi_k = \arctan\left( \frac{z_k - z_{k-1}}{||\alpha_k||} \right)$$ - Maximum Flight Altitude: Limits altitude
\(z_k\)to avoid excessively strong winds aloft (\(H_{\text{max}}\)).$$z_k \leq H_{\text{max}}$$
- Maximum Range: Total flight distance cannot exceed Unmanned Aerial Vehicle range
- Environmental Constraints (Modeled in the virtual scene & handled by PITB-RRT):
- Terrain Obstacles: Mountainous terrain represented as a 3D surface. UAV path must stay above ground level but below
\(H_{\text{max}}\). - Turbine Structures: Physical collision avoidance zones around each turbine tower and nacelle.
- Wake Exclusion Zones: Cylindrical no-fly zones downstream of each operational turbine (defined in Section 2.3).
- Terrain Obstacles: Mountainous terrain represented as a 3D surface. UAV path must stay above ground level but below
2.2 Virtual Wind Farm Scenario
A realistic virtual environment was constructed to model the challenges:
- Terrain: Based on elevation data from a real onshore wind farm in the Canary Islands. Geographic data was converted into a detailed 3D mesh surface model. Terrain slope
\(S(x,y)\)at any point was constrained for realism:$$S(x, y) = \sqrt{\left( \frac{\partial Z(x, y)}{\partial x} \right)^2 + \left( \frac{\partial Z(x, y)}{\partial y} \right)^2 } < S_{\text{max}}$$
Where\(Z(x, y)\)is the ground elevation. The positions and hub heights of 12 turbines were placed according to realistic distributions on this terrain. - Inspection Points: Defined at a safe distance upstream (along the prevailing wind direction, negative x-axis) of each turbine rotor center. The distance was set to Rotor Diameter (D) + 15m. Points are numbered corresponding to their turbine.
2.3 Wind Turbine Wake Modeling and Exclusion Zones
Operational turbine wakes pose a significant threat to UAV stability. To model this:
- Wake Velocity Deficit: Used the Cumulative-Curl wake model implemented within the FLORIS framework:
$$\frac{\Delta u}{U_h} = C_q \exp\left({\frac{-r^m}{2\sigma_q^2}}\right)$$
Where\(\Delta u\)is the velocity deficit,\(U_h\)is the hub-height inflow speed,\(C_q\)is the wake contribution,\(\sigma_q\)is the wake width,\(r\)is radial distance from wake center,\(m\)is the super-Gaussian order. - Wake Turbulence Intensity (TI): Used the Crespo-Hernández model:
$$I_w = \sqrt{I_a^2 + \Delta I^2}$$$$\Delta I = \begin{cases} 0.362[1-\sqrt{1-C_T}] & x/D \in [0,5] \\ 0.73a^{0.832} I_a^{0.032} (x/D)^{-0.32} & x/D \in [5,15] \end{cases}$$
Where\(I_w\)is wake TI,\(I_a\)is ambient TI,\(\Delta I\)is added TI,\(a\)is axial induction factor,\(C_T = 4a(1-a)\)is thrust coefficient,\(x/D\)is normalized downstream distance,\(D\)is rotor diameter. - Wake Exclusion Zones: Based on simulation results (Figure 3) and considering industrial UAV limits (max wind speed tolerance ~12-15 m/s, max TI tolerance ~15-20%), cylindrical exclusion zones were defined downstream of each turbine:
- Radius:
\(R_{ex} = D\)(87m in our case). - Length:
\(5D\)(435m). This covers the near-wake region where turbulence intensity is highest and most dangerous for a small Unmanned Aerial Vehicle.
- Radius:
Table 1: Key Parameters of the Virtual Wind Farm Scenario
| Component | Parameter | Value/Description |
|---|---|---|
| Turbines | Number | 12 |
| Rotor Diameter (D) | 87 m | |
| Layout | Based on real placement on terrain mesh | |
| Terrain | Source | Canary Islands elevation data |
| Representation | 3D Grid Surface Model | |
Max Slope (\(S_{\text{max}}\)) | Economically constrained value | |
| Wake Exclusion | Shape | Cylinder |
Radius (\(R_{ex}\)) | D = 87 m | |
| Length | 5D = 435 m | |
| Basis | FLORIS Sim (Cumulative-Curl & Crespo-Hernández) | |
| Inspection Points | Location | Upstream, Safe Distance = D + 15m = 102m |
| UAV (Reference) | Model | DJI Dock 2 Compatible |
Max Range (\(L_{max}\)) | 43 km | |
Endurance (\(T_m\)) | 50 min | |
Cruise Speed (\(v_m\)) | 46.8 km/h (13 m/s) | |
| Max Wind Speed | 12-15 m/s (Tolerance) | |
| Max TI | 15-20% (Tolerance) |
3. Methodology
Our solution framework consists of two main stages, as illustrated in Figure 1: 1) Feasible Path Planning between all pairs of inspection points using PITB-RRT, respecting all environmental and UAV dynamic constraints; 2) Global inspection sequence optimization using NSGA-II, utilizing the pre-computed feasible paths and their costs.
3.1 Stage 1: PITB-RRT for Feasible Path Planning
The Rapidly-exploring Random Tree (RRT) algorithm is renowned for its probabilistic completeness and ability to handle high-dimensional spaces efficiently. However, the basic RRT suffers from slow convergence and highly suboptimal paths due to its inherent random sampling. Variants like RRT-Connect improve connection speed, and RRT* provides asymptotic optimality but at a high computational cost. Biasing sampling towards the goal (\(x_{goal}\)) improves convergence but can lead the tree into obstacles. Obstacle-based biasing improves obstacle avoidance but can hinder path quality. Often, sampling and expansion strategies are optimized independently, leading to suboptimal synergy.
We propose the Policy Interactive Target Bias RRT (PITB-RRT) to overcome these limitations. Its core innovation is a dynamic, obstacle-aware sampling bias policy that directly interacts with and guides the tree expansion process, significantly improving both path quality and computational efficiency.
3.1.1 PITB-RRT Algorithm
- Initialization: Set start point (
\(x_{start}\)), goal point (\(x_{goal}\)), step size (\(StepSize\)), maximum iterations (\(MaxIters\)), initial target bias probabilities (\(P_{b1}\),\(P_{b2}\)where\(0 < P_{b1} \leq 0.5 < P_{b2} < 1\)). Initialize tree\(T\)with\(x_{start}\). - Sampling (
\(X_{rand}\)Generation):- Generate a random sample
\(x_{rand}\)in free space and a random probability\(P_{rand} \in [0, 1]\). - Determine the current bias probability
\(P_{bias}\)based on the obstacle check between the latest added node\(x_{new}\)(or\(x_{start}\)initially) and\(x_{goal}\)using function\(f_o(x_a, x_b)\):$$f_o(x_a, x_b) = \begin{cases} 1 & \text{Obstacle on line }(x_a, x_b) \\ 0 & \text{No obstacle on line }(x_a, x_b) \end{cases}$$$$P_{bias} = \begin{cases} P_{b1} & \text{if } f_o(x_{new}, x_{goal}) = 1 \\ P_{b2} & \text{if } f_o(x_{new}, x_{goal}) = 0 \end{cases}$$ - Generate the guided sample
\(X_{rand}\):$$X_{rand} = \begin{cases} x_{rand} & \text{if } P_{rand} > P_{bias} \\ x_{goal} & \text{if } P_{rand} \leq P_{bias} \end{cases}$$
- Generate a random sample
- Tree Extension:
- Find nearest node
\(x_{nearest}\)in\(T\)to\(X_{rand}\). - Generate new node
\(x_{new}\)by moving from\(x_{nearest}\)towards\(X_{rand}\)by\(StepSize\). - Check collision on path segment
\((x_{nearest}, x_{new})\). If collision-free, add\(x_{new}\)to\(T\)with parent\(x_{nearest}\).
- Find nearest node
- Policy Update: Update
\(P_{bias}\)based on\(f_o(x_{new}, x_{goal})\)(as in Step 2). - Goal Check: If
\(||x_{new} - x_{goal}|| \leq StepSize\)AND collision-free path\((x_{new}, x_{goal})\), add\(x_{goal}\)to\(T\)with parent\(x_{new}\). Trace parent pointers from\(x_{goal}\)to\(x_{start}\)to extract path. Terminate Successfully. - Loop: Repeat steps 2-5 until
\(MaxIters\)reached. Terminate Unsuccessfully.
Key Insight: The sampling policy (\(P_{bias}\) choice) dynamically interacts with the tree’s state (\(f_o(x_{new}, x_{goal})\)):
- Obstacle Blocking Goal (
\(f_o = 1\)): Sets\(P_{bias} = P_{b1} \leq 0.5\). This reduces the chance of sampling\(x_{goal}\)(\(X_{rand} = x_{rand}\)most of the time), encouraging exploration around the obstacle to find a way past it. This prevents wasting iterations trying to head directly towards an unreachable goal. - Clear Path to Goal (
\(f_o = 0\)): Sets\(P_{bias} = P_{b2} > 0.5\). This increases the chance of sampling\(x_{goal}\)(\(X_{rand} = x_{goal}\)most of the time), greedily biasing the tree expansion directly towards the goal. This exploits the clear path to converge rapidly and generate a direct, low-cost path.
This policy ensures efficient exploration around obstacles and rapid convergence in open spaces, simultaneously optimizing for path cost and computation time. The UAV flight dynamics constraints (Min/Max segment length, Yaw/Pitch angles, Max altitude) are enforced during the collision-checking and node-adding phase within the 3D environment containing terrain, turbine structures, and wake exclusion zones.
3.2 Stage 2: NSGA-II for Global Sequence Optimization
Given \(n\) inspection points, the number of possible visitation sequences is \((n-1)! / 2\). Finding the optimal sequence (shortest total path) is an NP-hard problem. We utilize the paths \(d_{ij}\) computed between all point pairs \((i,j)\) by PITB-RRT as input to solve the global TSP-like problem under the endurance constraint using NSGA-II.
NSGA-II Workflow:
- Initialization: Generate an initial population
\(P_0\)of size\(M\). Each individual (chromosome) represents a random permutation of the\(n\)inspection points (a candidate tour). The starting point can be any turbine; the tour is circular (returns to start). - Fitness Evaluation: Calculate the two objective functions for each individual:
\(f_1 = \sum d_{ij}x_{ij}\)(Total Path Length)\(f_2 = \left( \sum d_{ij}x_{ij} / v_m + n T_0 - T_m \right)^2\)(Endurance Penalty)
- Fast Non-dominated Sorting: Rank individuals into non-dominated fronts (F1, F2, …) based on Pareto dominance.
- Crowding Distance Calculation: Calculate crowding distance within each front to estimate solution density.
- Selection: Select parents from
\(P_t\)using binary tournament selection based on rank and crowding distance (prefer lower rank, higher crowding). - Crossover & Mutation: Apply genetic operators to parents to generate offspring population
\(Q_t\)of size\(M\).- Crossover: Simulated Binary Crossover (SBX) adapted for permutations.
- Mutation: Swap mutation or inversion mutation.
- Combined Population: Form
\(R_t = P_t \cup Q_t\)(size\(2M\)). - New Population (
\(P_{t+1}\)): Fill\(P_{t+1}\)by selecting the best\(M\)individuals from\(R_t\)using non-dominated sorting and crowding distance. - Termination: Repeat steps 2-8 for
\(G\)generations (or until convergence). - Output: Select the solution from the first front (Pareto front) with the smallest
\(f_1\)(shortest path) that also has\(f_2 = 0\)(meets endurance constraint).
*Table 2: NSGA-II Parameters for Global Optimization*
| Parameter | Symbol | Value | Description |
|---|---|---|---|
| Population Size | \(M\) | 100 | Number of individuals in each generation. |
| Maximum Generations | \(G\) | 500 | Stopping criterion. |
| Crossover Probability | \(p_c\) | 0.9 | Probability of applying crossover to parent pairs. |
| Mutation Probability | \(p_m\) | 0.1 | Probability of applying mutation to an offspring. |
| Selection Operator | – | Tournament | Binary tournament selection based on rank & crowding. |
| Crossover Operator | – | SBX (Permutation) | Simulated Binary Crossover adapted for TSP. |
| Mutation Operator | – | Swap/Inversion | Randomly swap two genes or invert a subsequence. |
4. Results and Analysis
The proposed methodology was implemented in Python 3.8.15 and evaluated on a PC (CPU: Ryzen 7 6800H, GPU: RTX 3060 6GB, RAM: 16GB). Unmanned Aerial Vehicle parameters were based on specifications compatible with the DJI Dock 2 system.
4.1 PITB-RRT Performance Validation (Point-to-Point Paths)
Before applying it within the wind farm, the performance of PITB-RRT was rigorously benchmarked against standard RRT and RRT* in two synthetic 2D obstacle environments of different complexities (100m x 100m and 200m x 200m). All algorithms used a step size of 5m and a maximum of 1000 iterations. RRT* used a rewiring radius of 20m. PITB-RRT used \(P_{b1} = 0.5\), \(P_{b2} = 0.8\). Metrics were averaged over 100 successful runs per scenario/algorithm.
*Table 3: PITB-RRT Benchmarking Results (Average ± Std Dev)*
| Scenario | Algorithm | Path Length (m) | Iteration Count | Planning Time (s) | Avg. Turning Angle (°) | Max Turning Angle (°) |
|---|---|---|---|---|---|---|
| 1 (100m) | RRT | 127.22 ± 11.70 | 189.73 ± 106.64 | 1.416 ± 0.855 | ~60 | ~120 |
| RRT* | 109.07 ± 12.14 | 146.29 ± 64.23 | 14.933 ± 10.719 | ~45 | ~90 | |
| PITB-RRT | 99.11 ± 11.17 | 33.48 ± 9.88 | 0.369 ± 0.110 | ~30 | ~60 | |
| 2 (200m) | RRT | 257.06 ± 20.58 | 358.41 ± 112.44 | 0.554 ± 0.309 | ~60 | ~120 |
| RRT* | 241.86 ± 17.31 | 363.46 ± 121.73 | 2.583 ± 1.428 | ~45 | ~90 | |
| PITB-RRT | 231.85 ± 17.46 | 135.72 ± 42.80 | 0.234 ± 0.140 | ~30 | ~60 |
Key Observations:
- Path Efficiency: PITB-RRT consistently found the shortest paths, outperforming RRT by 22.1% (Sc1) / 9.8% (Sc2) and RRT* by 9.1% (Sc1) / 4.1% (Sc2). Paths were significantly smoother, with average turning angles around 30° and maximum angles around 60°, compared to much larger angles for RRT and RRT*. This smoothness is crucial for stable and energy-efficient Unmanned Aerial Vehicle flight.
- Computational Efficiency: PITB-RRT was dramatically faster than both baselines. It reduced iteration counts by 82.4% (Sc1) / 62.1% (Sc2) vs RRT and 77.1% (Sc1) / 62.7% (Sc2) vs RRT*. Planning time reductions were even more substantial: 73.9% (Sc1) / 57.8% (Sc2) vs RRT and 97.5% (Sc1) / 90.9% (Sc2) vs RRT*. This speed is essential for practical application.
- Robustness: Lower standard deviations across all metrics for PITB-RRT indicate higher solution consistency and robustness compared to RRT and RRT*.
4.2 Wind Farm Path Planning (PITB-RRT Application)
PITB-RRT, configured with \(StepSize = 20m\), \(MaxIters = 20,000\), \(P_{b1} = 0.5\), \(P_{b2} = 0.8\), and incorporating all UAV flight constraints (\(L_{\text{min}} = 20m\), \(\psi_{\text{max}} = 45^\circ\), \(\phi_{\text{max}} = 30^\circ\), \(H_{\text{max}} = 4000m\)), was used to find feasible paths between all 66 unique pairs of the 12 inspection points in the virtual wind farm. It successfully found all 66 paths in approximately 30 seconds. Figure 7 illustrates these paths navigating the complex 3D terrain and avoiding wake exclusion zones and turbines.
Example Path Analysis (Points 1 & 12): The longest path (between points 1 and 12) consisted of 112 waypoints over a length of 3303.42m. Crucially, analysis of the yaw (\(\psi_k\)) and pitch (\(\phi_k\)) angles along this path (Figure 8b,c) confirmed adherence to the defined constraints (\(\psi_k \leq 45^\circ\), \(-30^\circ \leq \phi_k \leq 30^\circ\)). Pitch angles were relatively smooth, avoiding abrupt climbs or dives. This demonstrates PITB-RRT’s ability to generate complex, collision-free 3D paths suitable for stable Unmanned Aerial Vehicle navigation under stringent dynamic constraints.
4.3 Global Inspection Path Optimization Results (NSGA-II Application)
Using the 66 pre-computed \(d_{ij}\) values from PITB-RRT as input, NSGA-II was applied to find the optimal inspection sequence. The traditional sequence (often used in practice: row-by-row, nearest start: [1, 2, 3, 7, 6, 5, 4, 8, 9, 10, 12, 11]) had a total path length of 13,122.69m. NSGA-II parameters were \(M=100\), \(G=500\), \(p_c=0.9\), \(p_m=0.1\). For comparison, Multi-Objective Ant Colony Optimization (MOACO) and Multi-Objective Grey Wolf Optimization (MOGWO) were also tested.
Table 4: Global Inspection Sequence Optimization Results
| Optimization Algorithm | Optimal Inspection Sequence | Path Length (m) | Flight Time (min) | Avg. Runtime (s) | Reduction vs. Traditional |
|---|---|---|---|---|---|
| NSGA-II | [1, 5, 4, 8, 9, 11, 12, 10, 6, 7, 3, 2] | 9,342.41 | 25.3 | 1.59 | 28.8% |
| MOACO | [1, 2, 3, 7, 10, 12, 11, 9, 8, 6, 5, 4] | 9,355.52 | 25.4 | 1.94 | 28.7% |
| MOGWO | [1, 3, 10, 4, 8, 11, 12, 7, 9, 5, 6, 2] | 10,073.84 | 27.3 | 1.36 | 23.2% |
| Traditional | [1, 2, 3, 7, 6, 5, 4, 8, 9, 10, 12, 11] | 13,122.69 | 35.5 | – | – |
Key Observations:
- Effectiveness: All optimization algorithms significantly outperformed the traditional sequence, reducing path length by 23.2% to 28.8%. NSGA-II found the absolute shortest path (9342.41m).
- Efficiency: The flight time for the NSGA-II optimized path was only 25.3 minutes (based on
\(v_m = 13 m/s\)), well within the Unmanned Aerial Vehicle’s 50-minute endurance limit (\(T_m\)). This leaves ample time (approx. 24.7 minutes) for the required hover-and-scan inspection time at each turbine (\(nT_0 = 12 \times T_0\)), assuming\(T_0 \approx 2\)minutes per turbine is feasible. MOACO yielded a very close solution (9355.52m, 25.4 min flight time). MOGWO performed noticeably worse. - Computational Cost: NSGA-II achieved the best solution with an average runtime comparable to MOGWO and faster than MOACO (1.59s vs 1.94s), demonstrating its efficiency for this problem size.
- Solution: The NSGA-II sequence (1->5->4->8->9->11->12->10->6->7->3->2) represents an efficient traversal that minimizes backtracking and long jumps across the farm, effectively navigating the terrain and wake zone constraints embedded in the
\(d_{ij}\)costs. Figure 9 illustrates this optimal global path.
5. Conclusion
This study presented a comprehensive and effective methodology for autonomous Unmanned Aerial Vehicle path planning in operational wind farms, explicitly addressing the critical challenges of complex 3D terrain and hazardous turbine wake effects. The core contributions – the PITB-RRT algorithm for efficient and robust point-to-point path planning under UAV dynamic constraints and the integration with NSGA-II for global inspection sequence optimization – have been rigorously validated.
Key conclusions are:
- Holistic Problem Formulation: The developed multi-objective, multi-constrained optimization model effectively captures the real-world complexities of Unmanned Aerial Vehicle inspection in active wind farms, balancing path minimization with Unmanned Aerial Vehicle endurance limits while incorporating crucial flight dynamics and environmental threats.
- PITB-RRT Superiority: The novel PITB-RRT algorithm demonstrably outperforms classical RRT and RRT* in both path quality (shorter, smoother paths) and computational efficiency (significantly faster planning times). Its dynamic obstacle-aware sampling policy is key to this success, enabling efficient exploration around obstacles and rapid convergence in open spaces. Its application within a realistic 3D wind farm scenario confirmed its ability to generate feasible paths respecting UAV flight constraints and avoiding terrain, turbines, and wake exclusion zones.
- Effective Global Optimization: The NSGA-II algorithm efficiently solved the global inspection sequence optimization problem using the pre-computed feasible paths. It found the shortest possible tour (9342m, 25.3 min flight time), reducing the path cost by 28.8% compared to a traditional row-by-row approach and comfortably meeting the Unmanned Aerial Vehicle’s endurance constraint.
- Practical Viability: The entire methodology, from path planning to sequence optimization, operates within computationally feasible timeframes (seconds to tens of seconds for the tested scenario), making it suitable for practical deployment. The significant reduction in path length directly translates to shorter mission times, lower energy consumption, reduced operational costs, and potentially increased inspection frequency or coverage.
Future Work: Directions include integrating real-time wind condition updates into the wake model and path planner, extending the method to multi-Unmanned Aerial Vehicle cooperative inspection scenarios, incorporating detailed battery consumption models, and testing the approach with physical UAVs in controlled wind farm environments. The PITB-RRT algorithm also holds promise for path planning in other complex 3D environments beyond wind farms, such as urban air mobility or industrial inspection. This work provides a significant step towards fully autonomous, efficient, and safe Unmanned Aerial Vehicle operations within the critical renewable energy sector.