With the rapid advancement of UAV technology, surveying drones have become indispensable tools for proactive power system inspections. Path planning stands as a critical technology enabling autonomous surveying UAV operations, solving inspection routes to achieve full coverage while avoiding obstacles autonomously. Conventional approaches suffer from inefficient flight paths and prolonged inspection times, directly impacting operational productivity. To address these limitations, this study introduces a novel path planning algorithm specifically optimized for power line corridor inspections using surveying UAVs.
Global path planning identifies optimal routes in fully known environments, employing algorithms like RRT*, A*, Dijkstra, and ant colony optimization. Local path planning handles obstacle avoidance in partially known or unknown environments using methods like Dynamic Window Approach (DWA), genetic algorithms, artificial potential fields (APF), or neural networks. While APF creates virtual attractive/repulsive fields for navigation, it often ignores kinematic constraints and local minima. DWA simulates future trajectories from current velocities to ensure real-time obstacle avoidance. Though asymptotically optimal, classical RRT* exhibits slow convergence due to undirected random sampling. Our integrated framework overcomes these shortcomings through synergistic enhancements.
Algorithmic Foundations
Enhanced Bidirectional RRT*
Standard RRT* grows a tree from the start node by random sampling, rewiring neighbors to minimize path cost. Bidirectional RRT* accelerates this process by simultaneously expanding trees from start ($X_{start}$) and goal ($X_{goal}$) nodes. When new nodes from both trees lie within connection distance $L$, they merge into a complete path. However, isotropic sampling causes inefficient exploration. We introduce an obstacle-density heuristic function to direct tree growth:
$$Q(n) = \left(1 + \frac{1}{1 + e^{-m}}\right) \cdot I(n)$$
$$I(n) = \max(|x_i – x_j|, |y_i – y_j|)$$
$$m = \frac{\sum_{i=n_a}^{m_a} \sum_{j=n_b}^{m_b} \text{obs}(i,j)}{(m_a – n_a) \times (m_b – n_b)}$$
Here, $I(n)$ is the Chebyshev distance between nodes, $m$ represents obstacle spatial density, and $\text{obs}(i,j)$ marks obstacle grids (1: occupied, 0: free). This adaptive heuristic penalizes node expansion in cluttered regions, reducing redundant sampling by 63% compared to classical RRT*.
Keypoint Extraction Strategy
Raw RRT* paths contain excessive turns. We optimize this by extracting critical waypoints via collision checks:
- Define path node sequence $Q = \{q_1, q_2, \dots, q_n\}$.
- From $q_1$, connect $q_i$ to $q_{i+2}$. If the line intersects obstacles where minimal distance $D_{\min} < d$ (safety threshold), retain $q_{i+1}$ as keypoint.
- Repeat until reaching $q_n$, compiling keypoints into set $L$.
This simplifies global paths while preserving feasibility, as shown in Table 1.
| Metric | Original Path | Keypoint-Optimized Path | Reduction |
|---|---|---|---|
| Waypoints | 142 | 27 | 81.0% |
| Path Length (m) | 518.6 | 472.3 | 8.9% |
| Computation Time (ms) | 210 | 15 | 92.9% |
Adaptive Dynamic Window Approach
We modify DWA to incorporate global keypoints as sub-goals. The evaluation function becomes:
$$\max G(v_x, v_y, \omega) = \mu\left[\alpha \cdot \text{goal}(v_x, v_y, \omega) + \beta \cdot \text{dist}(v_x, v_y, \omega) + \gamma_t \cdot \text{vel}(v_x, v_y, \omega) + \tau \cdot \text{energy}(v_x, v_y, \omega)\right]$$
$$\text{goal}(v_x, v_y, \omega) = \sqrt{(x_g – x_t)^2 + (y_g – y_t)^2}$$
$$\text{energy}(v_x, v_y, \omega) = \int_t^{t+\Delta t} m \left( a_{xt} v_{xt} + a_{yt} v_{yt} + \lambda_t \omega \right) dt$$
where $\text{goal}(\cdot)$ minimizes distance to the next keypoint, and $\text{energy}(\cdot)$ penalizes high energy consumption from thrust and drag. Weights $\alpha, \beta, \gamma_t, \tau$ adapt based on obstacle proximity:
$$
\gamma_t =
\begin{cases}
k_1 \cdot \text{vel}_{\max} & \text{if } \text{Dist}(U, \text{obs}_i) < 2L \\
k_2 \cdot \text{vel}_{\text{nom}} & \text{otherwise}
\end{cases}
$$
Here, $L$ is the UAV step size. When obstacles are nearer than $2L$, velocity weight $\gamma_t$ increases to prioritize evasion. Surveying drone kinematics follow:
$$
\begin{bmatrix} x_{t+\Delta t} \\ y_{t+\Delta t} \\ \theta_{t+\Delta t} \end{bmatrix} =
\begin{bmatrix}
x_t + v_x \Delta t \cos \theta_t – v_y \Delta t \sin \theta_t \\
y_t + v_x \Delta t \sin \theta_t + v_y \Delta t \cos \theta_t \\
\theta_t + \omega \Delta t
\end{bmatrix}
$$
Fused Algorithm Framework
The hybrid algorithm operates in three phases:
- Global Planning: Enhanced bidirectional RRT* generates an initial path using obstacle-density heuristics.
- Path Simplification: Keypoints are extracted to create a minimized waypoint sequence.
- Local Execution: Adaptive DWA navigates between keypoints with real-time obstacle avoidance and energy optimization.
This fusion leverages rapid global exploration and reactive local adjustments, eliminating myopic behaviors in complex power corridor environments.
Simulation Results
Tests were conducted in MATLAB on 500m × 500m grid maps with varying obstacle densities. Performance metrics are summarized below:
| Algorithm | Path Length (m) | Planning Time (s) | Nodes Explored | Energy Cost (kJ) |
|---|---|---|---|---|
| Classical RRT | 643.2 ± 28.7 | 8.41 ± 1.32 | 892 ± 113 | 124.6 ± 9.8 |
| RRT* | 587.4 ± 24.5 | 12.63 ± 2.01 | 1,205 ± 98 | 112.3 ± 8.2 |
| Proposed Method | 407.8 ± 18.6 | 4.18 ± 0.74 | 318 ± 42 | 86.5 ± 6.3 |
Key observations include:
- Path Length: Reduced by 36.8% vs. RRT and 30.7% vs. RRT*.
- Planning Speed: 50.1% faster than RRT* and 60.9% faster than RRT.
- Energy Efficiency: 23% lower consumption than RRT* due to adaptive velocity tuning.
Conclusion
This research presents a fused path planning framework integrating enhanced bidirectional RRT* and adaptive DWA for power inspection surveying drones. By incorporating obstacle-density heuristics, keypoint extraction, and energy-aware velocity optimization, the algorithm achieves shorter, smoother, and more efficient flight paths. Simulations confirm significant improvements in planning speed, path quality, and energy utilization. Future work will explore GPU acceleration for real-time deployment in large-scale power networks and multi-drone coordination strategies.