A Hybrid ARO Algorithm and Key Point Retention Strategy Trajectory Optimization for UAV Path Planning
Abstract
:1. Introduction
- Considering more complex and realistic scenarios, we introduce a spherical obstacle model to better replicate scene characteristics. Subsequently, we propose a hybrid multi-strategy artificial rabbits optimization (HARO+) that utilizes spherical vector coordinates to enhance the efficiency of UAV path planning in intricate environments.
- To enhance early exploration capabilities and flexibility while ensuring better candidate solutions for the development phase, we propose a dual-exploration strategy switching mechanism, balancing exploration and exploitation stages. Additionally, we introduce a population migration memory mechanism to maintain population diversity during iterations, enhancing the ability to avoid falling into local optima.
- Considering the differential treatment of preliminary paths generated by HARO based on obstacle density, we propose the key point retention trajectory optimization strategy, HARO+. This approach effectively generates safe, smooth, and cost-effective UAV flight paths in complex 2D and 3D environments.
- HARO’s superior search performance is validated through comparisons with other methods using the CEC2017 test functions and various complex 2D/3D UAV flight scenarios. Additionally, the incorporation of the key point retention trajectory optimization strategy significantly reduces the fitness cost for both HARO+ and other methods (up to 4.5%), with a path point compression rate of approximately 50–80%, further validating the adaptability and compatibility of this optimization strategy in complex environments.
2. Related Work
2.1. UAV Path Planning
2.2. Artificial Rabbits Optimization Algorithm
3. Preliminaries
3.1. Definition of the UAV Path Planning Problem
3.1.1. Energy Constraint
3.1.2. Safety Constraint
3.1.3. Height Constraint
3.1.4. Attitude Angle Constraints
3.2. ARO Algorithm
3.2.1. Population Initialization
3.2.2. Detour Foraging (Exploration)
3.2.3. Random Hiding (Exploitation)
3.2.4. Energy Shrink
3.3. Douglas–Peucker Algorithm
4. The Proposed Methods
4.1. The Proposed HARO
4.1.1. Elite-Guided Exploration Strategy
4.1.2. Dual Exploration Strategy
4.1.3. Population Migration Memory Mechanism
4.1.4. The Algorithmic Process and Computational Complexity Analysis of HARO
Algorithm 1 Pseudocode of the HARO algorithm |
Input: The maximum iteration count T, the rabbit population size N, and the problem dimensionality D, and some other basic parameters. |
Output: The best position of the rabbit and its corresponding fitness value |
1: Initialize the positions of the rabbits using Equation (14). |
2: whiledo |
3: Determine the positions and fitness values of all individuals, and implement the memory storage mechanism. Compute the energy factor F as Equation (32). |
4: for to N do |
5: Calculate the factor A by using Equation (26); |
6: if then |
7: Select a rabbit at random from other individuals; |
8: if then |
9: Perform detour foraging by using Equations (15)–(18). |
10: else |
11: Perform other exploration strategy by using Equations (28)–(30). |
12: end if |
13: else |
14: Create d burrows and randomly select one for hiding by using Equation (24); |
15: Execute random hiding in accordance with Equation (22). |
16: end if |
17: Update the position of the individual by using Equation (25) |
18: end for |
19: Accomplish memory saving, and perform the population migration mechanism by using Equations (31)–(32). |
20: end while. |
4.2. HARO+ Trajectory Optimization
- (1)
- Considering the UAV safety constraints mentioned earlier, we define path points within the danger zone as key points. Based on the actual obstacle environment, set an appropriate threshold value, D.
- (2)
- Determine the Euclidean distance, , from each point in the flight path, P, to the centers of the obstacles it passes through. If is less than the preset danger zone radius, the path point belongs to a key point and needs to be retained; otherwise, path points outside this area can be ignored. According to the order in which the flight path passes through obstacles, these key points are sequentially stored in set , and the number of key points is denoted as n,
- (3)
- Utilize the DP algorithm to obtain the simplified set of path points . Then, traverse the key point set , adding the key point to set in order if it is not already present; otherwise, leave it unchanged. Set represents the final collection of simplified route points containing key points.
Algorithm 2 Calculate the distance between a point to a line segment in 3D space using the Douglas–Peucker algorithm |
Input: The point p, the starting point a of the line segment, and the ending point b of the line segment. |
Output: The distance from the point to the line segment. |
|
5. Simulation Experiments and Result Analysis
5.1. Numerical Experiments and Analysis
5.1.1. Operating Environment Setup
5.1.2. Results and Analysis of CEC2017 Benchmark Functions
5.1.3. Exploration–Exploitation Analysis
5.1.4. Non-Parametric Statistical Analysis
5.1.5. Ablation Study
5.2. Application of HARO+ in UAV Path Planning
5.2.1. Setting the Simulation Environment
5.2.2. HARO for 2D UAV Path Planning
5.2.3. HARO for 3D UAV Path Planning
5.2.4. HARO+ with Trajectory Optimization in 2D/3D
6. Conclusions and Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Fi | Index | AVOA | DBO | GWO | HHO | MPA | PSO | SSA | WOA | ARO | IARO | HARO |
---|---|---|---|---|---|---|---|---|---|---|---|---|
F1 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 5 | 7 | 10 | 8 | 6 | 11 | 3 | 9 | 4 | 1 | 2 | |
F3 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 4 | 10 | 8 | 5 | 3 | 9 | 7 | 11 | 6 | 1 | 2 | |
F4 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 6 | 7 | 9 | 8 | 3 | 11 | 4 | 10 | 5 | 1 | 2 | |
F5 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 7 | 6 | 5 | 8 | 2 | 11 | 9 | 10 | 3 | 4 | 1 | |
F6 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 7 | 6 | 5 | 9 | 4 | 11 | 8 | 10 | 2 | 3 | 1 | |
F7 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 7 | 6 | 5 | 8 | 2 | 11 | 9 | 10 | 3 | 4 | 1 | |
F8 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 6 | 9 | 4 | 7 | 2 | 11 | 8 | 10 | 5 | 3 | 1 | |
F9 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 6 | 8 | 5 | 9 | 2 | 10 | 7 | 11 | 3 | 4 | 1 | |
F10 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 6 | 7 | 4 | 9 | 2 | 11 | 8 | 10 | 5 | 3 | 1 | |
F11 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 5 | 9 | 8 | 7 | 2 | 11 | 6 | 10 | 3 | 4 | 1 | |
F12 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 6 | 8 | 9 | 7 | 2 | 11 | 5 | 10 | 4 | 3 | 1 | |
F13 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 6 | 9 | 10 | 8 | 2 | 11 | 5 | 7 | 4 | 3 | 1 | |
F14 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 7 | 8 | 10 | 9 | 2 | 5 | 6 | 11 | 4 | 3 | 1 | |
F15 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 7 | 9 | 11 | 8 | 2 | 6 | 5 | 10 | 4 | 3 | 1 | |
F16 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 6 | 7 | 4 | 9 | 1 | 11 | 8 | 10 | 5 | 3 | 2 | |
F17 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 8 | 6 | 4 | 10 | 2 | 11 | 7 | 9 | 5 | 3 | 1 | |
F18 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 8 | 10 | 7 | 9 | 2 | 5 | 6 | 11 | 4 | 3 | 1 | |
F19 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 6 | 8 | 10 | 9 | 2 | 7 | 5 | 11 | 4 | 3 | 1 | |
F20 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 7 | 6 | 5 | 9 | 2 | 11 | 8 | 10 | 4 | 3 | 1 | |
F21 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 6 | 7 | 5 | 9 | 1 | 11 | 8 | 10 | 4 | 3 | 2 | |
F22 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 6 | 8 | 5 | 9 | 4 | 11 | 7 | 10 | 2 | 3 | 1 | |
F23 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 8 | 6 | 5 | 10 | 1 | 11 | 7 | 9 | 3 | 4 | 2 | |
F24 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 8 | 6 | 4 | 10 | 2 | 11 | 7 | 9 | 3 | 5 | 1 | |
F25 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 5 | 8 | 9 | 7 | 1 | 11 | 4 | 10 | 6 | 3 | 2 | |
F26 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 7 | 6 | 4 | 9 | 1 | 11 | 8 | 10 | 3 | 5 | 2 | |
F27 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 7 | 6 | 4 | 9 | 1 | 11 | 8 | 10 | 3 | 5 | 2 | |
F28 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 5 | 8 | 9 | 7 | 3 | 11 | 4 | 10 | 6 | 1 | 2 | |
F29 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 7 | 6 | 5 | 9 | 2 | 11 | 8 | 10 | 4 | 3 | 1 | |
F30 | Mean | |||||||||||
Std | ||||||||||||
Best | ||||||||||||
Rank | 6 | 7 | 9 | 8 | 2 | 11 | 5 | 10 | 4 | 3 | 1 |
Function | AVOA | DBO | GWO | HHO | A, M.P. | PSO | SSA | WOA | ARO | IARO |
---|---|---|---|---|---|---|---|---|---|---|
F1 | ||||||||||
F3 | ||||||||||
F4 | ||||||||||
F5 | ||||||||||
F6 | ||||||||||
F7 | ||||||||||
F8 | ||||||||||
F9 | ||||||||||
F10 | ||||||||||
F11 | ||||||||||
F12 | ||||||||||
F13 | ||||||||||
F14 | ||||||||||
F15 | ||||||||||
F16 | ||||||||||
F17 | ||||||||||
F18 | ||||||||||
F19 | ||||||||||
F20 | ||||||||||
F21 | ||||||||||
F22 | ||||||||||
F23 | ||||||||||
F24 | ||||||||||
F25 | ||||||||||
F26 | ||||||||||
F27 | ||||||||||
F28 | ||||||||||
F29 | ||||||||||
F30 |
Function | Index | ARO | EARO | DEARO | MARO | Function | Index | ARO | EARO | DEARO | MARO |
---|---|---|---|---|---|---|---|---|---|---|---|
F1 | Mean | F17 | Mean | ||||||||
Std | Std | ||||||||||
Best | Best | ||||||||||
Rank | 3 | 4 | 2 | 1 | Rank | 4 | 3 | 2 | 1 | ||
F3 | Mean | F18 | Mean | ||||||||
Std | Std | ||||||||||
Best | Best | ||||||||||
Rank | 4 | 2 | 3 | 1 | Rank | 4 | 3 | 2 | 1 | ||
F4 | Mean | F19 | Mean | ||||||||
Std | Std | ||||||||||
Best | Best | ||||||||||
Rank | 4 | 2 | 3 | 1 | Rank | 4 | 3 | 2 | 1 | ||
F5 | Mean | F20 | Mean | ||||||||
Std | Std | ||||||||||
Best | Best | ||||||||||
Rank | 3 | 4 | 2 | 1 | Rank | 4 | 3 | 1 | 2 | ||
F6 | Mean | F21 | Mean | ||||||||
Std | Std | ||||||||||
Best | Best | ||||||||||
Rank | 3 | 4 | 2 | 1 | Rank | 4 | 3 | 1 | 2 | ||
F7 | Mean | F22 | Mean | ||||||||
Std | Std | ||||||||||
Best | Best | ||||||||||
Rank | 3 | 4 | 1 | 2 | Rank | 4 | 3 | 2 | 1 | ||
F8 | Mean | F23 | Mean | ||||||||
Std | Std | ||||||||||
Best | Best | ||||||||||
Rank | 4 | 3 | 2 | 1 | Rank | 4 | 3 | 1 | 2 | ||
F9 | Mean | F24 | Mean | ||||||||
Std | Std | ||||||||||
Best | Best | ||||||||||
Rank | 3 | 4 | 2 | 1 | Rank | 3 | 4 | 2 | 1 | ||
F10 | Mean | F25 | Mean | ||||||||
Std | Std | ||||||||||
Best | Best | ||||||||||
Rank | 4 | 1 | 3 | 2 | Rank | 4 | 2 | 3 | 1 | ||
F11 | Mean | F26 | Mean | ||||||||
Std | Std | ||||||||||
Best | Best | ||||||||||
Rank | 3 | 2 | 4 | 1 | Rank | 4 | 3 | 1 | 2 | ||
F12 | Mean | F27 | Mean | ||||||||
Std | Std | ||||||||||
Best | Best | ||||||||||
Rank | 4 | 2 | 3 | 1 | Rank | 4 | 2 | 3 | 1 | ||
F13 | Mean | F28 | Mean | ||||||||
Std | Std | ||||||||||
Best | Best | ||||||||||
Rank | 4 | 3 | 2 | 1 | Rank | 4 | 2 | 3 | 1 | ||
F14 | Mean | F29 | Mean | ||||||||
Std | Std | ||||||||||
Best | Best | ||||||||||
Rank | 4 | 3 | 2 | 1 | Rank | 4 | 3 | 2 | 1 | ||
F15 | Mean | F30 | Mean | ||||||||
Std | Std | ||||||||||
Best | Best | ||||||||||
Rank | 4 | 3 | 2 | 1 | Rank | 2 | 3 | 4 | 1 | ||
F16 | Mean | ||||||||||
Std | |||||||||||
Best | |||||||||||
Rank | 4 | 3 | 1 | 2 |
Scenario | Algorithms | Mean | Best | Std. | Rank | Scenario | Algorithms | Mean | Best | Std. | Rank |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | NGO | 5 | 2 | NGO | 3 | ||||||
DBO | 1 | DBO | 2 | ||||||||
IARO | Inf | - | 9 | IARO | Inf | - | 8 | ||||
PSO | 7 | PSO | 7 | ||||||||
SSA | 3 | SSA | 4 | ||||||||
WOA | 8 | WOA | Inf | - | 9 | ||||||
ARO | 4 | ARO | 5 | ||||||||
BWO | 6 | BWO | 6 | ||||||||
HARO | 2 | HARO | 1 | ||||||||
3 | NGO | 5 | 4 | NGO | 5 | ||||||
DBO | 3 | DBO | 3 | ||||||||
IARO | Inf | Inf | - | 9 | IARO | Inf | - | 9 | |||
PSO | 4 | PSO | 8 | ||||||||
SSA | Inf | - | 7 | SSA | 1 | ||||||
WOA | Inf | - | 8 | WOA | 6 | ||||||
ARO | Inf | - | 6 | ARO | 4 | ||||||
BWO | 1 | BWO | 7 | ||||||||
HARO | 2 | HARO | 2 |
Scenario | Algorithms | Mean | Best | Std. | Rank | Scenario | Algorithms | Mean | Best | Std. | Rank |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | NGO | 4 | 2 | NGO | 4 | ||||||
DBO | 2 | DBO | 3 | ||||||||
IARO | Inf | - | 9 | IARO | Inf | Inf | - | 9 | |||
SPSO | 6 | SPSO | 6 | ||||||||
SSA | 5 | SSA | 7 | ||||||||
WOA | Inf | - | 8 | WOA | 8 | ||||||
ARO | 3 | ARO | 2 | ||||||||
BWO | 7 | BWO | 5 | ||||||||
HARO | 1 | HARO | 1 | ||||||||
3 | NGO | 4 | 4 | NGO | 4 | ||||||
DBO | 2 | DBO | 3 | ||||||||
IARO | Inf | Inf | - | 9 | IARO | Inf | - | 9 | |||
SPSO | 5 | SPSO | 5 | ||||||||
SSA | Inf | - | 6 | SSA | Inf | - | 7 | ||||
WOA | Inf | - | 8 | WOA | Inf | - | 8 | ||||
ARO | Inf | - | 7 | ARO | 2 | ||||||
BWO | 1 | BWO | 6 | ||||||||
HARO | 3 | HARO | 1 | ||||||||
5 | NGO | 5 | |||||||||
DBO | 1 | ||||||||||
IARO | 9 | ||||||||||
SPSO | 6 | ||||||||||
SSA | 4 | ||||||||||
WOA | 7 | ||||||||||
ARO | 3 | ||||||||||
BWO | 8 | ||||||||||
HARO | 2 |
Scenario | Algorithms | Mean | Best | Std. | Algorithms | Mean | Best | Std. | Path Points | Improve | CR |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | NGO | NGO+ | 408 | 0.59% | 61.82% | ||||||
DBO | DBO+ | 316 | 0.11% | 47.88% | |||||||
ARO | ARO+ | 376 | 0.08% | 56.97% | |||||||
BWO | BWO+ | 386 | 1.76% | 58.48% | |||||||
HARO | HARO+ | 363 | 0.12% | 55.00% | |||||||
2 | DBO | DBO+ | 429 | 4.50% | 65.00% | ||||||
PSO | PSO+ | 444 | 4.47% | 67.27% | |||||||
ARO | ARO+ | 306 | 0.38% | 46.36% | |||||||
BWO | BWO+ | 361 | 2.48% | 54.70% | |||||||
HARO | HARO+ | 454 | 3.75% | 68.79% | |||||||
3 | NGO | NGO+ | 392 | 2.88% | 59.39% | ||||||
DBO | DBO+ | 414 | 0.65% | 62.73% | |||||||
PSO | PSO+ | 424 | 1.33% | 64.24% | |||||||
BWO | BWO+ | 135 | 0.11% | 20.45% | |||||||
HARO | HARO+ | 428 | 0.62% | 64.85% | |||||||
4 | DBO | DBO | 310 | 0.23% | 46.97% | ||||||
SSA | SSA | 287 | 0.33% | 43.48% | |||||||
BWO | BWO+ | 244 | 0.17% | 36.97% | |||||||
HARO | HARO | 327 | 0.29% | 49.55% |
Scenario | Algorithms | Mean | Best | Std. | Algorithms | Mean | Best | Std. | Path Points | Improve | CR |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | NGO | NGO+ | 436 | 0.63% | 66.06% | ||||||
DBO | DBO+ | 332 | 0.65% | 50.30% | |||||||
SPSO | SPSO+ | 504 | 0.46% | 76.36% | |||||||
SSA | SSA+ | 444 | 0.58% | 67.27% | |||||||
ARO | ARO+ | 418 | 0.69% | 63.33% | |||||||
BWO | BWO+ | 465 | 1.18% | 70.45% | |||||||
HARO | HARO+ | 368 | 0.75% | 55.76% | |||||||
2 | NGO | NGO+ | 544 | 0.87% | 82.42% | ||||||
DBO | DBO+ | 552 | 0.37% | 83.64% | |||||||
SPSO | SPSO+ | 547 | 0.59% | 82.88% | |||||||
SSA | SSA+ | 392 | 0.27% | 59.39% | |||||||
WOA | WOA+ | 414 | 0.11% | 62.73% | |||||||
ARO | ARO+ | 387 | 0.38% | 58.64% | |||||||
BWO | BWO+ | 514 | 1.23% | 77.88% | |||||||
HARO | HARO+ | 551 | 0.92% | 83.48% | |||||||
3 | NGO | NGO+ | 558 | 0.89% | 84.55% | ||||||
DBO | DBO+ | 532 | 0.81% | 80.61% | |||||||
SPSO | SPSO+ | 564 | 0.56% | 85.45% | |||||||
BWO | BWO+ | 269 | 0.22% | 40.76% | |||||||
HARO | HARO+ | 543 | 0.79% | 82.27% | |||||||
4 | NGO | NGO+ | 506 | 0.42% | 76.67% | ||||||
DBO | DBO+ | 505 | 0.83% | 76.52% | |||||||
SPSO | SPSO+ | 519 | 0.38% | 78.64% | |||||||
ARO | ARO+ | 518 | 0.58% | 78.48% | |||||||
BWO | BWO+ | 546 | 0.71% | 82.73% | |||||||
HARO | HARO+ | 502 | 1.21% | 76.06% | |||||||
5 | NGO | NGO+ | 437 | 0.91% | 66.21% | ||||||
DBO | DBO+ | 378 | 0.46% | 57.27% | |||||||
IARO | IARO+ | 503 | 1.44% | 76.21% | |||||||
SPSO | SPSO+ | 504 | 0.60% | 76.36% | |||||||
SSA | SSA+ | 421 | 0.56% | 63.79% | |||||||
WOA | WOA+ | 498 | 0.72% | 75.45% | |||||||
ARO | ARO+ | 374 | 0.23% | 56.67% | |||||||
BWO | BWO+ | 484 | 1.71% | 73.33% | |||||||
HARO | HARO+ | 406 | 0.23% | 61.52% |
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Share and Cite
Liu, B.; Cai, Y.; Li, D.; Lin, K.; Xu, G. A Hybrid ARO Algorithm and Key Point Retention Strategy Trajectory Optimization for UAV Path Planning. Drones 2024, 8, 644. https://doi.org/10.3390/drones8110644
Liu B, Cai Y, Li D, Lin K, Xu G. A Hybrid ARO Algorithm and Key Point Retention Strategy Trajectory Optimization for UAV Path Planning. Drones. 2024; 8(11):644. https://doi.org/10.3390/drones8110644
Chicago/Turabian StyleLiu, Bei, Yuefeng Cai, Duantengchuan Li, Ke Lin, and Guanghui Xu. 2024. "A Hybrid ARO Algorithm and Key Point Retention Strategy Trajectory Optimization for UAV Path Planning" Drones 8, no. 11: 644. https://doi.org/10.3390/drones8110644
APA StyleLiu, B., Cai, Y., Li, D., Lin, K., & Xu, G. (2024). A Hybrid ARO Algorithm and Key Point Retention Strategy Trajectory Optimization for UAV Path Planning. Drones, 8(11), 644. https://doi.org/10.3390/drones8110644