Stealth Aircraft Penetration Trajectory Planning in 3D Complex Dynamic Environment Based on Sparse A* Algorithm
Abstract
:1. Introduction
2. Algorithm
2.1. Aircraft Model
2.1.1. Aerodynamic Model
2.1.2. Engine Model
2.1.3. RCS Model
2.2. Flight Parameters and Radar Relative Angle Calculation
2.2.1. Solving Flight Parameters
2.2.2. Radar Relative Azimuth and Elevation Angle Calculations
2.3. Algorithm of Radar Detection Probability
2.3.1. Algorithm of Radar Detection Probability in a Single Position
2.3.2. Algorithm of Radar Detection Probability of the Entire Trajectory
2.4. Trajectory Planning Based on Sparse A* Algorithm
2.4.1. The Steps of the Sparse A* Algorithm
Algorithm 1. The sparse A* algorithm |
Input: Coordinates of the start node , coordinates of the goal node , weight, step size, grid properties, number of sectors S, radar layout. |
Output: Trajectory. |
1: Close Set = {};//Initialization |
2: Open Set = {};//Initialization |
3: Min Heap = {};//Initialization |
4: Current Node = ;//Initialization |
5: while () do |
6: Open Set = {Generated nodes} according to Figure 5; |
7: Remove the nodes in Min Heap from Open Set; |
8: Calculate the cost according to Equation (30); |
9: Min Nodes = nodes with least cost in each sector; |
10: Min Heap append the Min Nodes; |
11: Best node = node with least cost in Min Heap; |
12: Current Node = Best node;//Update the Current Node |
13: Close Set append the Current Node;//Update the Close Set |
14: Open Set = {} |
15: Record the parameters; |
16: if () then |
17: continue; |
18: else if |
19: break and exit. |
20: if (Min Heap is empty) then |
21: break and exit. |
20: end while |
21: Finish the calculation of the last step to the goal; |
21: Trace back the Close Set to get the Trajectory; |
22: return Trajectory |
2.4.2. Node-Generation Method
2.4.3. Cost Function Definition
3. Results
3.1. Stealth Aircraft Penetration in a Single-Radar Threat Environment
3.1.1. Conditions
3.1.2. Results of the Straight-Line Trajectory
3.1.3. Results of the Planned Trajectory
3.2. Stealth Aircraft Penetration in Three-Radar Threat Environments
3.2.1. Conditions
3.2.2. Results of the Straight-Line Trajectory
3.2.3. Results of the Planned Trajectory
3.3. Stealth Aircraft Penetration in Ten-Radar Threat Environment
3.3.1. Conditions
3.3.2. Results of the Straight-Line Trajectory
3.3.3. Results of the Planned Trajectory
3.4. Summary of the Simulation Results
4. Conclusions
- (1)
- The 3D-SASLRM method established in this paper is effective at reducing the radar detection probability during penetration compared to the trajectory before planning.
- (2)
- For the RCS fluctuation model based on azimuth and elevation angles in 3D space, executing minor maneuvers at dangerous positions is an effective method in scenarios with low-power radars to reduce radar detection probability, which essentially decreases the time of high RCS exposure to radar.
- (3)
- In scenarios with medium-power and high-power radars, a trajectory with low detection probability can be found using early large maneuvers to avoid approaching the radar valley radius.
- (4)
- When the area enclosed by the radar valley radius almost covers the entire penetration area and the number of radars is large, it becomes difficult for the aircraft to reach the destination safely in the penetration area.
- (5)
- There are several aspects of the study that still need more in-depth research.
- (a)
- The computation time for the scenario in Section 3.3 is around 10 h, which should be decreased.
- (b)
- The weight of the sparse A* algorithm needs to be adjusted manually, which should be made more automated.
- (c)
- More work needs to be carried out on trajectory smoothing in 3D space.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Radar Type | Power Factor | Single Valley Radius (km) |
---|---|---|
Low power | 16 | |
Medium power | 20 | |
High power | 50 |
Index | Location | (s) | N | ||||
---|---|---|---|---|---|---|---|
1 | (0, 50, 0) | 4 | 2 | 0.5 | 0 | 0 |
Radar Type | Step Size (km) | Lateral Angle (°) | Upward/Downward Angle (°) | Number of Expanded Nodes | |
---|---|---|---|---|---|
Low power | 3 | 8 | 0.5 | 9 | (, , , , ) |
Medium power | 3 | 8 | 0.5 | 9 | (, , , , ) |
High power | 3 | 8 | 0.5 | 9 | (, , , , ) |
Radar Type | Detection Probability before Planning | Detection Probability after Planning | Percentage Point Reduction in Detection Probability |
---|---|---|---|
Low power | 43.2% | 0.90% | 97.9% |
Medium power | 88.2% | 0.17% | 99.8% |
High power | 100.0% | 0.28% | 99.7% |
Index | Location | (s) | N | ||||
---|---|---|---|---|---|---|---|
1 | (−60, −60, 0) | 4 | 2 | 0.5 | 0 | 0 | |
2 | (−10, 50, 0) | 4 | 2 | 0.5 | 0 | 0 | |
3 | (60, −65, 0) | 4 | 2 | 0.5 | 0 | 0 |
Radar Type | Step Size (km) | Lateral Angle (°) | Upward/Downward Angle (°) | Number of Expanded Nodes | |
---|---|---|---|---|---|
Low power | 3 | 8 | 0.5 | 9 | (, , , , ) |
Medium power | 3 | 8 | 0.5 | 9 | (, , , , ) |
High power | 3 | 8 | 0.5 | 9 | (, , , , ) |
Radar Type | Detection Probability before Planning | Detection Probability after Planning | Percentage Point Reduction in Detection Probability |
---|---|---|---|
Low power | 42.0% | 0.57% | 98.6% |
Medium power | 91.7% | 7.82% | 91.5% |
High power | 100.0% | 4.20% | 95.8% |
Index | Location | (s) | N | ||||
---|---|---|---|---|---|---|---|
1 | (−80, 120, 0) | 4 | 2 | 0.5 | 0 | 0 | |
2 | (−80, 80, 0) | 4 | 2 | 0.5 | 0 | 0 | |
3 | (−80, 50, 0) | 4 | 2 | 0.5 | 0 | 0 | |
4 | (−80, −80, 0) | 4 | 2 | 0.5 | 0 | 0 | |
5 | (100, 100, 0) | 4 | 2 | 0.5 | 0 | 0 | |
6 | (100, 50, 0) | 4 | 2 | 0.5 | 0 | 0 | |
7 | (100, −60, 0) | 4 | 2 | 0.5 | 0 | 0 | |
8 | (−180, 150, 10) | 4 | 2 | 0.5 | 200 | 10 | |
9 | (−180, 80, 10) | 4 | 2 | 0.5 | 200 | 10 | |
10 | (−180, −120, 10) | 4 | 2 | 0.5 | 200 | 10 |
Radar Type | Step Size (km) | Lateral Angle (°) | Upward/Downward Angle (°) | Number of Expanded Nodes | |
---|---|---|---|---|---|
Low power | 3 | 8 | 0.5 | 9 | (, , , , ) |
Medium power | 3 | 8 | 0.5 | 9 | (, , , , ) |
High power | 3 | 8 | 0.5 | 9 | No solution |
Radar Type | Detection Probability before Planning | Detection Probability after Planning | Percentage Point Reduction in Detection Probability |
---|---|---|---|
Low power | 56.0% | 0.98% | 98.3% |
Medium power | 99.8% | 3.00% | 97.0% |
High power | 100.0% | No solution | No solution |
Scenario | Radar Type | Detection Probability before Planning | Detection Probability after Planning | Percentage Point Reduction in Detection Probability |
---|---|---|---|---|
1 | Low power | 43.2% | 0.90% | 97.9% |
Medium power | 88.2% | 0.17% | 99.8% | |
High power | 100.0% | 0.28% | 99.7% | |
2 | Low power | 42.0% | 0.57% | 98.6% |
Medium power | 91.7% | 7.82% | 91.5% | |
High power | 100.0% | 4.20% | 95.8% | |
3 | Low power | 56.0% | 0.98% | 98.3% |
Medium power | 99.8% | 3.00% | 97.0% | |
High power | 100.0% | No solution | No solution |
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Share and Cite
Guan, J.; Huang, J.; Song, L.; Lu, X. Stealth Aircraft Penetration Trajectory Planning in 3D Complex Dynamic Environment Based on Sparse A* Algorithm. Aerospace 2024, 11, 87. https://doi.org/10.3390/aerospace11010087
Guan J, Huang J, Song L, Lu X. Stealth Aircraft Penetration Trajectory Planning in 3D Complex Dynamic Environment Based on Sparse A* Algorithm. Aerospace. 2024; 11(1):87. https://doi.org/10.3390/aerospace11010087
Chicago/Turabian StyleGuan, Jingxin, Jun Huang, Lei Song, and Xiaoqiang Lu. 2024. "Stealth Aircraft Penetration Trajectory Planning in 3D Complex Dynamic Environment Based on Sparse A* Algorithm" Aerospace 11, no. 1: 87. https://doi.org/10.3390/aerospace11010087
APA StyleGuan, J., Huang, J., Song, L., & Lu, X. (2024). Stealth Aircraft Penetration Trajectory Planning in 3D Complex Dynamic Environment Based on Sparse A* Algorithm. Aerospace, 11(1), 87. https://doi.org/10.3390/aerospace11010087