Flight Plan Optimisation of Unmanned Aerial Vehicles with Minimised Radar Observability Using Action Shaping Proximal Policy Optimisation
Abstract
:1. Introduction
2. Related Work
2.1. Heuristic-Based Path Planning Approaches
2.2. Reinforcement Learning-Based Path Planning
2.3. Contributions
- A novel path-planning approach based on the PPO algorithm and an action-shaping mechanism that accelerates learning and avoids radar detection.
- A radar warning zone switching criteria is developed based on the Neyman–Pearson Criteria to improve the action selection in both warning and non-warning radar detection zones.
3. Problem Formulation
3.1. UAV Model
3.2. Technical and Theoretical Concepts
3.2.1. Radar Detection
3.2.2. Neyman–Pearson Criterion
- Signal-to-Noise Ratio (SNR): The SNR is a measure of the signal strength relative to the background noise. In the radar context, it helps to determine how easily a target can be detected by the radar. A higher SNR means better detectability of the target. SNR is calculated based on the distance between the UAV and the radar. The SNR decreases with the fourth power of the distance, i.e.,
- Eigenvalues of the Correlation matrix: The correlation matrix represents how similar or correlated the signals received by the radar are across different pulses or measurements. Suppose a radar transmits a series of pulses, and for each pulse, it receives a signal that may or may not contain the reflected signal from a target like a UAV. If the radar transmits N pulses, the signals it receives can be represented as a vector, where each entry corresponds to the received signal for one pulse. For a radar with N pulses and correlation , the eigenvalues of the correlation matrix are
- Detection threshold: The detection threshold is obtained by specifying the false alarm probability as [19]
- Detection probability: the detection probability is calculated by adding the contributions from each pulse while accounting for the SNR and the detection threshold, i.e.,
4. Methodology
- UAV and Radar State Information: these blocks provide the necessary information regarding both the locations of the UAV and radar, as well as the radar power, warning and detection ranges. This information plays a pivotal role in the decision-making process for action selection and manoeuvrability.
- Radar Warning: in this block, the state is analysed to verify if the UAV is within a radar’s warning zone. If the UAV is within a warning zone, then the PPO algorithm is applied for detection avoidance. Otherwise, it applies an action-shaping mechanism to select actions that drive the UAV towards the target location.
- Action-shaping mechanism: this mechanism is used only when the UAV is not within a radar’s warning range. Here, the action-shaping consists of reducing the action-space of the UAV to move only in the direction of the target goal and avoid using actions that may produce unnecessary movements.
- Actor-Critic PPO Module: this module consists of two main elements,
- Actor Network: which is responsible for the action selection based on a parametrised policy with parameters .
- Critic Network: which evaluates the value function with parameter that enables to improvement of the actor policy.
Both the actor and critic networks are updated using mini-batches of experiences collected from the environment–UAV interaction. - Reward function and policy update: the PPO algorithm uses a clipped objective function to prevent large and unstable updates. In the action-shaping implementation, the restricted action space complementary works with the clipped updates to stabilise the algorithm training and accelerate its convergence. The PPO updates the policy using a clipped objective based on the advantage estimate .The reward is designed to penalise actions leading to radar detection. This encourages the UAV to avoid those penalising paths, whilst moving towards to the location goal.
- Action and policy iteration: based on the reward and value function updates, the actor selects the next action that the UAV will apply to reach a new state that is not within the detection range of the radars. This process is repeated until the goal is reached or if a terminal condition is met (e.g., the maximum number of steps is reached).
4.1. Proximal Policy Optimisation (PPO)
4.2. Action Shaping PPO
Algorithm 1 Action shaping mechanism |
|
- Restricted Movement Integration: The action space is reduced based on the UAV’s position relative to the target goal and the radar warning zone. The UAV’s movement options are dynamically adjusted during training. Depending on its environment, the action space can be narrowed or expanded, ensuring the UAV avoids unnecessary movements that would lead to the exploration of suboptimal paths.
- Actor-Critic Structure: The use of separate actor and critic networks allows for more stable learning in environments with complex dynamics.
- Adaptive Action Selection: The model adapts the action space depending on whether the UAV is in a radar warning area, improving efficiency and safety.
- Faster Convergence: By limiting the action space to strategic movements, the model converges faster, requiring fewer training steps.
- Enhanced Safety: The restricted movement prevents the UAV from making large, unpredictable moves, ensuring it stays within safe zones during both training and deployment.
- If the UAV is in a non-detection zone, that is, the action-shaping mechanism is applied then the reward is where is the position of the UAV and is the position of the target goal.
- If the UAV moves to a previous visited state, then it is penalised with a reward of .
- If the UAV moves to a position that reduces the distance to the target, then a positive reward of is given.
- If the UAV enters into the radar detection range and exceeds a threshold of 0.2, then it is penalised by a reward of .
- If the UAV is within the radar range, then it is penalised by a reward of .
- If the UAV reaches the target then a positive reward of is given; otherwise, it is penalised with a reward of .
4.3. Modified Sparse Algorithm
- Total distance: this term accounts for the cumulative distance travelled. This term accounts for the cumulative distance travelled along the current path. The algorithm aims to minimise the overall distance, which aligns with operational efficiency and fuel conservation.
- Distance to Goal: This heuristic guides the path toward the goal. It is the Euclidean distance between the current node and the goal. This term encourages the UAV to move closer to the target in a straight line when possible.
- Cumulative Radar Detection Probability: It considers the cumulative radar detection probability encountered along the path. Lower detection probabilities are preferred, so paths that keep this metric low are favoured. The radar detection probability is computed using a Neyman–Pearson criterion-based model that accounts for factors like signal-to-noise ratio (SNR), and the characteristics of the radar (e.g., pulse number, correlation).
- Height Difference: This term measures the altitude change between consecutive nodes. Large altitude changes are undesirable due to aircraft performance limits, energy consumption, or increased radar visibility. For 2D environments, it can be set to zero.
- Immediate Radar Detection Probability: This term considers the radar detection probability at the current node. It ensures that paths moving into high-risk areas (high detection probability) are heavily penalised.
5. Results
5.1. Comparison against Traditional PPO
- Efficiency: the UAV using the action-shaping PPO reaches the goal much faster compared with the UAV using the standard PPO. This means that the action-shaping mechanism provides an effective tool to guide the UAV towards the goal without applying unnecessary actions.
- Detection probability: the cumulative detection probability is notably reduced which is critical for this particular implementation to ensure the survivability of the UAV.
- Path smoothness: as previously discussed, the path of the standard PPO is not smooth due to the random selection of actions in zones without radar detectability. In contrast, the proposed approach overcomes this issue such that the PPO is only applied in the coverage area of the radar.
- Distance travelled: this is a key benefit of the proposed approach since the UAV is capable of reaching the goal in less number of steps which directly affects the travel distance that is a critical element when the UAV resources are limited, e.g., battery time or fuel.
5.2. Scenario 1
5.3. Scenario 2
5.4. Scenario 3
5.5. Improvement of the Action-Shaping PPO
5.6. Limitations and Future Work
- Geometric Data of the Aircraft: this includes the dimensions of the aircraft such as its length, wingspan, height, and overall shape. In addition, the surface materials for the absorption of radar waves, and the panel configuration are critical aspects that affect the RCS.
- Data on Stealth Features: this covers the design features (e.g., edge alignment, RAM coating, cooling techniques) and operational profiles (e.g., typical flights and angles that the aircraft operates) that play important roles in the performance of the RCS.
- Radar Characteristics:
- -
- Radar frequencies that interact differently with the aircraft’s surface. Higher frequencies (shorter wavelengths) are more sensitive to smaller details on the aircraft’s surface, while lower frequencies (longer wavelengths) interact more with the overall shape.
- -
- Polarisation of the radar signal (vertical, horizontal, or circular) can affect how the radar waves interact with the aircraft. The RCS can vary depending on the polarisation of the incoming radar signal.
- -
- Incident Angle where the radar waves hit the aircraft is critical. RCS is highly dependent on the aspect angle, and the orientation of the aircraft relative to the radar source.
- Environmental Conditions: include both atmospheric conditions (e.g., humidity, temperature and pressure) and background noise which can reduce the radar signal strength and/or the radar readings.
- Radar Cross-section Data: such as monostatic and bistatic RCS. Here, the monostatic RCS is a measurement taken when the radar transmitter and receiver are at the same location. It is the most common method and provides a direct measure of how much energy is reflected back to the radar source. On the other hand, the bistatic RCS is the measurement taken when the radar transmitter and receiver are at different locations. These data help in understanding how radar waves are scattered in different directions, not just back towards the radar source.
- Computational Simulations:
- -
- Electromagnetic Modelling to predict the RCS, electromagnetic modelling techniques like the Method of Moments (MoM), Finite Element Method (FEM), or Finite Difference Time Domain (FDTD) are used. These simulations require detailed geometric and material data of the aircraft.
- -
- Simulation Parameters such as frequency range, incident angles, and polarisation settings, which need to align with the actual measurement conditions.
- Historical RCS Data: which consists of data from previous tests or from similar aircraft models used for comparison. This helps to understand the effectiveness of the stealth features and identify areas for improvement.
6. Conclusions
Author Contributions
Funding
Data Availability Statement
DURC Statement
Conflicts of Interest
Abbreviations
DC | Discretize continuous actions |
DQN | Deep Q-Networks |
FDTD | Finite Difference Time Domain |
FEM | Finite Element Method |
LSTM | Long Short-Term Memory |
MoM | Method of Moments |
PD | Probability Distribution |
PPO | Proximal Policy Optimisation |
RCS | Radar Cross section |
RA | Removing actions |
RL | Reinforcement Learning |
RPP | Real Path Planning |
UAV | Unmanned Air Vehicle |
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Symbol | Meaning |
---|---|
→ | Forward |
↑ | Upward |
↓ | Downward |
↗ | Forward-upward |
↘ | Forward-downward |
← | Backward |
↖ | Backward-upward |
↙ | Backward-downward |
No | Radar Detection | Warning Range | Radar Power | Pulse | Correlation | False Alarm |
---|---|---|---|---|---|---|
1 | 30 | 40 | 5 × 10−5 | 5 | 0.5 | 1 × 10−6 |
2 | 40 | 55 | 1 × 10−4 | 10 | 0.5 | 1 × 10−6 |
3 | 50 | 70 | 3.9063 × 10−3 | 15 | 0.5 | 1 × 10−6 |
No | Radar Detection | Weights |
---|---|---|
1 | 30 | (0, 1 × 10−4 , 0.8, 0, 0) |
2 | 40 | (1 × 10−6, 1 × 10−4, 8, 0, 1 × 102) |
3 | 50 | (1 × 10−9, 1 × 10−4, 8, 0, 9.5) |
Methods | Time Steps | Cum. Probability | Dist. Travelled |
---|---|---|---|
PPO | 74,879 | 49.99 | 86,048.72 km |
Action-shaping PPO | 887 | 15.99 | 1504.12 km |
Methods | Time Steps | Cum. Probability | Dist. Travelled |
---|---|---|---|
Modified sparse | 470 | 0.0 | 613.32 km |
Action-shaping PPO | 778 | 0.0 | 1394.76 km |
Methods | Time Steps | Cum. Probability | Dist. Travelled |
---|---|---|---|
Modified sparse | 636 | 0.0 | 767.72 km |
Action-shaping PPO | 681 | 0.0 | 1323.03 km |
Methods | Time Steps | Cum. Probability | Dist. Travelled |
---|---|---|---|
Modified sparse | 472 | 0.0 | 615.31 km |
Action-shaping PPO | 609 | 0.0 | 1197.18 km |
Methods | Time Steps | Cum. Probability | Dist. Travelled |
---|---|---|---|
Modified sparse | 472 | 0.0 | 615.31 km |
Action-shaping PPO | 609 | 0.0 | 1197.18 km |
Improved Action-shaping PPO | 444 | 0.0 | 1100.53 km |
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Ali, A.M.; Perrusquía, A.; Guo, W.; Tsourdos, A. Flight Plan Optimisation of Unmanned Aerial Vehicles with Minimised Radar Observability Using Action Shaping Proximal Policy Optimisation. Drones 2024, 8, 546. https://doi.org/10.3390/drones8100546
Ali AM, Perrusquía A, Guo W, Tsourdos A. Flight Plan Optimisation of Unmanned Aerial Vehicles with Minimised Radar Observability Using Action Shaping Proximal Policy Optimisation. Drones. 2024; 8(10):546. https://doi.org/10.3390/drones8100546
Chicago/Turabian StyleAli, Ahmed Moazzam, Adolfo Perrusquía, Weisi Guo, and Antonios Tsourdos. 2024. "Flight Plan Optimisation of Unmanned Aerial Vehicles with Minimised Radar Observability Using Action Shaping Proximal Policy Optimisation" Drones 8, no. 10: 546. https://doi.org/10.3390/drones8100546