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--- |
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license: mit |
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language: |
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- en |
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tags: |
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- model-predictive-control |
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- mpc |
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- pytorch |
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- aerospace |
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- flight-control |
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- boeing-747 |
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- learned-dynamics |
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- neural-network |
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- continuous-control |
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- gymnasium |
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library_name: tensoraerospace |
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pipeline_tag: reinforcement-learning |
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model-index: |
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- name: MPC-OneStepMLP-B747-PitchControl |
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results: |
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- task: |
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type: model-predictive-control |
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name: Pitch Angle Tracking Control |
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dataset: |
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type: custom |
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name: Boeing 747 Longitudinal Dynamics Simulation |
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metrics: |
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- type: overshoot |
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value: 0.27 |
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name: Overshoot (%) |
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- type: settling_time |
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value: 1.40 |
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name: Settling Time (s) |
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- type: rise_time |
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value: 0.80 |
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name: Rise Time (s) |
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- type: peak_time |
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value: 1.70 |
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name: Peak Time (s) |
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- type: static_error |
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value: 0.038 |
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name: Static Error |
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- type: oscillation_count |
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value: 5 |
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name: Oscillation Count |
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- type: performance_index |
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value: 72.62 |
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name: Performance Index |
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- type: iae |
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value: 41.25 |
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name: IAE |
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- type: ise |
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value: 147.43 |
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name: ISE |
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- type: itae |
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value: 33.99 |
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name: ITAE |
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- type: dynamics_loss |
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value: 8.69e-6 |
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name: Dynamics Model MSE Loss |
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--- |
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# TorchMPC with Learned Dynamics (OneStepMLP) for Boeing 747 Pitch Angle Control |
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<div align="center"> |
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**Model Predictive Control with Neural Network Dynamics for Longitudinal Aircraft Control** |
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[](https://github.com/TensorAeroSpace/TensorAeroSpace) |
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[](https://opensource.org/licenses/MIT) |
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[](https://pytorch.org/) |
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</div> |
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## Model Description |
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This model combines **Model Predictive Control (MPC)** with a **learned neural network dynamics model (OneStepMLP)** to control the pitch angle (θ) of a **Boeing 747** aircraft in a longitudinal flight dynamics simulation. The approach first learns the aircraft dynamics from exploration data, then uses gradient-based MPC optimization to compute optimal control actions for reference tracking. |
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### Key Features |
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- **Data-driven dynamics**: Learns one-step transition model f(x, u) → Δx from exploration data |
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- **Gradient-based MPC**: Differentiable optimization through learned dynamics |
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- **Step response optimization**: Custom cost function for overshoot/settling time minimization |
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- **Warm-starting**: Efficient action sequence initialization across timesteps |
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### Intended Uses |
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- **Primary Use**: Automatic pitch angle tracking and stabilization for Boeing 747 aircraft simulation |
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- **Research Applications**: Benchmarking learning-based MPC algorithms for aerospace control systems |
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- **Educational**: Learning MPC concepts with neural network dynamics in aerospace applications |
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- **Hybrid Control**: Can be combined with analytical models for robust flight control |
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## Model Architecture |
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### Dynamics Model (OneStepMLP) |
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The dynamics model predicts state transitions using a multi-layer perceptron: |
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| Layer | Configuration | |
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|-------|---------------| |
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| Input | 5 (state_dim=4 + action_dim=1) | |
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| Hidden 1 | Linear(5, 256) + ReLU | |
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| Hidden 2 | Linear(256, 256) + ReLU | |
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| Output | Linear(256, 4) | |
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| Mode | Predict Δx (delta dynamics) | |
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**Total Parameters**: ~70K |
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### MPC Controller |
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| Parameter | Value | |
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|-----------|-------| |
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| Horizon | 20 steps | |
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| Iterations per step | 60 | |
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| Optimizer | Adam | |
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| MPC Learning Rate | 0.02 | |
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| Warm Start | Enabled | |
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| Track Best | Enabled | |
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### State Space |
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The observation vector consists of 4 states representing the longitudinal dynamics: |
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| Index | State | Description | Units | |
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|-------|-------|-------------|-------| |
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| 0 | u | Forward velocity perturbation | m/s (rad internally) | |
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| 1 | w | Vertical velocity perturbation | m/s (rad internally) | |
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| 2 | q | Pitch rate | rad/s | |
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| 3 | θ | Pitch angle (tracking target) | rad | |
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### Action Space |
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| Dimension | Description | Range | Rate Limit | |
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|-----------|-------------|-------|------------| |
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| 1 | Elevator deflection | [-25°, 25°] | ±10°/step | |
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## Training Details |
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### Data Collection |
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| Parameter | Value | |
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|-----------|-------| |
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| Collection Episodes | 1500 | |
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| Transitions Collected | 297,000 | |
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| Exploration Strategy | Multi-signal exploration | |
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| Signal Types | random_steps, unit_step, multi_step, ramp, sinusoid, multisine, chirp, square_wave, triangular_wave, sawtooth, doublet, pulse, gaussian_pulse, exponential, damped_sinusoid | |
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| Action Amplitude | 100% of action space | |
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### Dynamics Training |
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| Parameter | Value | |
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|-----------|-------| |
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| Epochs | 120 | |
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| Batch Size | 2048 | |
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| Learning Rate | 1e-4 | |
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| Loss Function | MSE | |
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| Final Loss | 8.69e-6 | |
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| Normalization | Enabled | |
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### MPC Cost Weights |
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| Weight | Value | Description | |
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|--------|-------|-------------| |
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| W_θ | 2000.0 | Pitch tracking weight | |
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| W_q | 0.2 | Pitch rate weight | |
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| W_action | 0.01 | Control effort weight | |
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| W_Δu | 5.0 | Control rate weight | |
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| Terminal | 10.0 | Terminal cost multiplier | |
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### Step Response Cost Configuration |
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| Parameter | Value | |
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|-----------|-------| |
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| W_overshoot | 8,000 | |
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| W_settle | 8,000 | |
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| W_sse_steady | 40,000 | |
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| W_time | 800 | |
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| W_osc | 500 | |
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| W_jerk | 50 | |
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| Overshoot limit | 0.05° | |
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| Settle band | 0.10° | |
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| Settle time target | 1.0 s | |
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### Environment Configuration |
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| Parameter | Value | |
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|-----------|-------| |
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| Environment | `LinearLongitudinalB747-v0` | |
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| Time Step (dt) | 0.1 s | |
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| Episode Duration | 20 s | |
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| Initial State | [0, 0, 0, 0] | |
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| Reference Signal | Step function | |
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| Step Amplitude | 1.0° | |
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| Step Time | 5.0 s | |
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### Training Infrastructure |
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- **Hardware**: CUDA GPU (recommended) / CPU |
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- **Framework**: PyTorch 2.0+ |
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- **Compile Mode**: reduce-overhead (CUDA only) |
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## Evaluation Results |
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### Performance Metrics |
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| Metric | Value | |
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|--------|-------| |
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| **Overshoot** | 0.27% | |
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| **Settling Time (±5%)** | 1.40 s | |
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| **Rise Time** | 0.80 s | |
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| **Peak Time** | 1.70 s | |
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| **Static Error** | 0.038 | |
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| **Oscillation Count** | 5 | |
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| **Performance Index** | 72.62 | |
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| **Damping Degree** | -0.002 | |
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### Integral Criteria |
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| Criterion | Value | |
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|-----------|-------| |
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| IAE (Integral Absolute Error) | 41.25 | |
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| ISE (Integral Squared Error) | 147.43 | |
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| ITAE (Integral Time-weighted Absolute Error) | 33.99 | |
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### Step Response Characteristics |
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The MPC controller demonstrates good step tracking performance with: |
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- ✅ Very low overshoot (~0.27%) |
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- ✅ Fast settling time (1.4s) |
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- ✅ Quick rise time (0.8s) |
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- ⚠️ Some oscillations (5 cycles) |
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- ⚠️ Small static error (0.038) |
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## Usage |
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### Installation |
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```bash |
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pip install tensoraerospace |
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``` |
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### Quick Start |
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```python |
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import numpy as np |
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import gymnasium as gym |
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import torch |
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from tensoraerospace.signals.standart import unit_step |
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from tensoraerospace.agent.mpc import MPCAgent |
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def pick_device() -> str: |
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if torch.cuda.is_available(): |
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return "cuda" |
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if hasattr(torch.backends, "mps") and torch.backends.mps.is_available(): |
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return "mps" |
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return "cpu" |
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# Setup environment |
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DT = 0.1 |
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TN = 20.0 |
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N_STEPS = int(TN / DT) + 1 |
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T = np.arange(N_STEPS, dtype=np.float32) * DT |
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# Create step reference signal (1 degree step at t=5s) |
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reference_signal = unit_step( |
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tp=T, |
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degree=1.0, |
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time_step=5.0, |
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output_rad=True, |
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).reshape(1, -1) |
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env = gym.make( |
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"LinearLongitudinalB747-v0", |
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number_time_steps=N_STEPS, |
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initial_state=np.array([[0.0], [0.0], [0.0], [0.0]], dtype=np.float32), |
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reference_signal=reference_signal, |
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dt=DT, |
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) |
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# Load pretrained agent |
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agent = MPCAgent.from_pretrained("TensorAeroSpace/torchmpc-mlp-b747-step-response") |
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agent.env = env |
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agent.to_device(pick_device()) |
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# Run evaluation |
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_ = env.reset() |
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agent.reset() |
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ref_theta_rad = reference_signal[0] |
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x_ref = np.zeros((21, 4), dtype=np.float32) # horizon + 1 |
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for step in range(N_STEPS - 2): |
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k = int(env.unwrapped.current_step) |
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x0 = np.asarray(env.unwrapped.model.xt, dtype=np.float32).reshape(-1) |
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# Set reference for horizon |
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ref_k = float(ref_theta_rad[min(k, len(ref_theta_rad) - 1)]) |
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x_ref[:, 3] = ref_k |
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action = agent.select_action(x0, x_ref=x_ref) |
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obs, reward, terminated, truncated, info = env.step(action) |
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if terminated or truncated: |
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break |
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``` |
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### Custom Dynamics Training |
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```python |
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# Collect exploration data |
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agent.collect_data( |
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num_episodes=1500, |
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max_steps=199, |
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exploration="signals", |
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signal_kinds=["random_steps", "sinusoid", "chirp", ...], |
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dt=0.1, |
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action_amplitude_frac=1.0, |
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) |
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# Train dynamics model |
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metrics = agent.train_dynamics( |
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epochs=120, |
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batch_size=2048, |
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loss="mse", |
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) |
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print(f"Final dynamics loss: {metrics['loss']:.2e}") |
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``` |
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## Comparison with Other Methods |
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| Method | Overshoot | Settling Time | Rise Time | Static Error | |
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|--------|-----------|---------------|-----------|--------------| |
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| **MPC-MLP** | 0.27% | 1.40 s | 0.80 s | 0.038 | |
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| DSAC | 0.99% | 0.40 s | 0.40 s | 0.0002 | |
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| PID (tuned) | ~5% | ~2.0 s | ~1.0 s | ~0 | |
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## Limitations |
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- **Fixed Aircraft Model**: Trained specifically on Boeing 747 longitudinal dynamics; may not generalize to other aircraft |
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- **Step Reference Focus**: Optimized for step reference tracking; performance on other signal types may vary |
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- **Simulation Gap**: Trained in simulation; real-world deployment would require additional validation |
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- **Computational Cost**: MPC optimization at each step requires more computation than pure RL policies |
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- **Linear Dynamics**: Based on linearized aircraft model around trim conditions |
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- **Some Oscillations**: The controller exhibits 5 oscillation cycles during settling |
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## Ethical Considerations |
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- **Not for Real Flight Control**: This model is for research and educational purposes only. It should NOT be used for actual aircraft control systems without extensive testing, certification, and regulatory approval. |
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- **Simulation Only**: All training and evaluation performed in simulation environments. |
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## Citation |
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If you use this model in your research, please cite: |
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```bibtex |
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@software{tensoraerospace2024, |
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title = {TensorAeroSpace: Advanced Aerospace Control Systems \& Reinforcement Learning Framework}, |
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author = {TensorAeroSpace Team}, |
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year = {2024}, |
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url = {https://github.com/TensorAeroSpace/TensorAeroSpace}, |
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license = {MIT} |
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} |
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``` |
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## Model Card Authors |
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TensorAeroSpace Team |
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## Model Card Contact |
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- **GitHub**: [TensorAeroSpace/TensorAeroSpace](https://github.com/TensorAeroSpace/TensorAeroSpace) |
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- **Documentation**: [tensoraerospace.readthedocs.io](https://tensoraerospace.readthedocs.io/) |
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- **Hugging Face**: [TensorAeroSpace](https://huggingface.co/TensorAeroSpace) |
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``` |
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