SpaceX-Dragon-mpc

MPC control for the SpaceX Dragon spacecraft as it rendezvous with the ISS.

The ISS and the SpaceX Dragon spacecraft

The spacecraft is in circular orbit and its objective is to dock to the ISS. The simulation is implemented with a "sim to real gap" to account for unmodeled dynamics.

The MPC controller solves the following convex optimization problem :

$$ \begin{aligned} \min_{x_{1:N},u_{1:N-1}} \quad & \sum_{i=1}^{N-1} \bigg[ \frac{1}{2} (x_i - \tilde{x}_{ref, i})^TQ({x}_i - \tilde{x}_{ref, i}) + \frac{1}{2} u_i^TRu_i \bigg] + \frac{1}{2}(x_N- \tilde{x}_{ref, N})^TQ_f ({x}_N- \tilde{x}_{ref, N})\\ \text{st} \quad & x_1 = x_{\text{IC}} \\ & x_{i+1} = A x_i + Bu_i \quad \text{for } i = 1,2,\ldots,N-1 \\ & u_{min} \leq u_i \leq u_{max} \quad \text{for } i = 1,2,\ldots,N-1 \\ & x_i[2] \leq x_{goal} [2]\quad \text{for } i = 1,2,\ldots,N \end{aligned} $$

Docking with the MPC controller

State and control trajectories:

Technologies

The project was created with:

• Python 3.9.0
• numpy 1.24.2
• cvxpy 1.3.1
• matplotlib 3.6.2
• seaborn 0.12.2
• scipy 1.8.1

Installation

To use this project, install it locally via:

git clone https://github.com/elena-ecn/SpaceX-Dragon-mpc.git

The dependencies can be installed by running:

pip install -r requirements.txt

To execute the code, run:

python3 main.py