[MPC] Trajectory tracking with a quadrotor by LMPC

Trajectory tracking with a quadrotor by LMPC.

The non-linear dynamics are linearized about a linearization trajectory \(\bar{x}, \bar{u}\) while the quadrotor aims to track a different reference trajectory \(x_{ref}, u_{ref}\).

The MPC controller solves the following optimization problem :

\[ \begin{aligned} \min_{x_{1:N},u_{1:N-1}} \quad & \sum_{i=1}^{N-1} \bigg[ (x_i - x_{i,ref})^TQ(x_i - x_{i,ref}) + (u_i - u_{i,ref})^TR(u_i - u_{i,ref}) \bigg] + \frac{1}{2} (x_N - x_{N,ref})^TQ_f(x_N - x_{N,ref}) \\ \text{s.t.} \quad & x_1 = x_{\text{IC}} \\ & x_{i+1} = f(\bar{x}_i, \bar{u}_i) + \bigg[\frac{\partial f}{\partial x} \bigg|_{\bar{x}_i, \bar{u}_i} \bigg](x_i - \bar{x}_i) + \bigg[\frac{\partial f}{\partial u} \bigg|_{\bar{x}_i, \bar{u}_i} \bigg](u_i - \bar{u}_i) \quad \text{for } i = 1,2,\ldots,N-1 \\ & u_{\min} \leq u_i \leq u_{\max} \quad \text{for } i = 1,2,\ldots,N-1 \\ \end{aligned} \]

Installation ————

To use this project, install it locally via:

git clone https://github.com/phatcvo/Quadrotor-MPC.git

The dependencies can be installed by running:

pip install -r requirements.txt

To execute the code, run:

python3 main.py