[MPC] Trajectory tracking with a quadrotor by LMPC
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1 min
2023-11-01
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