quadrotor_mpc

Trajectory tracking with a quadrotor.

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

Quadrotor and reference trajectory

The MPC controller solves the following optimization problem :

$$\begin{array}{rl}\underset{x_{1:N},u_{1:N-1}}{min}& \sum _{i=1}^{N-1}[(x_i-x_{i,ref}{)}^{T}Q(x_i-x_{i,ref})+(u_i-u_{i,ref}{)}^{T}R(u_i-u_{i,ref})]+\frac{1}{2}(x_N-x_{N,ref}{)}^T{Q}_f(x_N-x_{N,ref})\\ \text{s.t.}& x_1=x_{\text{IC}}\\ & x_{k+1}=f({\overline{x}}_k,{\overline{u}}_k)+[\frac{\partial f}{\partial x}{|}_{{\overline{x}}_k,{\overline{u}}_k}](x_k-{\overline{x}}_k)+[\frac{\partial f}{\partial u}{|}_{{\overline{x}}_k,{\overline{u}}_k}](u_k-{\overline{u}}_k)\text{for }i=1,2,\dots ,N-1\\ & u_{min}\le u_i\le u_{max}\text{for }i=1,2,\dots ,N-1\\ \end{array}$$

Trajectory tracking with MPC controller

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
• pandas 1.5.3
• jax 0.3.25

Installation

To use this project, install it locally via:

git clone https://github.com/elena-ecn/quadrotor_mpc.git

The dependencies can be installed by running:

pip install -r requirements.txt

To execute the code, run:

python3 main.py

License

The contents of this repository are covered under the MIT License.