Table of Contents
Formula Student model-based trajectory optimization algorithm. This algorithm is shared as part of my Final Degree Thesis. Developed during the 2021-22 Formula Student season, it's an offline trajectory optimization approach relying on a dynamic bicycle model which is avaluated for the whole midline path in order to find the optimal path. This approach can be seen as a one-time MPC execution with an horizon lenght (or prediction horizon) as long as the given midline.
This is a tailored motion planning solution developed for CAT14X & CAT15X BCN eMotorsport cars. If you plan to use this algorithm in any Formula Student Competition the only thing I ask for is to ALWAYS REFERENCE the team BCN eMotorsport.
- Ubuntu 20.04
- ROS Noetic
- CasADi using Ipopt solver
- Eigen3
- as_msgs: self-defined ROS msgs pkg. You may change it for yours, adapting the necessary functions
NOTE: CasADi should be built from sources in your /home directory, where this pkg will look for it. If you have installed CasADi somewhere else adapt the CMakeLists.txt before building this pkg.
In order to install casadi from source, follow this tutorial.
When building CasADi from source the Ipopt solver is already included so the Building CasADi from sources section is the only one to follow from the tutorial mentioned above.
For specific information on how the trajectory optimization procedure is done please read this thesis.
The most important advantage of this optimization algorithm is that it is not based on any geometrical approach, but it tries to find the optimal race line by taking into account the constraints imposed by the dynamic bicycle model. This way, apart from the actual race line, an optimal state for each point of the trajectory is obtained. This means that it also outputs vx, vy and yawrate profiles as well as steering and throttle commands profiles.
FSG2019 track results:
For more results read this.
This pkg includes three different nodes (or executables), which are thought to be run in the following order:
midline(offline) executable is meant to be executed through midline.launch. It reads the detected cones during a complete run and saves the midline trajectory.optimizer(offline) executable is meant to be executed through optimizer.launch. It reads the midline trajectory, sets up the Optimization Problem and solves it. It saves the results in x_opt file.tro(online) executable is meant to be executed through tro.launch. It's the only node thought to run online. It reads the Optimization Problem solution and computes the optimal trajectory, as well as interpolating the optimal states, before publishing the partial trajectory data to the ROS network.
Explanation of all the parameters used:
| Parameter | Summary | Value [SI] |
|---|---|---|
| Qs | Progress rate weight | 1.0 |
| Qslip | Slip difference weight | 0.1 |
| Rd | Steering rate weight | 1.4 |
| Ra | Acceleration rate weight | 0.3 |
| RMtv | Additional moment weight | 1.0 |
| Bf | Pacejka Constant | 10.5507 |
| Br | Pacejka Constant | 10.5507 |
| Cf | Pacejka Constant | -1.2705 |
| Cr | Pacejka Constant | -1.2705 |
| Df | Pacejka Constant | 2208.0635 |
| Dr | Pacejka Constant | 2563.599 |
| Lf | Distance from CoG to front axis | 0.708 |
| Lr | Distance from CoG to rear axis | 0.822 |
| L | Total car's length | 2.72 |
| W | Total car's width | 1.5 |
| m | Car's mass | 210.0 |
| Iz | Inertial moment around z axis | 180.0 |
| rhoair | Air's density | 1.255 |
| Aaero | Drag area | 1.0 |
| Cd | Drag coefficient | 1.2727 |
| Cmotor | Motor Constant (max. N) | 4283.4645 |
| Cr | Rolling resistance (% of car's weight) | 0.45% |