Detailed, fast C/C++ vehicle physics based on acados

The python code in this project is used to generate C and C++ libraries that provide discretized car dynamics. In the current state, one can simulate a tenth-scale chassis with drive-train and tire friction dynamics.

Features

• 4 explicitly simulated wheels, independent 4-wheel steering
• Pacejka-type combined tire slip model (Similarity Method)
• Changes of friction coefficients / vertical load during runtime
• Underactuated differential gear simulation
• Drive-train with DC motor model (single motor)

How to integrate this in a multi-body simulator such as Gazebo?

Given the current velocities of a car body, vertical loads on the wheels and the controls (throttle and steering angles), this software can calculate the movement of the car in the form of force and torque to be applied to the car within the next millisecond.

• Set up a rigid body for the car in the employed simulator (e.g. Gazebo)
• Model wheels as spheres so that there is only a single contact point
• Turn off friction for the wheels (friction will be handled by the generated software)
• In each update:
  • Read the velocity states, vertical forces and controls from Gazebo.
  • Then, set those values as the current state for the car physics simulation.
  • Advance the car physics simulation.
  • Get force / torque and set it to the car body in Gazebo.

Installation

Prerequisites

• Install acados: https://github.com/acados/acados
• Install acados Python Interface: https://docs.acados.org/python_interface/index.html#installation
• Optional, for C++ demo: Python3 installation with numpy and matplotlib (dependency of matplotlibcpp)

Build

The CMakeLists.txt is set up so that the code is automatically re-generated using acados when the Python files are changed.

mkdir -p build/
cd build/
cmake -DCMAKE_BUILD_TYPE=Release ..
make -j6

Use

The build output to be linked in a C project consists of the libacados_sim_solver_car.so library. Refer to the acados API documentation on how to use it.

The build output to be linked in a C++ project consists of the libcar_physics_pacejka.so library (see CMakeLists.txt) and the libacados_sim_solver_car.so library. A simple C++ interface CarSimulation.h/.cpp is build into the library libcar_physics_pacejka.so which handles the interaction with the acados solver in the other library.

Appendix

Model

States: $v_x, v_y, r, \omega, \omega_{f \triangle}, \omega_{r \triangle}$
Linear velocities, angular velocity, motor velocity, differential velocities

Controls: $DC, \delta_{fl},\delta_{fr},\delta_{rl},\delta_{rr}$
Duty cycle, steering angles

Spatial view of the model

Spatial states: $v_x, v_y, r$

Drive-train view of the model

Drive-train states: $\omega, \omega_{f \triangle}, \omega_{r \triangle}$
$\omega_{f \triangle}, \omega_{r \triangle}$ are the relative velocities in-between front wheels and in-between rear wheels respectively.

Plots generated with the implemented Pacejka-type tire model