mpc_lib

Uses Model Predictive Control for path planning of a diffrential drive vehicle. Uses IPOPT

Moved to project-TARIV/mpc_lib . Based on project-TARIV/mpc_lib

Dependencties

• catkin OPTIONAL
  Project is made to be compiled with catkin for the ROS framework, but does work with just cmake.

• cmake: Build System

• Install cppad from your package manager
  For Ubuntu:

sudo apt-get install cppad

• Installing Ipopt Currently installs to /usr/local. Editing the script can change that.
  For Ubuntu:

sudo apt-get install gfortran
sudo apt-get install unzip
wget https://www.coin-or.org/download/source/Ipopt/Ipopt-3.12.7.zip && unzip Ipopt-3.12.7.zip && rm Ipopt-3.12.7.zip
sudo bash install_ipopt.sh ./Ipopt-3.12.7/

Working

We solve an optimisation problem for acceleration in each motor.

• A simple kinematic model has been selected
  If v_r and v_l are velocities in either frame, and a_r and a_l are the respective constraints.
  x_i = x_i-1 + (v_r + v_l) * dt * cos(theta_i-1) / 2 y_i = y_i-1 + (v_r + v_l) * dt * sin(theta_i-1) / 2 theta_i = theta_i-1 + (v_r - v_l) * dt / distance_between_wheels

• Constraints The path to follow has been defined as a polynomial f(x).

The objective function is of the form \sum{w_i*(a_i)^2}

The different terms (a_i) v_r + v_l - 2 * vref
v_r - v_l
a_r + a_l
a_r - a_l
f(x) - y

It is easy to expand to this list.

References

Based on project-TARIV/mpc_lib
Am a member of that organisation.