mpc_lib

Uses Model Predictive Control for path planning of a differential drive vehicle. Uses IPOPT to solve the non-linear optimization problem. Intended to be used with surajRathi/mpc_local_planner as a local planner for the ROS Nav Stack.

Forked from project-TARIV/mpc_lib to add documentation.

Dependencties

• cmake: Build System

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

• cppad For Ubuntu:

sudo apt-get install cppad

• Ipopt This installs it to /usr/local. You can edit the install_ipopt.sh before execution to modify 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 wheel.

1. A simple kinematic model has been selected where $v_r$ and $v_l$ are velocities of each wheel, $a_r$ and $a_l$ are the respective accelerations, and $L$ is the wheelbase.

   • $x_i = x_{i-1} + \frac{v_r + v_l}{2} * cos(\theta_{i-1}) * dt$
   • $y_i = y_{i-1} + \frac{v_r + v_l}{2} * sin(\theta_{i-1}) * dt$
   • $\theta_i = \theta_{i-1} + \frac{v_r - v_l}{L} * dt$

2. Constraints: We enforce maximum and minimum constraints on each wheel's velocity.

3. Objective Function: This is of the form $\sum{w_i*(\text{cost}_i)^2}$. The factors, $\text{cost}_i$ are listed below. We must choose appropriate weights, $w_i$ for each of them. The path to follow has been defined as a polynomial $f(x)$.

   • $v_r + v_l - 2 * v_{ref}$
   • $v_r - v_l$
   • $a_r + a_l$
   • $a_r - a_l$
   • $f(x) - y$

References