BeBOT_cpp

This repository contains the implementation of the Bernstein/Bezier Optimal Trajectories toolkit BeBOT. Python and Matlab implementations of this library are also available here Python BeBOT and MATLAB BeBOT.

Requirements

To run this examples you must have the following installed:

• CMake (https://cmake.org/)
• Ninja (https://ninja-build.org/)
• Ipopt (https://github.com/coin-or)
• Intel MKL libraries (https://www.intel.com/content/www/us/en/developer/tools/oneapi/onemkl.html)
• HSL libraries (https://licences.stfc.ac.uk/product/coin-hsl-archive)

We reccomed following the following guide to install Ipopt and its dependencies https://coin-or.github.io/Ipopt/INSTALL.html

Example 1

In the example provided, the following optimal control problem is solved using Bernstein polynomials.

$$ \min_{x(t),u(t),t_f} \int_0^{t_f} 1 , d\tau $$

subject to:

$$ \dot{x_1(t)} = x_2(t), \quad \dot{x_2(t)} = u(t), $$

$$ x_1(0) = -3, \quad x_2(0) = 0, \quad x_1(t_f) = 0, \quad x_2(t_f) = 0, $$

$$ u(t) \leq a_{\max}, \quad -u(t) \leq -a_{\min} $$