# Finding the nearest path point: A small comparison of optimisation methods

Mikhail Pak

TU München

Tuesday, May 10, 2016, 12:15

Room 01-012, Georges-Köhler-Allee 102, Freiburg 79110, Germany

Many path following control concepts rely on finding the point on the path nearest to the vehicle. If this point $\mu^*$ is known, it can be used to easily establish a reference coordinate frame based on the tangent space at $\mu^*$. One would usually formulate this problem as a quadratic program and solve it using few iterations of the Newton or Gauss--Newton method. In this talk, we will investigate global convergence of these two approaches and discuss the implications for path following controllers.