Abstract
The Markov-Dubins problem requires to find the shortest path that connects an initial point and angle to a final point and angle with bounded turning radius. Formally, this is equivalent to solve an interpolation problem with continuity up to the first derivative and with bounded curvature. We propose a mathematical framework that models with a single equation the different cases that arise, i.e., we can represent with the same function an arc of circle or a line segment by smoothly blending from one to the other. This allows us to restate the problem as a standard Mixed Integer Nonlinear Programming (MINLP), which can be relaxed into a standard Nonlinear Programming (NLP) and therefore opens the way to solve it using off-the-shelf solvers. Moreover, our formalism captures the symmetries of the problem in a more intuitive way with respect to previous works, thanks to the considered conformal bipolar transform. This approach is suitable for an effective solution of the extended problem of connecting multip...