Asymptotic constant-factor approximation algorithm for the Traveling   Salesperson Problem for Dubins' vehicle
  This article proposes the first known algorithm that achieves a constant-factor approximation of the minimum length tour for a Dubins' vehicle through $n$ points on the plane. By Dubins' vehicle, we mean a vehicle constrained to move at constant speed along paths with bounded curvature without reversing direction. For this version of the classic Traveling Salesperson Problem, our algorithm closes the gap between previously established lower and upper bounds; the achievable performance is of order $n^{2/3}$. 
Ketan Savla, Emilio Frazzoli and Francesco Bullo