This paper studies the Fast Marching Square (FM2$$) method as a competitive path planner for UAV applications. The approach fulfills trajectory curvature constraints together with a significantly reduced computation time, which makes it overperform with respect to other planning methods of the literature based on optimization. A comparative analysis is presented to demonstrate how the FM2$$ approach can easily adapt its performance thanks to the introduction of two parameters, saturation α$$ and exponent β$$, that allow a flexible configuration of the paths in terms of curvature restrictions, among others. The main contributions of the method are twofold: first, a feasible path is directly obtained without the need of a later optimization process to accomplish curvature restrictions; second, the computation speed is significantly increased, up to 220 times faster than other optimization-based methods such as, for instance, Dubins, Euler–Mumford Elastica and Reeds–Shepp. Simulation results are given to demonstrate the superiority of the method when used for UAV applications in comparison with the three previously mentioned methods.