Smoothness of mobile and vehicle navigation has become relevant to ensure the safety and the comfortability of riding. The robotics community has been able to render smooth trajectories in mobile robots by using non-linear optimization approaches and well-known fairness metrics considering the curvature variations along the path. In this paper, we evaluate the possibility of computing smooth paths from input reference trajectories by using higher order non-linear fairness functionals. Our approach is potential to enable the generation of simple and computationally-efficient path planning and smoothing for navigation in mobile robots.