An Euclidean norm based criterion to assess robots' 2D path-following performance

A current need in the robotics eld is the denition of methodologies for quantitatively evaluating the results of experiments. This paper contributes to this by dening a new criterion for assessing path-following tasks in the planar case, that is, evaluating the performance of robots that are required to follow a desired reference path. Such criterion comes from the study of the local dierential geometry of the problem. New conditions for deciding whether or not the zero locus of a given polynomial intersects the neighbourhood of a point are dened. Based on this, new algorithms are presented and tested on both simulated data and experiments conducted at sea employing an Unmanned Surface Vehicle.