Assessing path-following performance for Unmanned Marine Vehicles with algorithms from numerical commutative algebra

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

“…This method has been defined and tested for the first time in [15]; its feasibility has been proved on simulated data for the metric induced by the ∞-norm. However, for the specific goal of the path-following performance evaluation, the common sense suggests to design the methodology using the Euclidean distance, that is employing the 2-norm.…”

“…Using the new · 2 -norm crossing conditions (see Propositions 3,4,6 and 8), in the current paper we extend to the · 2 norm the methodology presented in [15] for evaluating surface path-following experiments executed employing marine robots. A two step strategy for evaluating the capability of a robot to follow a reference path and an overall index of performance are defined.…”

Adaptive Experimental Design for Path-following Performance Assessment of Unmanned Vehicles

“…Our group has addressed the definition of GEMs for path-following tasks from an engineering perspective in [13,14,15,16]. During path-following the vehicle has to follow a predefined target path without any time constraints.…”

“…• The crossing cell index, P CA counts the percentage of points in V that are classified as close to R more than a given tolerance. This classification is defined by two steps: 1) the reference path is approximated by a polynomial curve and 2) for each point in V the Crossing cell algorithm is applied for deciding whether the zero-locus of the given polynomial intersects the neighbourhood of the point [16,27].…”

“…Thus with an experiment we test a class of curves γ x with x ∈ X ⊂ R q , for example q = 2 in a sine wave. Both implicit as in [16] and explicit equations for the path curves can be adopted. We want to model univariate mean performance indices y and seek a model from x to y.…”