A Comparative Study: L1-Norm Vs. L2-Norm; Point-to-Point Vs. Point-to-Line Metric; Evolutionary Computation Vs. Gradient Search

Abstract

The study presented in this article compares the two most frequently used regularizations in the robotics area: L1-norm and L2-norm, for navigation purposes of an autonomous mobile platform in an inner environment with use of the 2D laser scanner. Sensorial data in a real environment are very often burdened by a noise, which unfavorably affects the classification process. Presented results show behavior of all tested algorithms under conditions in which the sensorial data are loaded by common types of the noise: moving objects, quantizing noise, artificially added noise with different types of characteristics that correspond to potentially real conditions. Basic navigation mechanisms presented here use methods of robust statistics and modern evolutionary optimizers. The methods selected in this study represent the two different types of metrics, commonly called point-to-point and point-to-line. The navigation algorithm that uses L1-norm regularization integrates several different evolutionary algorithms that occupy a position of very efficient optimizers, which, at the same time, do not cut down limits of usability of the tested methods. Correct working parameters settings of all used pose estimators play a key role in the robot pose and heading estimation, therefore, this article is extended by a description of several important working parameters and the way to use them.

Automatic correction of barrel distorted images using a cascaded evolutionary estimator

“…More may also be used, but computational demands are considerable for, say, a 12 dimensional task. The efficiency of the (LSQ) in comparison to the EA (CEE here) is discussed and analysed in (Moravec 2015;Moravec & Pošík 2014a,b). (Moravec 2015) particularly analyses in detail the efficiency, time demands and behaviour of the LSQ method in comparison to EA -lens function has identical features as lens function (20, 21) -see Fig.…”

A Practical Compensation Method for Differential Column Shortenings in High-rise Reinforced Concrete Buildings

“…Optimization methods are used to find out the most effective and efficient solution to a specific problem among several solutions [24]. These methods have become very useful tools in various ranges of applications including to find optimal feature subset in pattern recognition applications [25,26], optimal micro-structure parameters of a mechanical resonator design [27], optimal aerodynamic shape [28], optimal circuit elements for electrode design [29], and optimal path for mobile autonomous robots [30]. From the structural engineering point of view, optimization methods for differential shortenings of vertical members in highrise buildings aims to find the minimum number of vertical member groups by considering the practical applicability of the compensation process on site.…”

“…Alternatively, in some special cases, absolute values (L1-norm) can also be used since this gives robust solutions. In a recent study, Moravec [30] presented a comprehensive comparison for both norms. L2-norm gives stable solutions but L1-norm never guarantees the stability.…”