L1-L2-norm comparison in global localization of mobile robots

The global localization methods deal with the estimation of the pose of a mobile robot assuming no prior state information about the pose and a complete a priori knowledge of the environment where the mobile robot is going to be localized. Most existing algorithms are based on the minimization of an L2-norm loss function. In spite of the extended use of the L2-norm, the use of the L1-norm offers some alternative advantages. The present work compares the L1-norm and the L2-norm with the same basic optimization mechanism to determine the advantages of each norm when applied to the global localization problem. The algorithm has been tested subject to different noise levels to demonstrate the accuracy, effectiveness, robustness, and computational efficiency of both L1-norm and L2-norm approaches.