This paper presents algorithms implemented for positioning a wheeled robot on a production floor inside a factory by means of radio-frequency distance measurement and trilateration techniques. A set of radio-frequency transceivers located on the columns of the factory (anchors) create a grid with several triangular zones capable of measuring the line-of-sight distance between each anchor and the transceiver installed in the wheeled robot. After measuring only three of these distances (radii), an enhanced trilateration algorithm is applied to obtain X and Y coordinates in a Cartesian plane, i.e., the position of the robot on the factory floor. The embedded systems developed for the anchors and the robot are robust enough to establish communication, select the closest anchors for measuring radii, and identify in which of the grid zones the robot is located.

In previous investigations, the nonlinear hypothesis use the linear bounded maps. Nonlinear hypothesis are described as the combination of the first order terms, and after of the mentioned combination, one bounded map is applied to alter the result. This document proposes two nonlinear hypothesis which use different structures instead of using the linear bounded maps. They are termed as novel nonlinear hypothesis and second order nonlinear hypothesis and their goal is to improve the second order processes modeling. The proposed nonlinear hypothesis are described as the combination of the first order and second order terms. Since the delta parallel robot is a second order process, it is an excellent platform to prove the effectiveness of the two proposed hypothesis. INDEX TERMS Novel nonlinear hypothesis, second order nonlinear hypothesis, nonlinear hypothesis, delta parallel robot.

In this work, we study the structure regulator for the perturbations attenuation which is based on the infinite structure regulator. The structure regulator is able to attenuate the perturbations if the transfer function of the departures and perturbations has a numerical value almost equal to zero, and it does not require the perturbations to attenuate them. We apply the structure regulator and the infinite structure regulator to a quadrotor which maintains the horizontal position with respect to the earth for the step and sine perturbations.INDEX TERMS Quadrotor, perturbations attenuation, model, roll and pitch angles. I. INTRODUCTION

Actuators nonlinearities are unknown external perturbations in robots, which are unwanted because they can severely limit their performance. This research is focused on the stabilization of robots subject to actuators nonlinearities with a regulator containing the sigmoid mapping. Our regulator has the following three main characteristics: a) a sigmoid mapping is used to ensure boundedness of the regulator law terms, b) the chattering is reduced by the usage of the saturation mapping instead of the signum mapping, and c) the stabilization is ensured by the Lyapunov analysis. Finally, we evaluate our regulator for the stabilization of two robots.

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