Abstract
Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades due to the progress in the area of nonlinear dynamics. This article discusses several applications of fractional calculus in science and engineering, namely: the control of heat systems, the tuning of PID controllers based on fractional calculus concepts and the dynamics in hexapod locomotion. © 2009 Springer-Verlag Berlin Heidelberg.

Abstract
This paper studies periodic gaits of quadruped locomotion systems. The purpose is to determine the best set of gait and locomotion variables during walking, for different robot velocities, based on two formulated performance measures. A set of experiments reveals the influence of the gait and locomotion variables upon the proposed indices, namely that the gait and the locomotion parameters should be adapted to the robot forward velocity.

Abstract

Abstract
The interest in the development of climbing robots is growing rapidly. Motivations are typically to increase the operation efficiency by obviating the costly assembly of scaffolding or to protect human health and safety in hazardous tasks. Climbing robots are starting to be developed for applications ranging from cleaning to inspection of difficult to reach constructions. These robots should be capable of travelling on different types of surfaces, with varying inclinations, such as floors, walls, ceilings, and to walk between such surfaces. Furthermore, these machines should be capable of adapting and reconfiguring for various environment conditions and to be self-contained. Regarding the adhesion to the surface, they should be able to produce a secure gripping force using a light-weight mechanism. This paper presents a survey of different applications and technologies proposed for the implementation of climbing robots. Copyright © 2008 by World Scientific Publishing Co. Pte. Ltd.

Abstract
This paper studies the performance of a Fractional Order PD a controller in a hexapod robot with three dof legs and leg joint actuators having saturation. For that objective the robot prescribed motion is characterized in terms of several locomotion variables. Moreover, two indices measure the walking performance based on the mean absolute density of energy per travelled distance and on the hip trajectory errors. A set of simulation experiments reveals the influence of the different controller tuning upon the proposed indices. Copyright © 2006 IFAC.

Abstract
The performance of electrical devices, depending on the processes of the electrolytes, have been fully described and the physical origin of each parameter is well established. However, the influence of the irregularity of the electrodes was not a subject of study and only recently, this problem became relevant in the viewpoint of fractional calculus. This paper describes an electrolytic process in the perspective of fractional order capacitors. In this line of thought, are developed several experiments for measuring the electrical impedance of the devices. The results are analyzed through the frequency response, revealing capacitances of fractional order that can constitute an alternative to the classical integer order elements.