Abstract
This paper studies a fractional order proportional and derivative controller for a hexapod robot, having legs with three DoF and joint actuators with saturation, when walking over ground with varying properties. A simulation model is developed and the robot motion is characterized in terms of several locomotion variables. Two indices measure the walking performance based on the mean absolute density of energy per unit distance travelled and on the hip trajectory errors. A set of experiments reveal the influence of different controller tunings on the proposed indices, for different locomotion conditions.

Abstract

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 chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses FC in the study of system dynamics and control. In this perspective, this paper investigates the use of FC in the fields of controller tuning, legged robots, redundant robots, heat diffusion, and digital circuit synthesis.

Abstract
This paper presents the architecture of a climbing robot with wheeled locomotion and adhesion through permanent magnets. This machine is intended to be used in the inspection of ferromagnetic structures, in order to, for instance, detect weaknesses due to corrosion, particularly in aerogenerators towers, fuel tanks, ship hulls, etc. The vehicle is designed to have a semi-autonomous behavior, allowing a remote inspection process controlled by a technician, this way reducing the risks associated with the human inspection of tall structures and ATEX places. The particular characteristic of this robot is its dynamic adjustment system of the permanent magnets in order to assure the machine adhesion to the surfaces, even when crossing irregular and curved surfaces. ©2010 IEEE.

Abstract
Climbing robots are being developed for applications ranging from cleaning to inspection of difficult to reach constructions. These machines should be capable of travelling on different types of surfaces (such as floors, walls, ceilings) and to walk between such surfaces. Furthermore, these machines should adapt and reconfigure for various environment conditions and should be self-contained. Regarding the adhesion to the surface, they should be able to produce a secure gripping force using a light-weight mechanism. Bearing these facts in mind, this paper presents a survey of different technologies used for climbing robots adhesion to surfaces. © 2008 IEEE.

Abstract
Fractional calculus (FC) is being used in several distinct areas of science and engineering, being recognized its ability to yield a superior modelling and control in many dynamical systems. This article illustrates the application of FC in the area of robot control. A Fractional Order PD mu controller is proposed for the control of an hexapod robot with 3 dof legs. It is demonstrated the superior performance of the system by using the FC concepts.