Abstract
The synthesis and application of fractional-order controllers is now an active research field. This article investigates the use of fractional-order PID controllers in the velocity control of an experimental modular servo system. The systern consists of a digital servomechanism and open-architecture software environment for real-time control experiments using MATLAB/Simulink. Different tuning methods will be employed, such as heuristics based on the well-known Ziegler Nichols rules, techniques based on Bode’s ideal transfer function and optimization tuning methods. Experimental responses obtained from the application of the several fractional-order controllers are presented and analyzed. The effectiveness and superior performance of the proposed algorithms are also compared with classical integer-order PID controllers.

Abstract
This paper studies periodic gaits of multi-legged robot locomotion systems based on dynamic models, The purpose is to determine the system performance during walking and the best set of locomotion variables that minimizes the optimization indices. For that objective the prescribed motion of the robot is completely characterized in terms of several locomotion variables such as gait, duty factor, body height, step length, stroke pitch, foot clearance, link lengths, body and legs mass and cycle time. In this perspective, we formulate four performance measures of the walking robot namely, the locomobility of the foot, the mean absolute power, the mean power dispersion and the mean power lost in the joint actuators per walking distance. A set of model-based experiments reveals the influence of the locomotion variables in the proposed indices.

Abstract

Abstract
This paper studies the mechanical configuration and the periodic gaits of multi-legged locomotion systems based on its kinematic and dynamic models. The purpose is to determine the system performance during walking, and the best set of locomotion variables that minimize a set of optimization indices. In this perspective, two kinematic and four dynamic indices are formulated to quantitatively measure the performance of the walking robot. The kinematic indices consist of the perturbation analysis and the locomobility measure, and the dynamic performance indices of the walking robot locomotion are the mean absolute density of energy, the mean power density dispersion, the density of power lost and the mean force at the body-legs interface. A set of model-based simulation experiments reveals the system configuration and the type of movements that lead to a better performance, for a specific locomotion mode, from the viewpoint of the proposed indices.

Abstract
This paper describes a simulation model for a multi-legged locomotion system with joints at the legs having viscous friction, flexibility and backlash. For that objective the robot prescribed motion is characterized in terms of several locomotion variables. Moreover, the robot body is divided into several segments in order to emulate the behaviour of an animal spine. The foot-ground interaction is modelled through a non-linear spring-dashpot system whose parameters are extracted from the studies on soil mechanics. To conclude, the performance of the developed simulation model is evaluated through a set of experiments while the robot leg joints are controlled using fractional order algorithms.

Abstract
In this paper we propose the use of the least-squares based methods for obtaining digital rational approximations (IIR filters) to fractional-order integrators and differentiators of type s(alpha), alpha is an element of R. Adoption of the Pade, Prony and Shanks techniques is suggested. These techniques are usually applied in the signal modeling of deterministic signals. These methods yield suboptimal solutions to the problem which only requires finding the solution of a set of linear equations. The results reveal that the least-squares approach gives similar or superior approximations in comparison with other widely used methods. Their effectiveness is illustrated, both in the time and frequency domains, as well in the fractional differintegration of some standard time domain functions.