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
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
This paper studies the performance of different order Padé Fractional Order (FO) PD0.5 controllers applied to the leg joint control of a hexapod robot with two dof legs and joint actuators with saturation. For simulation purposes the robot prescribed motion is characterized through several locomotion variables and for the walking performance evaluation are used two indices, one based on the mean absolute density of energy per travelled distance and the other on the hip trajectory errors. A set of simulation experiments reveals the influence of the different order Padé PD0.5 controllers tuning upon the proposed indices. Copyright © 2006 IFAC.

Abstract
This paper describes a simulation model for a multilegged locomotion system with 3 dof legs and leg joint actuators having saturation. 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 behavior of an animal spine. A non-linear spring-dashpot system models the foot-ground interaction, being its parameters computed from studies on soil mechanics. To conclude, the performance of the developed model is evaluated through a set of experiments while the robot leg joints are controlled using a proportional and derivative algorithm.

Abstract
The idea of fractional calculus is not new. Fractional derivatives are almost as old as integer-order definition. In 1695 Leibniz discussed this problem with L'Hospital, but many other contributions are due to investigators such as Liouville, Abel, Heaviside and Riemann, that formalized the theory of the non-integer order systems. The area of fractional calculus has primarily been the domain of mathematicians, and only had the theoretical foundation. Nowadays, this concept is employed in physics, engineering, biology, economy and other scientific fields. In our work, we apply the concepts of fractional calculus and the theory of electrical impedance to botanical elements. The fractional order behaviour of these type of systems are studied and the relation with the electrical impedance is formulated.

Abstract
This work addresses the signal propagation and the fractional-order dynamics during the evolution of a genetic algorithm (GA). In order to investigate the phenomena involved in the GA population evolution, the mutation is exposed to excitation perturbations during some generations and the corresponding fitness variations are evaluated. Three distinct fitness functions are used to study their influence in the GA dynamics. The input and output signals are studied revealing a fractional-order dynamic evolution, characteristic of a long-term system memory.