Abstract
This paper studies the adoption of periodic gaits of quadruped animals by multilegged artificial locomotion systems. The purpose is to determine the gait to adopt at different velocities, under distinct robot and locomotion conditions, based on two performance measures. A set of experiments reveals the influence of the gait and the body and ground parameters upon the proposed indices. It is verified that the gait should be adapted to the robot forward velocity and to the conditions under which the robot is moving. The experiments also reveal that a gait that decreases the energy consumption generally implies an increase in the trajectory following errors.

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
This article studies several Fractional Order Control algorithms used for joint control of a hexapod robot. Both Pade and series approximations to the fractional derivative are considered for the control algorithm. The walking performance is evaluated through two indices: The mean absolute density of energy used per unit distance travelled, and the control effort. A set of simulation experiments reveals the influence of the different approximations upon the proposed indices. The results show that the fractional proportional and derivative algorithm, implemented using the Pade approximation with a small number of terms, gives the best results.

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
In this paper, we incorporate fuzzy reasoning in fractional-order PD controllers. The resulting fuzzy fractional PD controller is investigated in terms of its digital implementation and robustness. The combined features of both algorithms will result in a better control system performance. Also, the effectiveness and robustness of the new methodology is illustrated through an application example.

Abstract
This paper compares the performance of classical position PD algorithm with a cascade controller involving position and force feedback loops, for multi-legged locomotion systems and variable ground characteristics. For that objective the robot prescribed motion is characterized in terms of several locomotion variables. Moreover, we formulate several performance measures of the walking robot based on the robot and terrain dynamical properties and on the robot hip and foot trajectory errors. Several experiments reveal the performance of the different control architectures in the proposed indices.