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.

Abstract
This paper studies the dynamics of foot-ground interaction in hexapod locomotion systems. For that objective the robot motion is characterized in terms of several locomotion variables and the ground is modelled through a non-linear spring-dashpot system, with parameters based on the studies of soil mechanics. Moreover, it is adopted an algorithm with foot-force feedback to control the robot locomotion. A set of model-based experiments reveals the influence of the locomotion velocity on the foot-ground transfer function, which presents complex-order dynamics.

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During the last two decades the research and development of legged robots has grown steadily. Legged systems present major advantages when compared with "traditional" vehicles, because they allow locomotion in terrain inaccessible to vehicles with wheels and tracks. However, the robustness of legged robots, and specially its energy consumption, among other aspects, still lag being mechanisms that use wheels and tracks. Therefore, in the present state of development, there are several aspects that need to be improved and optimized. One of these aspects relates to the optimum parameters that these machines should adopt in order to minimize the energy consumption. Due to the large number of parameters involved in this optimization process, one way to achieve meaningful results is using evolutionary strategies. Genetic Algorithms are a way to "imitate nature" replicating the process that nature designed for the generation and evolution of species. This paper presents a genetic algorithm, running over a simulation application of legged robots, which allows the optimization of several parameters of a quadruped robot model.

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. It has been recognized the advantageous use of this mathematical tool in the modelling and control of many dynamical systems. Having these ideas in mind, this paper discusses a FC perspective in the study of the dynamics and control of several systems. The paper investigates the use of FC in the fields of controller tuning, legged robots, electrical systems and digital circuit synthesis.