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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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