Abstract

Abstract

Abstract

Abstract
This paper deals with the discretization of integrals and derivatives (i.e., differintegrals) of complex order. Several methods for the discretization of the operator s?, where ? = u+jv is a complex value, are proposed. The concept of conjugated-order differintegral is also presented. The conjugated-order operator allows the use of complex-order differintegrals while still resulting in real time responses and real transfer functions. The performance of the resulting approximations is evaluated both in the time and frequency domains. Copyright © 2006 IFAC.

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.