Polarisation diversity of conformal arrays based on geometric algebra via convex optimisation

A simple and general design procedure is presented for the polarisation diversity of arbitrary conformal arrays; this procedure is based on the mathematical framework of geometric algebra and can be solved optimally using convex optimisation. Aside from being simpler and more direct than other derivations in the literature, this derivation is also entirely general in that it expresses the transformations in terms of rotors in geometric algebra which can easily be formulated for any arbitrary conformal array geometry. Convex optimisation has a number of advantages; solvers are widespread and freely available, the process generally requires a small number of iterations and a wide variety of constraints can be readily incorporated. The study outlines a two-step approach for addressing polarisation diversity in arbitrary conformal arrays: first, the authors obtain the array polarisation patterns using geometric algebra and secondly use a convex optimisation approach to find the optimal weights for the polarisation diversity problem. The versatility of this approach is illustrated via simulations of a 7×10 cylindrical conformal array. © 2012 The Institution of Engineering and Technology.

Self-stabilization and behavioral diversity of embodied adaptive locomotion

Locomotion is of fundamental importance in understanding adaptive behavior. In this paper we present two case studies of robot locomotion that demonstrate how higher level of behavioral diversity can be achieved while observing the principle of cheap design. More precisely, it is shown that, by exploiting the dynamics of the system-environment interaction, very simple controllers can be designed which is essential to achieve rapid locomotion. Special consideration must be given to the choice of body materials. We conclude with some speculation about the importance of locomotion for understanding cognition. © Springer-Verlag Berlin Heidelberg 2004.