In the paper [7] we defined a map, called the hyperbolic Schwarz map, from the one-dimensional projective space to the three-dimensional hyperbolic space by use of solutions of the hypergeometric differential equation, and thus obtained closed flat surfaces belonging to the class of flat fronts. We continue the study of such flat fronts in this paper. First, we introduce the notion of derived S...

The purpose of this communication is to investigate the usefulness of the differential flatness control approach to solve the trajectory tracking problem for a four rotor aircraft. After introducing simplifying assumptions, the flight dynamics equations for the four rotor aircraft are considered. A trajectory tracking control structure based on a two layer non linear approach is then proposed. ...

We study some aspects of noncommutative differential geometry on a finite Weyl group in the sense of S. Woronowicz, K. Bresser et al., and S. Majid. For any finite Weyl group W we consider the subalgebra generated by flat connections in the left-invariant exterior differential algebra of W. For root systems of type A and D we describe a set of relations between the flat connections, which conje...

Differential flatness is a property which substantially reduces the difficulty involved in generating dynamically feasible trajectories for underactuated robotic systems. However, there is a large class of robotic systems that are not differentially flat, and an efficient method for computing dynamically feasible trajectories does not exist. In this paper we introduce a weaker but more general ...