Robot's hand and expansions in non-integer bases

We study a robot hand model in the framework of the theory of expansions in non-integer bases. We investigate the reachable workspace and we study some configurations enjoying form closure properties.Comment: 22 pages, 10 figure

Geometrical aspects of expansions in complex bases

We study the set of the representable numbers in base $q=pe^{i\frac{2\pi}{n}}$ with $\rho>1$ and $n\in \mathbb N$ and with digits in a arbitrary finite real alphabet $A$. We give a geometrical description of the convex hull of the representable numbers in base $q$ and alphabet $A$ and an explicit characterization of its extremal points. A characterizing condition for the convexity of the set of representable numbers is also shown.Comment: 23 pages, 5 figure

Optimal expansions of Kakeya sequences

We investigate optimal expansions of Kakeya sequences for the representation of real numbers. Expansions of Kakeya sequences generalize the expansions in non-integer bases and they display analogous redundancy phenomena. In this paper, we characterize optimal expansions of Kakeya sequences, and we provide conditions for the existence of unique expansions with respect to Kakeya sequences

Robot's finger and expansions in non-integer bases

International audience; We study a robot finger model in the framework of the theory of expansions in non-integer bases. We investigate the reachable set and its closure. A control policy to get approximate reachability is also proposed

Stabilizability in optimal control

We extend the well known concepts of sampling and Euler solutions for control systems associated to discontinuous feedbacks by considering also associated costs; in particular, we introduce the notions of Sample and Euler stabilizability to a closed target set C with W-regulated cost, which roughly means that we require the existence of a stabilizing feedback such that all the corresponding sampling and Euler solutions have finite costs, bounded above by a continuous, state-dependent function W, divided by some positive constant c. We prove that the existence of a special Control Lyapunov Function W, called c-Minimum Restraint function, c-MRF, implies Sample and Euler stabilizability to C with W-regulated cost, so extending [Motta, Rampazzo 2013], [Lai, Motta, Rampazzo, 2016], where the existence of a c-MRF was only shown to yield global asymptotic controllability to C with W-regulated cost