Nonholonomic and robotics day
(an informal, explorative meeting)

July 4, 2016
Dipartimento di Matematica dell'Universita` di Padova
Torre Archimede - Via Trieste 63
Aula 1AD100

9:30 Inizio Incontro    
9:45-10:30 E. Menegatti
DEI, Universita` di Padova.		 "Perception for service and industrial robotics"

Parlerò delle linee di ricerca attive presso il nostro laboratorio IAS-Lab:
Robotics.dei.unipd.it

 
Break      
11:00-11:25 M. Zoppello.
Universita` di Trento.		 "Swimming and geometric control" The study of swimming strategies of biological organisms is attracting increasing interest in the literature, moreover recently is emerging a connection between swimming and geometric control theory.
We present the geometrical setting of the swimming problem in terms of Lie groups, principal fiber bundles and fluid dynamic connection. Then we reinterpret the equation of motion of a deformable body immersed either in an ideal or viscous fluid, as a drift less affine control system assuming to be able to prescribe the shape of the swimmer. Finally we give some results on its controllability.
11:30-11:55 N. Sansonetto.
Universita` di Verona.		  "Some aspects of the integrability of nonholonomic systems with symmetry"
In Hamiltonian mechanics, symmetry implies the existence of first integrals, and the link with integrability is described by the Liouville-Arnol’d Theorem and its noncommutative generalizations. In nonholonomic mechanics the situation is different and not fully understood: symmetries not necessarily produceds first integrals. In this talk we discuss a possible link between symmetries and first integrals and  give some preliminary results related to the integrability of a nonholonomic system with symmetry.
Break      
12:15-13:00 P. Fiorini e R. Muradore.
Universita` di Verona.		  "Over- and under-actuated robotic systems: applications and challenges"  
Lunch      
15:00-15:45 L. Garcia-Naranjo.
UNAM, Mexico.		 "The dynamics of an articulated n-trailer vehicle". We derive the reduced equations of motion for an articulated n-trailer vehicle that moves under its own inertia on the plane. We show that the energy level surfaces in the reduced space are (n + 1)-tori and we classify the equilibria within them, determining their stability. A thorough description of the dynamics is given in the case n=1. The main results of this work were recently published in Bravo-Doddoli A. and Garcia Naranjo L.C., The dynamics of an articulated $n$-trailer vehicle, Regular and Chaotic Dynamics, 20, 497-517, (2015).
15:45 Discussion    

Organizers: F. Cardin, F. Fasso`