We present several results on the inverse problem and equivalent contact Lagrangian systems. These problems naturally lead to consider smooth transformations z variable (i.e., reparametrizations of action). extended systems formalize this notion. With structure we define horizontal equivalence Lagrangians, which generalizes symplectic case. also some for

A partial solution of the quaternionic contact Yamabe problem on the quaternionic sphere is given. It is shown that the torsion of the Biquard connection vanishes exactly when the trace-free part of the horizontal Ricci tensor of the Biquard connection is zero and this occurs precisely on 3-Sasakian manifolds. All conformal deformations sending the standard flat torsion-free quaternionic contac...

We investigate the problem of using contact sensors to estimate the pose of an object during planar pushing by a fixed-shape hand. Contact sensors are unique because they inherently discriminate between “contact” and “no-contact” configurations. As a result, the set of object configurations that activates a sensor constitutes a lower-dimensional contact manifold in the configuration space of th...

In this paper we consider the problem of letting an aerial robot exploiting its contact with the environment in order to enhance its motion possibilities, in a way reminiscent of legged robots exploiting contact forces for locomotion purposes. As a representative and initial case study, we consider a quadrotor equipped with a 1-DOF arm able to hook at some pivot points, and needing to perform a...