Ricerc@Sapienza

We investigate optimal reachability and grasping problems for a planar soft manipulator, from both a theoretical and numerical point of view. The underlying control model describes the evolution of the symmetry axis of the device, which is subject to inextensibility and curvature constraints, a bending moment and a curvature control. Optimal control strategies are characterized with tools coming from the optimal control theory of PDEs. We run some numerical tests in order to validate the model and to synthetize optimal control strategies.

We solve the reachability problem for a coupled wave-wave system with an integro-differential term. The control functions act on one side of the boundary. The estimates on the time is given in terms of the parameters of the problem and they are explicitly computed thanks to Ingham type results. Nevertheless some restrictions appear in our main results. The Hilbert Uniqueness Method is briefly recalled. Our findings can be applied to concrete examples in viscoelasticity theory