Ricerc@Sapienza

We address an optimal reachability problem in constrained environments for hyper-redundant and soft planar manipulators. Both the discrete and continuous devices are inextensible and they are characterized by a bending moment, representing a natural resistance to leave the position at rest, an inequality constraint forcing the bending below a fixed threshold, and a control term prescribing local bending.

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 investigate a reachability control problem for a soft manipulator inspired to an octopus arm. Cases modelling mechanical breakdowns of the actuators are treated in detail: we explicitly characterize the equilibria, and we provide numerical simulations of optimal control strategies.

We present a control model for an octopus tentacle based on the dynamics of an inextensible string with curvature constraints and curvature controls. We derive the equations of motion together with an appropriate set of boundary conditions, and we characterize the corresponding equilibria. The model results in a system of fourth-order evolutive nonlinear controlled PDEs, generalizing the classic Euler's dynamic elastica equation, that we approximate and solve numerically by introducing a finite difference scheme.