Optimal reachability with obstacle avoidance for hyper-redundant and soft manipulators

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. After introducing the model and characterizing the associated equilibria, we set the problem in the framework of optimal control theory and we present some simulations related to its numerical solution.