Mathematical control models and applications.
We aim to investigate mathematical control models for bio-inspired flexible structures, with particular attention to evolutive systems characterized by distributed, stop-and-go and/or variable-domain controls. The interest in this subject is motivated by applications to soft-robotics, with particular attention to the motion planning octopus-like manipulators. More generally, the project aims to contribute to those applicative frameworks demanding for a non-standard application of the optimal control theory and exact controllability theory of partial differential equations.
The project includes the following goals. First, we focus on a control, evolutive model for an octopus arm, based on a controlled version of Euler's dynamic Elastica equation. We aim to derive open-loop control strategies for fine manipulation tasks, e.g., grasping and reachability tasks. More generally, to cope with those situations in which only a portion of a general, flexible (bio-inspired) structure can be controlled, we also plan to address exact controllability problems for controls with time-varying domains. In order to develop, further (possibly sub-optimal) control strategies, we finally plan a "merging phase" of the project devoted to the application of the general, theoretical background to the particular octopus arm model under exam.