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.
The present object aims to investigate models and control strategies for flexible structures inspired by biology. The key point is to work from both modelling and theoretical point of view to cope with some of the real-life limitations characterizing biological, robotics as well as networking processes.
From the modeling point of view, the originality of the our proposal relies on taking account a model in which internal reaction elastic and control forces (i.e., the resistance to bending given by the elasticity of the octopus tissue) are conjugated with an inextensibility exact constraint (describing the smaller ability to stretch of the octopus arm with the respect to the bending). The aim is to develop time-varying optimal controls for complex manipulations, i.e., to synthesize, beside the stationary and quasi-static approach, also fully dynamic controls. Moreover, the case of a temporary or local unactuability of the controls is taken into account.
Another element of originality is given by the fact that further real-life limitations in the actuation of the controls are considered: to this end, we plan to endow ourselves also with some original results concerning the exact controllability of wave equation with internal and/or stop-and-go controls.
We expect this research to have a two-fold impact. On the one hand, we expect our contribution to enrich the wide family of models for biology, with particular reference to the biomechanics of the octopus arm. On the other hand, we remark the possible applications to the control of soft manipulators. These aspects are indeed deeply entangled, because of the wide use of bio-inspired devices in robotics.
Finally, the modelling activity is planned to be coupled with a more general, theoretical investigation of the exact controllability of evolutive systems. The auspicated theoretical developments can be possibly be applied to wider settings.