Symbolic Control with Biologically Inspired Motion Primitives

Outline of the Thesis This thesis is about the control of nonlinear dynamical systems with the superposition of a finite number of modules. Practically, admissible control actions are constrained to be within the space spanned by a finite number of elementary controls, called motion primitives. This control paradigm was inspired by recent experiments sheding a new light on the organization of sensory-motor structures in biological systems. The motivation of the thesis is twofold. First, we are interested in understanding how to reduce the complexity of planning movements in articulated structures with many degrees of freedom. Second, we want to understand if biology can be helpful in formulating a control paradigm for realistically simulating human movements. The thesis is organized into five different papers. All the papers make use of concepts and tools typical of system control theory. Paper A presents the motion primitives control paradigm and shows how to choose the modules so as to preserve the system controllability. Paper B deals with the problem of choosing the modules so as to compensate for parametric changes in the controlled system. Moreover, the problem of performing movements with arbitrary execution time is considered. Paper C proves some results on the minimum number of primitives necessary to preserve controllability. Paper D looks at the control paradigm from a different point of view and tries to answer questions which are related to the biologically inspired nature of the paradigm. Moreover, it gives solution the problem of optimally choosing the elementary modules to compensate for disturbances affecting the system. Finally, Paper E considers the problem of estimating the cost function that best approximates a given set of trajectories. The estimation problem is shown to be connected to the problem of realistically simulating human movements. Riassunto della Tesi In questa tesi si propone un paradigma di controllo innovativo. L’idea è quella di controllare un sistema dinamico nonlineare utilizzando la sovrapposizione di un numero finito di moduli di controllo. Sostanzialmente, l’insieme dei controlli ammissibili è costituito da uno spazio vettoriale generato da un numero finito di azioni elementari di controllo, chiamateprimitive del movimento . Questo paradigma di controllò e motivato da alcuni recenti esperimenti che hanno messo in luce un’organizzazione modulare dei sistemi senso-motori biologici. La motivazione della tesi è duplice. Da un lato ci interessa capire sè e possibile ridurre la complessit à della pianificazione dei