Cenedese, Angelo (Univ. of Padova), Beghi, Alessandro (Univ. of Padova)

How to Represent the Shape of a Deformable Object and Ease the Control of the Deformation?

Scheduled for presentation during the Regular Session "Physics and Control" (WeA08), Wednesday, July 26, 2006, 10:25−10:50, Room I

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 26, 2024

Abstract

Consider the behaviour of a flock of birds chased by a predator. The entire flock system can be considered as a deformable object of complex shape, which moves according to its own dynamics and is subject to external inputs such as, in this case, the presence of a predator. The evasion maneuver implies that the flock modifies the planned trajectory, as well as it alters its shape. This collective behaviour example helps us in introducing the problem of how to represent the shape of a deformable object, how to analyse the evolution of the shape as a space continuum, and how to control the deformation. As a matter of fact, the definition itself of shape as a technical term is hazy, so that when it comes to understand the deformation and study the evolution we need to refer mainly to the intuition. One common approach to describe the shape of an object makes use of landmarks, that can be, for example, the points of minimum or maximum curvature of the boundary, or points of particular interest. The representation of the shape has implications on the control capability of the object, and landmarks prove particularly useful when the object is a connection of rigid structures. Conversely, when considering the control of -loosely speaking- a freely deformable shape, the landmark approach appears to be inadequate for the purpose in that it does not represent the spatial continuum of the shape. In this work we propose a novel approach to the control of shape by resorting to a curve based description of the boundary. By employing a suitable description of the object border, such as a spline based representation, we show how it is possible to formulate an optimal problem, whose solution is efficient in control the deforming shape and present nice properties of consistency with the physics of the body dynamics.