This thesis is centred on the development and application of a model to reason about shape and about movement in a qualitative way (in a way similar to the human reasoning), The interest of this study originates from the necessity to find solutions for the recognition of objects and the description and reasoning about the movement in situations with high uncertainty, as it is the case of robotic applications, where robots only have limited and vague sensorial information. In these situations the use of a qualitative reasoning, that allows us to handle ambiguities and errors, will be the most suitable. This PhD thesis presents a motion model as a qualitative representational model for integrating qualitatively time and topological information for reasoning about dynamic worlds in which spatial relations between regions and between regions and objects may change. On the other hand, the thesis develops a theory for the recognition of shapes able to describe several types of shapes: regular and non-regular polygons, with or without holes, with or without curved segments and completely curvilinear forms. Each shape is described by a string containing its qualitative distinguished features, which is used to match an object against the others. This theory has been applied, in an industrial domain, for the automatic and intelligent assembly of ceramic mosaics. Moreover, the part of the theory that describes polygonal objects, jointly with the theory of movement has been applied for the simulated navigation of a real robot.
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