On the Stability Problem of Equilibrium Discrete Planar Curves

We study planar polygonal curves with the variational methods. We show a unified interpretation of discrete curvatures and the Steiner-type formula by extracting the notion of the discrete curvature vector from the first variation of the length functional. Moreover, we determine the equilibrium curves for the length functional under the area-constraint condition and study their stability.

Trajectory Control of an Automated Guided Vehicle Using Feedback Linearization

In this paper, the dynamics and control of an automated guided vehicle (AGV) is described. The objective is to control the vehicle direction and location with respect to a prescribed trajectory. This is accomplished based on an optimum control strategy using vehicle state variables. A four-wheel vehicle with three degrees of freedom including longitudinal, lateral and yaw motion is considered. The nonlinearity of the tire and steering mechanism is also included. The control system design for circular, straight forward and composite path is presented based on feedback linearization. Some trajectory simulation for discrete curvatures is carried out. The controller was implemented within MATLAB environment. The design was also evaluated using ADAMS full vehicle assembly. The results demonstrated the accuracy of the model and the effectiveness of the developed control system.

Discrete Curvature Approximations for the Segmentation of Polyhedral Surfaces

The segmentation of digitized data to decompose a free form surface into patches is one of the key processes used to perform the reverse engineering of an object. To this end, discrete curvature approximations are introduced that form the basis of a segmentation process which lead to a decomposition of digitized data into areas that will help the construction of surface patches. The approach presented relies on the use of a polyhedral representation of an object built from the digitized data input. Then, it is shown how noise reduction techniques, edge swapping techniques and adapted remeshing schemes can participate to different preparation phases which provide a geometry that highlights useful characteristics for the segmentation process. The segmentation process is performed with various approximations of discrete curvatures evaluated on the polyhedrons issued by the preparation phases. The segmentation process proposed involves two stages: the identification of characteristic polylines and the identification of polyhedral regions. Discrete curvature criteria are adapted to each stage and concepts of invariant are introduced to generate criteria, which are constant over equivalent meshes. An outline of the segmentation procedure is provided together with examples of results for free form objects.