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In this paper we present the design of a device to guide the visually impaired person who normally uses a cane. We propose a non-invasive device that will help blind and visually impaired people to navigate. The system uses stereoscopic vision, a RGB-D sensor and an IMU to process images and to compute the distances from obstacles relative to cameras and to search for free walking paths in the scene. This computing is done using stereo vision, vanishing points, and fuzzy rules. Vanishing points are used to obtain a main orientation in structured spaces. Since the guidance system is related to a spatial reference system, the vanishing point is used like a virtual compass that helps the blind to orient him- or herself towards a goal. Reinforced with fuzzy decision rules, the system supports the blind in avoiding obstacles, thus the blind person is able to cross structured spaces and avoid obstacles without the need for a cane.

This paper presents an algorithm to model volumetric data and other one for non-rigid registration of such models using spheres formulated in the geometric algebra framework. The proposed algorithm for modeling, as opposite to the Union of Spheres method, reduces the number of entities (spheres) used to model 3D data. Our proposal is based in marching cubes idea using, however, spheres, while the Union of Spheres uses Delaunay tetrahedrization. The non-rigid registration is accomplished in a deterministic annealing scheme. At the preprocessing stage we segment the objects of interest by a segmentation method based on texture information. This method is embedded in a region growing scheme. As our final application, we present a scheme for surgical object tracking using again geometric algebra techniques.

The geometric relationships between the elements of a humanoid robot manipulator are defined by the kinematics of the robot. The synthesis of the kinematical model for this type of robots is presented in this work using the Conformal Geometric Algebra framework. Moreover, two controllers are developed, one for the position tracking problem using a error feedback controller and another using sliding modes for the position tracking problem in precense of perturbations. The stability analysis is carried out for both controllers, and their application to a humanoid robot arm, composed of 5 DOF is presented. By proposing the error feedback and Lyapunov functions in terms of geometric algebra, we are opening a new venue of research in control of manipulators which involves the use of geometric primitives like lines, circles, planes and spheres.