Visually Guided Robotics Using Conformal Geometric Computing

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In this chapter the authors have used a single non?standard mathematical framework, the Conformal Geometric Algebra, in order to simplify the set of data structures that we usually use with the traditional methods. The key idea is to define and use a set of products in CGA that will be enough to generate conformal transformations, manifolds as ruled surfaces and develop incidence algebra operations, as well as solve equations and obtain directed distances between different kinds of geometric primitives. Thus, within this approach, all those different mathematical entities and tasks can be done simultaneously, without the necessity of abandoning the system. Using conformal geometric algebra we even show that it is possible to find three grasping points for each kind of object, based on the intrinsic information of the object. The hand`s kinematic and the object structure can be easily related to each other in order to manage a natural and feasible grasping where force equilibrium is always guaranteed. These are only some applications that could show to the robotic and computer vision communities the useful insights and advantages of the CGA, and we invite them to adopt, explore and implement new tasks with this novel framework, expanding its horizon to new possibilities for robots equipped with stereo systems, range data, laser, omnidirectional and odometry.

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