Abstract
A general method to obtain the obstacle representation in the robot configuration space is presented. The method is based on a solid mathematical formalism that has as a key element a mathematical expression to evaluate the C-obstacle representation. The use of the proposed method and the choice of a suitable coordinate system, in the workspace as well as in the configuration space, lead to the fact that the obstacle representation in the configuration space could be seen as a convolution of two functions that describe the robot and the obstacles, respectively. The computational load can then be reduced drastically if convolution properties are applied. The method is directly applicable to mobile and articulated robots without any kind of adaptation or restriction of the shape of the elements that constitute the robot and the shape of the obstacles. Hence, its utilization is quite suitable to motion planning and control problems.
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