Obstacle evaluation of the configuration space for cylindrical manipulators

In this paper it is shown a practical method wich lets evaluate the full set of robot configurations that produce collisions between the environment and the cylindrical manipulator. The method is based on a sound mathematical formalism so the feasibility of the results is guaranteed. The application of the formalism is performed by means of choosing a suitable coordinate functions, in the workspace, as well as in the configuration space. It leads to the fact that the obstacle representation in the configuration space could be seen as a convolution of two functions that describe the cylindrical robot and the obstacles respectively. Additionally, the computational load is independent of the shape and number of obstacles and of the robot shape. The algorithmic tool that has been used is FFT (Fast Fourier Transform), since it eases the parallel implementation of the resulting algorithms reducing significantly the computational load, so the computational time is highly optimized.