L. E. Kavraki, “Computation of Configuration Space Obstacles Using the Fast Fourier Transform,” IEEE Transactions on Robotics and Automation, vol. 11, no. 3, pp. 408–413, 1995.
This paper presents a new method for computing the configuration-space map of obstacles that is used in motion-planning algorithms. The method derives from the observation that, when the robot is a rigid object that can only translate, the configuration space is a convolution of the workspace and the robot. This convolution is computed with the use of the fast Fourier transform (FFT) algorithm. The method is particularly promising for workspaces with many and/or complicated obstacles, or when the shape of the robot is not simple. It is an inherently parallel method that can significantly benefit from existing experience and hardware on the FFT.