Efficient SE(3) Reachability Map Generation via Interplanar Integration of Intra-planar Convolutions

Abstract

Convolution has been used for fast computation of reachability maps, but it has high computational costs when performing SE(3) convolution operations for general joint arrangements in industrial robots and 3D workspace. Its application is also limited to planar robots, 2D workspace, or robots with special spatial arrangements for joints. In this paper, we find that the SE(3) convolution can be decomposed into a set of SE(2) convolutions, which significantly reduces the computational complexity when computing the reachability map of high-DOF robotic manipulators in the 3D workspace. We also leverage GPU parallel computing and Fast Fourier transform to further accelerate the computation procedure. We demonstrate the time efficiency and quality of our approach using a set of numerical experiments for constructing reachability maps and also present a multi-robot plant phenotyping system that uses the computed reachability map for efficient viewpoint selection and path planning.