Distance and Collision Probability Estimation from Gaussian Surface Models

Abstract

This paper describes methodologies to estimate the collision probability, Euclidean distance and gradient between a robot and a surface, without explicitly constructing a free space representation. The robot is assumed to be an ellipsoid, which provides a tighter approximation for navigation in cluttered and narrow spaces compared to the commonly used spherical model. Instead of computing distances over point clouds or high-resolution occupancy grids, which is expensive, the environment is modeled using compact Gaussian mixture models and approximated via a set of ellipsoids. A parallelizable strategy to accelerate an existing ellipsoid-ellipsoid distance computation method is presented. Evaluation in 3D environments demonstrates improved performance over state-of-the-art methods. Execution times for the approach are within a few microseconds per ellipsoid pair using a single-thread on low-power embedded computers.