Odometry Error Covariance Estimation for Two Wheel Robot Vehicles

Abstract

This technical report develops a simple statistical error model for estimating position and orientation of a mobile robot using odometry. Once the errors are characterised, other sensor data can be combined sensibly in the estimation of position, using the Extended Kalman Filter [Kleeman, 1992 #100; Jazwinski, 1970 #117]. A closed form error covariance matrix is developed for (i) straight lines and (ii) constant curvature arcs and (iii) turning about the centre of axle of the robot. Other paths can be composed of short segments of constant curvature arcs without great loss of accuracy. The model assumes that wheel distance measurement errors are exclusively random zero mean white noise. Systematic errors due to wheel radius and wheel base measurement are ignored, since these can be removed by calibration. Previous work on developing odometry covariance relies on incrementally updating the covariance matrix in small times steps. The approach taken here integrates the noise theoretically over the entire path length to produce simple closed form expressions, allowing efficient covariance matrix updating after the completion of path segments. 1