Representation of Uncertain Occupancy Maps with High Level Feature Vectors

This paper presents a novel method for representing an uncertain occupancy map using a “feature vector” and an associated covariance matrix. Input required is a point cloud generated using observations from a sensor captured at different locations in the environment. Both the sensor locations and the measurements themselves may have an associated uncertainty. The output is a set of coefficients and their uncertainties of a cubic spline approximation to the distance function of the environment, thereby resulting in a compact parametric representation of the environment geometry. Cubic spline coefficients are computed by solving a non-linear least squares problem that enforces the Eikonal equation over the space in which the environment geometry is defined, and zero boundary condition at each observation in the point cloud. It is argued that a feature based representation of point cloud maps acquired from uncertain locations using noisy sensors has the potential to open up a new direction in robot mapping, localisation and SLAM. Numerical examples are presented to illustrate the proposed technique.