Vector Distance Function Based Map Representation for Robot Localisation

Abstract

This paper introduces the use of the vector distance function (VDF) for representing environments, particularly for the use in localisation algorithms. It is shown that VDF has a continuous derivative at the object boundary in contrast to unsigned distance transform, and does not require an environment populated with closed object as in the case of the signed distance transforms, the two most common strategies reported in the literature for representing environments based on distances to nearest occupied regions. As such VDF overcomes the main disadvantages of the existing distance transform based representations in the context of robot localisation. The key properties of VDF are demonstrated and the use of VDF in robot localisation using an optimization based algorithm is illustrated using three examples. It is shown that the proposed environment representation and the localisation algorithm is effective in providing accurate location estimates as well as the associated uncertainties