A relative map approach to SLAM based on shift and rotation invariants

This paper presents a solution to the Simultaneous Localization and Mapping (SLAM) problem in the stochastic map framework based on the concept of the relative map. The idea consists in introducing a map state, which only contains relative quantities among the features invariant under shift and rotation. The estimation of this relative state is carried out through an Extended Kalman Filter. The shift and rotation invariance of the state allows us to significantly reduce the computational burden. In particular, the computational requirement is independent of the number of features. Furthermore, since the estimation process is local, it is not affected by the linearization introduced by the EKF. The cases of point features and corner features are considered. Furthermore, in the case of corners, it is considered a realistic case of an indoor environment containing structures consisting of several corners. Finally, since a relative map contains dependent elements, the information coming from all the constraints which express the elements dependency, is exploited. For this, an approximated solution with low computational requirement is proposed. Its limitation arises at the loop closure since it cannot exploit the information in this case. This is discussed in depth for the case of point features. Experimental results carried out on a real platform in our laboratory and by using the Victoria park dataset show the performance of the approach.