On the Monte Carlo Representation of Uncertain Spatial Constraints

We present a novel approach to the problem of simultaneous localization and mapping (SLAM), that is not based on any of the three major SLAM paradigms: extended Kalman filters, particle filters and graph-based optimizers. In this approach, the uncertain spatial constraints are represented as ordered sets of Monte Carlo samples drawn from the space of coordinate frame transformations. Such a representation enables fusion of two or more spatial constraints even if they are correlated, under certain assumptions. The spatial constraints are organised in a compact data structure which models the full posterior over the robot's pose and landmark locations. The number of Monte Carlo samples necessary to accurately represent the posterior does not grow exponentially with the number of state-space dimensions as in conventional particle filters; in fact, it is a constant parameter. This data structure provides a constant time access to marginal distributions and a newly observed spatial constraint can be accommodated in time linear to the number of landmarks tracked, regardless of the number of spatial constraints that have been observed previously. We provide an experimental evaluation of the method, and discuss its strengths and weaknesses with respect to the well-established SLAM approaches.