Near-optimal SLAM exploration in Gaussian processes

In this paper we examine near-optimal SLAM exploration in Gaussian processes. We propose a submodular sensing quality function that extends studies from discrete sensor placement to an autonomous sampling scheme where sensing sites must be visited frequently. This is beneficial in the SLAM context, where sensing sites themselves bear uncertainties. Also in time-critical applications, we have to balance modeling accuracy against sensing time, which introduces noisy samples with only limited replications at each site. Our SLAM studies were inspired by our previous studies on indoor mobile robot localization that utilizes ambient magnetic fields. Those studies were based on observations that most indoor magnetic field distortions originate from concrete structures, which make these spatial fluctuations stable over time. Magnetic vector fields can be modelled by three orthogonal Gaussian processes that provide a flexible framework for localization. In the first part of this paper we prove that, in Gaussian processes, mutual information provides near-optimal solutions when each sensing site can be visited infinite times. We also conjecture that the optimal sites are within a set of sensing sites where the quality of processes is to be estimated. This enables near-optimal sensing when the sensing sites are defined in a probability space. In the second part we provide technical details and equations required when working in a SLAM context. We show that, considering pose uncertainties, we can use a greedy policy to select sensing sites that provide a near-optimal solution for modeling and give information required to decrease pose uncertainties. Finally, in order to evaluate our approach, we built preliminary simulations of vector fields.