For long-term operations, graph-based simultaneous localization and mapping (SLAM) approaches require nodes to be marginalized in order to control the computational cost. In this paper, we present a method to recover a set of nonlinear factors that best represents the marginal distribution in terms of Kullback-Leibler divergence. The proposed method, which we call nonlinear factor recovery (NFR), estimates both the mean and the information matrix of the set of nonlinear factors, where the recovery of the latter is equivalent to solving a convex optimization problem. NFR is able to provide either the dense distribution or a sparse approximation of it. In contrast to previous algorithms, our method does not necessarily require a global linearization point and can be used with any nonlinear measurement function. Moreover, we are not restricted to only using tree-based sparse approximations and binary factors, but we can include any topology and correlations between measurements. Experiments performed on several publicly available datasets demonstrate that our method outperforms the state of the art with respect to the Kullback-Leibler divergence and the sparsity of the solution.

Abstract-In this paper we present a novel framework for nonlinear graph sparsification in the context of simultaneous localization and mapping. Our approach is formulated as a convex minimization problem, where we select the set of nonlinear measurements that best approximate the original distribution. In contrast to previous algorithms, our method does not require a global linearization point and can be used with any nonlinear measurement function. Experiments performed on several publicly available datasets demonstrate that our method outperforms the state of the art with respect to the KullbackLeibler divergence and the sparsity of the solution.

Human-centered environments are rich with a wide variety of spatial relations between everyday objects. For autonomous robots to operate effectively in such environments, they should be able to reason about these relations and generalize them to objects with different shapes and sizes. For example, having learned to place a toy inside a basket, a robot should be able to generalize this concept using a spoon and a cup. This requires a robot to have the flexibility to learn arbitrary relations in a lifelong manner, making it challenging for an expert to pre-program it with sufficient knowledge to do so beforehand. In this paper, we address the problem of learning spatial relations by introducing a novel method from the perspective of distance metric learning. Our approach enables a robot to reason about the similarity between pairwise spatial relations, thereby enabling it to use its previous knowledge when presented with a new relation to imitate. We show how this makes it possible to learn arbitrary spatial relations from non-expert users using a small number of examples and in an interactive manner. Our extensive evaluation with realworld data demonstrates the effectiveness of our method in reasoning about a continuous spectrum of spatial relations and generalizing them to new objects.1 The Freiburg Spatial Relations Dataset and a demo video of our approach running on the PR-2 robot are available at

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