We present a novel interval-based visual-inertial LiDAR SLAM (i-VIL SLAM) method that solely assumes sensor errors to be bounded and propagates the error from the input sources to the estimated map and trajectory using interval analysis. The method allows us to restrict the solution set of the robot poses and the position of the landmarks to the set that is consistent with the measurements. If the error limits are not violated, it is guaranteed that the estimated set contains the true solution. The accumulation of the uncertainty is stabilized by anchoring poses derived from GNSS/INS data. Furthermore, for the first time we compare confidence ellipses determined by a classical SLAM graph optimization approach with the interval estimates of the robot poses provided by our method. In this work, we experimentally show that the marginal co-variances computed by the classical SLAM graph optimization are too overconfident and underestimate the uncertainty of the poses. While the 99.9 %-ellipsoids derived from the marginal covariances of the poses only enclose less than 64 % of the ground truth in the worst case, our method provides interval bounds for the pose parameters that enclose the ground truth for more than 96 % of all frames.

Localization and mapping are essential tasks in mobile robotics. A purely odometry-based pose estimation accumulates errors caused by factors such as unequal wheel-diameters or wheel-slippage and is, therefore, inaccurate. The resulting error can be corrected by recognizing previously observed places and constraining the robots' relative poses. A common challenge of such place recognition methods arises from the incorrect association of different places, which can corrupt the resulting pose correction and, consequently, any map update. Therefore, we propose a novel place recognition method that enables the selection of a correct place recognition hypothesis from a set of possible matches.In this work, we make use of the fact that multiple robots' trajectories run parallel in many scenarios, like in warehouse corridors or on public roads. In such situations, place recognition can be regarded as a sequential task along the robots' trajectories. We study the problem of repetitive, periodic and indistinguishable landmarks for place recognition on regularly-spaced guideposts on German rural roads. By interpreting place recognition hypotheses as nodes of a k-partite graph, we introduce our novel selection method, the Hierarchic Single Cluster Graph Partitioning, that enables the robust selection of the correct hypotheses by finding the optimal path within the graph. The selected place recognition information is used to build a map incorporating multiple observations acquired from multiple vehicles.