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.

To fuse information from a 3D Light Detection and Ranging (LiDAR) sensor and a camera, the extrinsic transformation between the sensor coordinate systems needs to be known. Therefore, an extrinsic calibration must be performed, which is usually based on features extracted from sensor data. Naturally, sensor errors can affect the feature extraction process, and thus distort the calibration result. Unlike previous works, which do not consider the uncertainties of the sensors, we propose a set-membership approach that takes all sensor errors into account. Since the actual error distribution of off- the-shelf sensors is often unknown, we assume to only know bounds (or intervals) enclosing the sensor errors and accordingly introduce novel error models for both sensors. Next, we introduce interval-based approaches to extract corresponding features from images and point clouds. Due to the unknown but bounded sensor errors, we cannot determine the features exactly, but compute intervals guaranteed to enclose them. Subsequently, these feature intervals enable us to formulate a Constraint Satisfaction Problem (CSP). Finally, the CSP is solved to find a set of solutions that is guaranteed to contain the true solution and simultaneously reflects the accuracy of the calibration. Experiments using simulated and real data validate our approach and show its advantages over existing methods.

To properly fuse IMU and camera information for robotics applications, the relative timestamp offset between both sensors' data streams has to be considered. However, finding the exact timestamp offset is often impossible. Thus, it is necessary to additionally consider the offset's uncertainty if we want to produce reliable results. In order to find the offset and its uncertainty, we determine orientation estimates from IMU and camera under interval uncertainty. Subsequently, these intervals are used as a common representation for our bounded-error approach that finds an interval enclosing the true offset while also modeling the uncertainty. Calibration data can be acquired in a few seconds using a simple setup of IMU, camera and camera target. Results using both simulated and real data demonstrate that we are able to determine the offset to an accuracy of 20 ms with a computation time that is suitable for future online applications. Here, our approach could be used to monitor the timestamp offset in a guaranteed way. Additionally, our method can be adapted to determine an interval for the rotation between both sensors. While this increases the computation time drastically, it also enhances the accuracy of the timestamp offset to less than 10 ms.