User Feedback and Sample Weighting for Ill-Conditioned Hand-Eye Calibration

Hand-eye calibration is an important and extensively researched method for calibrating rigidly coupled sensors, solely based on estimates of their motion. Due to the geometric structure of this problem, at least two motion estimates with non-parallel rotation axes are required for a unique solution. If the majority of rotation axes are almost parallel, the resulting optimization problem is ill-conditioned. In this paper, we propose an approach to automatically weight the motion samples of such an ill-conditioned optimization problem for improving the conditioning. The sample weights are chosen in relation to the local density of all available rotation axes. Furthermore, we present an approach for estimating the sensitivity and conditioning of the cost function, separated into the translation and the rotation part. This information can be employed as user feedback when recording the calibration data to prevent ill-conditioning in advance. We evaluate and compare our approach on artificially augmented data from the KITTI odometry dataset.

Adaptive Patched Grid Mapping

In this work, we propose a novel adaptive grid mapping approach, the Adaptive Patched Grid Map, which enables a situational aware grid based perception for autonomous vehicles. Its structure allows a flexible representation of the surrounding unstructured environment. By splitting types of information into separate layers less memory is allocated when data is unevenly or sporadically available. However, layers must be resampled during the fusion process to cope with dynamically changing cell sizes. Therefore, we propose a novel spatial cell fusion approach. Together with the proposed fusion framework, dynamically changing external requirements, such as cell resolution specifications and horizon targets, are considered. For our evaluation, real-world data were recorded from an autonomous vehicle driving through various traffic situations. Based on this, the memory efficiency is compared to other approaches, and fusion execution times are determined. The results confirm the adaptation to requirement changes and a significant memory usage reduction.

Extrinsic Infrastructure Calibration Using the Hand-Eye Robot-World Formulation

We propose a certifiably globally optimal approach for solving the hand-eye robot-world problem supporting multiple sensors and targets at once. Further, we leverage this formulation for estimating a geo-referenced calibration of infrastructure sensors. Since vehicle motion recorded by infrastructure sensors is mostly planar, obtaining a unique solution for the respective hand-eye robot-world problem is unfeasible without incorporating additional knowledge. Hence, we extend our proposed method to include a-priori knowledge, i.e., the translation norm of calibration targets, to yield a unique solution. Our approach achieves state-of-the-art results on simulated and real-world data. Especially on real-world intersection data, our approach utilizing the translation norm is the only method providing accurate results.

Globally Optimal Multi-Scale Monocular Hand-Eye Calibration Using Dual Quaternions

In this work, we present an approach for monocular hand-eye calibration from per-sensor ego-motion based on dual quaternions. Due to non-metrically scaled translations of monocular odometry, a scaling factor has to be estimated in addition to the rotation and translation calibration. For this, we derive a quadratically constrained quadratic program that allows a combined estimation of all extrinsic calibration parameters. Using dual quaternions leads to low run-times due to their compact representation. Our problem formulation further allows to estimate multiple scalings simultaneously for different sequences of the same sensor setup. Based on our problem formulation, we derive both, a fast local and a globally optimal solving approach. Finally, our algorithms are evaluated and compared to state-of-the-art approaches on simulated and real-world data, e.g., the EuRoC MAV dataset.

Online Extrinsic Calibration based on Per-Sensor Ego-Motion Using Dual Quaternions

In this work, we propose an approach for extrinsic sensor calibration from per-sensor ego-motion estimates. Our problem formulation is based on dual quaternions, enabling two different online capable solving approaches. We provide a certifiable globally optimal and a fast local approach along with a method to verify the globality of the local approach. Additionally, means for integrating previous knowledge, for example, a common ground plane for planar sensor motion, are described. Our algorithms are evaluated on simulated data and on a publicly available dataset containing RGB-D camera images. Further, our online calibration approach is tested on the KITTI odometry dataset, which provides data of a lidar and two stereo camera systems mounted on a vehicle. Our evaluation confirms the short run time, state-of-the-art accuracy, as well as online capability of our approach while retaining the global optimality of the solution at any time.