Vladyslav Usenko

Nikolaus Demmel, David Schubert, Christiane Sommer et al.

In this paper we propose a novel square root sliding-window bundle adjustment suitable for real-time odometry applications. The square root formulation pervades three major aspects of our optimization-based sliding-window estimator: for bundle adjustment we eliminate landmark variables with nullspace projection; to store the marginalization prior we employ a matrix square root of the Hessian; and when marginalizing old poses we avoid forming normal equations and update the square root prior directly with a specialized QR decomposition. We show that the proposed square root marginalization is algebraically equivalent to the conventional use of Schur complement (SC) on the Hessian. Moreover, it elegantly deals with rank-deficient Jacobians producing a prior equivalent to SC with Moore-Penrose inverse. Our evaluation of visual and visual-inertial odometry on real-world datasets demonstrates that the proposed estimator is 36% faster than the baseline. It furthermore shows that in single precision, conventional Hessian-based marginalization leads to numeric failures and reduced accuracy. We analyse numeric properties of the marginalization prior to explain why our square root form does not suffer from the same effect and therefore entails superior performance.

Nikolaus Demmel, Christiane Sommer, Daniel Cremers et al.

We propose a new formulation for the bundle adjustment problem which relies on nullspace marginalization of landmark variables by QR decomposition. Our approach, which we call square root bundle adjustment, is algebraically equivalent to the commonly used Schur complement trick, improves the numeric stability of computations, and allows for solving large-scale bundle adjustment problems with single-precision floating-point numbers. We show in real-world experiments with the BAL datasets that even in single precision the proposed solver achieves on average equally accurate solutions compared to Schur complement solvers using double precision. It runs significantly faster, but can require larger amounts of memory on dense problems. The proposed formulation relies on simple linear algebra operations and opens the way for efficient implementations of bundle adjustment on hardware platforms optimized for single-precision linear algebra processing.

David Schubert, Thore Goll, Nikolaus Demmel et al.

Visual odometry and SLAM methods have a large variety of applications in domains such as augmented reality or robotics. Complementing vision sensors with inertial measurements tremendously improves tracking accuracy and robustness, and thus has spawned large interest in the development of visual-inertial (VI) odometry approaches. In this paper, we propose the TUM VI benchmark, a novel dataset with a diverse set of sequences in different scenes for evaluating VI odometry. It provides camera images with 1024x1024 resolution at 20 Hz, high dynamic range and photometric calibration. An IMU measures accelerations and angular velocities on 3 axes at 200 Hz, while the cameras and IMU sensors are time-synchronized in hardware. For trajectory evaluation, we also provide accurate pose ground truth from a motion capture system at high frequency (120 Hz) at the start and end of the sequences which we accurately aligned with the camera and IMU measurements. The full dataset with raw and calibrated data is publicly available. We also evaluate state-of-the-art VI odometry approaches on our dataset.

Lukas von Stumberg, Vladyslav Usenko, Jakob Engel et al.

Micro aerial vehicles (MAVs) are strongly limited in their payload and power capacity. In order to implement autonomous navigation, algorithms are therefore desirable that use sensory equipment that is as small, low-weight, and low-power consuming as possible. In this paper, we propose a method for autonomous MAV navigation and exploration using a low-cost consumer-grade quadrocopter equipped with a monocular camera. Our vision-based navigation system builds on LSD-SLAM which estimates the MAV trajectory and a semi-dense reconstruction of the environment in real-time. Since LSD-SLAM only determines depth at high gradient pixels, texture-less areas are not directly observed so that previous exploration methods that assume dense map information cannot directly be applied. We propose an obstacle mapping and exploration approach that takes the properties of our semi-dense monocular SLAM system into account. In experiments, we demonstrate our vision-based autonomous navigation and exploration system with a Parrot Bebop MAV.

Jakob Engel, Vladyslav Usenko, Daniel Cremers

We present a dataset for evaluating the tracking accuracy of monocular visual odometry and SLAM methods. It contains 50 real-world sequences comprising more than 100 minutes of video, recorded across dozens of different environments -- ranging from narrow indoor corridors to wide outdoor scenes. All sequences contain mostly exploring camera motion, starting and ending at the same position. This allows to evaluate tracking accuracy via the accumulated drift from start to end, without requiring ground truth for the full sequence. In contrast to existing datasets, all sequences are photometrically calibrated. We provide exposure times for each frame as reported by the sensor, the camera response function, and dense lens attenuation factors. We also propose a novel, simple approach to non-parametric vignette calibration, which requires minimal set-up and is easy to reproduce. Finally, we thoroughly evaluate two existing methods (ORB-SLAM and DSO) on the dataset, including an analysis of the effect of image resolution, camera field of view, and the camera motion direction.