Nonlinear ego-motion estimation from optical flow for online control of a quadrotor UAV

Abstract

Abstract-For the control of Unmanned Aerial Vehicles (UAVs) in GPS-denied environments, cameras have been widely exploited as main sensory modality for addressing the UAV state estimation problem. However, the use of visual information for ego-motion estimation presents several theoretical and practical difficulties, such as data association, occlusions, and lack of direct metric information when exploiting monocular cameras. In this paper, we address these issues by considering a quadrotor UAV equipped with an onboard monocular camera and an Inertial Measurement Unit (IMU). First, we propose a robust ego-motion estimation algorithm for recovering the UAV scaled linear velocity and angular velocity from optical flow by exploiting the so-called continuous homography constraint in presence of planar scenes. Then, we address the problem of retrieving the (unknown) metric scale by fusing the visual information with measurements from the onboard IMU. To this end, two different estimation strategies are proposed and critically compared: a first one exploiting the classical Extended Kalman Filter (EKF) formulation, and a second one based on a novel nonlinear estimation framework. The main advantage of the latter scheme lies in the possibility of imposing a desired transient response to the estimation error when the camera moves with a constant acceleration norm w.r.t. the observed plane. We indeed show that, when compared against the EKF on the same trajectory and sensory data, the nonlinear scheme yields considerably superior performance in terms of convergence rate and predictability of the estimation. The paper is then concluded by an extensive experimental validation, including an onboard closed-loop control of a real quadrotor UAV meant to demonstrate the robustness of our approach in real-world conditions.

A direct optic flow-based strategy for inverse flight altitude estimation with monocular vision and IMU measurements

“…When the robot hovers at ∼1.2 m, the altitude estimation error is ∼10 cm. This is comparable to the results from in [22], where a robust feature-based ego-motion estimation algorithm was shown to provide the RMS error of 9.23 cm for a flight at 1 m altitude. Our results indicate the effectiveness of the proposed implementation of the direct optic flow method and the EKF scheme that are relatively simple in comparison.…”

“…In evidence of this, in [21], it was reported that the RMS errors in velocity estimates in flight were higher than those from a handheld experiment, citing the vibrations and motion blur as the cause of inaccuracies. Similarly, in [22], the results showed that the RMS errors of the estimated velocity To further inspect this claim, performed additional handheld experiments to imitate vertical flights in section 5. In this situation, the robot was manually moved vertically with the amplitude of ∼10 cm at the altitude of ∼40 cm, similar to the previous vertical flights.…”

“…Recently, researchers have explored the integration of optic flow information with other known quantities [19] or measurements from other sensors to exploit the 'scaling' information, allowing true velocity or distance to be estimated [18,[20][21][22]. In [20], the opto-aeronautic algorithm was developed for estimation of wind speed and flight height using inputs from optic flow and air velocity sensors, whereas in [18], an ultrasonic sensor was incorporated.…”

“…In [21,23], extended Kalman filters (EKF) were employed to recover a scale factor. In [22], the authors formulated a nonlinear estimation scheme for the task, allowing the transient response of the observer to be tuned. Based on the knowledge of control inputs, optic flow was used to robustly estimate the distance for landing in [19].…”

“…Compared to popular alternative keyframe-based visual-SLAM methods that involve building and maintaining a map of visual features [26][27][28], these optic-flow based approaches are potentially less computationally intensive and more robust against failures as they do not need prolonged continuous feature tracking [21,22].…”