Deterministic observer design for vision-aided inertial navigation

Abstract

The purpose of this tutorial is to report results developed over the last three years for state estimation problems arising with unmanned mobile robots equipped with a monocular camera and a 3-axis gyrometer, complemented with either a velocity sensor, or a 3-axis accelerometer, or an optical flow sensor. Definition and characterization of uniform observability for linear time-varying systems, followed by an observer design framework exploiting first-order approximations of a class of nonlinear systems, are first recalled. The resulting Riccati observers are locally uniformly exponentially stable when associated uniform observability conditions are satisfied. This framework is subsequently applied, with detailed explanations, to a set of practical problems, namely i) classical PnP camera pose estimation using known source points and bearing measurements, ii) the adaptation of this problem to unknown source points by using epipolar constraints, iii) camera pose and velocity estimation using bearing and IMU measurements, and iv) camera velocity and depth estimation using optical flow and IMU measurements from the observation of a planar target. The observer solutions proposed for these last two problems are validated with experimental data.

Signal corrector and decoupling estimations for UAV control

“…However, even small measurement error or very weak non-zero mean noise in acceleration through integrations can cause velocity and position to drift over time. The observer-based INS methods were used to estimate unknown variables in navigation [14,15]. However, position signals are limited to be local and bounded, but not global.…”

“…In signal corrector (14) and uncertainty observer (15), for the nonlinear function | * | α i sign ( * ), by selecting * = A i sin (ωt), its describing function can be expressed by 4 π when α i ∈ (0, 1). For the corrector (14), define:…”

Signal corrector and decoupling estimations for UAV control

“…However, even small measurement error or very weak non-Gaussian noise in acceleration through integrations can cause velocity and position to drift over time. The observer-based INS methods were used to estimate unknown variables in navigation [14,15]. However, position signals are limited to be local and bounded, but not global.…”

Homography-based Riccati observer design for camera pose estimation

“…The present paper introduces a novel direct approach to solving the homography-based pose estimation problem as an alternative to the classical homography estimationdecomposition process. Such that to obtain an estimate of the camera motion, the planar homography constraint between the two views of the scene is used directly to construct the system measurement equation needed for the Riccati observer design [3]. The design of the proposed observer builds on previous work of the authors [6] on pose estimation using epipolar constraints, itself an extension of their previous work on the PnP pose estimation problem, but departs from it in the modeling of the system and the output measurements.…”

“…The design of the proposed observer builds on previous work of the authors [6] on pose estimation using epipolar constraints, itself an extension of their previous work on the PnP pose estimation problem, but departs from it in the modeling of the system and the output measurements. The output measurement equation used in [6] is slightly modified in this work to meet the requirements of the Riccati observer framework [3] when using the planar homography constraint.…”