Range Identification for Perspective Vision Systems: A Position-Based Approach

Abstract

In this paper, a new estimator using a single moving calibrated camera is developed to asymptotically recover the range (depth) and the 3D Euclidean position of a static object feature. The position and the orientation of the camera is assumed to be measurable unlike in existing observers where velocity measurements are assumed to be known. To estimate the unknown depth along with the 3D coordinate of a feature an adaptive least squares estimation strategy is employed based on a novel prediction error formulation and a Lyapunov stability analysis. The developed estimator has a simple mathematical structure, can be used to identify range and 3D Euclidean coordinates of multiple features, and is easy to implement. Numerical simulation results along with experimental results are presented to illustrate the effectiveness of the proposed algorithm.

Euclidean Position Estimation of Static Features Using a Moving Uncalibrated Camera

“…To proceed with the error development, the term is multiplied to the both sides of (8) that results in the following expression: (14) The estimate of (14) can be written as follows: (15) where and are the estimates of and , respectively, and denote and , respectively, where are the estimates of and , respectively. To facilitate the development, the terms and are added and subtracted from the right-hand side and the left-hand side of (14), respectively, that yields the following expression: (16) After subtracting (15) from (16), the following expression is obtained: (17) where is the prediction error for the th feature point , is the structure estimation error, and denotes , where . After adding and subtracting the term to the left-hand side of (17) and simplifying, the following expression can be obtained: (18) where denotes and .…”

“…To facilitate the development, the terms and are added and subtracted from the right-hand side and the left-hand side of (14), respectively, that yields the following expression: (16) After subtracting (15) from (16), the following expression is obtained: (17) where is the prediction error for the th feature point , is the structure estimation error, and denotes , where . After adding and subtracting the term to the left-hand side of (17) and simplifying, the following expression can be obtained: (18) where denotes and . To ease the subsequent analysis, we combine these individual vectors to obtain their respective compact forms.…”

“…Remark 3: The projection algorithm utilized in (37), and (41) ensures that is bounded . Furthermore, it satisfies the following inequalities (see [17] for a detailed description):…”

“…However, this work assumed a calibrated camera, i.e., the intrinsic and the extrinsic camera calibration parameters were assumed to be known. The work in [16] was extended and evaluated experimentally in [17] where it was realized that calibrating a camera is tedious and complicated, especially calibration of the camera's extrinsic parameters.…”

Range identification for nonlinear parameterizable paracatadioptric systems

“…doi:10.1016/j.automatica.2010.03.017 identify the range when the motion parameters were known (Chen & Kano, 2002Dixon, Fang, Dawson, & Flynn, 2003;Jankovic & Ghosh, 1995;Karagiannis & Astolfi, 2005;Ma, Chen, & Moore, 2004). More recently, in Nath, Braganza, and Dawson (2008a), the measurement of camera position was utilized to develop an adaptive estimator to recover the structure; this was extended in Nath, Braganza, Dawson, and Burg (2008b) to recover the range.…”