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Extended Kalman Filter for Stereo Vision-Based Localization and Mapping Applications

[+] Author and Article Information
Xue Iuan Wong

Department of Mechanical and
Aerospace Engineering,
University at Buffalo,
Amherst, NY 14260-4400
e-mail: xuewong@buffalo.edu

Manoranjan Majji

Aerospace Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: mmajji@tamu.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received February 22, 2017; final manuscript received August 4, 2017; published online November 8, 2017. Assoc. Editor: Puneet Singla.

J. Dyn. Sys., Meas., Control 140(3), 030908 (Nov 08, 2017) (16 pages) Paper No: DS-17-1119; doi: 10.1115/1.4037784 History: Received February 22, 2017; Revised August 04, 2017

Image feature-based localization and mapping applications useful in field robotics are considered in this paper. Exploiting the continuity of image features and building upon the tracking algorithms that use point correspondences to provide an instantaneous localization solution, an extended Kalman filtering (EKF) approach is formulated for estimation of the rigid body motion of the camera coordinates with respect to the world coordinate system. Recent results by the authors in quantifying uncertainties associated with the feature tracking methods form the basis for deriving scene-dependent measurement error statistics that drive the optimal estimation approach. It is shown that the use of certain relative motion models between a static scene and the moving target can be recast as a recursive least squares problem and admits an efficient solution to the relative motion estimation problem that is amenable to real-time implementations on board mobile computing platforms with computational constraints. The utility of the estimation approaches developed in the paper is demonstrated using stereoscopic terrain mapping experiments carried out using mobile robots. The map uncertainties estimated by the filter are utilized to establish the registration of the local maps into the global coordinate system.

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Figures

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Fig. 1

Binocular stereopsis: image formation

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Fig. 2

Three out of 200 pairs of stereo images input to experiment 1: (a) left frame 1, (b) left frame 100, (c) left frame 200, (d) right frame 1, (e) right frame 100, and (f) right frame 200

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Fig. 3

Views of estimated global 3D map at different view direction and estimated camera pose of the experiment 1

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Fig. 4

Estimated relative translation of the experiment 1 (solid line) and estimated standard deviation bound (dashed line): (a) q1, (b) q2, (c) q3, (d) tx, (e) ty, and (f) tz

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Fig. 5

(a)–(c) Estimated relative CRP rate of the experiment 1 (solid line) and (d)–(f) estimated standard deviation bound (dashed line): (a) q˙1, (b) q˙2, (c) q˙3, (d) σq˙1, (e) σq˙2, and (f) σq˙3

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Fig. 6

(a)–(c) Estimated relative translation velocity of the experiment 1 (solid line) and (d)–(f) estimated standard deviation bound (dashed line): (a) t˙x, (b) t˙y, (c) t˙z, (d) σt˙x, (e) σt˙y, and (f) σt˙z

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Fig. 7

Views of estimated global 3D map at different view direction and estimated camera pose of the experiment 2

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Fig. 8

Estimated relative translation of the experiment 2 (solid line) and estimated standard deviation bound (dashed line): (a) q1, (b) q2, (c) q3, (d) tx, (e) ty, and (f) tz

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Fig. 9

(a)–(c) Estimated relative CRP rate of the experiment 2 (solid line) and (d)–(f) estimated standard deviation bound (dashed line). The large covariance around frame 160 corresponding to the sudden increment in velocity as being shown in second and third camera from the right-hand side in Fig. 7(a): (a) q˙1, (b) q˙2, (c) q˙3, (d) σq˙1, (e) σq˙2, and (f) σq˙3.

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Fig. 10

(a)–(c) Estimated relative translation velocity of the experiment 2 (solid line) and (d)–(f) estimated standard deviation bound (dashed line): (a) t˙x, (b) t˙y, (c) t˙z (d) σt˙x, (e) σt˙y, and (f) σt˙z

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Fig. 11

Views of estimated global 3D map at different view direction and estimated camera pose of the experiment 3

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Fig. 12

Estimated relative translation of the experiment 3 (solid line) and estimated standard deviation bound (dashed line): (a) q1, (b) q2, (c) q3, (d) tx, (e) ty, and (f) tz

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Fig. 13

Stereo camera trajectory of the experiment 3

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Fig. 14

(a)–(c) Estimated relative CRP rate of the experiment 3 (solid line) and (d)–(f) estimated standard deviation bound (dashed line): (a) q˙1, (b) q˙2, (c) q˙3, (d) σq˙1, (e) σq˙2, and (f) σq˙3

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Fig. 15

(a)–(c) Estimated relative translation velocity of the experiment 3 (solid line) and (d)–(f) estimated standard deviation bound (dashed line): (a) t˙x, (b) t˙y, (c) t˙z, (d) σt˙x, (e) σt˙y, and (f) σt˙z

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Fig. 16

A comparison of EKF filtered (top) and pre-EKF filtered (bottom) result from experiment 1. The misalignment in the maps produced using the prefiltered estimates indicates better accuracy for EKF solution.

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Fig. 17

Comparison of the EKF and prefiltered estimates. EKF estimates are shown in solid line, and prefiltered estimates are shown in solid line. Errors are computed relative to ICP estimated translation. The EKF estimated (dashed line) and prefiltered (dashed line) standard deviations are also plotted: (a) q1, (b) q2, (c) q3, (d) tx, (e) ty, and (f) tz.

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Fig. 18

Comparison of residual error of transformed 3D scene points with EKF and L.S

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