The experimental results are as follows:
In Table 14, the research reaches a similar conclusion that
the mean localization accuracy by
WTLS
is equal to that of par-
allaxBA or
TLS
and higher than that of
BA±LS
and
BA±LM
. From
the fourth column, the mean relative localization accuracies
based on
WTLS
,
TLS
,
BA±LS
,
BA±LM
, and parallaxBA are 1.86%,
1.88%, 1.92%, 1.90%, and 1.86%, respectively. Meanwhile,
the localization accuracy is clearly higher than that in the
previous Section, which indicates that the effect of the errors
in the coordinate system transformation framework degrades
the positioning accuracy.
Conclusions
In this paper, a new localization algorithm for a planetary
rover is proposed. This algorithm is based on the weighted
total least squares adjustment, which considers error in both
the coefficient matrix and observation vector instead of
OLS
.
It includes two parts: (1) estimation of the epipolar geometry
of binocular cameras, and (2) planetary rover localization.
Rigorous analysis has been presented regarding why the new
planetary rover’s localization algorithm is superior to the
existing
OLS
and
BA
methods.
Various experimental results from the dataset of China’s
first lunar rover demonstrate the following: (1) the proposed
relative orientation algorithm based on
WTLS
has higher preci-
sion than
OLS
does in the epipolar geometry estimation of the
binocular cameras; (2) the weight matrix of the 3D coordi-
nate observations is more effective than the equal-precision
observations for the rover’s visual localization; and (3) the
proposed algorithm has equal accuracy and better efficiency
and convergence property than
BA
+
LS
, parallaxBA and
BA
+
LM
.
The main reason is that the aforementioned defects merely
caused by errors in the observation vector and dependency
on the initial parameters in existing
OLS
and
BA
algorithms
can be avoided in the proposed algorithm, resulting in more
theoretical rationality and direct convergence. In the actual
task, the rover’s localization system on the earth control
center read real-time data exactly and ran steadily using both
our method and
BA
algorithms. These methods strengthen the
effectiveness and credibility of the conclusions of the pose
estimation analysis by mutual authentication.
However, the proposed algorithm cannot guarantee con-
vergence to the true minimum under all conditions. Further
investigation is needed for the robustness of
WTLS
for the
planetary rover’s visual localization with respect to outliers.
Furthermore, the adaptive image matching and target tracking
algorithms in varying stations with the “front-back” overlap-
ping
FOV
are also very interesting themes for further research
of the planetary rover’s visual
SLAM
and automatic navigation.
Acknowledgments
Ma YouQing, Liu ShaoChuang and Peng Song are supported
by the National Natural Science Foundation of China (No.
41601494). Thanks to the reviewers and the associate editor
for providing the comments and hard work on our manu-
script.
References
Achtelik, M., M. Achtelik, S. Weiss, and R. Siegwart, 2011. Onboard
IMU and monocular vision based control for MAVs in unknown
in-and outdoor environments,
Proceedings of the 2011 IEEE
International Conference on Robotics and Automation (ICRA),
pp. 3056-3063.
Alexander, D.A., R,G. Deen, P.M. Andres, P. Zamani, H.B. Mortensen,
A.C. Chen, and C.L. Stanley, 2006. Processing of Mars
Exploration Rover imagery for science and operations planning,
Journal of Geophysical Research: Planets
, 111(E2).
Alismail, H., B. Browning, and S, Lucey, 2016. Photometric bundle
adjustment for vision-based SLAM,
Proceedings of the Asian
Conference on Computer Vision
, pp.324-341.
Bay, H., T. Tuytelaars, and L. Van Gool, 2006. Surf: Speeded up robust
features,
Computer Vision–ECCV 2006
, pp. 404-417.
Blanco, J.L., J. González-Jiménez, and J.A. Fernández-Madrigal,
2013. Sparser relative bundle adjustment (srba): Constant-time
maintenance and local optimization of arbitrarily large maps,
IEEE International Conference on Robotics and Automation
(ICRA),
(pp. 70-77).
Bouguet, J.Y., 2000. Matlab camera calibration toolbox,
CalTech
Technical Report
.
Davison, A.J., I.D. Reid, N.D. Molton, and O. Stasse, 2007.
MonoSLAM: Real-time single camera SLAM,
IEEE Transactions
on Pattern Analysis and Machine Intelligence
, 29(6).
Di, K., F. Xu, J. Wang, S. Agarwal, E. Brodyagina, R. Li, and L.
Matthies, 2008. Photogrammetric processing of rover imagery
of the 2003 Mars Exploration Rover mission,
ISPRS Journal of
Photogrammetry and Remote Sensing
, 63(2):181-201.
Engel, J., T. Schöps, and D. Cremers, 2014. LSD-SLAM: Large-
scale direct monocular SLAM,
Proceedings of the European
Conference on Computer Vision
, Springer, pp. 834-849.
Engel, J., V. Koltun, and D. Cremers, 2016. Direct sparse odometry,
arXiv preprint arXiv
:1607.02565.
Engels, C., H. Stewénius, and D. Nistér, 2006. Bundle adjustment
rules,
Photogrammetric Computer Vision
,
2
:124-131.
Fang, X, 2013. Weighted total least squares: necessary and sufficient
conditions, fixed and random parameters,
Journal of Geodesy
,
87(8), pp. 733-749.
Fraser, C.S, 1997. Digital camera self-calibration,
ISPRS Journal of
Photogrammetry and Remote Sensing
, 52(4):149-159.
Fusiello, A., and F. Crosilla, 2015. Solving bundle block adjustment
by generalized anisotropic Procrustes analysis,
ISPRS Journal of
Photogrammetry and Remote Sensing
, 102 :209-221.
Igual, L., X. Perez-Sala, S, Escalera, C. Angulo, and F. De la Torre,
2014. Continuous generalized procrustes analysis,
Pattern
Recognition
,
47
(2):659-671.
Indelman, V., A. Melim, and F. Dellaert, 2013. Incremental light
bundle adjustment for robotics navigation,
2013 IEEE/RSJ
International Conference on Intelligent Robots and Systems
(IROS),
pp. 1952-1959).
Table 14. Summary localization results of the simulated stereo camera system in the test field.
Number
Relative
distance (m)
Absolute localization accuracy (mm)
Relative localization accuracy (%)
BA+LS parallaxBA BA+LM TLS WTLS BA+LS parallaxBA BA+LM TLS WTLS
S1-S2
25.1
743.0
730.4
743.0 735.5 732.9 2.96
2.91
2.96 2.93 2.92
S2-S3
25.1
351.7
344.1
349.2 349.2 344.1 1.40
1.37
1.39 1.39 1.37
S3-S4
25.9
344.0
320.7
336.3 338.8 325.9 1.33
1.24
1.3
1.31 1.26
I1-I2
26.3
300.1
276.4
289.6 281.7 279.1 1.14
1.05
1.1
1.07 1.06
I2-I3
22.4
615.1
606.2
608.4 606.2 601.7 2.75
2.71
2.72 2.71 2.69
I3-I4
39.8
760.2
740.3
760.2 740.3 736.3 1.91
1.86
1.91 1.86 1.85
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
October 2018
617
