Technique of positioning and navigation of lunar surface vehicle
Natalia Kozlova
Moscow State University of Geodesy and Cartography (MIIGAiK) Extraterrestrial Laboratory
(MExLab), Moscow (natally.ko@gmail.com)
Introduction
Nowadays, Russia is preparing significant Lunar program [1], starting with landers (Luna-25 in
2018, Luna-27 in 2020), orbital mission (Luna-26 in 2019) and delivery of lunar polar soil to
Earth (Luna-28). Future plans include studying of the Moon with rovers (Luna-29) and even
establishment of a research and industrial Lunar base to support manned flights to the Moon.
Still for a long time exploration of the Moon will be carried out using mobile surface vehicles
(rovers). Therefore, to optimally plan future missions, it is now very important to review the
experience accumulated during driving and navigation of the Soviet missions Lunokhod-1 and
Lunokhod-2.
Experience of the Soviet Lunokhod-1 and -2 missions
Soviet Lunokhods studied mare regions in the Sea of Rains and in Le Monnier crater in 19701973. They covered distances of 9.9 and 39.1 km, and obtained about 180 and 90 surface
panoramic images, respectively. However, many important data, such as coordinates of
observation points, pointing directions, shooting date and time, was lost. We have assembled
all panoramas from archive fragments and recovered some part of this information using
methods and special programs developed at MExLab. The study showed that it is easier to
pinpoint the observation point if we have mountains or hills on the horizon of the image as we
see in Lunokhod-2 panoramas. In case of Lunokhod-1 the territory is very plain that makes
determination of exterior orientation for the images nearly impossible. Hills on the horizon also
help to navigate the rover during the mission.
No doubt, many things have changed since the 1970s but the problem of positioning and
navigation remained. Therefore, the described below technique allows us to solve the problem
on the basis of orbital images of the landing site using artificial modeling of surface images. It
is known that landing of future Russian missions is planned into a big crater [2] (such as
Boguslawsky and other craters at the South polar area), so will not face the problem which we
have with Lunokhod-1 panoramas, where it is not possible to find enough objects (mountains,
etc.) on the horizon to help with positioning and navigation.
Developed technique
To determine the rover coordinates the following technique is proposed.
1. First step includes selection and preparation of surface images which observation points are
to be determined. Here we also need to gather all service information, such as camera
parameters, date and time of shooting, approximate coordinates of the rover, etc.
2. On the second step, we need to prepare reference data – DEMs and orthomosaics for the
landing site.
Surface images and reference data have to satisfy a number of criteria. Firstly, the prepared
DEMs and orthomosaics must have accurate coordinates and cover sufficient area to capture
objects which can be seen on the horizon in surface images. Second criterion is high resolution
of images. It should be possible to distinguish individual objects on the horizon and use them as
reference points. Thirdly, it is good illumination conditions. Under good illumination we mean
that it is much easier to work if both images (surface and orbital) were obtained with
approximately the same Sun azimuth and height. In this case it is easier to identify objects
which can be used as reference points.
3. On the third step we use reference
orthomosaic and DEM to model
several artificial surface images from
different observation points so that
they have some identical features with
the selected one. This step is carried
out by means of special programming
module ‘OrthoDem2Cam’ which has
been created at our Laboratory.
Fig. 1. Comparison of the assembled archive
panorama obtained by Lunokhod-2 (above) and
modeled panoramic image (below).
Figure 1 shows that modeled image is
in good agreement with the real one.
However, one should pay attention that
on archival panoramas more details are visible in the foreground, while on the modeled images
- in the background.
4. Step four includes search and measurements of reference points, which tie the surface image
with ones modeled at the previouse step and with the coordinate frame.
Fig. 2. Search for reference points and their Fig. 3. Measurements of reference points in
coordinates in ‘OrthoDem2Cam’
PHOTOMOD
5. Processing of the prepared data in PHOTOMOD. For the adjustment we consider the
modeled images (their coordinates and orientation) error-free, while for the surface image we
use approximate position. As the result we obtain adjusted coordinates of observation point and
pointing direction for the surface image - coordinates and orientation of the lunar rover.
Significance of the proposed technique is in artificial modeling of lunar surface image based on
orbital image mosaic and DEM. Such approach allows us to model a visual panoramic image
which the driver of lunar rover would see from the particular point and direction. Therefore,
using this modeling, we can plan the lunokhod route in detail, providing the safest and optimal
way.
Lunar coordinate systems
We estimate the relative accuracy of the object (rover) coordinates on the lunar surface,
obtained using nadir orbital images (LRO spacecraft), as 1.1-2.3" (10-20 m on the lunar
surface). To assess this value a series of comparative evaluation of the potential accuracy of
coordinate systems ME and PA, as well as ephemeris DE405 and DE421 was performed ().
Table 1. Extreme differences in the position of the lunar North Pole and the sub-Earth point in
the Mean Earth (ME) and Principal Axes (PA) coordinates, as well as in the ephemeris DE405
and DE421 during the 10-year period (2000-2010).
МЕ–РА
Value
In
longitude
In
latitude
Min, "
67,088
Max, "
DE405–DE421
sub-Earth
point, m
In
longitude
In latitude
sub-Earth
point, m
77,798
3,46
0,28
69,042
78,560
3,48
0,36
Average, "
68,065
78,179
3,47
0,32
Min, m
565,55
655,84
861,766
29,2
2,4
29,1
Max, m
Average, m
582,02
573,79
662,26
659,05
874,746
868,256
29,3
29,3
3,0
2,7
29,4
29,3
The Table shows that differences in orientation of the axes between ME and PA coordinate
systems have an effect upon the coordinates of the surface point of about 868 m. Axes of
reference frames DE405 and DE421 are also turned for 3.47" in longitude and 0.32" in latitude
which results in 29 m difference in the lunar coordinates of the same point in different systems.
Differences in coordinates of the Lunar Pole and sub-Earth point, caused by the use of different
ephemeris are systematic. So, when preliminary calculations, this displacement of about 30 m
will not affect the adequacy of the results of calculations. However, for precise calculations,
where it is supposed to change from one version of the ephemeris to another, this longitudinal
shift should be taken into account.
Conclusion:
Modeling of the situation, based on orbital data using approximate exterior orientation
parameters and especially developed at the Laboratory software, helps to solve two basic
problems of rover navigation: 1) to plan the best and safest route; 2) to determine the
coordinates of the rover.
Acknowledgments
The research leading to these results has received funding from the European Community’s
Seventh Framework Program (FP7/2007-2013) under grant agreement № 312377 Planetary
Robotics Vision Data Exploitation (PRoViDE). We also would like to thank Russian State
Archive of Scientific and Technical Documentation which provide image fragments of archive
panoramas for research.
References
[1] Reports of meeting of subsection "Planets and small bodies of the Solar System" (section
"Solar System" Council on Space RAS) from 18.03.2015.
[2] L. Zelenyi et al. The sequence of missions “Luna-Glob”, “Luna-Resours” and “LunaGrunt” // 5MS3-MN-09, Moscow, IKI, 2014