SELENESafe Exploration for Lunar Environments: Navigation Experts |
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Starting the Exploration As
the astronaut first exits the lunar lander, his location is determined
by three fixed RFID tags which are mounted at a known location on the
lunar lander. Using the time difference of arrival between the
transmitted RFID code and the received code, the Distance (d) = (c * 2) / (TDOA); Where c = Velocity of Light; TDOA = Time Difference of Arrival.
After exiting the lunar lander, the astronaut will be able to explore the near vicinity of the lander while maintaining knowledge of his exact coordinates provided that he maintain communication with the three RFIDs mounted on the lander. Given that the maximum distance of the astronaut to RFID tag to maintain a BER of 10-4 with an RFID tag is 3.4 m, it will be necessary for the astronaut to begin establishing his “bread crumb trail” very soon after exiting the lander. The bread crumb trail is established taking care of the non line of sight communication with the Lunar Lander. The procedure for creating a bread crumb trail is outlined next. Building a Trail Once the astronaut is prepared to begin laying out his RFID trail, he must first come to a stop, and drop an RFID tag. It is imperative that the astronaut place the tag directly at his feet, as his current location will be logged as the coordinates for the newly placed RFID tag. If the astronaut were to throw the tag, the procedure for ascertaining its spatial location would be much more complex an overall larger density of RFID tags including a larger number of tags needed to be within reliable communications range. Based on the initial reference locations of the tags and their distances from the astronaut using triangulation we can find the location for tag T4. The following system of quadratic equations can be used to find the position for the new tag dropped. Where (xn,yn) are the coordinates for tag N (N=4 for the first tag dropped) and (x1,y1), (x2,y2), and (x3,y3) are the locations for tag 1, tag 2, tag 3 respectively. This procedure then continues as the astronaut continues his expedition further from the lander. As he moves away from tag T4 he must drop another RFID tag before losing communication with three tags. As shown above, the location for tag T5 can be calculated based on the distances from three other tags with known locations. Once again we can use triangulation to establish a location for tag T5. Hence at any given time the astronaut should be in communication with at least three tags for the triangulation algorithm to work and provided that the three tags are not part of a straight line to accurately predict the location for the next tag dropped. Hence as the astronaut goes along the path he can know the map of the path along which he would be going. Initially the astronaut would start randomly and would know the trail as he is walking. The trail would be displayed on a hand held device based on the tag locations that he has already recorded. Constraints As the astronaut has to communicate with at least
three tags to find out its current location the astronaut would throw a
tag after Another constraint is that the astronaut cannot move
along a straight line in order for triangulation algorithm to work so
there is
Return Path: Since the astronaut is not moving in the exact straight line while returning back the optimum distance can be found based on the range of the astronaut and the position of the tags. The astronaut would search for the tags in descending order and the centroid of the triangles formed by the tags would give the optimum path. Several different algorithms can be implmented for tracing the return path at the expense of more processing time and cost (Dijkstra Algorithm). Errors and Limitations While developing the location algorithm a flat terrain was assumed and as the locations were calculated based on the 2-D system there would be some error component in calculating the 2-D co-ordinate However it can safely assumed that the realative positions of the tags does not get affected while doing the triangulation as the area covered by the tags used for triangulting would be small enough to considered as flat. The processing delay of the received signal may also lead to some error while calculting TDOA (Time differnce of arrival). The error can be minimized by subtracting the correction factor for processing delay from the TDOA to estimate the correct distance of the tag from the astronaut.
Find Complete Location Algorithm Code Here
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