AIAA Space 2007 Conference & Exposition Technology for Autonomous Optical Planetary Navigation and

Precision Landing

Tom Weismuller David Caballero

Manny Leinz

Electronic and Sensor Systems Advanced Network and Space Systems

The Boeing Company Abstract This paper describes techniques to enable unmanned planetary orbiters (or landers) to successfully navigate over terrain by use of optical imagery which is dynamically generated along the nadir and continuously compared against a stored database of significant craters or other features. These techniques can be a key technology enabling precision descent guidance for autonomous landing and hazard avoidance. This initial work is focused on the moon, but is extensible to Mars and other bodies such as asteroids. Low cost visible and infrared imagers will be used to provide input to the automatic feature recognition algorithm, which primarily identifies the location of craters of selected radii in terms of focal plane coordinates, while eliminating extraneous features not used for comparison. This method could also be used to identify secondary features such as rills and ridges, but the predictable shape and abundance of craters over the lunar surface makes them the logical choice as the primary feature to be used for the initial evaluation. Use of both IR and visible input allows enhancement of the observed surface features by registration of the images through affine transformation and image fusion, especially when lighting conditions are difficult. Comparison to the stored database of lunar craters is analogous to celestial star tracking, but in this case the storage elements consist of the locations of selected craters in lunar coordinates along with their nominal radius. Use of the radius information greatly reduces the risk of false pattern matches. The algorithms described in this paper which are used to autonomously detect the lunar craters employ a combination of edge generation of the input image along with a Hough transformation of the resultant edge image to locate craters of a selected radius. Dynamic thresholding is used to manage the amount of edges produced and produce a population of candidate craters consistent with a realistic lunar environment. False alarms are subsequently reduced by analyzing the angular slope distribution of the edges produced for each crater

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AIAA SPACE 2007 Conference & Exposition18 - 20 September 2007, Long Beach, California

AIAA 2007-6173

Copyright © 2007 by The Boeing Company. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

and producing a score weighted according to the deviation of the expected slope against the actual slope measured. In practice, this eliminates false craters formed from clusters of edges in the scene which may be arranged roughly in a circle, but which in fact belong to unrelated features. When the altitude of the vehicle is known by independent means, this information can be used to convert the location of the observed craters to actual lunar coordinates. However, if the altitude is not known precisely, the crater patterns generated can be used to create normalized ratios of crater locations and compared against normalized map data to actually estimate altitude. Whether or not the altitude needs to be determined, once an initial estimate of the craft location is obtained through an exhaustive search, subsequent updates will be comparatively fast, since only a local region around the last position need be searched. Data fusion of the techniques described in this paper with available LIDAR data can add robustness and redundancy to the navigation solution. Mission risk reduction is realized through use of these two independent methods, which can provide both position and altitude information as input to an appropriate device such as a Kalman filter for an enhanced overall navigation solution. Introduction The current national goal for achieving manned exploration of Mars calls first for a return to the moon. Lunar bases may even serve as way stations for outbound expeditions. Unlike earlier lunar missions, astronauts will stay for greatly extended periods at these bases, which requires a fundamental change in the way lunar missions operate. Instead of keeping a manned presence aboard the command module while the lunar module descends to the lunar surface for a short period and then returns, the plan now calls for all astronauts to descend together and leave the command module vacant. The command module would remain unoccupied in lunar orbit for up to several months before astronauts reboard and return to earth. The effect of local irregularities in lunar gravitational fields creates uncertainty in orbital position over time. Although these irregularities have been comprehensively characterized for the earth, this is not true for the moon and other planetary bodies. Therefore, a reliable method must be devised to allow the command module to autonomously and continually provide latitude, longitude, and altitude updates to its onboard navigation system. This can be accomplished through the use of crater navigation. Although the work described in this paper has been focused to date on the orbiter scenario described above, the crater navigation method is equally applicable to use in the lunar lander, In this case, the position of the lander as it deorbits over the moon’s surface can be tracked precisely up to the point of touchdown.

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Crater navigation is the ability to determine spacecraft position and attitude using sensor measurements of the lunar surface and correlating those measurements with predefined database parameters derived from maps of craters on the entire lunar surface. These required sensor measurements consist of images collected from visible or IR cameras. Figure 1 shows an example of a lunar surface image collected for this purpose using a visible sensor. For the work done in this project, a map of a 0.2% area of the moon1 in the vicinity of Oceanus Procellarum was created. The edges of the map were modified to seamlessly loop the map’s terrain from north to south and east to west, in essence creating the effect of a continuous globe. This area of the moon was selected because it contained a reasonable variety of lunar features such as plains, mountain ridges, variation in density of the crater population, and variation in crater sizes as well. The database of crater parameters consists of coordinates of crater centers and the nominal radius for each crater. The craters used for this database are selected from a survey of all craters on the lunar surface (which will be greatly enhanced after launch of the Lunar Reconnaissance Orbiter, now scheduled for fall of 2008). The selection criteria include using only well-formed, nearly circular craters; avoiding craters that impinge on each other; using craters of only a narrowly defined set of radii; and attempting to keep the spatial density of included craters reasonably constant and sufficient to insure detection of several craters in any particular field of view.

1 The source of the imagery was NASA’s Lunar Topographic Orthophotomap series, collected photographically by Apollo 15 in August, 1971.

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Figure 1. Example Of Lunar Surface Imagery Using Visible Sensor.

The following steps are required to determine lunar orbital position from a single sensor image: 1. Capture the image from the sensor, which can either a visible or infrared

type. 2. Create a binary edge image to outline each crater from the sensor input

image. Also assign a progression angle to each edge pixel in the binary image.

3. Determine areas in the edge image which fit well to circles with radii included in the crater database. Create an image showing these well-fitting areas and their corresponding radii.

4. Obtain each crater’s location from this resultant image. 5. Remove any craters from this image which are too closely spaced, or which

do not have a progression of angles about the perimeter which fit well with a circular object.

6. Using the distances between crater centers determined above and the radii of these craters, attempt to identify each remaining crater with an entry in the crater database.

7. Use the successful matches in the above step to determine the location and attitude of the sensor over the lunar surface.

Figure 2 shows pictorially the flow of the steps outlined above. These steps are discussed in more detail below.

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Sensor input image Binary edge image

Final crater detection Crater detection locationsNon crater-like, or closely spaced, object rejection

Compare to database crater entries

Hough transform image(Circular Fit Process)

(Latitude, Longitude)

Final position determination

Figure 2. Crater Detection Algorithm Flowchart.

Detailed Description of Algorithms The raw sensed image may be input directly to the algorithm for creating a binary edge image. However, low pass filtering can be used first to reduce pixel to pixel noise, if necessary. A spatial averaging or median filter can be employed for this purpose. Alternatively, a high pass filter (such as a Laplacian or morphing filter) could be used instead to augment edge

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enhancement. Use of these options is dependent on the camera systems selected for the mission2.

Two standard methods have been successfully used in this project for generation of detected edges. These include a Sobel filter and a Boie-Cox filter, both of which create similar appearing edge images such as shown in Figure 3.

Figure 3. Sobel Filter Applied To Figure 1.

The output of the edge filter is a grayscale edge image. A threshold is applied to this grayscale image as the first step in producing a binary image. To obtain the threshold, a normalized histogram of the edge image data is created by binning pixels according to their grayscale intensity. This histogram is normalized by dividing the number of pixels in each bin by the total number of pixels in the image array. Starting with the first bin, the number in each bin is summed until a value of N is reached, where N represents the fraction of pixels to be excluded. The intensity value corresponding to the last bin summed is determined to be the threshold. Figure 4 shows a histogram of Figure 3, where N is about 0.97, and the resulting threshold is about 282.

2 For a reference on standard methods of filtering, see Seul, Michael, Image Analysis Description, Examples, And Code, Cambridge University Press, 2005.

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.25

.20

.15

.10

.050.0

Fraction N of data in this area

Threshold ~282

Figure 4. Histogram Of Figure 3.

The binary edge image is obtained by setting all pixel values that are greater than or equal to the threshold to one. All other pixels are set to zero. Figure 5 shows the resulting binary image of Figure 3 using a 0.97 value for N.

Figure 5. N = 0.97 Threshold Binary Image Of Figure 3.

For all pixels that have been set to one in the binary edge image, the

direction of the corresponding pixel in the filtered image is also determined. If the Sobel filter is used, the pixel direction is determined from the gradient directions which are generated when the Sobel image is created.

If the Boie-Cox filter is used, then images are generated during the filtering process where each image corresponds to a particular direction. The pixel direction associated with the binary pixel value is determined by

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comparing the corresponding pixel in each Boie-Cox direction image. The direction associated with the image with the maximum value for a given pixel is then assigned to the binary image pixel. Figure 6 shows the direction image for the Boie-Cox image obtained from Figure 1.

Figure 6. Boie-Cox Angle Image Of Figure 1.

The left hand side of Figure shows an enlargement of the box inset into the image on the right hand side. In this enlargement there are four discrete directions or angles: 0 or 180 degrees represented by red, 45 or 225 degrees represented by blue, 90 or 270 degrees represented by yellow, and 135 or 315 degrees represented by green. This angle data associated with each detected binary edge pixel is important later in the process when discriminating true craters against false alarms. Following creation of the binary edge image, the next step is to determine the location of craters of certain sizes in the image. Craters are seldom, if ever, perfectly round. They may have jagged edges, areas of poor edge definition which result in missing sections in the binary image, and they may be more ellipsoidal than truly circular. For these reasons, when searching for a crater of a specific radius, an upper and lower bound is given to the radius to allow for irregularities. For example, if a crater has a nominal radius of nine pixels, the upper and lower bounds for examining the crater might be six and twelve pixels. To create an image showing the location of craters of interest, first all pixel values in the new image are set to zero. Then, for each discrete unit radius (that is, from the lower bound to the upper bound stepping in unit increments), a pixelwise scan across the binary edge image is made. For each

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above-detection pixel encountered, a circle is generated around the detected pixel having a radius of the current search value. For every pixel intersected by the generated circle, the intensity of that pixel is incremented by one. A very simple example is shown in Figure 7 using a search circle with both the upper and lower bounds equal to the nominal radius, and with only three detected edge pixels on the original binary edge image.

1

1

2

3

1 1 11

1

1

1

111

1

11

1

1 1 1 111

1

11

111

11

1

1

1

11

1

1

1

111

1

11

12

2

3 points on circledetected in binaryimage.

Circles of radius rgenerated abouteach detected pixeland summed incrater location image

The location with the highestcounts is the center of the original circle.

Figure 7. Crater Location Image Example.

As mentioned above, real-world usage involves searching not just at the nominal radius value, but rather a band of radii. The resulting search will then produce a pattern with local peaks which will ideally indicate the location of centers of craters having a radius value within the band searched. These peaks are isolated from background clutter by thresholding. This algorithm is a modification of the standard circular Hough transform3.

Figure 8 shows an example of a modified Hough transform image applied to the binary image of Figure 5, processed within a band of radii with a lower bound of three pixels and an upper bound of nine (the nominal desired radius was six pixels). Each local bright area indicated by a sharp white point represents the central location of a crater with a radius falling within these bounds.

3 For a description of the Hough transform, see Salas, Renato, Image Processing and Computer Vision Circle Detection Assignment, University Of Bristol.

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Figure 8. Hough Transform Image of the Binary Image of Figure,

with a Radius Search Band from Six to Nine Pixels. The thresholds used to isolate the crater center locations in the modified Hough transform image are determined in the same manner as described above for thresholding the grayscale Sobel or Boie-Cox edge image. Pixel clusters found above the threshold are assumed to indicate the center locations of craters in the scene. The centroid of each cluster is computed and stored in a list as a possible location for a crater with the associated search radius.

For each radius, a closely spaced object (CSO) rejection is then performed. If two objects with the same search radius are detected in the list and are within a predefined close distance of each other, then the object with the brightest peak in the corresponding Hough transform image is kept in the list and the other object is deleted from the list. It is useful to make the predefined threshold spacing a function of the radius.

A second check is performed to eliminate objects in the list that are not

sufficiently crater-like. This involves looking at the detected pixels in the binary edge image within the search band of radii for each list entry and evaluating their angular component. A well-defined circle should have a continuous progression of angular direction along the circumference. Figure 9 shows an example of a series of well-defined circles contained within a particular radial search band.

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yellow = 67.5 to 112.5

red = -22.5 to 22.5 blue = 22.5 to 67.5

green = 112.5 to 157.5

rr u

rl

bin2bin1

bin0

bin7 bin6

bin5

bin4

bin3

(x,y)

Figure 9. Expected Angle Bins For A Crater.

Eight angle bins are generated by the edge processing algorithms

described above. Using the angle image shown in Figure 6, for example, every pixel located within the radius bound for each crater examined is counted and checked against the expected angle for that crater. If the edge pixel's angle falls within the expected angle range for a particular bin, then the bin counter for that angle is incremented. If the edge pixel's angle is perpendicular to the expected angle, then the bin counter for that angle is decremented. If the edge pixel’s angle falls in any other bin, then the bin counter is neither incremented nor decremented.

After all pixels have been summed in this manner, each individual bin is

examined to see if it is valid overall. It is declared valid if the normalized bin count for that bin is greater than a threshold. Following this, the number of valid bins for the entire circle is counted. If this count is greater than a given threshold, then this feature passes the overall test and is considered sufficiently crater-like (i.e., circular about one fixed center). Figure 10 shows two examples of crater testing. The left side of the figure shows a test case with a score surpassing the threshold to be considered a valid crater (note most of the bins have positive overall counts). The right side, on the other hand, shows a test case with fewer positive bins and some negative bins as well. This one fails the crater validity test.

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r r u

r l r

r u r l

Angle image looks like a crater

Does not look like a crater

(x,y)( x,y )

+ +

+ + + +

+

+ + + +

+ +

+ + +

+ + +

- -

- -

++ + +

+ + ++

+ +

-

-

Figure 10. Test Cases for Determining Crater Validity

Based on Edge Angle Values

Following the crater validity testing, an algorithm is employed to identify which craters in the crater database match with the validated craters in the field of view, thereby fixing the position of the spacecraft over the lunar surface. This algorithm is based on a generic star tracking algorithm described in the literature4. Figure 11 shows an overall flow diagram of the crater identification algorithm.

4 Shucker, Brian; Ground-Based Prototype Of CMOS Navigational Star Camera For Small Satellite Applications, University Of Arizona, 15th AIAA/USU Conference On Small Satellites.

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IdentificationList Found?

Local Search Algorithm

For eachlocal patch

All PatchesExamined?

Done (search successful)

Done (search unsuccessful)

No

No

IdentificationList Found?

YesPick The Best

Find craters which closely match database entries

If successful, refine list by searching for additional neighboring database

craters using relaxed error bounds

Normal Search AlgorithmFind craters which closely match database entries

If successful, refine list by searching for additional neighboring database

craters using relaxed error bounds

Yes

Yes

No

Figure 11. Crater Identification Options and Modes. The normal crater identification algorithm is used with the crater database for the entire moon. For cases where this search fails to reveal a unique set of lunar coordinates, a local search algorithm is employed to find possible solutions using database information from many smaller lunar regions, which then collectively include all areas of the moon. From this, the best choice is selected from the set of multiple solutions. As mentioned above, the crater tracking algorithm uses a database of crater positions in lunar coordinates and radius size (Az, El, R)m. This database is reduced in size by keeping only craters whose sizes are less than a desired size related to the maximum field of view of the sensor. This reduced database is referred to as the Crater Position Database (CPD).

From the CPD a list is generated by computing the angular distance, Δ, between all possible pairs of craters (S1, S2). Crater pairs whose angular distance is greater than a threshold (e.g. the sensor field of view) are not maintained in this list. The list consists of the angular separation and designation of the craters (Δ, S1, S2). This list is called the Crater Distance List (CDL). This list is ordered either from minimum separation distances to the maximum, or vice versa.

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From the sensor measurement detections, a list of estimated crater

positions on the sensor array and their associated radii (Az, El, R)FPA are input into the crater identification algorithm. This list is also pared down by removing all detections from the Crater Position Database whose radius is either too small or too large. From this list the angular distance, ΔFPA, is computed for all pairs of detections, (D1, D2). This list, called the Detection Distance List (DDL), consists of a list of triplets (ΔFPA, D1, D2).

Based on the performance of the sensor, an error is associated with the measurement of the crater position and radius size. For position, this error is called Angular Measurement Precision (AMP) and for radius this error is called Radius Measurement Precision (RMP).

The first phase of crater identification compares all distances between

detected craters to the distances in the CDL. A crater count array (CCA) is used to count up the number of times the crater separation distance from the database is the same (within bounds) as a detected crater pair. This array consists of bins corresponding to each crater in the CPD.

For each detected crater in the measurement list, the CCA is initially set to zero. For a given detected crater, the distance to all other detected craters is computed. Using the AMP a bound is obtained for the angular distance measurement Δmin<ΔFPA<Δmax for each measured pair. For each pair of measurements the CDL is searched for any pairs of craters (C1,C2) whose distance lie with in the bounds (Δmin<Δ<Δmax). Each pair of CDL craters that lie within this bound have their crater count bins incremented by one.

D 1

D 2

D 3 D 4

D 5

Detection 1, compute distance to all other detections

Δ12

Δ13Δ 14

Δ 15

Δab,Ca,CbΔyz,Cy,CzΔjk,Cj,CkΔmn,Cm,CnΔav,Ca,CvΔpb,Cp,Cb

...Δzc,Cz,CcΔrf,Cf,CfΔmc,Cm,CcΔco,Cc,CoΔps,Cp,CsΔxk,Cx,Ck

OrderedCDL

Δmin

Δmax

Δ12 range

Ci counta 1b 1c 0d 0e 0f 0g 0...u 0v 1w 0x 0y 1z 1

CCAafter lookingat Δ12

C i counta 1b 1c 0d 0e 0f 2g 0...u 0v 4w 0x 2y 1z 1

CCA after lookingat Δ 12,...Δ15

Figure 12. Crater Distance Check

For any given detected crater, after all comparisons have been made the

bin with the maximum counts is noted. This bin count is compared to a

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threshold. If the threshold is exceeded, then that crater, Ci, is said to correspond to the given detection. In the example shown in Figure 12, Ci=v is the crater that corresponds to the detection D1. If the maximum bin count is less than the threshold, the given detection is not assigned to a crater from the crater database.

To reduce the uncertainty of correct crater identification, at this point a

check is performed on the differences between the radius of the detected crater and the expected size of the radius from the crater database. If the difference is greater than a limiting range, then this is labeled a bad identification and the detected crater is deleted from the detection list. The limiting range is a function of the radius and the RMP. If the maximum bin count is tied between two or more craters, and this count exceeds the minimum threshold, then the one with the radius most closely matching the database expected value is chosen as the correct match. This additional radius check is shown in Figure 13.

R 1 R 3

Δ13

R jR k

Δ jk

From DDL

From CDL

To increase CCA for C j and C kNot only must Δmin<Δ jk< Δ max But we must also have R1min<Rj<R1max and R 3min <R k <R 3maxor R1min<Rk<R1max and R 3min< R j<R 3max

Figure 13. Additional Radius Check for Crater Identification

The output at this point is a detected crater list that consists only of

detections that have been associated with craters found in the database.

The next phase performs an additional check on all identified crater detections. An array of size equal to the number of identified craters is created to act as a validation counter. This array is initially set to zero. For each pair of craters identified earlier as potentially assigned to known entries in the crater database, the distance between the craters in the database is compared to the distance between the actual measurements. If, within tolerable limits, the distances are the same, the detection count bin assigned to each crater under investigation is incremented by one.

If there are N of these identified craters in total, and all craters match their associations, then each bin should have a count of N-1 to have a perfect match. If this is the case, then the identified crater list is deemed valid and this routine is exited. Otherwise, the median count of the array is computed. If the median is equal to the minimum count, then the median count is

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incremented by one. All craters whose count is less than the median count are then deleted from the identified crater list.

This process is then repeated for this new list, and is iterated until the routine results in a perfect match, or the maximum number of iterations is exceeded. If a perfect match is not found within the number of allowable iterations, then the original identified crater list is declared invalid. Figure 14 shows an example of using this process to eliminate one crater from a sample identified crater list.

D 2

D 1

D 3D 4

D 5

D 6

Det CountD 1 4D 2 5D 3 4D 4 4D 5 4D 6 1

N=6

median = 4Drop all Detswhose countis less than 4 D2

D1

D3D 4

D 5

Det CountD1 4D2 4D3 4D4 4D5 4

N=5

indicates detectiondistance matches catalog distances

Perfectmatch

indicates detection distance does not match catalog distances

Figure 14. Phase 2 Iteration To Obtain Perfect Match. If, at this point, there is a surviving valid detection list, then the

refinement algorithm is implemented. This algorithm recomputes the validation detailed above in a modified form using information about the known identified craters in an attempt to identify any further detected craters in the original detection list. The error bounds (AMP and RMP) used in the initial algorithm are relaxed in the refinement algorithm. This allows more of the unidentified detected craters to be identified if the problem was due to uncertainties in the initial measurements. The process proceeds as before, except that when creating the detection distance list, each element will contain one previously identified crater and one unidentified crater. Thus when distance is compared in the ordered crater detection list, if the comparison passes the count threshold, a new crater may be added to the identified crater list. In this process, however, previously identified craters will not be deleted from the detection list. This process only acts as a method of potentially identifying craters that were previously detected, but not identified. If the above described normal search algorithm fails to identify a sufficient number of craters to uniquely fix location in lunar orbit (that is, more than one possible location is found), then the identification algorithms are rerun using a set of local crater databases. This method will allow a best solution to be chosen. This method would probably not be necessary for landing operations, where the search area is already limited, or even for orbital operations where a

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valid track has already been established. In this case, the search area would also be limited to regions near the current track point. Before this algorithm is called the original crater database is broken into M crater databases each covering a local region or patch on the moon. Note that each local region has overlap into other local regions along their boundaries. From each of these, regional Crater Position Databases are created (CPDi, where i is the ith Crater Position Database: 1 < = i <= M). Figure 15 shows a notional depiction of a lunar region as might be used for this purpose.

ith region with partial lunar coverage (Note: Illustration is simplified. In actual usage, the moon probably would be divided into many smaller regions)

Figure 15. Notional Area of Lunar Surface for Creating Local Crater Databases

The crater identification algorithm is then run as previously described, but now once for each regional crater database. If a valid crater location list is made using the ith map, the list is stored as the ith location list. If no valid crater identification list is obtained using any of the regional crater databases, then this routine is exited without a valid list. Otherwise, the list having the most number of identified craters is selected as the valid list and this routine is exited. If there is more than one list with the maximum number of craters identified, then those lists are compared to determine if they contain identical craters, which can happen due to the overlap area in the regional crater databases. If so, then a list containing these craters is selected as the valid list and this routine is exited. Otherwise, this routine is exited without a valid list. Figure 16 shows the logical flow of the routine using local crater databases.

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Original PositionDatabase

) ( x,y,Rad

Crater PositionDatabase

( x,y,Rad , OI)

Reducevia Radius Crater

DistanceDatabase(Δ, C1,C2)

Pairs thatare closerthan maxseparation(FOV)

ith Regional Crater PositionDatabase

( x,y,Rad , OSI)

ith Regional Crater DistanceDatabase(Δ, C1,C2)

Pairs thatare closerthan maxseparation(FOV)

Separatedatabase intoregional databases

ID 1 ID 2 cos

OI = index of this crater in original database OSI = sub index of this crater in regional database Ci = index of < - > database of this crater

Figure 16. Sub-Crater Map(s) Logical Progression. Assuming the orbiter’s sensor is pointed toward the nadir, following successful crater identification the location of the orbiter can be reported from the crater positions on the focal plane, which are then converted to lunar latitude and longitude. Averaging the offsets of the center positions of all identified craters with the nadir position on the focal plane (usually near the center of the field of view) will reduce error caused by measurement uncertainty. The rotation of the orbiter about the nadir axis can be determined as well by comparing the angles between crater centers compared to the focal plane reference. After an initial position has been found using the above technique, updates to the position probably will not require an exhaustive search of the entire lunar crater database. Only searching the local regions surrounding the last reported position should be necessary, which will reduce computation time. In the event where a new solution cannot be found, an exhaustive search is a viable option. To extend the method for orbital navigation described above to lunar landing navigation, additional craters must be added to the database along the descent trajectory. These entries will be continuously smaller in radius as the descent progresses, until only very small craters will be included at the point of landing. The objective is to choose crater sizes which will always remain close to constant in angular extent, based on the expected altitude estimates at each point in the descent. Because of this, the size of craters of interest will

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decrease by several decades from orbital altitude to the last few hundred meters. Mapping of extremely small craters will probably require special surveys of the proposed landing site, although the imagery from the Lunar Reconnaissance Orbiter is likely to be sufficient for this task, as it should provide centimeter-scale resolution. Figure 17 depicts the decreasing size of the field of view of a lunar lander on its descent.

Altitude

Fields of View

Descent

(Note: Illustration is simplified. Frames should overlap over entire descent in actual usage)

Distance Traversed Across Lunar Surface

Figure 17. Field of View of Camera During Lunar Descent

Results of Using Crater Navigation with an Abridged Lunar Crater Database Using the lunar map created from Apollo 15 surveys of Oceanus Procellarum previously described5, a series of 1024 x 1024 pixel images was generated, each of which simulated a visible sensor view from an orbiting spacecraft at a fixed altitude of about 110 kilometers directly along the nadir to the lunar surface. Each view encompassed about 875 square kilometers of the lunar surface. The rotation of simulated sensor images about the pointing vector was randomly generated at any value from zero to 360 degrees. The center position of the image was also randomly selected from anywhere in the map region, including along the edges where looping of the image in either the vertical or horizontal direction to the opposite edge of the map could occur, simulating the effect of a closed sphere. For each randomly placed image, the crater navigation algorithms were applied to determine the measured center position of the image referenced to the lunar map, as well as the measured rotation angle of the image about the 5 As mentioned earlier, this area of the moon was selected because it contained a reasonable variety of lunar features such as plains, mountain ridges, variation in density of the crater population, and variation in crater sizes.

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nadir from the map reference position. These were then compared to the actual selected values to determine the precision of the position and rotation measurements. In addition, the fraction of cases where no determination could be made was evaluated, as well as cases where a completely incorrect match was made. The crater database used for this evaluation is a preliminary version, which contains only 1200 craters scattered across the entire map region. These craters range in size from a radius of six pixels to 120 pixels. The total map area is about 100 million square pixels, representing about 81,000 square kilometers. The resulting crater distribution provides an average of three to six identified craters per image, but in sparse areas there may be few or no identified craters. In mountainous areas, larger craters may be difficult to elucidate if they are similar in size to the high frequency component of clutter presented by the rugged background, which can also result in inability to establish location. In these cases, it is beneficial to add more small-radius craters to those regions, which are easier to recognize against the terrain features. Future enhancements to the database will include these improvements. Figure 18 shows an overall view of the map used for this evaluation, with two sample image frames inset into the figure. A total of 135 images were generated and analyzed from this map. Table 1 shows the results of the lunar position and angle determination for these images.

Figure 18. Lunar Map Used for Orbital Navigation Analysis

(Rectangles Indicate Typical Sensor Image Views)

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Number of Images in Plains Region

100

Images with Successful Determinations in Plains Region (%)

71 (71%)

Number of Images in Mountain Region

35

Images with Successful Determinations in Mountain Region (%)

8 (23%)

Mean Deviation in X -0.041 pixels -34 meters Mean Deviation in Y -0.119 pixels -99 meters Mean Deviation in Rotation 0.0378 degrees Standard Deviation in X 1.02 pixels 851 meters Standard Deviation in Y 0.899 pixels 750 meters Standard Deviation in Rotation 0.114 degrees Note: Statistics above computed using all successful images

Table 1. Results of Analysis of Lunar Position and Rotation Angle Table 1 shows that when a determination was successful, the deviation from the values associated with the reference craters used in the database was quite small, with about a one-sigma deviation of one pixel for both the X and Y directions, and a little over a tenth of a degree in rotation. This means that there is little incidence of false positive determinations with this method for this test case. The design of the algorithms was intended to reduce false positive results, since sending erroneous information to the navigation system is undesirable. The unsuccessful determinations were primarily due to the limited size of the crater database and the rather low resolution imagery associated with the Apollo 15 survey. The available imagery will improve dramatically with the launch of the Lunar Reconnaissance Orbiter, scheduled for 2008. The improvement in resolution6 is expected to be better than a factor of 103. Many areas of the current map are low contrast, and have washed out areas that have no recognizable craters. In the meantime, the regions of the map which are currently not well represented in the database can be dramatically improved just by selectively adding existing craters where needed. As mentioned above, it is not surprising that mountainous areas are more difficult to analyze successfully. This is evident in the much lower percentage of success for these areas as seen in Table 1 (23% vs. 71% in the lunar plains areas). Adding small craters to the database for these regions is

6 About 850 meters for Apollo 15 vs. 0.30 meters for the Lunar Reconnaissance Orbiter.

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expected to increase the success rate significantly. But even as it stands with dropouts occurring in some areas, the ability to navigate from orbit can be accomplished successfully, since new areas are constantly being observed and updates to position can be processed as they occur. It is most important to receive continual updates during the critical descent phase of landing operations. In this case, the landing trajectory maps must be carefully prepared and well-populated to assure success for a high percentage of the images analyzed. Results of Crater Detection with Variable Sun Elevation Angles Since the lunar crater database used in the analysis above was created from an Apollo 15 photographic survey with a nearly fixed sun angle, a separate evaluation was performed using a three-dimensional model of a simulated lunar surface as observed with a visible sensor. For this evaluation, the sun could be placed anywhere over the surface, so four sunrise-to-sunset scenarios were generated. These consisted of an east-west track, a north-south track, a northeast-southwest track, and a northwest-southeast track. Overhead images of the simulated lunar surface were created in one degree intervals from zero to 180 degrees. The purpose of this evaluation was to see how radically changing sun angles and directions, with their accompanying changes in shadowing, would affect the ability of the algorithms to detect craters built into the scene.

Figure 19 shows a view of the scene with the sun overhead, with five test craters having radii within the search bounds of the algorithm identified. Table 2 reports the nominal length and width of each test crater. Five craters were chosen as a reasonable number of database craters expected to be present in any particular field of view.

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1 2 3 4 5

Figure 19. Overhead View of Simulated Lunar Terrain with

Test Craters Identified

Table 2. Nominal Size of Test Craters Evaluated for Simulated Lunar Terrain

Crater Number Crater Width (pixels) Crater Length (pixels) 1 26 26 2 21 21 3 22 23 4 27 27 5 32 33

Figure 20 shows the extensive variations in lighting which occur as the sun progresses from sunrise to sunset. At a sun angle of 0°, almost the entire scene is in shadow, and craters are very difficult to detect. At a 90° sun angle,

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the shadowing is minimized and the craters are much easier to detect. Values between these two extremes have an intermediate degree of difficulty of being detected.

0 degrees 15 degrees 30 degrees 45 degrees

60 degrees 75 degrees 90 degrees

Figure 20. Progression of Lighting Change in Simulated Lunar Terrain (Angles given are for sun elevation)

For each image of each track generated in one-degree increments in sun elevation angle from zero to 180 degrees, the algorithm was run in an attempt to find all craters having a radius of eight to sixteen pixels. This range was chosen because it covered the range of the five test craters built into the simulation. The results are shown graphically in Figure 21, where the total count of the craters of interest was computed. With a maximum possible count of five, it can be seen from the figure that between sun elevation angles of 20 to 160 degrees, four or five of the craters were consistently counted, regardless of the shadow effects. This result supports the conclusion that lunar position can reliably be found with this method for all but extremely low sun angles when using visible sensors. For a lunar position to be found, not all database craters need be detected, since as few as three craters is sufficient to be successful. Conditions where fewer than three craters are detected are relatively uncommon. Since new images are constantly being generated, if a single frame dropout occurs, the navigational track can be expected to be refreshed without a significant impact on the navigation system.

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Crater Matches vs. Sun Elevation

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Figure 21. Numbers of Database Craters Detected with Varying Sun Angle (Max Possible = 5 in This Scenario)

Many of the issues involving difficulty of detection under conditions of low sun angle or even night observation can be solved by use of infrared sensors. Imagery from the high-resolution IR sensors aboard the Mars Reconnaissance Orbiter collected during night conditions are very encouraging. Shadows are largely eliminated as a source of concern, although overall feature noise can be higher. A comparison of a typical Martian night image collected in the long wave infrared region to a visible image collected during the day is shown in Figure 22. Both views are of the same region. Note that the cratered areas shown in the infrared image have distinct edges marking the craters. A useful future task will be to investigate the performance of the crater navigation routine described in this paper using real and simulated infrared images.

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THEMIS LWIR Image (night)

Visible Sensor Image (day)

Figure 22. Comparison of Mars Infrared Night Imagery (THEMIS)

With Visible Day Imagery of the Same Region Summary The above described method has shown to be a promising approach for accomplishing autonomous lunar/planetary navigation using only visual imagery of the body’s surface. Crater patterns can be used to determine location over the planetary surface by virtue of their unique sets of distances from one another, along with discrimination based on their radial sizes. Since individual measurements of location do not rely on previous measurements, propagation of errors leading to erroneous navigation is eliminated as a risk. On the other hand, finding a valid track across the surface adds confidence to the overall location assessment and allows the possibility of narrowing the search area as the track propagates. This approach will support the stated goal of sustained lunar exploration and colonization by allowing unmanned orbiters to be in a dormant state with minimum power demands during orbit. For landers, it will allow continual monitoring of the descent path independent of other navigation methods by use of visual imagery alone. This adds an important element of reliability and a backup to this critical phase of the flight. It also supports the future goal of exploration of Mars and other planetary bodies, such as asteroids. The use of both infrared and visible sensors can enhance the effectiveness of this method and allow operation seamlessly over all lighting conditions. Combining these sensors adds robustness and reliability to the system while using a common software approach to the issues of navigation during orbit and landing operations.

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