Study on Algorithm of Selecting Safe Landing Area on Ground During Asteroid Soft Landing (EEIC2013 +161)

OUATTARA Sie, RUAN Xiaogang, Yan yan

Institute of Artificial Intelligence and Robots, School of Electronic Information and Control Engineering

Beijing University of Technology Beijing, China  

^' = ∑b₁^' (i) ² /(n₁ × p₁ )                      (15)

i=1 n2×p2

                             f ₂^' = ∑b₂^' (i) ² /(n₂ × p₂ )                     (16)

j=1

Step8: get the threshold α₁ of shadow area and α₂ of lighting area：

                               a2                     b2                    c2

Figure 2.  Binary Design sketch

 

Fig. 2 includes the shadow area and the lighting area, which are acquired by binary algorithm under different lighting conditions. b,b1,b2 are the binary result of shadow area; c,c1,c2 are the binary result in lighting area.

 

                       II.   DILATATION OF BINARY IMAGE

This article deal with the binary image by using dilation of morphology for finding the suitable area. Suppose M, N are both sets in R (two-dimensional space). Here N is called as structural element. M is dilated by N and defined as:

∧

                                M⊕N = {a | (N)_a IM ≠Φ}             (19)

Among  {w | w =−n,n∈ N} , shows the reflection for N.

        a,n       , shows translate the

reflection of N to the position of a = (a₁,a₂).

In Fig. 3, if a is the set M, c acts as the structure element N and its mapping. N is equal to its mapping, should be Symmetric about the Origin. C is the result that M is dilated for N. The white area is the dilated area.

        a: M                             b: N                       c:        M_⊕:N               

Figure 3.  Diagram of Dilatation Algorithm

 

Using dilatation theory to look for character of the target has good reason. It chooses the structure with the size of n^×n to dilatate the binary topographic map. All the lighting point is dilated by the structure. Even the smallest size is nearly reached n/2 . After dilatation, the black part in the image is flat and smooth, more far away from the obstacles.

 

            III.   THE CHOSEN OF THE SAFE LANDING AREA  

Choosing the safe landing area in the image which has been dilated binarily should be following the rules as shown in bellow:

（1）   For let the chosen landing area to be near the central part of the image, if M1 × M2 is the original size, n1 ×n2 is the structure size, the original image should delete the n1and n2 of the both ends of length and width and get the result （M1 -2×n1)×(M2 -2×n2) .

（2）   The size of landing area is usually the maximum inscribed rectangular of the undilated area. 

（3）   For convenience to track the chosen landing area, it is better exist some reference feature like rocks and meteor crater around it. Therefore, it may develop the real-time navigation for the space machine

using the center of safe landing area as the target and reference feature as the landmark.

 

 

                       IV.   EXPERIMENTS AND ANALYSIS

 Figure 4.  Image of experiment

 

This article uses the pictures of Small Bodies 433 EROS of NEAR exploration in 2001 to test the performance of the algorithm. As showing in Fig. 4, from picture a to d, the high of shot is from high to low, and there exists the big different lighting condition. In this experiment, it introduces the projecting experiment for shadow area and lighting area of binary algorithm for the four pictures in Fig. 4. As Fig.5 showing:

 Figure 5.  Binary image

 

Seeing from Fig. 5, shadow area and lighting area in Fig. 4 has been shown very well. The following is using dilatation algorithm to dilatate the shadow area and lighting area in Fig. 5. The size of the dilated structure may be adjusted according to the image size. Usually, the side length of structure should be the 1/20 of the minimum side length of the image. The size of the four pictures of this article is 388x496. Therefore, the size of the structure is 20x20.

 

Figure 6.  The effect picture of dilated binary image

 

Fig. 6 is the dilated picture of the binary image in Fig. 5. Seeing from the picture, the shadow area and lighting area are enlarged obviously, the undilated area has not the obstacles, which has a distance from the area with obstacles. This area can be the safe landing area for the space machine. According to the above rules, the red rectangular area can be the best choice for safe landing. While there exists much more noise and more complicated texture, which decrease the size of safe landing area in the dilated image. For this can use the filter to filt the noise and the trivial texture.

The algorithm in this article is real-time effectively, which calculates the four images of Fig. 4 only in 1 second separately.

 

                                       V.    CONCLUSION

This article provides an algorithm for searching safe landing, which focus on dilatation of binary image for shadow area and lighting area. There are several advantages: (1) it is a new binary algorithm for extracting shadow area and lighting area in the image. (2) Using morphologic dilatation to dilatate shadow area and lighting area in the binary image shows the improvement of safe landing for the space machines. (3) This algorithm is real-time and timesaving, which is valid for choosing the safe landing area.

There also has some limitation of this algorithm. One is the threshold in shadow area and lighting area of binary algorithm is the global threshold, which has uncertainty under the circumstance of the more complicated topography and lighting condition. The other is the filter for the noise and complexes texture in the image should be chosen one more suitable to deal with the image. 

 

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