La ciència per a qui i per a què? Assegurar el rigor científic

As opposed to relative navigation, which depends on a unique origin or previous motion informa-tion to locate the current posiinforma-tion of a space craft, absolute navigainforma-tion computes the locainforma-tion of a space craft without a unique origin point or previous motion information using only the avail-able terrain information. In other words, it extracts the spacecraft position referred to a general, fixed, coordinate system.

The basic approach consists in extracting some kind of information, from the images taken by the spacecraft, characterizing the landing zone and trying to match these information with the ones stored in a reference database.

In order to ensure the proper definition of the absolute position, the database stores the infor-mation related to a planetary surface portion wider than the target landing area.

Existing approaches for Video-Based Absolute Navigation can be classified into three main groups:

• Orbiter-assisted

• Shape-based

• Crater-based.

The Orbiter-assisted approach [169] is depicted in Figure 2.24. It requires the presence of an orbiter, or satellite, equipped with a high resolution camera. As shown in Figure 2.24, the Field of View (FoV) of the spacecraft camera must be completely covered by the FoV of the orbiter camera.

The picture taken by the Orbiter has the purpose of reference image. The reference database is created by extracting features from this image. The image taken by the spacecraft is firstly scaled and rectified according to the orbiter attitude, provided by the Inertial Measurement Unit (IMU) (i.e., a module equipped in every spacecraft involved in a space exploration mission), in order to align the picture with the one taken by the orbiter (i.e., after rectification the two pictures lie on the same plane). After that, features are extracted from the rectified picture, and compared with the database. After features matching, since the orbiter position is known, the absolute position

Figure 2.24: Orbiter-assisted Absolute Navigation

of the spacecraft can be defined with respect to the orbiter reference system.

This method has a lot of benefits, since it provides a good precision, it does not require specific landmark on the planet surface, it does not require an internal database, and it is not susceptible to different illumination conditions, since the compared pictures are acquired at the same time.

However, the method is based on two main hypothesis that are not feasible for the majority of space exploration missions. In particular, it requires:

• the presence of an orbiter that monitors the overall descending phase of the spacecraft;

• a permanent communication channel between the two entities, that is not always guaran-teed during the spacecraft descending phase.

The Shape-based and Crater-based [33] approaches are both based on a pre-computed refer-ence database.

In the former, the information composing the database are landmarks templates, characterized by an absolute position w.r.t. a reference system. The image rectification is performed to align the acquired pictures with the one composing the surface atlas (in the sequel called atlas image). This task is accomplished by exploiting the current attitude and altitude of the descent module. After image alignment, regions of interest (i.e., landmarks) are extracted from the spacecraft picture, and they are compared with the reference database to find the most robust match. Commonly, the matching task is done by extracting from the spacecraft acquired images a set of image tem-plate containing region of interest. These temtem-plates are then stepped over the atlas image to find the regions having the higher number of pixels in common, and so to find a valid matches.

Even-tually, after the matching task, from the absolute position characterizing the matched database template, it is possible to define the absolute position of the spacecraft.

As it can be noted from this brief description, Shape-based methods involves simple operations and work for different kind of landmarks. However, they are not able to provide good precision when the planet surface contains landmarks with similar shape, and, in addition, they are not invariant to the spacecraft attitude.

The crater-based approach exploits a similar method but it exclusively uses craters as land-marks. The crater matching can be commonly done in two different ways: Conic-pair Invariants matching [118] or Cross-correlation matching (Section 2.5.1.2).

In the former, for each possible pair of craters in the acquired pictures and in the atlas image, an invariant operator, called conic-pair invariant, is defined. This operator allows to create a signature, invariant to geometrical transformation, identifying each couple of craters. Thanks to the invariance of this operator, the matching can be done without knowing the attitude of the spacecraft in the atlas reference system. Thus, the spacecraft image rectification can be avoided.

However, this methods presents an important drawback, being efficient only if the planet surface is picked by a high number of craters.

Instead, in the cross-correlation matching, for each crater detected in the acquired image, a sur-rounding image template is extracted. This template is then stepped over the atlas image in order to find a crater match through the cross-correlation operation (Section 2.5.1.2). The main positive aspect of this approach concerns the required simple operations that allow to limit the execution time. However, this methods is not able to provide acceptable performance when the atlas im-age and the acquired imim-ages have different photometric properties (i.e., illumination, contrast, etc.). Moreover, this method is not invariant to the spacecraft attitude, it can find a lot of fake matches when different craters have similar structure, and it requires a huge dataset to store the atlas image.

Even if Shape-based and Crater-based approaches have some drawbacks, they are preferred to the Orbiter-assisted ones since they present less critical limitations.

Analyzing the literature, a lot of these methods have been presented.

[146] proposes a VISion aided Inertial NAVigation (VISINAV) system. It is an hybrid relative and absolute navigation system for planetary landing applications. It utilizes both information extracted from an IMU and pictures acquired from an imaging camera. The visual measurements are combined in an optimal fashion with measurements from an IMU, to produce estimates of the spacecraft position and attitude during EDL.

As aforementioned, this system does not implement a pure absolute navigation approach, since it combines the extraction and matching of two types of features: mapped landmarks (i.e., craters whose global coordinates can be inferred from a map) and opportunistic features. Just the former are related to the absolute navigation, while the latter represent the features used in the standard relative navigation computation described in section 2.5.1.1.

Taking into account just the absolute navigation part of VISINAV, the landmarks matching is done with a cross-correlation based crater matching, optimized to reduce the required computation time. In order to avoid to step the crater templates over the overall atlas image, a Fast Fourier Transform (FFT) map matching forego the actual landmarks matching. This added task allows to rapidly approximate the horizontal position of the spacecraft w.r.t. the atlas reference system.

This approximation, even if not really accurate, enables to create a searching window inside the atlas image that strongly reduces the searching area of potential landmark matches.

However, this approach, even if it provides a really high execution speed, it embeds all the draw-backs of the cross-correlation based crater matching.

In [32] an approach based on the Conic-pair Invariants matching is proposed. This work in-creases the robustness of the matching task by comparing, in addition to the conic-pair invariant associated with each crater couples, a set of peculiar crater attributes. In particular, to remove potential fake matches identified by the basic method, this work compares also the radius and the orientation of each detected craters. This improvement allows to increase the robustness of the Conic-pair Invariants matching, but, at the same time, it increases the size of the reference database, resulting in a higher memory requirement.

[34], in order to even more increase the matching robustness, exploits in parallel the Conic-pair Invariants matching and Cross-correlation matching, plus the so called context based match-ing [57]. This considers the positions and sizes of a set of craters found in an image. Their con-stellation usually forms a unique pattern, which could be used to identify the correspondences between the acquired images during the descending phase and the atlas image. Basically, this approach randomly selects three craters in the acquired image. These three craters have to form a triangle in order to avoid an ill conditioned problem. Knowing the attitude and altitude of the spacecraft (provided by the IMU), the epipolar geometry (Section 2.6.1) can be generated and used, together with the size and shape of each crater to find the corresponding crater triplets in the atlas and spacecraft images.

The combination of these techniques provides a great increase in the accuracy, but at the same time, it strongly increase the execution time. In fact, the main drawback of this techniques is the huge time required to find valid matches, that is not compatible with the timing performance re-quired by an absolute navigation system. In addition, the memory requirements are higher than the previously presented methods, since the internal atlas must contain the information required by all of the three exploited matching approaches.

Eventually, [195] proposes a hardware infrastructure that implements an innovative crater-based absolute navigation . This solution aims at identifying each landmark (i.e., craters) through a characterizing point, and then applying the same approach used in Planar triangle-based (PT) Star trackers [36]. PT Star trackers are used to define the attitude of a satellite depending on which stars are within the satellite camera field of view. The basic steps performed by a PT Star tracker are: (i) develop a triangle from a combination of three stars, (ii) characterize the triangle with

its area and polar moment, and, eventually, (iii) compares the extracted area and polar moment with the database of all possible star triangles in order to find a match.

In this approach the characterizing points associated with landmarks act as stars.

The proposed method can be split in two main tasks: Reference database development, to be performed off-line, and Absolute position estimation, executed at run-time. The database de-velopment task is carried out by creating a surface map of the landing zone. The surface map can be obtained by stitching a set of images taken by satellites orbiting around the target planet.

Then, landmarks, i.e., craters, are extracted and the associated characterizing points are defined.

Characterizing points are defined in terms of centroids of the detected craters, and the associated absolute position. In addition to centroids, the database contains the set of all possible triangles (among all centroids), defined by the triangle surface area, perimeter and polar moment.

This approach strongly reduces the database size, w.r.t. existing methods. In this approach the database requires three numeric values for each triangle, plus the absolute position of each cen-troid, instead of an image template for each landmark.

The Absolute position estimation is a sequence of consecutive operations to be performed on the input image at run-time. First, the images acquired by the spacecraft, during the descend-ing phase, are pre-processed to reduce the level of noise and enhance the overall quality. Image pre-processing mainly consists of noise filtering (e.g., by applying a Gaussian filter [81]) and recti-fication, needed to align the plane of the acquired spacecraft image with the plane of the images used for the database development. The rectification process is essential in order to apply the Planar Triangle-based Star tracking algorithm, that in general, does not take into account the spacecraft attitude because stars can be considered as point at an infinite distance. On the other hand, during the descending phase, craters, and consequently the associated centroids, changes their relative position in the camera field of view depending on the spacecraft attitude.

These pre-processing operations ensure to increase the performances of the following image pro-cessing algorithms.

After image pre-processing, craters are extracted. This operation can be accomplished by us-ing image segmentation [191]. This kind of algorithm provides better results with respect to a standard edge detector (e.g., Canny [28]), since it does not require information about the sun el-evation and it is more robust to illumination condition variations.

If less than three craters are extracted, the star tracking approach cannot be applied and a new picture must be acquired. Otherwise, each extracted crater is characterized by the centroid.

Exploiting the altitude information, provided by a LIDAR sensor (commonly equipped on space-crafts involved in space exploration missions), the absolute distance among centroids is com-puted. Then, all possible triangles are defined, and characterized by the area, perimeter and polar moment. Finally, these information are compared with the ones stored in the database to find potential matches. The matching task is very simple since it consists of searching numerical values in the pre-computed database table. Matches are used to compute the absolute position

of the spacecraft by exploiting the absolute position of the centroids composing the matched tri-angles.

However, even if this approach solves many issues in terms of memory requirement and execu-tion speed, it requires to land on a surface picked by at least three craters, making this approach not suitable for every landing site.

From this analysis of the current state-of-the-art, it can be noted that an efficient way to solve all the issues characterizing the absolute navigation system has not yet been found. Thus, a huge research effort must still be spent on this topic. However, as already mentioned at the beginning of this chapter, the space agencies are reducing their research efforts on this approach in favour of relative navigation approaches.