American Journal of Computer Science and Engineering Survey Open Access

Keywords

Faster R-CNN; CubeSats Detection; Attitude Estimation

Introduction

Since 1960, there have been numerous launches of different types of satellites (Sats) aiming at studying different disciplines, mainly focusing on engineering applications and atmospheric chemistry [1]. The Aerospace Corporation is one of the major industries that constructed and launched CubeSats for the purpose of technological demonstrations [2]. The structure of a CubeSat is significant to resolving the problem of space object identification. The CubeSat reference design, proposed by Professor Jordi Puig- Suari from California Polytechnic State University and Professor Bob Twiggs from Stanford University in 1999, aimed to build a spacecraft with similar capabilities to the first spacecraft, Sputnik [1]. A CubeSat consists of one or more 10 cm by 10 cm by 11.35 cm units with mass no more than 1.33 kg per unit [3]. Larger CubeSat platforms have been proposed from time to time. Among them, common are the 6U and 12U CubeSats, which are used for academic and technological validation applications [1].

Real-time object detection is crucial for many space-related applications. Although higher accurate object detection is becoming important, there are many loopholes in current object detection methods. Therefore, robust object detection systems are needed to precisely understand the environment. Recently, convolutional neural networks (CNNs) have been used as a powerful tool for recognizing image content and are widely considered in the computer vision community [4]. One disadvantage of CNNs is that it is computationally demanding, which requires a GPU that requires higher power consumption. With the development of the software industry, there are many advances that have been done in the fields of computer vision and machine learning. One major contribution is the Faster R-CNN [4] which shows promising results. This context motivated the researcher to participate in this research and to develop robust Faster R-CNN based object detection models that will perform a key role in the computer vision community. This research was focused on generating new CubeSats databases and development of CubeSats detection models using the Faster R-CNN [4]. In this research, CubeSats with various dimensions are referred as “1U CubeSat,” “2U CubeSat,” “3U CubeSat,” and so on [5]. Latest development the Faster R-CNN achieves near real-time performances using deep networks [4]. Faster R-CNN models described in this research for CubeSat detection were trained and tested on both Web-searched images and synthetic images rendered using CAD models. A series of sensitivity analyses were performed to measure the accuracy of the developed CubeSats detection models. Results showed the potential to be a general CubeSat detection tool.

CubeSat attitude estimation using the detection results from the Faster R-CNN

Increasing the number of CubeSats launches leads to an increase in the number of small Sats in the lower-earth orbit (LEO). This causes an increase in space traffic and the possibility of the collision of Sats and asteroids. This requires more service missions to remove Sats debris. To better service these missions, it is important to understand the environment. Therefore, fast and accurate space objects detection and attitude estimation methods need to be developed. Sat’s attitude can be determined by using several different ways. In this research, the singular value decomposition (SVD) method [6] has been examined to estimates a spacecraft attitude by minimizing Wahba’s loss function [7]. In this paper, a coarse range of attitude estimation is obtained for a Sat using the centroids of the bounding boxes of detected CubeSats in the environment.

Related Work

The development of image datasets used to train artificial neural networks (NNs) progresses with the computer vision demand. Computer vision is a research field that is used to perform many object detections experiments with image datasets [8-13]. The use of visual data from the internet is a good source to develop a vision-based system. There is good amount of literature in the computer vision community [14-18] that has been devoted to designing object detection systems using images texture and shape cues. With the recent improvements, the CNNs have been successfully used on red-green-blue (RGB) images for a variety of tasks [4,19-24] in computer vision (e.g. classification and object detection). CNNs have the power of learning features accurately.After learning from a large database like ImageNet [4], CNNs have the ability to generalize the learned features on new image datasets as well. However, there are drawbacks of these systems with the limited data availability. Because of this, researchers were focused on developing detection models using synthetic image data [25-27].

Synthetic images for training

Many researchers tried to use synthetic images to train CNNs due to the lack of training images [28-31]. There have been a few works published on shape descriptors considering the 3D-CAD data representation [32-34]. There are many ways to represent the shape information in a vision system [35,36]. This research had been focused on a few more experiments to increase the accuracy of the object detection process using 3D-CAD-based images. When preparing a massive image dataset using 3D-CAD models, the dataset needs to consist of a large number of images with higher variation in features (e.g., color, scale, texture, etc.) to increase the accuracy of training with higher learning capacity [37]. When rendering an image, many different parameters such as different lighting conditions and camera configurations can be used. This research introduces an innovative path (using Autodesk Maya) [38] to render images from 3D-CAD models for the Faster R-CNN training purposes.

Experimental Setup

Faster R-CNN has the capability of learning powerful image data patterns. All these image data patterns are hidden under huge number of parameters [4]. It is worth it to study what these parameters represent to understand the behaviour of the Faster R-CNN. In this paper, the Faster R-CNN is evaluated on two tasks: Web-searched images based CubeSats detection and CAD images based CubeSats detection (Sat’s attitude estimation). The mean average precision (mAP), precision and recall curves are reported to evaluate the accuracy of trained CubeSats models [5]. The section experiment setup includes discussions for data -sets and important considerations that are followed towards developing an accurate CubeSats detection system [39].

Data

For the preliminary works in this research two new datasets are collected. They are Web-searched CubeSats images and 3D-CAD models-based images with texture. This subsection includes discussions about datasets, annotation process, and experimental setup in detail for the collected Web-searched dataset.

Web-searched dataset: This dataset is collected as a part of the research to detect CubeSats in Web-searched images. Main problems when working with images are the partial observability, scale, and recognition of the correct shape of the object with different viewpoints [40]. However, these problems could be solved by introducing more information such as increasing the training data with various data augmentation techniques.

Augmented web-searched dataset: This dataset is prepared by incorporating data augmented techniques, as shown in Figure 1 [41]. The dataset is divided into two: original images (970 images) and augmented images (9,067 images) with corresponding annotation files. 10,037 images (with data augmentation) are used for training and four types of image datasets are used for testing. Data augmentation techniques rotation, jitter, gray, and flip are used to increase the Web-searched training dataset to 10,037 images with corresponding annotation files [5].

Figure 1: Data augmented techniques: rotation, gray, flip, and jitter [41].

Test dataset: Test datasets include 255 Web-searched gray images, 317 CAD with texture images, 313 CAD images without texture, and 255 Web-searched color images. In addition, for a fair comparison 1,014 Web-searched test images are prepared using all data augmented techniques. These images are collected to evaluate the ability of the trained CubeSats models on detecting correct CubeSats classes.

Image annotation: Training and testing CubeSat datasets are annotated as follows. Inputs to the annotation process are a CubeSat image, predefined classes (e.g., 1U CubeSat, 3U CubeSat, etc.), and a user defined bounding box around the object-ofinterest in the image. When it comes to image annotation process, two assumptions are made about the images [42]: the object class (e.g., 1U CubeSat, 3U CubeSat, etc.) and the location of the object in each image. Each CubeSat image is annotated by drawing rectangular boxes for each predefined object (e.g., CubeSats) and labeled every object-of-interest with predefined keywords found in its image [41]. All annotated files for positive images are in the pascal challenge format [34].

Important considerations

How to handle the scale of an image: One of the biggest challenges when training the Faster R-CNN is the scale of images [37]. Sometimes, the CubeSats detection process fails due to the difficulty of detecting CubeSats. One limitation of Web-searched images for CubeSats detection is that there are a limited number of images available for CubeSats. To overcome this situation, one possibility is preparing the CubeSat dataset including CubeSats images with different scales [39]. In order to evaluate how the scale of the image effects on Web-searched-based CubeSats dataset, the Faster R-CNN is trained at the image scale of 600 1,000 (default scale) and results are tested at different scales [39]. Results show that image scaling considerably affects the detection process (Table 1). When reducing the scaling of the image, the resolution of the image drops by reducing the CubeSat detection probability.

Table 1: CubeSats detection results on different image scales (tested on the Web-searched augmented image dataset).

How object proposal matters: In the Faster R-CNN, detection accuracy depends on the number of object proposals [39]. The Faster R-CNN architecture is flexible on choosing the number of object proposals to be sent to the classifier at test-time [4]. Experiments are conducted on the number of the object proposal at test time to find out how the accuracy changes on the Websearched CubeSats detection system (Table 2). In this experiment, the test-time number of object proposals varies between 10 and 1,000 [39]. Figure 2a shows variations of the mAP with a different number of object proposals. According to the Table 2 it shows increasing the number of object proposals does not largely help to increase the detection accuracy. To save the computational cost, for this research selected 100 object proposals at test time.

Table 2: CubeSats detection results by varying number of object proposals (tested on the Web-searched augmented image dataset).

Figure 2: Memory usage (MiB) of GTX-1080 GPU and Number of object proposals versus mAP.

Iterative training: The Faster R-CNN is an iterative method [4]. Experiments are conducted to monitor how the iterative ways improve the accuracy of the CubeSats detection [39]. Multiple networks are trained with two different feature extractors: the VGG-M and VGG-16. VGG-M is a smaller CNN architecture with seven layers [1]. For the Web-searched image dataset, it showed that increasing the number of iterations does not largely help to improve the accuracy of the CubeSats detection model (Table 3). For the VGG-16, it is worth applying early stopping at 70K to prevent unnecessary computation [43]. In addition, the researcher measured the memory consumption of GTX-1080 GPU for the VGG-M and VGG-16 feature extractors. Also, the size of CubeSats models generated by each extractor is recorded. The graph shown in Figure 2b shows that the VGG-16 has higher memory consumption compared to VGG-M feature extractor.

Table 3: Performance of each feature extractor on GTX-1080 GPU (tested on the Web-searched augmented image dataset).

Performances of the CubeSats detection process: In this section, the mAP [4] is reported for the Web-searched CubeSats detection models. The detection accuracy of CubeSats model is evaluated by plotting the precision and recall curve. Figure 3 shows how the precision and recall curve change with the type of tested image datasets. Figures 3a-3c show higher accuracy while maintaining a high precision with a high recall compared to Figure 3d. Figure 3d shows that the Web-searched CubeSats detection model shows a very low accuracy when tested on CAD-no-texture CubeSats image dataset compared to other precision and recall curves. Rendered images from 3D-CAD models are lack of realistic nature which significantly reduces the performance when testing on Web-searched CubeSat model [25]. It is possible to overcome such situations to some extent by adding real image texture on to CAD models [25]. This process is time-consuming and needs supervision to select the appropriate texture for each CubeSat category [25].

Figure 3: Precision and recall curves for different test datasets.

Training methods: To train the Faster R-CNN both the “approximate joint training” (end-to-end) and the “alternating training” [4] methods can be used. Table 3 shows results of both training methods. From results on Table 3, it shows that deep architectures like VGG-16 trained using the one-stage method learned better on new CubeSat datasets than the small architecture like VGG-M which has used the two-stage training method [4]. What makes alternating training special is it first trains the region proposal network (RPN) and uses the proposals to train the Fast R-CNN [4]. For the alternating training, the learning rate is fixed at 0.001, momentum to 0.9, and trains for 80K iterations, then lowers the learning rate to 0.0001 and trains for another 40K iterations [4]. For the approximate joint training (end-toend), the learning rate is fixed at 0.0001, momentum to 0.9, and has trained for both 70K and 100K iterations. The intersection of union (IoU) threshold for the non-maximum suppression (NMS) is fixed at 0.7 to get around 2,000 proposal regions per image [4]. The experiments are conducted on a Dell desktop computer with 32GB RAM, an i7-6700 Intel CPU, and a Nvidia Ge Force GTX-1080 GPU [5]. It took below 0.2 seconds to process a test image by all CubeSats models on the GTX-1080 GPU (Table 3). This training process applied widely used Faster R-CNN pre-trained weights for 1,000 object categories on Image Net [4].

Effect of the training batch size: In order to measure the impact of the size of image datasets, two CubeSats models are trained with Web-searched image datasets varying from 970 original images to 10,037 images with data augmentation techniques [39]. VGG- 16 feature extractor is evaluated on the training batch size (Table 4) [5]. The performances are increased considerably (from mAP of 83.7 percent to 95.8 percent for VGG-16) when increasing the size of training images dataset [39].

Table 4: Performance with training images batch size (tested on the Web-searched augmented image dataset).

Detection Accuracy after Increasing the Number of CubeSat Classes: 1U, 2U, 3U, and 6U CubeSats

When it comes to CubeSats configuration, there are different CubeSats configurations such as “2U” and “6U” CubeSats. In this section, the researcher set a goal of developing a CubeSat detection model by increasing the number of the CubeSat classes: “1U, 2U, 3U, and 6U” CubeSats. In order to start the process, the researcher collected a dataset for four different classes of cubesats.The dataset contains images from the Web using the Google search engine. 29,210 images (with data augmentation) are used for the training process. Data augmentation techniques rotation, jitter, gray and flip is used to increase the training dataset to 29,210 images with corresponding annotation files. 4201 images (with data augmentation) are used for the testing process. The CubeSat detection model is trained using the “approximates joint training” method. The IoU, threshold for NMS, set at 0.7 for this experiment to get around 2000 proposal regions per image [4]. For the approximate joint training, the learning rate is fixed at 0.0001, momentum to 0.9, and has trained for 70K iterations. The size of the sliding window used in this experiment is 3×3, as it is a good scale to detect the likelihood of the presence of a CubeSat in the proposal generation stage [4]. To extract more accurate features the “cov5_3” layer of VGG-16 architecture has been used. It took below 0.2 seconds to process a test image on the GTX-1080 GPU.

When developing a vision-based model, it is important to have a way to measure the accuracy of the developed vision system to handle unseen test data [44]. Supervised learning models which are acquired from a dataset can be categorized into three types [44]: under-fitted, well-trained, and over-fitted models. Overly simple models named as under-fitted models. Overly complex training methods lead to over-fitted models by learning noisy data, which then leads to bad generalization [44]. The following experiments are conducted to evaluate the performance of the trained CubeSat model: when the test image is that of a “1U, 2U, 3U, and/or, 6U” CubeSats, when the test image is an asteroid or a planet, and if there are no CubeSats at all to find out when the trained CubeSat detection model fails. mAP for detecting four CubeSats classes are shown on Table 5. Figure 4 shows the precision and recall curve after increasing the number of CubeSat classes: 1U, 2U, 3U, and 6U CubeSats. From the mAP, the precision and recall curve can conclude that the developed Web-searched CubeSat model with four classes shows acceptable results to become a general CubeSat detection tool.

Table 5: mAP after increasing the number of CubeSat classes: 1U, 2U, 3U, and 6U in Web-searched dataset.

Figure 4: Precision and recall curve after increasing the 1U (%) 3U (%) mAP (%) 1U 2U (%) 3U (%) 6U (%) number of CubeSat classes: 1U, 2U, 3U, and 6U.

CubeSats detection results are evaluated on how illumination affects the detection process and the prediction probability when there are no CubeSats at all. The detection results for four CubeSats classes are shown in Figures 5 and 6. If the Websearched CubeSats detection model has to detect low-resolution images (Table 1) there is a high chance for a false detection. Figure 6 shows that the Web-searched CubeSats detection models assigned lower probabilities to non-CubeSat objects. Due to the intra-class variation of CubeSats models available in the Web-searched image dataset, Web-searched-based CubeSats detection model learned the 1U, 2U, 3U, and 6U CubeSats shapes with higher accuracy. There are false positives for Web- Searched-based CubeSats detection system. The Web-searched CubeSats detection model detected cylinders (e.g., Hubble space telescope) as 3U CubeSats (Figure 6). This is expected fault detection as the viewpoint of the Hubble space telescope image is similar to a side view of a 3U CubeSat. Sometimes, the Web-searched-based CubeSats detection models detect wrong shape (e.g., a 2U CubeSat as a 3U CubeSat) as shown in Figure 6. These are some major challenges with the developed CubeSat models which focus to solve in the future works. However, the developed Web-searched-based CubeSats detection model has a high capability on rejecting irregular shapes and circles (asteroids and planets) as shown in Figure 6 and showed the potential to be a general CubeSat detection tool.

Figure 5: Detection results after increasing the number of CubeSat classes: 1U, 2U, 3U, and 6U [36-43].

Figure 6: Trained for 1U, 2U, 3U, and 6U CubeSats detection, no red-box means no detection [44-47].

CubeSat Attitude Estimation Using the Detection Results from the Faster R-CNN

This section presents a single-point coarse attitude estimation method based on the detection results by a spacecraft in the close proximity of two or more CubeSats. The method can be used as a contingent attitude estimation solution for a spacecraft. The attitude is defined not as the orientation of the spacecraft relative to one of the CubeSats in close proximity, but the orientation of the spacecraft with respect to a global reference frame such as the Earth-Centered Inertial frame or the Earth-Centered Earth-Fixed frame. Determining the former would require the use of CubeSat surface feature points in the image, which are unavailable from the output of the CubeSat detection system. Instead, the attitude determination system leverages the coordinates of the bounding boxes surrounding the CubeSats. The centroid of a bounding box can be readily calculated from the coordinates of the four corners of the bounding box. These bounding box centroids approximate the centroids of the CubeSats in the image, which in turn approximates the center of mass of the CubeSats in the image.

Algorithm development

The attitude estimation algorithm is developed under the following assumptions: the spacecraft body frame is the same as the camera frame, the CubeSat image is provided by a pin-hole camera with known focal length onboard the spacecraft, two or more CubeSats are detected in the image, the position vectors of the detected CubeSats and the spacecraft are provided by GPS, the position information of the detected CubeSats is shared with the spacecraft. The bounding box coordinates and the camera focal length determine the LOS vectors from the spacecraft to the CubeSats in the body frame. The GPS data are used to determine the LOS vectors in the reference frame. Then, the three-axis attitude is obtained by solving Wahba’s problem [7]. Suppose there are n≥2 bounding boxes with centroids The n LOS vectors in the body frame are given by:

where f denotes the focal length of the camera. The LOS vectors in the reference frame are given by:

Where are the CubeSat positions in the reference frame and is the space craft position in the reference frame. The attitude matrix estimate is the solution to Wahba’s problem, which minimizes the following cost function:

Where the superscript T denotes matrix transpose, det denotes matrix determinant, I_3x3 is the three-dimensional identity matrix, and is the effective noise level. Suppose the noise variances of and respectively. Therefore, σ_i² ≈ σ_ri² +σ_bi². Many solutions to Wahba’s problem exist. In this research Markley’s singular value decomposition method [6] has been used to solve the attitude estimation problem. First, an attitude profile matrix B is constructed:

The attitude estimate is given by:

The 3×3 attitude error covariance matrix is given by:

Where are the noise-free LOS vectors in the body frame.

Illustrative example

In this subsection, an example is used to show the attitude determination process. Simulated images are generated using Autodesk Maya, a 3D software application developed by Autodesk [56]. A Faster R-CNN with four CubeSat classes is built on Caffe [57]. A total of 90,956 synthetic training images in 1,000 random camera viewpoints are generated using Autodesk Maya. In Maya, the default method of rotation is Euler [58]. Euler rotations are calculated using three Euler angles, which represent rotations about the X, Y, and Z axis, with an order of rotation [58]. The user can specify the order of rotation for an object (CubeSat) by setting its rotation order (e.g., XYZ). For example, if the user sets a CubeSat’s rotation order to XZY, the CubeSat will first rotate on the X axis, then the Z axis, and finally the Y axis. The synthetic test images of rotating CubeSats are simulated based on rigid-body kinematics and dynamics under zero external torque. The camera is assumed to be sufficiently close to the CubeSat, but the relative translational motion is not simulated.

Object space versus world space: Maya has two coordinate systems: the local coordinate system and global coordinate system. The local coordinate system is called object space and the global coordinate system is called world space [56]. In Maya, the world coordinate system is always fixed. Figure 7a shows three CubeSats representation in the world frame and XYZ coordinates of a one CubeSat in the world frame. It is necessary for each CubeSat to have its own axis independent of the worldaxis. When a CubeSat rotates or moves, its object space rotates or moves with it. This is called the object space [56].

Figure 7: Autodesk Maya world and camera frames.

Camera frame: When a user creates a camera in Maya, its view is perspective [59]. To render a scene the user needs to create a rendering camera as shown in Figure 7b.

Focal Length: In Maya, the focal length is represented in millimeters (mm) [59]. The object’s (CubeSat’s) size in the rendering frame is proportional to the focal length of the camera. Therefore, the user needs to be careful when selecting a focal length as it causes the CubeSat to appear larger or smaller in the rendering frame.

Simulated scenario 1: 1U CubeSats detection

In this example, three 1U CubeSats are present in the close proximity of a camera onboard a spacecraft. The detection result is shown in Figure 8. The centroids of the bounding boxes are [units: centimeters (cm)]:

Figure 8: 1 U CubeSats detection.

The focal length of the camera is f =3.5 cm. Thus, the three LOS vectors in the body frame are:

The position vectors of the CubeSats and the spacecraft are (cm):

From the position vectors, the LOS vectors in the reference frame are:

The attitude estimate is given by:

From the attitude-error covariance matrix in Equation 10, the attitude estimation method has two primary error sources: GPS and bounding box coordinates. The effect of the GPS positioning error on σ_ri is well understood. Roughly speaking, σ_ri ≈ σ_GPS/ri where r_i is the distance from the camera to the i-th CubeSat. The noise level σ_bi is a complicated function of the attitude of the CubeSats and the tightness of the bounding box and need to be determined by experimentation. In addition, σ_bi is approximately proportional to the pixel size of the camera and inversely proportional to the field of view of the camera. The field of view of the camera limits the number of CubeSats that simultaneously appear in the image. When the number drops below two, the attitude cannot be uniquely determined.

Conclusion

The goal of this research framework is to provide an introduction and crucial knowledge to develop accurate CubeSats detection models using the Faster R-CNN. A wide range of experiments is conducted to develop accurate CubeSats detection models. For the preliminary work of this research, a CubeSats detection model using the Faster R-CNN with Web-searched images is developed. Then, experiments are analyzed Web-searched CubeSats detection model on images with and without texture features. The biggest challenges with these experiments are to detect small-scale CubeSats and to detect the correct shape of CubeSats. There are situations where the CubeSats detection process failed due to the difficulty of detecting the CubeSat. Therefore, this paper proposed important considerations that need to be considered to improve the accuracy of CubeSats detection models. Another objective of this research is to solve an attitude estimation problem using the detection results from the Faster R-CNN. This paper proposed a coarse singlepoint attitude estimation method utilizing the centroids of the bounding boxes surrounding the CubeSats in the image. Future research will focus on generalizing the CubeSats detection model to an extent that can detect more CubeSats classes (12U, 27U) in dynamic environments while optimizing the Faster R-CNN network. Moreover, to increase the estimation accuracy, future works will focus on more quantitative error analysis for the attitude estimation problem.

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