VISUAL POSE ESTIMATION SYSTEM FOR AUTONOMOUS RENDEZVOUS OFSPACECRAFT

Mark A. Post1, Junquan Li2, and Craig Clark3

1Lecturer, Space Mechatronic Systems Technology Laboratory. Department of Design, Manufacture and EngineeringManagement, University of Strathclyde, Glasgow, United Kingdom

2Marie Curie Experienced Researcher, Clyde Space Ltd. Glasgow, United Kingdom3CEO, Clyde Space Ltd. Glasgow, United Kingdom

ABSTRACT

In this work, we consider a tracker spacecraft equippedwith a short-range vision system that must visually iden-tify a target and determining its relative angular veloc-ity and relative linear velocity using only visual informa-tion from an onboard camera. By means of visual featuredetection and tracking across rapid, successive frames,features detected in two-dimensional images are matchedand triangulated to provide three-dimensional featuremaps using structure-from-motion techniques. Triangu-lated points are organized by means of orientation his-togram descriptors and used to identify and track targetsover time. The state variables with respect to the camerasystem are extracted as a relative rotation quaternion andrelative translation vector that are tracked by an embed-ded unscented Kalman filter. Inertial measurements overperiods of time can then be used to determine the relativemovement of tracker and target spacecraft. This methodis tested using laboratory images of spacecraft movementwith a simulated spacecraft movement model.

Key words: Satellite; Pose Estimation; Vision.

1. INTRODUCTION

Visual Pose Estimation technology has attracted a lot ofinterest for spacecraft navigation as an enabling tech-nology for rendezvous and docking manoeuvres. Guid-ance and Control of a spacecraft has been studied exten-sively, but in order for such systems to work effectivelybetween spacecraft close to each other, the relative po-sition, attitude and and velocity between each spacecraftmust be robustly estimated. The desired result is that twosatellites will be able to reliably and autonomously ren-dezvous with each other, but visual position estimationfor satellites in orbit is far from a solved problem.

Traditionally, RF radar trades off precision for wide rangeof operation, and is not as suitable for uncooperative orsmall targets. The TriDAR system used a LIDAR and

Iterative Closest Point system outside the ISS withoutapproach or autonomy [RLB12]. Recent automated ren-dezvous and docking systems make use of optical, laserranging, and LIDAR systems [HCDS14] [PHAR12] andvisually-aided systems have been tested in proximity op-erations with NASA’s Space Shuttle, JAXA’s ETS-VIIsatellite [Oda00], and other satellites such as the DARTmission [RT04].

However, the complexity, size, and power requirementsof current LIDAR systems are still out of reach for smallsatellites and nanosatellites, and there is great potentialin the use of multiple-view imaging and feature mappingsince only one camera may be necessary. Many pose es-timation techniques have been proposed for this, and typ-ically focus on shape tracking and recognition, featuredetection and triangulation [Sha14], or a combination ofshape and features [TBB11]. The SPHERES experimentuses SURF feature matching with stereo vision for navi-gation inside the ISS [TSSO+14].

In this work, we propose a different approach to themonocular visual estimation problem: recognition andtracking of features for ego-motion from a sequence ofimages, which can then be inserted into a point cloud,which in turn provides a way to recognize the position ofthe target. This method is derived from structure-from-motion computer vision methods used in robotics and inphoto-tourism reconstructions from large image sets, andrequires that only rigid transformations are present be-tween images. To speed the development process andminimize coding errors and complexity, we make use ofthe open-source OpenCV (Open Computer Vision) andPCL (Point Cloud Library) for most of the computer vi-sion programming.

2. APPROACH AND TRACKING

To allow a tracker spacecraft to to identify and estimatethe movement of a target spacecraft, we approach thisproblem as illustrated in Fig. 1 First, we build up a fea-ture set of points located in three dimensions by triangu-lation of keypoints on successive images of the target in

the “Approach” phase. We then locate the camera rel-ative to the matched points by Perspective-n-Point (PnP)solution during the “Track” phase. By projecting the key-points into three dimensions, we build up a point cloudof the target over many more images in the “Observe”phase, which can then be matched in shape to a pointcloud model, and the pose of the model accurately ob-tained by three-dimensional keypoint correspondences inthe “Identify” phase.

Feature-based vision methods reduce complete images toa set of distinct, reproduceable “features” that are rep-resented by small numerical sequences. We apply ORB(Oriented FAST and Rotated BRIEF) point descriptorsfor 2-D feature matching with high rotation invariance[RRKB11]. We then use structure-from-motion methodsto triangulate these points in space.

2.1. System Overview

A flowchart of the process we propose is shown in Fig. 2,with details on each step provided in the following sec-tions. A sequence of images can be captured or cached,features extracted using two-dimensional point descrip-tors that are stored in memory and matched in pairs toobtain a list of images with features, and also a list offeatures tracked across images. This list of feature cor-respondences is used to track the movement of keypointsacross several poses, and.if the triangulation is not goodenough, a more different pose containing those featuresis selected. Using a pose solution, the points and cam-era are projected into global coordinates. The resultingscene point cloud can then be compared with a modelcloud to identify the target by choosing a set of keypointsand extracting histogram descriptors for each with respectto point normals. By matching descriptors between thescene and model, the model and its pose can be foundwithin the scene. An OptiTrak Trio optical tracking sys-tem is currently used as an external high-speed referencefor pose estimation. The pose estimates are then filteredover time using an Unscented Kalman Filter to reducenoise. Sensor fusion of the triangulation and correspon-dence tracker-target measurements is planned, but has notbeen implemented yet.

2.2. Keypoint Detection and Matching

A method of keypoint detection must be used to obtainkeypoints from a sequence of images. The FAST key-point detector (Features from Accelerated Segment Test)is frequently used for keypoint detection due to its speed,and is used for quickly eliminating unsuitable matches inORB. Starting with an image patch p of size 31x31, eachpixel is compared with a Bresenham circle built 45 de-grees at a time by x2n+1 = x2n − 2y(n) − 1. The radiusof the surrounding circle of points is nominally 3, but is 9for the ORB descriptor, which expands the patch size andnumber of points in the descriptor. If at least 75% of the

pixels in the circle are contiguous and more than somethreshold value above or below the pixel value, a featureis considered to be present [RD05]. The ORB algorithmintroduces an orientation measure to FAST by computingcorner orientation by intensity centroid, defined as

C =

(m10

m00,m01

m00

)where mpq =

∑x,y

xpyqI(x, y).

(1)

The patch orientation can then be found by θ =atan2(m01,m10) and is Gaussian smoothed. ORBthen applies the BRIEF feature descriptor fn(p) =∑

1≤i≤n 2i−1τ(p; ai, bi), a bit string result of binary in-

tensity tests τ , each of which is defined from the intensityp(a) of a point at a relative to the intensity p(b) at a pointat b by [RD05]

τ(p; a, b) =

{1 : p(a) < p(b)0 : p(a) ≥ p(b)

}(2)

The descriptor is also steered according to the orienta-tions computed for the FAST keypoints by rotating thefeature set of points (ai, bi) in 2xn matrix form by thepatch orientation θ to obtain the rotated set F [RRKB11].

F = Rf

(a1 · · · anb1 · · · bn

). (3)

The steered BRIEF operator used in ORB then becomesgn(p, θ) = fn(p) ∨ (ai, bi) ∈ F . A lookup tableof steered BRIEF patterns is constructed from this tospeed up computation of steered descriptors in subse-quent points.

Keypoints are then matched between two images in thesequence by attempting to find a corresponding keypointa′ in the second image that matches each point a in thefirst image, which can be done exhaustively by an XORoperation between each descriptor and a population countto obtain the Hamming distance. However, The FLANN(Fast Library for Approximate Nearest Neighbor) searchalgorithm built into OpenCV is used in current work as itperforms much faster while still providing good matches[ML09].

The more features in common between these images,the more potentially good matches Mf can be found,but it is essential that matches be correct correspon-dences or a valid transformation between the two im-ages will be impossible. The matches Mf are firstcoarsely pruned of bad pairings by finding the maxi-mum distance between points dmax and then removingall matches that have a coordinate distance da of morethan half the maximum distance between features usingMg =Mf (a)|da < dmax/2.

Figure 1. Process of Ego-Motion and Target Pose Estimation

Figure 2. Flowchart of Optical Pose Estimation System

2.3. Three-Dimensional Projection

To obtain depth in a 3-D scene, an initial baseline for3-D projection is first required using either stereoscopicvision, or two sequential images from different angles..The Fundamental Matrix F is the transformation matrixthat maps each point in a first image to a second image,and the set of “good” matches Mg is used where eachkeypoint ai in the first image is expected to map to a cor-responding keypoint a′i on the epipolar line in the sec-ond image by the relation a′Ti Fai = 0, i = 1, . . . , n[LF95]. For three-dimensional space, this equation is lin-ear and homogeneous and the matrixF has nine unknowncoefficients, so F can be uniquely solved for by us-ing eight keypoints with the method of Longuet-Higgins[LH87]. However, due to image noise and distortion, lin-ear least squares estimation (i.e. minF

∑i(a′Ti Fai)

2) orRANSAC [FB81] must be used to ensure that a “best”solution can be estimated. We use RANSAC for its speedto estimate F for all matches Mg and estimate the associ-ated epipolar lines [FH03]while removing outliers morethan 0.1 from their epipolar line from Mg to yield a final,reliable set of keypoint matches Mh. To perform a pro-jection into un-distorted space, a calibration matrix K isneeded, either from calibration with a known pattern suchas a checkerboard [Har97], or estimated for a size w × himage as

K =

(max(w, h) 0 w/20 max(w, h) h/20 0 1

). (4)

A camera matrix is defined as C = K[R|t] with the ro-tation matrix R and the translation vector t defining thepose of the camera in space, and for two images, we de-fine two camera matrices C1 and C2. To localize a pointin un-distorted space, we formulate the so-called essen-tial matrix E = t×R = KTFK that relates two match-ing undistorted points x and x′ in the camera plane asa′Ti Eai = 0, i = 1, . . . , n [HS97]. In this way, E in-cludes the “essential” assumption of calibrated cameras[Shi12b], and is related to the fundamental matrix by E

After calculating E, we can find the location of a secondcamera C2 by assuming for simplicity that the first cam-era is uncalibrated and located at the origin (C1 = [I|0]).We decompose E = t ×R into its component R and tmatrices by using the singular value decomposition of E[HZ04]. We start with the orthogonal matrix W and andsingular value decomposition (SVD) of E, defined as

W =

(0 −1 01 0 00 0 1

)SVD(E) = U

(1 0 00 1 00 0 0

)V.

(5)

The matrix W does not directly depend on E, but pro-vides a means of factorization for E. Detailed proofscan be found in [HZ04] and are not reproduced here,

but there are two possible factorizations of R, namelyR = UWTVT and R = UWVT, and two possi-ble choices for t, namely t = U(0, 0, 1)T and t =−U(0, 0, 1)T . Thus when determining the second cam-era matrix C2 = K[R|t], we have four choices in total.

it is now possible to triangulate the original un-distortedpoint positions in space with E and a pair of matchedkeypoints [a = (ax, ay),b = (bx, by)] ∈Mh using itera-tive linear least-squares triangulation [HS97]. A point inthree dimensions x = (xx, xy, xz, 1) written in the ma-trix equation form Ax = 0 results in four linear nonho-mogeneous equations in four unknowns for an appropri-ate choice of A4x4. To solve this, we can write the systemas Ax = B, with x = (xx, xy, xz), and A4x3 and B4x1

as defined by Shil [Shi12a]. The solution x by SVD istransformed to un-distorted space by x = KC1x, as-suming that the point is neither at 0 nor at infinity. Thistriangulation must be performed four times for each com-bination of R and t and tested by perspective transforma-tion with C1 and xz > 0 to ensure the resulting points piare in front of the camera.

2.4. Image Selection

Using adjacent pairs of images in a closely-spaced timesequence allows feature points to be tracked more reli-ably between images, as there is less chance of condi-tions or change in angle causing a feature to change sig-nificantly. However, the disadvantage of using closely-spaced images for pose estimation is that a very smallangular difference between two images will prevent trian-gulation solutions, like very distant points. Therefore, wetrack, match, and store keypoints between closely-spacedimages, but only triangulate with images that are well-separated that contain tracked keypoints between the two.Unusable images in the matching process are most com-monly due to:

• Not enough feature points being matched to obtainF or triangulate

• Inaccurate estimates of rotation R and translation t

• Inaccuracy of the fundamental matrix F, preventingdecomposition to E, R, and t

If two few features are matched between image Pt at timestep t and Pt−1, the next image to be obtained Pt+1 isused with Pt−1, if it fails then Pt+2 is used, and so onuntil a predefined “reset” limit. Valid matches from thenew image Pt or later are added the the existing trackedkeypoint list to associate feature numbers across the se-quence of images. When obtaining the fundamental ma-trix F, only keypoints that have been associated betweenboth images are used.

2.5. Position Estimation

To finding the ego-motion of the tracker’s camera relativeto feature points represents the Perspective & Point (PnP)problem. For this, we apply the OpenCV implementationof the EPnP algorithm [MNLF07]. For the n-point cloudwith points p1 . . .pn, four control points ci define theworld coordinate system and are chosen with one pointat the centroid of the point cloud and the rest oriented toform a basis. Each reference point is described in worldcoordinates (denoted with w) as a linear combination ofci with weightings αij . This coordinate system is con-sistent across linear transforms, so they have the samecombination in the camera coordinate system (denotedwith c. The known two-dimensional projections ui of thereference points pi are linked to these weightings by Kconsidering that the projection involves scalar projectiveparameters wi, leading to the following.

pwi =

4∑j=1

αijcwj , p

ci =

4∑j=1

αijccj ,

4∑j=1

αij = 1 (6)

Kpci = wi

(ui

1

)= K

4∑j=1

αijccj (7)

The expansion of this equation has 12 unknown controlpoints and n projective parameters. Two linear equa-tions can be obtained for each reference point to ob-tain a system of the form Mx = 0, where the nullspace or kernel of the matrix M2nx12 gives the solu-tion x = [cc1

T , cc2T , cc3

T , cc4T ] to the system of equa-

tions, which can be expressed as x =∑m

i=1 βivi. Theset vi is composed of the null eigenvectors of the prod-uct MTM corresponding tom null singular values of M.The method of solving for the coefficients β1 . . . βm de-pends on the size of m, and four different methods areused in the literature [MNLF07] for practical solution.

Let the translation and rotation in world coordinatesof the previous pose be tw(t − 1) and Rw(t − 1),and that of the current pose be tw(t) and Rw(t), forwhich we need to find the current camera matrix inworld coordinates Cw(t). The relative transformationbetween the camera positions t(t) and R(t) is usedto incrementally advance the current pose (assumedto be attached rigidly to the camera) as Cw(t) =[Rw(t− 1)R(t)|R(t) (t(t) + tw(t− 1))] ., and featurepoints are incrementally projected into world coordi-nates with x′ = (Rw(t− 1)R(t))

Tx + Rw(t −

1) (t(t) + tw(t− 1)). Orientation is stored as a quater-nion from the elements rij of Rw.

q =

wxyz

=

√1+r00+r11+r22

2r21−r12

2√1+r00+r11+r22

r02−r202√1+r00+r11+r22

r10−r012√1+r00+r11+r22

(8)

3. OBSERVATION AND IDENTIFICATION

The PnP solution across a sequence of images allows usto track the pose of the tracker spacecraft relative to fea-tures on the target spacecraft. However, in most casesit is necessary to identify what the actual orientation ofthe target is with respect to a known geometric model,or to identify specific parts of the target for interactionor analysis. For this task, we use the positional corre-spondences of three-dimensional keypoints selected fromthe constructed point cloud with respect to keypoints se-lected from a reference model point cloud that can be ob-tained in advance or on-line from another sequence ofimages with known relative pose. Model recognition isdone on a per-pose basis with accumulated points in thepoint cloud once a sufficient number of images has beenacquired during the “Observation” phase. This makes itpossible to match parts of a structure without requiringthe entire structure to have keypoints, for example if thetarget is in partial shadow. We use an Unscented Kalmanfilter (UKF) for reducing noise over time for pose esti-mates. Separate filtering is performed for the pose esti-mates obtained from PnP solutions and target pose esti-mation, both translation and quaternion rotation, using afast embedded UKF implementation with adaptive statis-tics [LPL13].

3.1. Object Pose Estimation

A set of three-dimensional keypoints are chosen fromboth the scene and the model by picking individual pointsfrom the cloud separated by a given sampling radius.Normals are calculated for these keypoints relative tonearby points so that each keypoint has a repeatable ori-entation. The keypoints are then associated with three-dimensional SHOT (Signature of Histograms of Orien-Tations) descriptors [STDS14]. SHOT descriptors arecalculated by grouping together a set of local histogramsover the volumes about the keypoint, where this volumeis divided into by angle into 32 spherically-oriented spa-tial bins. Within a given radius of the keypoint, pointcounts from the local histograms are binned as a cosinefunction cos(θi) = nu · nvi of the angle θi between thepoint normal within the corresponding part of the struc-ture nvi and the feature point normal nu. This has thebeneficial effects of creating a general rotational invari-ance since angles are relative to local normals, accumu-lating points into different bins as a result of small differ-ences in relative directions, and creating a coarse parti-tioning that can be calculated fast with small cardinality.

Comparing the scene keypoint descriptors with themodel keypoint descriptors to find good correspon-dence matches is done using a FLANN search on a k-dimensional tree (k-d tree) structure, similarly to thematching of image keypoints. Additionally, the BOrderAware Repeatable Directions algorithm for local refer-ence frame estimation (BOARD) is used to calculate localreference frames for each three-dimensional SHOT de-

scriptor [PDS11] to make them independent of global co-ordinates for rotation and translation invariance. Once aset of nearest correspondences and local reference framesis found, clustering of correspondences to given clus-ter sizes is performed by pre-computed Hough voting tomake recognition of shapes more robust to partial occlu-sion and clutter [TDS10].

Evidence of a particular pose and instance of the modelin the scene is initialized before voting by obtaining thevector between a unique reference point CM and eachmodel feature point FM

i and transforming it into lo-cal coordinates by the transformation matrix RM

GL =[LM

i,x, LMi,y, L

Mi,z]

T from the local x-y-z reference frameunit vectors LM

i,x, LMi,y , and LM

i,z . This precomputationcan be done offline for the model in advance and is per-formed by calculating for each feature a vector VM

i,L =

[LMi,x, L

Mi,y, L

Mi,z] · (CM − FM

i ). For online pose estima-tion, Hough voting is performed by each scene featureFSj that has been found by FLANN matching to corre-

spond with a model feature FMi , casting a vote for the po-

sition of the reference point CM in the scene. The trans-formationRMSL that makes these points line up can thenbe transformed into global coordinates with the scene ref-erence frame unit vectors, scene reference point FS

j andscene feature vector V S

i,L as V Si,G = [LS

j,x, LSj,y, L

Sj,z] ·

V Si,L+FS

j . The votes cast by V Si,G are thresholded to find

the most likely instance of the model in the scene, al-though multiple peaks in the Hough space are fairly com-mon and can indicate multiple possibilities for model in-stances. Due to the statistical nature of Hough voting, itis possible to recognize partially-occluded or noisy modelinstances, though accuracy may be lower.

3.2. Processing Times

To profile the processing requirements of the describedalgorithms on a system that could potentially be embed-ded into a satellite, the algorithm was run on a 667MHzARM Cortex-A9 processor with pre-defined images of aCubeSat engineering model in VGA resolution and pre-computed point clouds, and raw timing statistics gatheredfor the processing time of each algorithm. Tests 1 and 2were performed with 6524 model points and 5584 scenepoints from 220 images, and tests 3 and 4 were performedwith 6524 model points and 1816 scene points from 32images. Tests 1 and 3 were performed with a descriptorradius of 0.05 and cluster size of 0.1, and Tests 2 and 4were performed with a descriptor radius of 0.1 and clustersize of 0.5. Tab. 1 and Tab. 2 show the timing informa-tion obtained for each of the described algorithms in thesecases.

3.3. Identification Accuracy

To illustrate the accuracy of pose estimation while vary-ing the descriptor radius and cluster size and therefore

Table 3. Correspondences and Error resulting from vary-ing Descriptor Radius and Cluster Size

Estimate Descr.Radius

ClusterSize

Corresp-ondences

Trans.Error

RotationError

1 2.0 1.0 507 1% 2%2 2.0 0.1 507 7% 3%3 0.5 1.0 45 3% 4%

processing times, a set of pose estimation tests were per-formed using a CubeSat engineering model as a target forpose identification. In three examples of target identifica-tion shown in Fig. 3, Fig. 4, and Fig. 5, high-densitymodel points are in yellow with selected keypoints ingreen, and low-density scene keypoints are shown inblue. The model instance found in the scene is over-laid in red from a high-density model composed of 26339points, while the scene is composed of 1960 points trian-gulated from 52 images. The number of keypoints wasreduced by radius to 2042 in the model and 1753 in thescene. The descriptor radius and cluster size for theseestimates, with the resulting number of correspondencesand rounded cumulative errors in translation and rotationare shown in Tab. 3.

As more scene points are added over time, accuracy canincrease, but only if they are consistent with the exist-ing scene. We can see from these results that increasingthe size of the SHOT descriptor will increase the numberof keypoints available and result in better accuracy andhigher likelihood of identifying a shape, but also will re-quire longer processing times. Cluster sizes must be setappropriately for the point cloud size, as a cluster size toosmall or too large will prevent valid instances from beingfound, and result in decreased accuracy.

4. CONCLUSIONS

In this work, we have described a feature-based visualidentification system that allows a tracker spacecraft totrack relative movement to a target and ultimately ac-quire pose estimates using point cloud techniques. Us-ing projective geometry, we perform three-dimensionalreconstruction of features on the target from a sequenceof images taken with a single camera. The patent-freeORB algorithm that combines FAST keypoint detectionand BRIEF feature descriptors provides good toleranceto rotation and scaling of features for this purpose. Foruseful reconstruction, it is important to identify as manyfeatures as possible, so target spacecraft with many col-ors, edges, and shapes generally provide the best resultsfor feature-based systems such as this. It is important tonote that this method of motion estimation provides bestsolutions through post-processing of results. The moreimages that are included when creating the structure, thebetter triangulation will be. If processing power and stor-

Table 1. Timing for Features, Triangulation and PnP

TestNumber

FeatureDetect.

FeatureMatching

FeatureSelection

Fundam.Matrix

EssentialMatrix

Triangu-lation

PnPRANSAC

Ego-Motion

TotalTime

1-2 0.12 0.058 0.015 0.083 0.0017 0.038 0.0033 0.0005 0.323-4 0.12 0.061 0.010 0.048 0.0014 0.025 0.0026 0.0004 0.27

Table 2. Timing for Correspondence and Identification

TestNumber

ModelNormals

SceneNormals

ModelSampling

SceneSampling

ModelKeypoints

SceneKeypoints

FLANNSearch

Cluster-ing

TotalTime

1 0.17 0.15 0.027 0.020 1.26 0.84 107.7 0.92 112.12 0.17 0.15 0.029 0.024 3.37 2.19 118.0 2.00 127.23 0.17 0.043 0.031 0.0083 3.31 0.37 42.5 0.63 48.44 0.17 0.041 0.031 0.0078 3.31 0.37 42.6 1.36 49.1

Figure 3. Pose Correspondence for Estimate 1, Descriptor Radius 2.0, Cluster Size 1.0

Figure 4. Pose Correspondence for Estimate 1, Descriptor Radius 2.0, Cluster Size 0.1

Figure 5. Pose Correspondence for Estimate 1, Descriptor Radius 0.5, Cluster Size 1.0

age is available to include a large number of recent im-ages, such as by observing the target through multiplerotations, a better solution for motion will be obtained.To additionally decrease the processing time if desired,the camera image can be lowered in resolution, or pixelscan be under-sampled by choosing only every 2nd pixelor every 4th pixel in a staggered pattern over the imagefor feature matching [AZK09].

It is intended that even small spacecraft such asnanosatellites with a single camera could take advantageof this system. Work is underway to scale this system toa level suitable for nanosatellite use, which could providea technology demonstration with a minimum of cost andrisk. As the performance of feature tracking depends veryheavily on the design of the feature descriptor and methodof matching, further comparison of descriptor types forboth two-dimensional and three-dimensional matching iswarranted. Future work also includes the validation ofthese methods on a variety of models, and under a broaderset of varying conditions to evaluate the robustness offeature-based systems. A wide variety of applications forthis technology is also available, including robotic usesand planetary rover navigation and sensing.

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