Pose measurement of large non-cooperative satellite using structured light vision sensor(英文版)

Abstract —In final approach of rendezvous between a space robot and a large non-cooperative target, a single camera of the space robot can not observe a whole feature image of the large target to measure relative pose (attitude and position). To overcome this problem, a structured light is introduced to aid measurement. A partial rectangular framework of the target is chosen as measurement object. Firstly, the measurement model is built and four measurement coordinates systems are presented. Secondly, according to projection constraints on rectangle and circular points, a whole rectangle feature is reconstructed. Thirdly, using the whole rectangle and the structured light, transform matrix between camera and target coordinates systems is computed. Lastly, the relative pose of the partial rectangular framework is derived from the transform matrix. Several numerical simulations are studied to verify the method under different scenarios. The results show that the pose measurement is feasible and effective.

I. I NTRODUCTION

PACE robotic systems are expected to play an increasingly important role in on-orbit servicing (OOS) [1]-[3]. In recent years, more and more attentions have been paid to the OOS in geostationary orbit (GEO). Some malfunctioned communication satellites are main objects to be serviced [4][5]. To repair a malfunctioned satellite in GEO, the space robotic systems should have the ability of autonomous rendezvous. Especially, the determination of relative pose between the space robot and the malfunctioned satellite is the key technology in final approach of rendezvous. Vision based system is commonly used to achieve this work. The Proximity Sensor (PXS) system of Engineering Test Satellite VII (ETS-VII) and Advanced Video Guidance Sensor (AVGS) system of Orbital Express (OE) are all vision based systems for relative pose measurement [6]-[8]. The two vision based systems depend on corner-cubes mounted on serviced satellites to work, i.e. the serviced satellites are cooperative. However, these malfunctioned communication satellites are non-cooperative. No artificial sign for measurement are mounted on these satellites. Their nature

Received November 30, 2011. Astronautics, Harbin Institute of Technology, Harbin, 150001, China and

Aerospace Dongfanghong Development Ltd. Shenzhen, Shenzhen 518057, China (corresponding author phone: +86-755-26727118; fax: +86-755-26994863; e-mail: xhgao@https://www.360docs.net/doc/01940076.html,, bliang@https://www.360docs.net/doc/01940076.html,, xddu@https://www.360docs.net/doc/01940076.html,).

of Technology, Shenzhen, 518055, China (e-mail: wfxu@https://www.360docs.net/doc/01940076.html,).

This work is supported by National Nature Science Foundation of China

under research grants 60805033. surface features can be used for relative pose measurement. Stereo visions can be used to estimate the motion and pose of non-cooperative satellite [9]-[13]. These methods seem to be a costly and complex operation for space missions. Considering that rectangular features are common in the configuration of a satellite and can be chosen as the recognized object to determinate relative pose. Based on single vision system, the pose of rectangle can be determined by the methods in papers [14]-[18]. But the rectangle feature is usually very large, in final approach it will go beyond the camera’s field of view (FOV). The image of rectangle becomes partial and the above-mentioned methods are not effective.

In this paper, a method based on single camera and structured light is proposed to calculate the pose of a large non-cooperative satellite using a partial rectangle feature. The

structured light vision sensor can reconstruct a whole rectangle to achieve pose measurement. This paper is

organized as follows. In section 2, the structured light vision

sensor is designed for pose measurement. In section 3, the pose measurement model of structured light vision sensor is introduced. In section 4, a whole rectangle is reconstructed and the relative pose is determined. In section 5, some numerical simulations of typical cases are performed to verify the proposed pose measurement method. The last section is the conclusion. II. S TRUCTURED L IGHT V ISION S YSTEM FOR P OSE M EASUREMENT A. A Typical Non-cooperative Satellite A typical on-orbit failure of GEO satellites is the failure of mechanisms to deploy. For instance, TV-Sat-1 suffered the failure of one solar panel deployment in 1987. Due to a clamping bolt, the array deployment was inhibited and the whole mission failed totally. Another recent example is the Chinese satellite SinoSat-2 launched on October 29, 2006. After less than one month in orbit, the satellite lost its function because of un-deployed solar panels and antennas.

According to these malfunctioned satellites, it is assumed that the non-cooperative target satellite which will be serviced is a malfunctioned satellite with one un-deployed

solar panel and two un-deployed communication antennas. The structure and mechanism of the target satellite are the same as SinoSat-2. The target satellite encounter three mechanical malfunctions: (a) The +Y solar wing fails to

deploy; (b) The +X communication antenna is unfolded; (c) The –X communication antenna is unfolded. These statuses of the target satellite are shown in Fig. 1.

Pose Measurement of Large Non-cooperative Satellite using

Structured Light Vision Sensor

Xuehai Gao, Bin Liang, Xiaodong Du, and Wenfu Xu

S

Xu Wenfu is with the Shenzhen Graduate School, Harbin Institute

Xuehai Gao , Bin Liang, Xiaodong Du are with the School of

2012 IEEE International Conference on Information Science and Technology Wuhan, Hubei, China; March 23-25, 2012

B.The Design of Measurement Sensor

In former rendezvous and docking missions, measurement sensors usually rely on the artificial markers which can simplify the measurement task. However, the given target satellite which is non-cooperative can not provide effective cooperative information for the relative pose measurement. We have to use the natural features of the target satellite to determine the relative pose.

According to the investigation of the target satellite, it is found that there exists framework on the backboard of antenna which can increase the strength of the whole structure, as shown in Fig. 1. The framework which is designed to be a regular pattern can be taken as the feature for the pose measurement. And rectangular feature is very common in the frame work. Consequently, it is of great significance to perform the pose determination by recognizing the rectangular structure. Finally, the middle rectangular structure is chosen as the recognition object.

A vision camera commonly used in current space operations is available at a relative low cost and has low mass and energy requirement. A feasible camera should be designed to recognize the rectangular feature. Usually, the GEO communication satellites are very huge i.e. the rectangular structure is very large. The FOV of vision camera should be wider. However, the FOV is wider, the lens distortion is worse and it is more difficult to exactly extract the recognition feature. Therefore, the FOV of vision camera is limited and only a partial rectangle feature can be detected. The attitude of target satellite can be determined by the partial rectangle feature [18]. But it is a problem to obtain the position of the target satellite, because the target satellite is non-cooperative and the size of partial rectangle feature is unknown.

To solve this problem, a structured light is introduced to the vision measurement system to calculate the position of target satellite. The structured light can form a point on the plane of partial rectangle feature. And the point is always in the FOV of the camera. The structured light vision sensor system is shown in Fig.1.

Based on the structured light vision sensor system, a novel pose measurement of non-cooperative satellite is presented in following sections. The method can reconstruct a virtual whole rectangle by the partial rectangle to calculate the attitude and position of non-cooperative satellite at the same time. The demonstration of relative pose determination in

final approach of rendezvous, the structured light vision sensor system and the malfunctioned non-cooperative satellite are shown in Fig. 1.

III.P OSE M EASUREMENT M ODEL

A partial rectangular structure on the backboard of antenna

is chosen as the recognition object. A structured light vision system composed of a structured light and a single camera is

used to determine the pose of rectangle. The pose measurement model is shown in Fig. 2.

Four measurement coordinates systems are necessary in

the model. t

∑is target coordinates system. Its coordinate

is T

[,,,1]

t t t t

X Y Z

=

P. c

∑is camera coordinates system. Its coordinate is T

[,,,1]

c c c c

X Y Z

=

P. l

∑is light coordinates system. Its point coordinate is T

[,,,1]

l l l l

X Y Z

=

P.p

∑is

image coordinates system. Its coordinate is T

[,,1]

u v

=

p. The relationships of these coordinate systems are introduced and

the question of pose measurement is presented.

A.Image and Camera Coordinates Systems

A camera can be described by pinhole model which is a

linear model. Then, the transformation between image coordinate and camera coordinate can be given by:

[]()

c p c

c

Z=0

p M P (1) Where

o

o

/0

0/

001

u

p

c v

f d u

f d v

??

??

=??

??

??

M

c

M

Fig. 2. Pose Measurement Model Fig. 1. Relative Pose Measurement in Final Approach

p c

M is the intrinsic parameters of camera. It can be obtained by camera calibration [19]. f is the focus of camera. u d and v d are the effective pixel pitch in direction of axes u and v. o o [,]u v stands for the center of image plane.

B. Light and Camera Coordinates Systems

The transformation matrix between light and camera coordinates systems can also be calibrated [20]. Therefore, the relationship of the two coordinates systems is:

()c

c l l =P M P (2)

Where

123T

1231[,,][,,]c c

c l l l c c c c l l l l c c c c l

l l l t t t ??=??

??==R T M 0

R r r r T c l

R is rotation matrix. It is an orthonormal unit matrix. c l T is

translation vector.

C. Target and Camera Coordinates Systems

The relationship between target and camera coordinates systems can be described by:

()c

c t t =P M P (3)

Where

123c c c c T

t

t 1t 2t 31[,,][,,]

c c

c t t t c c c c t t t t t t t ??=??

??==R T M 0

R r r r T c t

R is rotation matrix. It is an orthonormal unit matrix. c

t

T is

translation vector.

D. Question of Pose Measurement

The question of pose measurement is to determine relative rotation angles and position between target and camera coordinates systems using the image of partial rectangle feature and structured light i.e. the question is to compute the

transformation matrix c t M . The relative position is c

t T .

Defined that the rotation sequence of coordinates system is

Z X Y →→, and the corresponding rotation angle is

γαβ→→. Then, the rotation matrix c t R will be:

c

t C C S S S C S S S C C S C S C C S S C S C S S S S C C C C βγαβγβγαβγαβαγαγαβγαβγβγαβγαβ??

+?+??=?????

?++??R (4)

S stands for sine. C stands for cosine. IV. P OSE M EASUREMENT A. Rectangle Reconstruction

Because the target is non-cooperative, the size of partial

rectangle feature is unknown. Therefore, it is difficulty to calculate the relative pose by the half rectangle. It is necessary

to reconstruct a whole rectangle. For this purpose, projection

constraint on rectangle will be concluded. However, it still lacks conditions to reconstruct a whole rectangle. Circular points will be introduced to assist rectangle reconstruction. If a point is on a plane (i.e.0Z =), its target coordinate can be rewritten to T [,,1]t t t X Y =P . Using (1) and (3), we can have:

12[,,]()c

p c c c t

c t t t Z =p M r

r T P (5) Assumed that target coordinates of rectangle apex are:

T 1T

2T

3T 4

[0,0,1][,0,1]

[0,,1][,,1]t t

t t d rd d rd ?=?=??=??=?P P P P d is the width of rectangle and is unknown. r is the

proportion of length and width and is also unknown. Their image coordinates and camera coordinates respectively are:

T

T [,,1]

, 1,2,3,4[,,,1]i i i c c c c

i

i i i u v i X Y Z ?=?=?=??p P Substituting target coordinates and pixel coordinates into (5), we can obtain the equation:

(),

1,2,3,4p t

i i t i i λ==p M P (6)

Where

4124

/ (1,2,3,4)

[,,]/c c

i i p p c c c c

t c t t t Z Z i Z λ?==??=??M M r r T Because the target coordinates of points 1P , 2P and 3P are not on a same line, the matrix 123[,,]t t t P P P is nonsingular. From (6), we have:

141231231234[,,](,,)[,,]()t t t t diag λλλ?=p p p p P P P P (7) The four points 1P , 2P , 3P and

4P have the following characteristic:

1T 1234[,,]()[1,1,1]t t t t ?=?P P P P (8)

Because the pixel coordinates of points 1P , 2P and 3P are

also not on a same line. The matrix 123[,,]p p p is

nonsingular. Substituting (8) into (7), we have: T 11231234[,,][,,]λλλ??=p p p p (9) Equation (9) is the projection constraint on rectangle. However, the information is not enough to reconstruct a

rectangle. The relationship between circular points and

rectangle will be introduced. Circular points are the intersections of infinite straight line and circle. Circular points are imaginary and conjugate points. In infinite plane, circular points are on absolute conic, i.e. they satisfy the equation:

T

0=Q CQ (10)

Where

T

1T

2

[1,,0]

[1,,0]j j ?=??=???Q Q 1Q and 2Q are circular points. C is absolute conic. It is a third-order identity matrix.

The image coordinates of circular points are also on the

image of absolute conic C [21]:

T 0=q cq (11)

Where

T

1

()()p p c

c

??=c M M c is the image of absolute conic C , it is only relative to

the intrinsic parameters of camera.

Similar to (6), the image coordinates of circular points can be given by:

, 1,2p i i t i i τ==q MQ (12)

i τ is a constant.

Substituting (12) into (11), the projection constraint on circular points can be described as:

T

T

()()0, 1,2p p i

t

t

i i ==Q M c M Q (13)

To reconstruct a whole rectangle, it is necessary to substitute apex of rectangle for circular points. The left sides of (13) are complex numbers. The real part and imaginary

part are all equal to zero. From (13), we have:

T T

[1,0,0]()()[0,1,0]0p p t t =M c M (14)

From (6), we can derive the description as follows:

T T 12123T T

13123()[1,0,0][,,][,,]

()[0,,0][,,][,,]p t p t d d r λλλλλλ?=???=??

?M p p 0M p 0p (15) Substituting (9) and (15) into (14), equation (14) can be

transformed to the following forms finally:

T T T 1412312131234[,,][,,][,,][,,]0

??=p p p p p p 0c p 0p p p p p (16) Equation (16) fuses the two projection constraints on rectangle and circular points. It will be used for rectangle reconstruction.

From the image of partial rectangle, three image lines

((,),1,2,3)i i i l k b i =can be extracted by image processing.

The image coordinate 1p of point 1P is the intersection of lines 1l and 3l . The image coordinate 2p of point 2P is the intersection of lines 1l and 2l . Choosing an image coordinate

3p of point 3P on line 3l , the image coordinate of point 4P

can be calculated by the equations:

T 442

240

[,1,]0k b ?=??

?=??p Np p (17) Where

T T 11231213123[,,][,,][,,][,,]??=N p p p p p 0c p 0p p p p

2k and 2b are the parameters of line 2l .

Until now, a whole rectangle is reconstructed. Its image coordinates are 1p , 2p , 3p and 4p . B. Pose Determination

In order to calculate the relative pose, the camera coordinates of rectangle apex (1,2,3,4)c i i =P are necessary. From (6), we have

4() ,=1,2,3,4c i c c p

i i c i c i X Y Z i Z λ?????=??????

1M p (18) In (18), only 4c Z is unknown. The structured light will be

used to calculate it.

In camera coordinates system, the plane of rectangle can be described by:

[],,1c i c i c i X m n p Y Z ????

=????

??

(19) Where

11

1T T 11

1T T 2224T T 333,0,01110,,01110,0,c p c c c c m n Z p λλλ???????????????????????????==????????????

???????????

?????????????P p M P p P p

Assumed that the camera coordinate of structured light is 5c

P . Its image coordinate 5p can be extracted by image processing. From (2), we have:

5535()c c l c c

l l c X Y Z Z ??

??=+??????

r T (20) Where

T 1T 1

53[0,1]()()

[(),]

l c l p c c l Z ???=??=???H H H T H M p r Substituting (20) into (19), the 4c Z can be computed:

T

T

T

T 115T T 4225T 533,0,0110,,010,0,c c

p c

c c X Z Y Z λλλ????

??

????

????????=????????

??????????

??

??

??

p p M p (21)

Substituting (21) into (18), 1c P , 2c P , 3c P and 4c P are obtained. And the target coordinate can be:

T 1T 2122T

3

132T 4

121322[0,0,1][,0,1][0,,1][,,1]t t

c c t c c t

c c c c ?=?=???

?=???=????P P P P P P P P P P P P The symbol 2? stands for 2-Norm. From (3), we have:

12[,,]1c t i i c c c c t i t t t i c i X X Y Y Z ????

????=????

????

????

r r T (22) Substituting c i P and (1,2,3,4)t i i =P into (22), we can obtain:

12c t c t c t ????=??????

r

A r

B T (23) Where

11111144444

4

129

0000100000001000000010000100000001000

1t t

t t t t t t t t t t X Y X Y X Y X Y X Y X Y ×??????????=???????????

?#########A T 1

114

4

4121

c

c

c

c

c

c

X Y Z X Y Z ×??=??

"B

The result of (23) is:

1

T

1T 2()c t c t c t ?????=??????

r r A A A B T Because the matrix c t R is an orthonormal unit matrix, the vector 3c t r is:

3

12c

c c

t t t =×r r r

Now, the relative rotation angels between target and

camera coordinates systems are:

2313332122arcsin()arctan(/)arctan(/)c

t c c t t c c t t R R R R R αβγ?????????=?

???????????

And the relative position between target and camera

coordinates systems is:

c t =T T

Until now, the attitude and position of non-cooperative satellite is determined.

V. S IMULATION S TUDY

To verify the proposed method is feasible and effective, several representative computer simulations are presented in this section. We experiment with three typical scenarios.

By analyzing the pose measurement algorithm, the factors effecting measurement precision are: (1) The precision of intrinsic parameters p c M and matrix c l M which can be calibrated on ground. (2) The precision of inputs (,)i i i l k b and 5p which can be extracted by image processing. Because

the accuracy of 5p is relatively high, only a small bias is

added to it. Assumed that the FOV of camera is 55o , and its image

plane size is 10241024×. Then, the intrinsic parameter p c M with calibration errors is:

983.50

5120983.551200

1u p

c v

I u I v +Δ+Δ????=+Δ+Δ?????

?

M

In the matrix, ,,,u v I I u v ΔΔΔΔ are calibration errors.

In theory, the rotation matrix c l R of c

l M is a unit matrix. However, the calibration has rotation errors which are l αΔ,

l βΔ and l γΔ. The rotation matrix c l R is similar to (4). The

translation vector c l T of c l M with calibration errors is:

T [300mm ]c

l

l l l X Y Z =Δ?+ΔΔT

In the vector, ,,l l l X Y Z ΔΔΔ are calibration errors.

The image line (,)i i i l k b

can be extracted by Hough Transform whose parameters are θ and ρ [22]-[24]. The relationship between (,)k b and (,)θρ is:

ctg()

/sin()k b θρθ=???

=?

Therefore, random errors θΔ and ρΔ are added to θ and

ρ to simulate input errors.

A. Scenario 1: Planned Path Approach

In scenario one, the space robot will approach to the non-cooperative satellite through a planned path to verify the feasibility of the pose measurement. The calibration errors and random errors of input are shown in Table I.

It is assumed that the space robot has performed a

proximity to the target satellite at the range of about 2m by

using other navigation method. The current situation is that the rectangle used for pose measurement is beyond the FOV of camera and the navigation method is invalid. In final approach, the proposed pose determination of this paper will

be applied to navigate sequentially. The initial relative attitude and position between camera frame and target frame are given by:

o o o x y z

[,,][7.4, 6.6,6.3][,,][425.1mm,363.5mm,1642.6mm]T T T αβγ?=???

?

=??? To perform on-orbit operations, the space robot will close to the target satellite at a berthing position (1.0m). The desired relative pose is:

o o o

x y z

[,,][0,0,0]

[,,][383.9mm,480.1mm,999.6mm]T T T αβγ?=??

=???

The proximity to the target satellite spends about 200

control periods. In every control period, the vision system

will provide relative pose information until it arrives at the

berthing position. The relative attitude and position tracking trajectory and the tracking errors are shown in Fig. 3 and Fig.

4.

From the simulation results, the proposed method for pose

determination of non-cooperative satellite in final approach is

feasible. Comparing the three angles, the angle γ is more Fig. 4. The Result of Positions and Errors

Fig. 3. The Result of Angles and Errors

TABLE I

C ALIBRATION E RRORS AN

D I NPUT

E RRORS Error Name

Errors

u I Δ,v I Δ 10,10

u Δ,v Δ 5,5 l αΔ,l βΔ,l γΔ(°) 0.1,0.1,0.1 l X Δ,l Y Δ,l Z Δ(mm) 5,5,5

θΔ(°)

[-0.1,0.1] ρΔ

[-2,2]

precise than the other two angles. For a rectangle, the pixel variation caused by angle γ is more than that caused by the other two angles in the same rotation i.e. angle γ is more sensitive to pixel variation. Comparing the three positions, the position error of the Z axis is a little larger than that of the other two axes. The explanation is that the relative motion along the normal direction of a rectangle plane (the direction along the line of vision) is relatively difficult to be computed.

B.Scenario 2: Random Noises in Line Extract

The orbital environment has significant effect on electronic components. It may result in degradation of optical sensors. Therefore, images from a camera of space robot may be corrupted by intense noises. These noises will effect on the precise of image processing. The main embodiment is that the parameters θand ρof line extracted by Hough Transform exist random errors. These errors will be transferred into pose measurement algorithm.

In order to evaluate the performance of the proposed algorithm, modeled images at initial and desired relative poses are taken as the test sample. The Case A and Case B denote the initial and desired relative poses respectively. It is assumed that the three ideal lines of partial rectangle are extracted. And different random noises are added in the parameters θand ρ of the three ideal lines.

The strategy of the experiment is that the maximum absolute values of random noise added in parameter θ are [-0.1,0.1], [-0.2,0.2] and [-0.4,0.4] degrees and the maximum absolute values of random noise added in parameter ρ are [-2,2], [-4,4] and [-8,8] pixels. Then, 9 different states will be experimented in each case. The calibration errors are the

same as scenario one. The proposed algorithm will be executed about 1,000 times in each state. The results of these experiments are shown in Table II and Table III.

The maximum absolute errors of Case A and Case B are shown in Table II and Table III. Observing each table, the random noise of θ has more obvious effect on the proposed pose determination than the random noise of ρ. The angle γis more precise than the other two angles. The position error of the axis Z is a little larger than that of the other two axes. The two results consist with the result of scenario one. Comparing Table II and Table III, if the distance between the space robot and target satellite is closer, the error of relative pose will be smaller. From this experiment, the image processing has an important impact on the pose determination algorithm. Therefore, the precision of image processing should be insured. rectangle. The structured light calibration has effect on calculation of camera coordinate.

To observe the influence on pose measurement by calibration error, three different calibration errors are given to experiment. The calibration errors are shown in Table IV.

The strategy of the experiment is that the maximum absolute values of random noise added in parameter θ are [-0.1,0.1] degrees and the maximum absolute values of random noise added in parameter ρ are [-2,2] pixels. Three different states will be experimented at initial relative pose. The proposed algorithm will be executed about 1,000 times in

TABLE III

M AXIMUM A BSOLUTE E RROR OF C ASE B

θΔ

(o)

ρΔαΔ

(o)

βΔ

(o)

γΔ

(o)

x

T

Δ

(mm)

y

T

Δ

(mm)

z

T

Δ

(mm) [-0.1,0.1] [-2,2] 0.215 0.404 0.136 3.23 4.64 17.5 [-0.2,0.2] [-2,2] 0.424 0.679 0.228 4.33 5.78 19.4 [-0.4,0.4] [-2,2] 0.967 1.539 0.377 6.88 9.90 26.7 [-0.1,0.1] [-4,4] 0.243 0.436 0.138 5.43 6.48 16.6 [-0.2,0.2] [-4,4] 0.503 0.746 0.209 5.64 8.06 20.2 [-0.4,0.4] [-4,4] 0.870 1.43 0.350 8.76 10.4 28.9 [-0.1,0.1] [-8,8] 0.250 0.422 0.139 8.84 10.1 17.1 [-0.2,0.2] [-8,8] 0.480 0.671 0.211 8.81 13.3 20.1 [-0.4,0.4] [-8,8] 1.01 1.52 0.402 9.92 12.4 28.1

TABLE II

M AXIMUM A BSOLUTE E RROR OF C ASE A

θΔ

(o)

ρΔαΔ

(o)

βΔ

(o)

γΔ

(o)

x

T

Δ

(mm)

y

T

Δ

(mm)

z

T

Δ

(mm) [-0.1,0.1] [-2,2] 0.517 0.634 0.167 7.85 6.93 38.3 [-0.2,0.2] [-2,2] 0.814 0.736 0.244 9.15 6.27 42.4 [-0.4,0.4] [-2,2] 1.62 1.51 0.397 10.8 8.59 49.1 [-0.1,0.1] [-4,4] 0.465 0.776 0.171 11.2 7.93 41.6 [-0.2,0.2] [-4,4] 0.825 0.919 0.238 12.5 10.7 43.6 [-0.4,0.4] [-4,4] 1.66 1.36 0.303 13.5 10.9 49.9 [-0.1,0.1] [-8,8] 0.578 0.625 0.187 16.9 12.2 42.1 [-0.2,0.2] [-8,8] 0.936 1.27 0.212 16.2 10.8 47.6 [-0.4,0.4] [-8,8] 1.43 1.69 0.434 16.1 14.4 51.7

TABLE IV

C ALIBRATION E RRORS

Calibration Errors Case C1 Case C2 Case C3

u

IΔ,

v

IΔ 10,10

20,20

10,10 uΔ,vΔ5,5 10,10 5,5 l

αΔ,

l

βΔ,

l

γΔ(°) 0.1,0.1,0.1 0.1,0.1,0.1 0.2,0.2,0.2 l

X

Δ,

l

Y

Δ,

l

Z

Δ(mm) 5,5,5 5,5,5 10,10,10

C.Scenario 3: Errors in Calibration

The calibration error is one of the important factors effecting measurement precision. The calibration includes camera calibration and structured light calibration. The camera calibration has effect on the reconstruction of

each state. The results of these experiments are shown in Table V.

From the results in Table V, we can conclude that the intrinsic parameters p

c

M have more effect on the pose

measurement than the matrix c

l

M do. Especially, the errors of Z axis are worse than that of the other two axes i.e. the depth information is more difficult to be computed. If the

intrinsic parameters p

c M an

d matrix c

l

M can be calibrated

on orbit, the pose determination of non-cooperative satellite will be more accurate.

The results of the three numerical simulations show that the pose determination of large non-cooperative satellite based on structured light vision sensor is feasible and effective.

VI.C ONCLUSION

In this paper, a method for pose determination of a large non-cooperative target is presented. The method relies on a rectangular structure on the target. Though lacking the whole information of rectangle, the proposed method can determine the pose of the large non-cooperative target by using the structured light vision system. The method overcomes the problem that single camera can not observe the whole scene of a large-scale rectangle to determine relative pose in final approach of rendezvous. The results of computer simulations validate the proposed method.

The application of this method may be extended to determine pose information for any large-scale spacecraft with rectangular structures. The possible rectangular features include the antenna frame, the solar panel, the heat delivery surface, or even the spacecraft itself and so on.

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TABLE V

M AXIMUM A BSOLUTE E RROR OF C ASE C

Maximum Errors

αΔ

(o)

βΔ

(o)

γΔ

(o)

x

T

Δ

(mm)

y

T

Δ

(mm)

z

T

Δ

(mm)

Case C1 0.517 0.634 0.167 7.85 6.93 38.3 Case C2 0.605 0.741 0.178 12.6 10.9 57.2 Case C3 0.558 0.603 0.154 7.17 8.80 35.9