INTRODUCTION
The third step of manned space flight is to build a large space station for
astronauts longterm residence, but the future of the large space station is
a combination of many cabin space station and track complexes. At present, the
assembly of the large space station is generally by the use of space robot to
implement capturing and docking the cabins and track complexes to instead the
astronauts to complete the dangerous or impossible tasks. At the same time,
the space robot also can do the recovery, repair and maintenance of the satellite.
However, these activities are based on precise robot motion control and compare
with the traditional fixed based robots the base of the freefloating space
robot is moveable and one mainly difference is that the base body of the freefloating
robot has six degrees of freedom that the control methods for terrestrial robot
can not be easily applied to freefloating space robot directly (Wenfu
et al., 2009). The position and posture of the base body would change
when the freefloating space robot is moving its manipulator to the position
to capture a target that take a great challenge to the control of the free floating
space robot. Therefore, it has received the domestic and foreign scholars’
great attention.
Yoshida (2003) derived the general form of the Jacobian
matrix of the space robot by using the conservation of the angular momentum
theorem and based this new form generalized Jacobian matrix a resoled motion
rate control method is proposed. In the ETSVII validated the control method
based the generalized Jacobian matrix. Belousov et al.
(2005) proposed a motion planning method by two iterative, for a wide range
space robot based on complex dynamics. Huang et al.
(2006), Wenfu et al. (2007) and Xu
et al. (2007) proposed a control method for freefloating space robots
that can track, approach and capture the target in Cartesian space with the
spiral trajectory.
In this study, the target capturing for freefloating space robot based on
binocular stereo vision (Malamas et al., 2003;
Van der Zwaan et al., 2002) is studied and the
method does not require accurate modeling of the system with the external feedback
(Chaumette and Hutchinson, 2008). In the general methods,
the feedback is used to implement the target capturing avoid identifying the
parameters of the freefloating space robot system. In the visual servoing control
system a computer is employed for processing the acquired images. This is achieved
by applying special purposed image processing analysis and classification software.
One or more cameras placed at the sence under inspection usually acquire images.
And the main problem of the machine vision task is to understand what kind of
information the machine vision system is to retrieve and how this is translated
into measurements or features extracted from images (Ruf
and Horaud, 2000). There are two methods to design the visual servoing system
(Christie et al., 2005). One is imagebased visual
servoing method and the other is positionbased visual servoing method. Usually,
the position of the cameras are fixed but in the freefloating binocular stereo
vision control system, the position of the cameras mounted on the base body
of the space robot is changing all the time that takes a great challenge to
the space robot system. In this study, the external feedback binocular stereo
vision device is used to calculate the target position in realtime for the
control system to compensate for the error of the conservation of the momentum
caused by the movement of the freefloating space robot.
THE DYNAMICS OF FREEFLOATING SPACE ROBOT
Consider an n degrees of freedom manipulator with freefloating base body which
considered as link n+1, as shown in Fig. 1 and each joint
of the manipulator is a single degree of freedom, it can be rotational or translational
joint. Based on Lagrange equations the freefloating space robot dynamic equations
can be found by HongTao and YouLun (2000) and FuYang
et al. (2010). The linear and angular momentum conservation equations
of the freefloating space robot are as follows:
where, ρ_{i} denotes the density of link i, m_{i} denotes
the mass of link i , drives, actuators and other rigid bodies, m_{0} denotes
the mass of the base body of the freefloating space robot, J^{r}_{i}
denotes the inertia tensor of unit length of the link i according the mass centre
of the link i, J_{v} denotes the inertia tensor of the base body of the
freefloating space robot according to the mass centre of the base body, L_{s}
and L_{r} denote the initial linear and angular momentum of the freefloating
space robot system which make the degrees of freedom increase to n+6.

Fig. 1: 
The freefloating space robot 
THE DESIGN OF BINOCULAR STEREO VISION
The binocular stereo vision is based on the parallax principle that get the three dimensional geometric information of the object by multiple images. In the machine vision system, the binocular stereo vision system is generally comprise of two or more cameras apart at some distance with different angles or with one movable camera at different place taking two different images. The parallax principle is based on the triangular method and the projectional transformation to recover the three dimensional geometric objects. Although, the real scene is three dimensional, the image could be twodimensional or threedimensional. When we do not need to determine the depth of the scene or scene features, we can use two dimensional images, for example, in determining the contours of the object or image side that we do not need the depth information of each point of the objects, so we could use the two dimensional image. The three dimensional images processing is mainly used for those that need motion detection, depth measurements, remote sensing, relative positioning and navigation during the operation. In the freefloating space robot binocular stereo vision control system, the three dimensional images are used to calculate the position and posture of the target and feedback to the robot control system for the space robot approaching and capturing the target.
Assumed that in the space there is a target point p. Points p_{1} and
p_{2} denote the points in the image coordinates of camera C_{1}
and camera C_{2} respectively, and the projection matrix (Shuqing
et al., 2005) of the cameras are M_{1} and M_{2}.
o_{t} (x_{t}, y_{t}, z_{t}) denotes the coordinate
system of the base body of the freefloating space robot and according to the
perspective projection matrix transformation (Guangjun, 2004)
could obtain equations as follows:
The geometry locations of the two CCD cameras are shown in Fig. 2. (u_{1}, v_{1}, 1) and (u_{2}, v_{2}, 1) denote homogeneous coordinates of the points p_{1} and p_{2 }in the image coordinate systems of the cameras C_{1} and C_{2}, respectively and (x_{t}, y_{t}, z_{t}, 1) denotes homogeneous coordinate of point p. From Eq. 3, the parameters z_{c1} and z_{c2} can be eliminated and could obtain 4 linear equations:
From the analytic geometry theorem, combining two plane equations we could get a space linear equation. The geometric meaning of Eq. 3 is the line o_{c1} p_{1} and line o_{c2} p_{2} and the space point p (x_{t}, y_{t}, z_{t}) is the intersection point of the line o_{c1} p_{1} and the line o_{c2} p_{2} by which we could calculate the coordinate of point p. For the posture of the target, we could measure the four points of a square ABCD to calculate the posture; the posture can be calculated by following equations:
where, L = AB denotes the side length of the square ABCD.
THE CONTROL SYSTEM OF SPACE ROBOT
In the robot kinematics, the position and posture of robot endeffector could
be obtained from solving the robot kinematic equations and the turning angle
of each joint can be calculated when the robot endeffector is moving.

Fig. 2: 
Geometry of binocular stereo vision 
The movements of robot joints are not independent but associational and coordinational
and the control system is actually achieved through the joint servoing systems.
The movement of robot endeffector decomposed to each joint velocity, acceleration,
force and torque and each joint is controlled independently. In this study,
the decomposition acceleration control method with binocular stereo vision feedback
is used to control the freefloating space robot capturing the target. The decomposition
acceleration control method requests drivers of each joint simultaneously to
move at calculated acceleration that to guarantee the robot endeffector moving
smoothly and stably in Cartesian coordinate. Before control the robot, we need
to decompensate the position and posture of the robot endeffector into joint
angle acceleration and then control the joints of the space robot (Jifeng,
2006).^{.}
Supposed that the robot has n degrees of freedom, and the position and posture of the endeffector in the Cartesian coordinates in vector form are written as follows:
The generalized robot joint coordinate vector could be defined as:
The relationship between Eq. 5 and Eq. 6 are:
Supposed that the robot has m degrees of operational space freedom and the relationship of joint angle and Cartesian coordinates are written in nonlinear function Eq. 7. Derivate Eq. 7 we could obtain:
where, j (q) denotes the generalized Jacobian matrix of joints, defined as:
denotes the desired velocity of the robot endeffector in Cartesian coordinate,
q (t) denotes the joint velocity in the joint space coordinate and Eq.
9 has established the relationship of the two velocities. When degrees of
freedom of the robot in operational space is equal to the degrees of freedom
in robot joint space, the robot is nonredundant and the inverse of generalized
Jacobian matrix can be calculated directly as follows:
When m<n, the robot is redundant and the generalized Jacobian matrix does not exist. According to the generalized inverse matrix theory, we could obtain:
j^{+} (q) denotes the inverse generalized Jacobian matrix. When j (q) has the full rank, we could obtain following equation:
Derivate Eq. 12, we could obtain the acceleration of the robot end effector, written as follows:
Equation 13 denotes the relationship between the acceleration
of joints in Cartesian coordinate and in joint space coordinate, in fact, the
goal of acceleration control method is to achieve the error between the actual
and desire position and posture of robot endeffector converging to zero, supposed
that:
where, e denotes the error between the actual and desire position and posture of the robot endeffector, X_{d} and X denote the desire and actual position and posture of the robot endeffector, respectively. To meet the requirement of the converging condition that must satisfy:
where, k_{1}, k_{2 }are proportional coefficient, and should
make sure that the real root of Eq. 15 is negative. With
Eq. 1315, we could obtain:
The closed loop acceleration decomposition control method is based on Eq. 16, if we have known the desire trajectory of the robot endeffector that is desire position, posture, velocity and acceleration of the robot endeffector, we could calculate the joint acceleration of each joint in joint space coordinate, then we could control the robot.
SIMULATION
In this study, the free floating space robot with a 6 degrees of freedom manipulator capturing the moving target is simulated. The freefloating space robot is modeled in OpenGL and using DirectShow acquiring the images of the two cameras and the colour is used to get the position of the target in the image coordinate and at last use the OpenCV for image processing and send the position and posture of the target to the control system realtimely to modify the movement of the manipulator.
Figure 3 is the simulation software of the target capturing
of the free floating space robot. Figure 4 is the position
of the target in the robot coordinate that calculated from the processed images.
Figure 5 is the trajectory of the robot end effector that
approaches the target from the feedback of the binocular stereo vision system.

Fig. 3: 
The simulation software 

Fig. 4: 
The calculated spatial points 

Fig. 5: 
Trajectory of the space robot endeffector 
CONCLUSION
In this study, the target capturing of the freefloating space robot based on binocular stereo vision method is proposed. This method does not need to consider the nonholonomic constraints characteristics that caused by linear and angle momentum conservation constraints and just need to set up the dynamic model of the manipulator of the freefloating space robot which does not need to model the accurate dynamic model of the whole freefloating space robot system. The control method for the traditional fixed based manipulator is introduced into the freefloating space robot control system successfully and avoids the complex process of the parameter identification and prevents the robot endeffector collision with the target that provides a new method for space station assembly, inorbit satellite service.
ACKNOWLEDGMENT
My research project was sponsored by Commission of Science, Technology and Industry for National Defense Preresearch Foundation of China (No. C4220062501) (period: 20082011).