Visual Tracking of a Hand-eye Robot for a Moving Target Object with Multiple Feature Points: Translational Motion Compensation Approach

Transcription

1 Visual Tracking of a Hand-eye Robot for a Moving Target Object with Multiple Feature Points: Translational Motion Compensation Approach Masahide Ito Masaaki Shibata Department of Electrical and Mechanical Engineering, Seikei University, Kichijoji-kitamachi, Musashino-shi, Tokyo , JAPAN, and masahide i@st.seikei.ac.jp Abstract In this paper, we propose a visual tracking control method of a hand-eye robot for a moving target object with multiple feature points. The hand-eye robot is composed of a three degrees-offreedom planar manipulator and a single CCD camera that is mounted on the manipulator s endeffector. The control objective is to keep all feature points of the target object around their desired coordinates on the image plane. In many conventional visual servo methods, it is assumed that the target object is static. Consequently, the visual tracking error arises in the case of a moving target object. We have already proposed a visual tracking control system that takes into consideration the target object motion. This method can reduce the visual tracking error, but can only deal with a single feature point. Therefore, this paper extends such a visual tracking control method to multiple feature points. The effectiveness of our control method is evaluated experimentally. keywords: visual servoing, moving target object, feature points, eye-in-hand configuration, hand-eye robot 1 INTRODUCTION Robotic systems need to understand their external environment to behave autonomously. For this purpose, the camera is a very useful sensory device to provide a vision function for robots. An image captured via the camera contains a vast amount of information of the environment. Introducing visual information extracted from the image into the control loop has the potential to increase the flexibility and accuracy of a given task. From such background, vision-based control method has attracted attention of many researchers and engineers. In particular, feedback control with visual information, so-called visual servoing or visual feedback control, is an important technique for robotic systems [1 6]. 1

2 CCD Camera 2nd joint 1st joint 3rd joint 3-DoF Planar Manipulator Figure 1: Hand-eye Robot. Visual servoing is classified roughly into position-based visual servoing (PBVS) and image-based visual servoing (IBVS) approaches. The difference between the two approaches depends on how to use visual features of the target object which are extracted from the image. In the PBVS approach, the controller is designed using the relative three-dimensional (3D) pose between the camera and the target object, which is estimated from the visual features. This approach also needs a priori 3D model of the target object for the 3D reconstruction. On the other hand, the controller in the IBVS approach is designed directly using the visual features; i.e., there is no need for the 3D reconstruction. As a consequence, one advantage of the IBVS approach over the PBVS approach is robustness against modeling errors and external disturbances. The IBVS approach for a robot in the eye-in-hand configuration is focused on in this paper. In many conventional IBVS methods [1 5], it is assumed that the target object is static. Consequently, a steady-state error between the actual and desired features on the image plane, which we call the visual tracking error, arises in the case of a moving target object. In our previous works, we have proposed a visual tracking control method that takes into consideration the target object motion for a robot with two charged-coupled device (CCD) cameras [6, 7] or a robot with a single CCD camera [8]. Although we have demonstrated experimentally that our proposed method can reduce the visual tracking error, this method can only deal with a single feature point. This paper extends such a visual tracking control method to multiple feature points. The controlled object is a hand-eye robot, which is a typical example of eye-in-hand system with a single camera. As depicted in Figure 1, the hand-eye robot considered in this paper is composed of a three degrees-offreedom (3-DoF) planar manipulator and a single CCD camera that is mounted on the manipulator s end-effector at a constant tilt angle. In the case of single camera systems, we need to estimate the depth from the camera to the target object. The structural features of the hand-eye robot used in our study derive a certain relationship between image information and the depth. We can estimate the depth through this relationship. The rest of the paper is organized as follows. In the next section, we divide the kinematics of a 2

3 Camera frame Σ c c y y (, ) Σ f z v c x x World frame Σ w u (u, v ) s p c c p oi Image plane s y c z s p oi s x s z Standard camera frame i-th feature point on image plane (u i, v i ) i-th marker on target object Σ s Figure 2: Coordinate frames for vision system. hand-eye robot into of the vision and the manipulator to show two kinds of Jacobian matrices. Based on the Jacobian matrices, in Section 3 we present a visual tracking control method for the moving target object with multiple feature points. In Section 4, we show experimental results. Finally, we summarize the main contributions of the paper and discuss future works. 2 KINEMATICS OF HAND-EYE ROBOT In this section we divide the kinematics of the hand-eye robot into those of the vision and the manipulator to provide two kinds of Jacobian matrices. 2.1 Vision kinematics A target object is equipped with k markers. We refer to the markers as feature points on the image plane. The geometric relation between the camera and the i-th marker is depicted in Figure 2, where the coordinate frames Σ w, Σ c, Σ s, and Σ f represent the world frame, the camera frame, the standard camera frame, and the image plane frame, respectively. The frame Σ w is located at the base of the manipulator. The frame Σ s is static on Σ w at a given time. Let s p oi := [ s x oi, s y oi, s z oi ], s p c := [ s x c, s y c, s z c ], and c p oi := [ c x oi, c y oi, c z oi ] be the position vectors of the i-th marker on Σ s, the camera on Σ s, and the i-th marker on Σ c, respectively. The coordinates of the i-th feature point and the center on the image plane are denoted as f i = [ u i, v i ] and f = [ u, v ], respectively. When the camera moves at a certain translational and angular velocity, the translational velocity of the i-th marker on Σ c can be represented as cṗ oi = s ṗ oi s ṗ c s ω c c p oi 1 c z c oi y oi = 1 c z oi c x oi 1 c y c oi x oi s ṗ c s ṗ oi s ω c (1) 3

4 where s ω c := [ s ω cx, s ω cy, s ω cz ] is the angular velocity of the camera on Σ s. Using the pinhole camera model with a perspective projection, image deviations can be represented as f i = ūi := u i u = 1 λ x c x oi v i v i v c (2) z oi λ c y y oi where λ x, λ y are the horizontal and vertical focal lengths, respectively. Differentiating (2) with respect to time and using (1) and (2), we obtain f i = J img ( f i, c z oi ) s ṗ c s ω c J (1,1) img ( f i, c z oi ) s ṗ oi (3) where [ ] J img ( f i, c z oi ) = J (1,1) img ( f i, c z oi ) J (1,2) img ( f i ) R 2 6, λx ū c z oi i c z oi, J (1,1) img ( f i, c z oi ) := J (1,2) img ( f i ) := 1 λ y ū i v i λy c z oi v i c z oi ( ) λ x + ū2 i λ x λ y + v2 i λ y 1 λ x ū i v i λ x λ y v i λ y λ x ū i, and [ s ṗ c, s ω c ] is called the velocity twist of the camera. Furthermore, summarizing (3) in terms of k feature points, we obtain f = J img ( f, c z o ) s ṗ c s ω c J (1,1) img ( f, c z o ) s ṗ o (4) where f := [ f 1,, f k ] R 2k, c z o := [ c z o1,, c z ok ] R k, s ṗ o := [ s ṗ o 1,, s ṗ o k ] R 3k, J img ( f 1, c z o1 ) J img ( f, c z o ) :=. R2k 6, J img ( f k, c z ok ) J (1,1) img ( f 1, c z o1 ) J (1,1) img ( f, c z o ) :=... R2k 3k. J (1,1) img ( f k, c z ok ) The matrix J img is the so-called image Jacobian matrix or interaction matrix. 2.2 Manipulator kinematics The hand-eye robot system has five coordinate frames which consist of the base frame Σ b, the i-th joint frame Σ i, i = 1, 2, 3, and the camera frame Σ c, as shown schematically in Figure 3. Let θ i, α i, d i and h i denote the i-th joint relative angle, the relative angle and distance from i 1 y to i y and the distance 4

5 Σ b b x b z 1 x θ 1 1 z Σ Σ 2 1 θ 2, 2 z 2 x Σ 3 Σ c 3 z, c z h 1 h 2 h 2 h 3 Σ b b z Σ 1 1 y Σ 3, Σ c Σ 2 1 z 2 y c y d 1 d 2 d 3 α 3 3 z c z 3 y 2 z 3 x, c x θ 3 b y (a) Top view (b) Side view in the case of θ i =, i = 1, 2, 3 Figure 3: Joint frames on hand-eye robot. from i 1 z to i z, respectively. The homogeneous transformation matrices from Σ i to Σ i 1 and from Σ c to Σ 3 are derived as cos θ i sin θ i d i sin θ i 1 i 1 1 h H i (θ i ) = i, 3 cos α H c = 3 sin α 3. (5) sin θ i cos θ i d i cos θ i sin α 3 cos α Note that the left-superscript i 1 is replaced by b when i = 1. Using (5), the homogeneous transformation matrices from Σ c to Σ i 1, i = 1, 2, 3, are given by 2 H c (θ 3 ) = 2 H 3 (θ 3 ) 3 H c, 1 H c (θ 23 ) = 1 H 2 (θ 2 ) 2 H 3 (θ 3 ) 3 H c and b H c (θ) = b H 1 (θ 1 ) 1 H 2 (θ 2 ) 2 H 3 (θ 3 ) 3 H c, where θ 23 := [ θ 2, θ 3 ] and θ := [ θ 1, θ 2, θ 3 ]. Now, regarding i 1 H c, i = 1, 2, 3, as i 1 H c = r cx i 1 r cy i 1 r cz i 1 p c 1 that consist of vectors i 1 r cx, i 1 r cy, i 1 r cz and i 1 p c R 3, we obtain the following manipulator 5

6 Jacobian matrix: c J (θ 23 ) = = b p c b r cx, e 2 1 p c 1 r cx, e 2 2 p c 2 r cx, e 2 b p c b r cy, e 2 1 p c 1 r cy, e 2 2 p c 2 r cy, e 2 b p c b r cz, e 2 1 p c 1 r cz, e 2 2 p c 2 r cz, e 2 b r cx, e 2 1 r cx, e 2 2 r cx, e 2 b r cy, e 2 1 r cy, e 2 2 r cy, e 2 b r cz, e 2 1 r cz, e 2 2 r cz, e 2 d 1 cos(θ 2 + θ 3 ) + d 2 cos θ 3 + d 3 d 2 cos θ 3 + d 3 d 3 d 1 sin α 3 sin(θ 2 + θ 3 ) d 2 sin α 3 sin θ 3 d 2 sin α 3 sin θ 3 d 1 cos α 3 sin(θ 2 + θ 3 ) + d 2 cos α 3 sin θ 3 d 2 cos α 3 sin θ 3 cos α 3 cos α 3 cos α 3 sin α 3 sin α 3 sin α 3, (6) where e 2 = [, 1, ] is the second basis vector in R 3. Thus, using (6), the angular velocity of joints is related to the velocity twist of the camera by the formula s ṗ c s ω c = c J (θ 23 ) θ. (7) 3 VISUAL TRACKING FOR MOVING TARGET OBJECT WITH MULTIPLE FEATURE POINTS This section presents a visual tracking system based on the kinematics of the hand-eye robot. The controller of the 3-DoF planar manipulator consists of a disturbance observer [9] and a PD controller. The desired angle and angular velocity assigned to the PD controller are designed by the kinematics of the hand-eye robot without neglecting the target object velocity. 3.1 Visual tracking system The manipulator dynamics is linearized and decoupled with the use of a disturbance observer [9], and the controller of the linearized system adopts the PD control law. We obtain the closed system θ(t) = K p (θ(t) θ d ) K v ( θ(t) θ d ), (8) where the superscript d refers to the desired value. Matrices K p and K v are the positive gain matrices. It is well known that the control system based on the disturbance observer is robust against system parameter variations and external disturbances. The control objective is to keep all feature points of the target object around their desired coordinates on the image plane. We design the desired angle θ d and angular velocity θ d in (8) using visual 6

7 information to achieve the control objective. Substituting (7) into (3) yields All solutions of (9) are expressed as f = J img ( f, c z o ) c J (θ 23 ) θ J (1,1) img ( f, c z o ) s ṗ o. (9) { } { } θ = J + vis ( f, c (1,1) z o, θ 23 ) f + J img ( f, c z o ) s ṗ o + I 3 J + vis ( f, c z o, θ 23 )J vis ( f, c z o, θ 23 ) φ (1) where J vis := J c img J R 2k 3, J + vis = J vis(j vis J vis) 1, for k = 1 and rank J vis = 2 (J visj vis ) 1 J vis, for k > 1 and rank J vis = 3 (11) denotes the pseudo-inverse of J vis, (I 3 J + vis J vis) R 3 3 is the orthogonal projection operator into the null-space of J vis, ker J vis, and φ R 3 is an arbitrary vector, respectively. Setting φ 3, the motion of the target object on the image plane is related to the angular velocity of the joints by the following formula: { θ = J + vis ( f, c (1,1) z o, θ 23 ) f + J img ( f, c z o ) s ṗ o }. (12) Hence, based on (12), the desired angular velocity of the joints is given by: { } θ d = J + vis ( f, c z o, θ 23 ) K img (f f d (1,1) ) + J img ( f, c z o ) s ṗ o (13) where K img = block diag {K img 1,, K img k }, K img i := diag{k u img i, K v img i} >, i = 1,..., k, denotes the positive gain matrix and f d = [ (f d 1),, (f d k) ], f d i := [ u d i, vi d ], i = 1,..., k, denotes the desired coordinates of all feature points on the image plane. The desired angle of the joints θ d can be calculated by the step-by-step integration of θ d. Our proposed method is basically classified as IBVS. In many conventional IBVS methods [1 5] it is assumed that the target object on Σ s is static, i.e., s ṗ o 3, even if the target object is moving. Thus, it is usually necessary to increase the value of K img in the conventional method when the target object is moving. However high gain control may cause instability of the control system itself. In contrast, our proposed method is appropriate to the vision kinematics, as designed using s ṗ o without annihilating it. Hence our proposed method can suppress the value of K img. Now, note that the depth c z o and the target object velocity s ṗ o are not directly measured. We need to estimate them. The details will be given in the following subsections. 7

8 3.2 Depth estimation The hand-eye robot considered in this paper is a single camera system. Hence, the depth of the target object on Σ c, c z oi, cannot be measured directly. For this problem, a number of depth observers have been proposed so far; see, for example, [1 16] and the references. These observers can estimate c z oi for a static target object under some conditions, but they are inapplicable to a moving target object. Here we introduce an appropriate assumption to estimate c z oi. The hand-eye robot has the following structural features: 1) The motion space of the manipulator s end-effector is planar. 2) And the CCD camera of the hand-eye robot is mounted on the manipulator s end-effector at a constant tilt angle, as shown in Figures 1 and 3 (b). Under the following assumption, these structural features generate certain one-to-one correspondence between the depth c z oi and v i on the image plane. Assumption 1 The motion of the target object is constrained in a horizontal plane at an appropriate height so that the height of the target object is lower than the height of the camera. As shown in Figure 4, the value of the coordinate v increases when the camera approaches the target object, which is static on Σ w at a given time, along 3 z-axis. Similarly, the value of the coordinate v decreases when the camera moves away from the target object along 3 z-axis. Consequently, collecting some measured data of set ( c z oi, v i ) in advance, we can estimate the depth c z oi as a function that depends on v i. We call the function c z oi (v i ) depth estimation function. The concrete depth estimation function c ẑ oi (v i ) used in the experiment would be shown in Section Target object velocity estimation The vector s ṗ o, which we call the target object velocity, consists of translational velocity of each marker. Each marker does not behave freely because all markers are attached on a single rigid body. Let us locate the target object frame Σ o at the first marker, as shown in Figure 5. Differentiating the geometric 2 1 u Σ c c y c z v 2 1 c z oi i-th feature point Image plane Figure 4: Relationship between v and c z oi. 8

9 1st marker s p o1 o p o1 o i s p oi i-th marker Standard camera frame Σ s Target object frame Σ o Figure 5: Geometric relation between Σ s and target object. relation s p oi = s p o1 + s R o o p o1o i with respect to time and using o ṗ o1o i 3, we obtain sṗ oi = s ṗ o1 + s ω o ( s R o o p o1 o i ), (14) where o p o1 o i, s R o, and s ω o are the position vector from the first marker to i-th marker on Σ o, the rotational matrix, and angular velocity of the target object frame on Σ s, respectively. Now, the following assumption is introduced. Assumption 2 The rotational motion of the target object is enough small, i.e., s ω o 3. Under this assumption, (14) can be approximated as follows: sṗ oi s ṗ o1. (15) Next, we estimate s ṗ o1 by the difference approximation of the estimated position sˆp o1. When we can estimate the depth c z o1 as stated in the previous subsection, the estimation of s p o1 can be calculated by sˆp o1 (v 1 ) = [ cẑ o1 (v 1) λ x, cẑ o1 (v 1) λ y, c ẑ o1 (v 1 )]. We estimate the translational velocity s ṗ o1 (t), t [t s, t s + t) as follows: where sˆṗ sˆp o1 (t) = o1 (t s ) s p o1 (t s t), (16) t s p o1 (t s t) := c H b (θ(t s )) b H c (θ(t s t)) sˆp o1 (t s t), (17) 1 }{{} 1 b H 1 c (θ(t s)) }{{} [ b ˆp o (t 1 s t), 1 ] t s and t are the time to update the estimation and the time interval, respectively. The frames Σ s at t = t s t and Σ s at t = t s are generally different. Accordingly, (17) transforms the estimated position information of the first marker on Σ s at t = t s t to the quantity on Σ s at t = t s. In general, the sampling period of the image data is longer than that of the controller. And the appropriate value of t is determined by trial and error so as to be longer than the sampling period of the image data. Finally, using (13), (16), and the depth estimation function c ẑ o = [ c ẑ o1 (v 1 ),..., c ẑ ok (v k ) ], the desired angular velocity of joints is rewritten as: { θ d = J + vis ( f, c ẑ o, θ 23 ) K img (f f d (1,1) ) + J img ( f, c ẑ o ) sˆṗ o1 }. (18) 9

10 Camera System f + f d + f K img f J + vis (,, ) + + J (1,1) img (, ) sˆṗ o1 Obj. Motion Estimator cẑ o1 cẑ o Depth Estimator θ d 1 s θd + + K p K v - - Robot with Disturbance Observer θ 1 s θ Figure 6: Block diagram of control system. Table 1: Physical parameters. Symbol (Unit) i = 1 i = 2 i = 3 d i (m) h i (m) α i (rad) π/6 The block diagram of the whole control system is shown in Figure 6. This control system can reduce the visual tracking error by compensating the translational motion of the target object, and therefore can achieve visual tracking precisely. Our proposed method is basically applicable to a n-dof hand-eye robot if only the structural features 1), 2) and Assumption 1, 2 are satisfied. In next section, we evaluate the effectiveness of the proposed control method experimentally. 4 EXPERIMENT This section presents an experimental result to show the effectiveness of our proposed method. We here consider a case that the number of feature points is three, i.e., k = 3. The overviews of the hand-eye robot system and the experimental setup are shown in Figures 7 and 8. The target object is equipped with two markers which are in the same horizontal plane. The 3-DoF planar manipulator is controlled by a PC running a real-time Linux OS. The rotating angle of each joint is obtained from an encoder attached to each DC motor via a counter board. And armature currents based on control law (8) and (18) are interpolated to each DC motor by a D/A board through each DC servo driver. The main physical parameters of the 3-DoF planar manipulator are shown in Table 1. The image resolution and the focal lengths of the CCD camera are pixels, λ x = 8. pixels, and λ y = pixels, respectively. The frame rate of the CCD camera is 12 fps. Hence, the image 1

11 Target Object 2nd marker 1st marker Hand-eye Robot 3rd marker Cart Target Object on Cart (a) Target object on the cart (b) Hand-eye robot and target object Figure 7: Overview of hand-eye robot system. PC (real-time Linux OS) Visual tracking algorithm Coordinates of feature points 1(msec) period Shared memory Counter board D/A board about 8.3 (msec) period DC Servo driver DC Servo driver DC Servo driver PC (Windows OS) Feature point extracting algorithm Image capture board Hand-eye robot 1st joint DC Motor Encoder 2nd joint DC Motor Encoder 3rd joint DC Motor Encoder 64x48 monochrome image 12 (fps) CCD Camera Figure 8: Overview of experimental setup. data is updated every 8.3 ms. On the other hand, the sampling period of the controller is 1 ms. In consideration of the gap between both periods, we set t = 1 ms. The tilt angle of the CCD camera, α 3, is 3 deg. Collecting some measured data of set ( c z o1, v 1 ) and fitting them to a second-order polynomial function c z o1 = av1 2 + bv 1 + c, we obtain a = , b = , c = (19) Therefore, we adopt here the following function with (19) to estimate the depth: cẑ oi (v i ) = avi 2 + bv i + c, i = 1, 2, 3. (2) Note that the estimation of c ẑ o2 (v 2 ) and c ẑ o3 (v 3 ) is also based on (19) and (2) because all markers of the target object are in the same horizontal plane. Measured data of set ( c z o1, v 1 ) and the depth estimation function are shown in Figure 9. The procedure of the experiment is presented as follows: Step 1: We set θ d = [ π/4, π/4, ] and θ d = 3 in (8) to drive the hand-eye robot to the initial configuration, as shown in Figure 1, so that the target object is inside the boundaries of the 11

12 czo1 (m) czˆo1 (v) Measured data v (pixels) Figure 9: Measured data and depth estimation function. π 4 (rad) Σ c Target object on cart c z Σ b π 4 (rad) c x Moving forward Moving backward b x b z.65 (m) Figure 1: Top view of initial configuration. image plane and the 3-DoF planar manipulator is not in a singular configuration. As a result of such control, the target object is located at left side of the image plane against the central axis. Step 2: The target object starts to move forward. If u 1 338, we change the control mode to the proposed visual tracking based on (8) and (18) with f d 1 = [ 338, 21 ], f d 2 = [ 36, 228 ], f d 3 = [ 354, 249 ]. Step 3: The target object moves parallel to b x-axis at an almost constant speed. After moving forward by.23 m, the target object goes backward at the same speed and stops at the start point. The experimental result is shown in Figures 11 and 12. Figure 11 shows the trajectories of feature points on the image plane. Figures 12 (a) and (b) show the time responses of u i u d i, v i vi d, i = 1, 2, 3, respectively, for 6 s in Steps 2 and 3. For comparison, the experimental result in the case of the conventional method, i.e., sˆṗ o1 3 in (18), is shown additionally. This experiment in Step 2 and 3 was carried out with initial condition f 1 () = [ 338, 21 ], f 2 () = [ 34, 228 ], f 3 () = [ 351, 249 ], θ() = [ π/4, π/4, ], θ() = 3 and gain matrices K p = diag{ 144, 144, 144 }, K v = diag{ 48, 48, 48 }, K img = diag{ 4, 4, 4 }. And the gain of the disturbance observer was 15. If they are stabilized asymptotically, then it means that each feature point is kept around the desired one. The target object is going forward and backward in a straight line at a constant speed for t <

13 6 12 Conv. method Proposed method 1st desired point 2nd desired point 3rd desired point 18 v (pixels) u (pixels) Figure 11: Trajectories of feature points on image plane and is static for the rest of the time. The visual tracking error arises in the case of the conventional method. On the other hand, visual tracking by the proposed method works well almost without such error. 5 CONCLUSIONS AND FUTURE WORKS We proposed a visual tracking control method of a hand-eye robot for a moving target object with multiple feature points. Our proposed method can reduce the visual tracking error by compensating the target object motion, and hence can achieve precise visual tracking. Using the structural features of the hand-eye robot and introducing an appropriate assumption, the depth from the camera to the target object can be estimated. The validity of the proposed method was demonstrated by an experiment. The main future works present as follows: Precision improvement of the target object velocity estimation. Development of a dynamic depth estimator for a moving target object. REFERENCES [1] S. Hutchinson, G. D. Hager, and P. I. Corke, A tutorial on visual servo control, IEEE Trans. on Robotics and Automation, 12, (1996). [2] K. Hashimoto, A review on vision-based control of robot manipulators, Advanced Robotics, 17, (23). [3] F. Chaumette and S. Hutchinson, Visual servo control, Part I: Basic approaches, IEEE Robotics and Automation Magazine, 13, 82 9 (26). 13

14 u1 u1 d (pixels) u2 u2 d (pixels) u3 u3 d (pixels) Target obj. is moving forward moving backward Time: t (s) Conv. method Proposed method Target obj. is moving forward moving backward Time: t (s) Conv. method Proposed method Target obj. is moving forward moving backward Time: t (s) Conv. method Proposed method (a) Time response of u i u d i, i = 1, 2, 3 v1 v1 d (pixels) v2 v2 d (pixels) v3 v3 d (pixels) Conv. method Proposed method Target obj. is moving forward moving backward Conv. method Proposed method Target obj. is moving forward Time: t (s) moving backward Conv. method Proposed method Target obj. is moving forward Time: t (s) moving backward Time: t (s) (b) Time response of v i vi d, i = 1, 2, 3 Figure 12: Deviations on image plane. [4] F. Chaumette and S. Hutchinson, Visual servo control, Part II: Advanced approaches, IEEE Robotics and Automation Magazine, 14, (27). [5] F. Chaumette and S. Hutchinson, Visual servoing and visual tracking, Springer Handbook of Robotics, B. Siciliano and O. Khatib (Eds.), Chap. 24, (28). [6] N. Oda, M. Ito, and M. Shibata, Vision-based motion control for robotic systems, IEEJ Trans. on Electrical and Electronic Engineering, 4, (29). [7] M. Shibata and N. Kobayashi, Non-delayed visual tracking of a moving object with target speed compensation, in Proc. IEEE Int. Conf. on Mechatronics (ICM 7), Kumamoto, Japan, No. WA1- A-4 (27). [8] M. Ito and M. Shibata, Non-delayed visual tracking of hand-eye robot for a moving target object, in Proc. ICROS-SICE Int. Joint Conf. 29 (ICCAS-SICE 9), Fukuoka, Japan, pp (29). 14

15 [9] K. Ohnishi, M. Shibata, and T. Murakami, Motion control for advanced mechatronics, IEEE/ASME Trans. on Mechatronics, 1, (1996). [1] L. Matthies, T. Kanade, and R. Szeliski, Kalman filter-based algorithms for estimation depth from image sequences, Int. J. of Computer Vision, 3, (1989). [11] S. Soatto, R. Frezza, and P. Perona, Motion estimation via dynamic vision, IEEE Trans. Automatic Control, 41, (1996). [12] X. Chen and H. Kano, A new state observer for perspective systems, IEEE Trans. Automatic Control, 47, (22). [13] W. E. Dixon, Y. Fang, D. M. Dawson, and T. J. Flynn, Range identification for perspective vision systems, IEEE Trans. Automatic Control, 48, (23). [14] A. Astolfi, D. Karagiannis and R. Ortega, Nonlinear and Adaptive Control with Applications, Communications and Control Engineering Series, Springer-Verlag (28). [15] A. De Luca, G. Oriolo and P. R. Giordano, Feature depth observation for image-based visual servoing: theory and experiments, Int. J. of Robotics Research, 27, (28). [16] F. Morbidi and D. Prattichizzo, Range estimation from a moving camera: an Immersion and Invariance approach, in Proc. IEEE Int. Conf. on Robotics and Automation (ICRA 9), Kobe, Japan, pp (29). 15