Data-Driven Kinematic Control for Robotic Spatial Augmented Reality System with Loose Kinematic Specifications
Data-Driven Kinematic Control for Robotic Spatial Augmented Reality System with Loose Kinematic Specifications
ETRI Journal. 2016. Apr, 38(2): 337-346
Copyright © 2016, Electronics and Telecommunications Research Institute (ETRI)
  • Received : August 06, 2015
  • Accepted : October 29, 2015
  • Published : April 01, 2016
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About the Authors
Ahyun Lee
Joo-Haeng Lee
Jaehong Kim

We propose a data-driven kinematic control method for a robotic spatial augmented reality (RSAR) system. We assume a scenario where a robotic device and a projector-camera unit (PCU) are assembled in an ad hoc manner with loose kinematic specifications, which hinders the application of a conventional kinematic control method based on the exact link and joint specifications. In the proposed method, the kinematic relation between a PCU and joints is represented as a set of B-spline surfaces based on sample data rather than analytic or differential equations. The sampling process, which automatically records the values of joint angles and the corresponding external parameters of a PCU, is performed as an off-line process when an RSAR system is installed. In an on-line process, an external parameter of a PCU at a certain joint configuration, which is directly readable from motors, can be computed by evaluating the pre-built B-spline surfaces. We provide details of the proposed method and validate the model through a comparison with an analytic RSAR model with synthetic noises to simulate assembly errors.
I. Introduction
Spatial augmented reality (SAR) can be used to enhance the efficiency of real-world tasks by directly projecting relevant information over the surface of the work environment, rather than relying on an external monitor such as glasses or a smart phone as in augmented reality [1] , [2] . It is conventional to install a large projector near the ceiling of the work space because securing a wide projection area is critical to SAR. In a real-world scenario, however, this type of installation is not always feasible owing to various constraints. For example, a near-ceiling installation may be highly inefficient for an ad hoc task in a spacious room. In such a case, robotic spatial augmented reality (RSAR) can be an effective solution to handle the installation problem [3] , [4] . RSAR, which combines a simple robotic mechanism with an SAR technique, enables the position and orientation of a projector to be changed for a wider workspace, as shown in Fig. 1 . However, an RSAR system requires an additional procedure to control and monitor the status of the robotic device it employs (where the projector and camera unit are mounted). If the exact kinematic specifications of the parts and assembly involved are available, such as the link lengths and joint orientations, then it can be applicable to a traditional robot kinematics technique.
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Configuration of RSAR system considered in this paper: (a) installation on table-top environment and (b) PCU and pan-tilt motors.
Assuming that the kinematic specifications are available, Fig. 2 shows a typical execution flow of an RSAR application. It is composed of two steps: on-line and off-line processes. In the off-line process, we calibrate a projector-camera unit (PCU) and formulate the kinematic equations using the known specification. In particular, we set up the kinematic relation between the camera and the projector assuming they are relatively fixed during the operation.
The on-line process of Fig. 2(b) assumes a typical RSAR application where a real-world object is detected from a camera image and the relevant information is augmented through a projector. In the system model of Fig. 2 , we use inverse kinematics to determine the position of the projection area and forward kinematics to compute the extrinsic parameters of the moving PCU. The extrinsic parameters of a projector can be computed using the extrinsic parameters of a camera computed during the on-line process and the relative relation calibrated during the off-line process. Finally, a projection image is transformed according to the extrinsic parameters of the projector.
In Fig. 2 , computations of both the forward and inverse kinematics are shown based on kinematic equations set up during the off-line process, assuming that the exact kinematic specifications (for example, from a CAD file) are available [5] [7] . However, in our RSAR scenario, we assume that a moving mechanism (such as a pan-tilt mount) is assembled in an ad hoc manner using an off-the-shelf robot kit and consider the conditions of the work environment. Hence, it is difficult to assume that the exact kinematic specifications are available. Moreover, even if such a user-created robotics (UCR) system is assembled based on a CAD model, it is susceptible to assembly errors, which may invalidate the kinematic equations. To handle this situation, we propose a data-driven kinematic control method for an RSAR system.
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Typical execution flow of RSAR application: (a) off-line and (b) on-line processes.
- 1. Related Works
A feature of the SAR technique is that a user’s physical environment is augmented with a projected virtual image using a projector, as shown in Fig. 3 . Jones and others [8] ; Oswald and others [9] ; and Wilson and others [10] augment the existing physical environment with projected visualizations to enhance traditional gaming experiences. PlayAnywhere [11] , Interactive Dining Table [12] , and ActivitySpace [13] are interactive projection vision systems with a compact table projection and sensing system. Their multiple-touch interfaces naturally support a direct manipulation style of interaction with virtual objects, where a user can initiate object interaction through touch and natural gestures. HP Sprout [14] is a new computing platform using SAR. Hewlett Packard’s Sprout touch mat takes the place of a traditional mouse and keyboard. Its projector can place a virtual keyboard on a capacitive touch panel; thus, users can interact with the PC and its applications.
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Example of SAR/RSAR systems: (a) MS IllumiRoom [8], (b) HP sprout [14], (c) MIT LuminAR [16], and (d) ETRI Future Robotic Computer [4].
VisiCon [15] is a robot navigation game using a handheld projector. It enables a user to intuitively control a robot and share the displayed robot information with others through a projected display. LuminAR [16] , developed by MIT Media Lab, is a robotic projector-camera system that can dynamically change projection parameters. The robotic system is similar to a desk lamp, but uses a pico-projector instead of a light bulb for projecting a virtual image at the user-desired position. A projector system [17] and a ubiquitous display [18] are used in movable mobile projection robots. These platforms enable images to be projected on any surface, such as a wall, a floor, or an object.
The Future Robotic Computer [4] , developed by the Electronic Telecommunications Research Institute (ETRI), enables the end position of a robot device equipped with a PCU to be changed. The Future Robotic Computer is the leading RSAR system, and actively applies an SAR technique with a robotic device for user interaction. It can be applied to various applications that need to expand or change the projection area or the user environment.
The initial idea of data-driven control was conceived in [19] . In this paper, we advance this technique in multiple ways to be applied in a real-world scenario. First, sampling is performed to cover an entire work area, rather than a fixed area, by moving the calibration markers. The sample data are then merged into a single parametric form. We evaluate the accuracy of the proposed approach by comparing with an analytic RSAR model with synthetic noises.
The rest of this paper is structured as follows. In Section II, we overview the RSAR system model and describe the limitations of the previous control method under loose kinematic specifications. In Section III, we describe the proposed method in detail in the context of a proof-of-concept application. In Section IV, we show our experimental results. Finally, in Section V, we conclude the present paper with a discussion of future works.
II. RSAR System Model
The RSAR system, which has an attached PCU at the end position of the robot device, recognizes real-world objects using a camera, and projects virtual images on the surface of the objects. In this section, we describe the projector-camera calibration, RSAR kinematic control, and loose kinematic specifications.
- 1. Projector-Camera Calibration
We use Zhang’s method [20] for the camera calibration. The correlation between p c , which is a point in the camera coordinates, and p w , which is a point in the real-world coordinates, is defined through homography matrix H wc . In (1), H wc is combined with intrinsic parameter M c and extrinsic parameter X wc of a camera.
(1) p c = M c X wc p w = H wc p w = H cw −1   p w .
In the case of projector calibration, we use Tsai’s method [21] instead of Zhang’s method, which has to know in advance the resolution of a projected image. As a result, the transformation matrix X cp between the camera and the projector coordinates is defined as [22] [26]
(2) X wp X wc −1 = X wp X cw = X cp = X pc −1 .
The projector homography matrix H wp is computed using X wc , projector intrinsic parameter M p , and the correlation matrix X cp between the camera and the projector.
(3) M p X cp X wc = M p X wp = H wp = H pw −1 ,
(4) p c = H wc H pw p p = H pc p p .
Figure 4 shows the correlation of the coordinate system for the RSAR. The camera, projector, and real-world coordinate systems are defined by the calibrated PCU in the RSAR system [27] . To combine the virtual image in Fig. 4(a) and the printed image on paper, shown in Fig. 4(b) , the projection source needs to be warped according to the position and orientation of a projector, such as in Fig. 4(c) . Figure 4(d) shows the registered result of the warped projection image and the printed image on paper, such as the original image in Fig. 4(e) .
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Major coordinate system in RSAR and transformation among coordinates: (a) circular sub image of (e), (b) modified (e) by removing (a) and printed on paper, (c) transformation of (a) as projection source, (d) projection of (c) onto (b) captured using external camera, (e) The Vitruvian Man by Leonardo da Vinci, and (f) image of (d) from camera of PCU.
- 2. RSAR Kinematic Control
An end-effector is the interaction force device of a robot, which is placed at the end position of a robot arm. On the other hand, an end-effector is defined differently in the RSAR system. In this paper, end-effector is taken to mean the position of the center point of a projected image. In Fig. 5(a) , the analytic RSAR model is designed as a two-axis robotic arm based on the kinematic specifications, such as the lengths of the links and the positions of the joints.
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Comparison of calculation method of postion of end-effector based on (a) explicit kinematic specification and (b) camera pose estimation using pattern marker.
(5) End-effector =[ 1 cos q 0 ( l 1 + l 2 + l 0 sin q 0 )   1 cos q 0 { l 0 +( l 1 + l 2 )sin q 0 } 0 ],
(6) l 3 =− l 0 + l 1 sin q 0 + l 2 sin q 0 cos q 0 cos q 1 .
In (5), q 0 is the angle of the tilt motor, and q 1 is the angle of the pan motor. The length of link l 0 is from the origin point to the axis of rotation of the tilt motor, and l 1 is the length of a link from the tilt motor to the pan motor. The length of link l 2 is from the axis of rotation of the pan motor to the principal point of the projector. The length of the last link, l 3 , is variable according to the joint angles in (6).
The forward kinematic equation is geometrically defined based on the joints and links. In the case of an inverse kinematic equation, we use the inverse matrix of the forward kinematic equation through pseudoinverse or Jacobian transpose methods. In the absence of links or joints based on the kinematic specifications, the position of the end-effector can be computed using a camera and a pattern marker in the RSAR, as shown in Fig. 5(b) . However, whenever a PCU is moved, it needs to conduct camera pose estimation using a pattern marker. In addition, it is impossible to use the inverse kinematics without kinematic specifications.
- 3. Loose Kinematic Specifications
A minimalism-based UCR has a strong point (which is of a reduced complexity), seeks the lowest cost, and minimizes the development time [28] . Users can easily make a robot system using robot kits available on the market. Our UCR-based RSAR system, which was designed to fit a table-top environment, as shown in Fig. 1 , enables the usable range to be dynamically expanded through a moving PCU.
However, the UCR is usually fabricated without a CAD model. Even if the UCR is made based on a CAD model, it easily incurs assembly errors. Thus, it is difficult to integrate the kinematic equations for a UCR-based system with loose kinematic specifications. In this paper, we propose a data-driven kinematic control method with loose kinematic specifications for a UCR-based RSAR system.
III. Proposed Method
The proposed method is composed of the acquisition, representation, and evaluation of sample data for kinematic control. We assume that the UCR-based RSAR system is a two-axis robotic arm without kinematic specifications. In addition, it can compute the projector extrinsic parameters by conducting only a camera pose estimation because the calibrated camera and projector are physically fixed.
- 1. Acquisition of Sampled Data
The sampled-data for kinematic control are composed of joint angles and camera extrinsic parameters, as shown in Table 1 . The rotation radius of the joints should be preset prior to the acquisition of the sampled data depending on the user’s application environment. Pan and tilt motors are rotated at regular intervals within the range of configured rotation radii. In addition, the camera pose estimation is conducted by detecting a pattern marker in the camera input frames at each rotated motor angle. The finding-a-pattern-marker algorithm is implemented based on OpenCV-based marker recognition [29] .
Sampled data.
Index Joint angles Camera extrinsic parameter
i θi, φi Xwei
In previous research [19] , we had a problem in that the acquisition area of the sampled data was too narrow, because of a fixed pattern marker used on the ground. In this paper, we enabled moving the pattern marker to expand the acquisition area of the sampled data. First, a pattern marker should be fixed on the ground of the table-top environment. In addition, the motors are rotated at regular intervals within the range of the configured rotation radii. Camera extrinsic parameters are computed at each angle of the rotated motors in Fig. 6(b) . After acquisition of the sampled data, if a user wants to acquire the sampled data in another area, then they can move the marker to a desired area, as shown in Fig. 6(c) . In addition, the position of the moved marker in the world coordinate in Fig. 6(d) should be computed. The acquisition process of the sampled data is repeated by moving to Fig. 6(a) .
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Acquition process of sampled data using printed pattern marker at multiple locations.
To compute the position of the moved marker, the following steps should be conducted:
  • 1) Compute the camera extrinsic parameterXwcbefore the marker is moved.
  • 2) After moving the marker, compute the corner pointspcof the moved marker in the camera coordinate.
  • 3) Computepw0(=Xwcpc) and perspective transformation matrixTbetweenpcandpw0using RANSAC for minimizing reprojection errors.
  • 4) Finally, compute the moved positionpw1(=Tpc) of a marker in the world coordinates.
The acquired sampled data are classified as input or output data according to the forward or inverse kinematics. In the case of forward kinematics, the position of the end-effector is computed by measuring the angle of the joints. At this time, the joint angles are the input data, and a camera extrinsic parameter is the output data used to compute the position of the end-effector. In the case of inverse kinematics, the target position of the end-effector is the input data, and the joint angles are the output data. Table 2 shows the form of the classified input and output data for kinematic control.
Input and output data for kinematic control.
Forward kinematics Inverse kinematics
Input (θ, φ) Position of end-effector (cx, cy)
Output Xwc (θ, φ)
To compute the output data at unacquired joint angles, we need to interpolate the set of sampled data. In particular, in the case of forward kinematics, the sampled data need to be decomposed. The camera extrinsic parameter X wc , which is the output data of the forward kinematics, is decomposed into a total of six factors: the rotation values, rx , ry , and rz , and the translation values, tx , ty , and tz , of the x -, y -, and z -axis, respectively. In (8), R ij indicates the i th row and j th column of R [30] .
(7) X wc =[R|t]=[ R(rx,ry,rz)| (tx,ty,tz) T ],
(8) rx= tan −1 ( R 21 , R 11 ), ry= sin −1 ( − R 31 ), rz= tan −1 ( R 32 , R 33 ).
The six decomposed factors are recomposed with joint angles θ and φ , as shown in Table 3 , for the forward kinematics.
Recomposed sampled data for proposed forward kinematics.
Input data Output data
Rotation Translation
Index Pan Tilt rx ry rz tx ty tz
i θi φi rxi ryi rzi txi tyi tzi
- 2. Representation of Sampled Data and Evaluation for RSAR Kinematic Control
In this paper, we use B-spline surface fitting for estimating the output data at the unacquired joint angles. B-spline surface fitting is suitable for interpolating in various unpredictable forms of the surfaces. In (9), N d0,i ( u ) and N d1,j ( v ) are basis functions for generating the B-spline surface function B ( u , v ), and d 0 and d 1 are degrees of the B-spline surface function. The B-spline surface has control point matrix Q , which is formed in two-dimensional arrays [31] [33] .
(9) B(u,v)= ∑ i=0 n ∑ j=0 m    N d 0 ,i (u) N d 1 ,j (v) Q i,j .
The sampled data need to be recomposed as three-dimensional coordinates to present a B-spline surface. For example, in the case of the rotation factor, rz of the z -axis in a camera extrinsic parameter is recomposed as ( θi , φi , rzi ) for the forward kinematics. The recomposed sampled data are shown in Fig. 7(a) . The results of the presented B-spline surface are shown in Fig. 7(b) .
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Sampled data and their B-spline surface form.
To compute the output data from the presented surfaces, we compute the z -axis value according to the input data value of the x - and y -axis. In the case of forward kinematics, we measure the joint angles ( θ , φ ) as input data, and compute the output data rx , ry , rz , tx , ty , and tz from the six represented surfaces. In addition, the six computed factors are recomposed into the camera extrinsic parameter X wc in (10). A total of eight surfaces (six for the forward kinematics, and two for the inverse kinematics) are presented for the proposed kinematic control. Figure 8 shows the results of surfaces presented by 8 × 8 control points; d 0 and d 1 are cubic values in (9).
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Representation results of sampled data: (a) through (f) surfaces for forward kinematics, and (g), (h) surfaces for inverse kinematics.
(10) X wc =[ cosrycosrz sinrxsinrycosrz−cosrysinrz cosrxsinrycosrz+sinrxsinrz tx cosrysinrz sinrxsinrysinrz+cosrycosrz cosrxsinrysinrz−sinrxcosrz ty −sinry sinrxcosry cosrxcosry tz 0 0 0 1 ].
- 3. Example of UCR-Based RASR System
An example of the UCR-based RSAR system enables a real-world object to be detected by a camera [34] and virtual contents to be projected by a projector. When an object is moved out of the projection area, the RSAR system can maintain the image registration by dynamically changing the kinematic parameters through the proposed inverse kinematics shown in Fig. 9(a) . In addition, we compute the position of the PCU using the proposed forward kinematics. The source of projection image P w is designed in the world coordinates. So, depending on the computed position of the PCU, an augmented projection image P p is rendered in Fig. 9(b) [27] .
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Example for RSAR application: (a) change in position of PCU according to real moving object, (b) warped image source for projection, and (c) projection result.
(11) P p = M p X cp X wc P w = M p X wp P w = H wp P w .
Finally, the rendered image is projected onto the surface of an object, as shown in Fig. 9(c) .
IV. Experiments
The experiments were conducted on a desktop computer with a 2.67 GHz Intel® core™ i7 CPU, using a USB 2.0 camera (Logitech C920 with a 640 × 480 resolution), a projector (Optoma P320 with a 1,280 × 720 resolution), and joints (Robotis Dynamixel MX-64). We acquired 12 × 12 sampled data for the preset rotation radii of the joints, at a pan motor angle of 17.58º to 149.45º, and a tilt motor angle of 237.36º to 263.73º. Our computer vision algorithm was programmed with OpenCV [29] .
We measured the accuracy of the proposed kinematic control in a UCR-based RSAR system without kinematic specifications by making an analytic RSAR model, as shown in Fig. 5(a) . The correlation between joint angles and the position of the end-effector is presented through the contour plots in Fig. 10 . The contour plots show changes in the joint angles according to the fixed values of cx and cy . To model a UCR-based RSAR system in which irregular movements occur during the system operation, we added random noise (−0.5 mm to 0.5 mm) at the position of the joints where were acquired of the sampled data.
Figure 10(b) shows a contour plot with random noise. The red and green lines represent the results through kinematic control based on the kinematic specifications. The blue points indicate the results of the proposed kinematic control. We acquired the sampled data with random noise, represented by B-spline surfaces, and computed joint angles θ and φ according to the fixed value of the end-effector ( cx , cy ). The distribution form of the blue points is dependent on random noise generated at the time of the sampled data acquisition.
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Correlation between joint angles and position of end-effector with loose kinemtatic specifications through contour plot: (a) changes in joint angles according to fixed values of cx and cy in analytic RSAR model, (b) contour plot with random noise, where blue points are results of proposed method, and (c) magnified image of (b).
In another experiment, we examined the accuracy of the proposed method by changing the position of the end-effector along the outline of a circle with various radii of random noises. First, we computed 126 points of the outline of a circle in real-world coordinates, and computed the joint angles corresponding to each point through inverse kinematics using the kinematic specifications shown in Fig. 11(a) . Second, we used the sampled data with various radii of random noises for modeling with loose kinematic specifications. Finally, we applied the proposed forward kinematics for computing the position of the end-effector through the computed joint angles. The position results of the end-effector are shown in Figs. 11(b) through 11(d) . The distorted form of a circle is dependent on random noise generated at the time of acquisition of the sampled data.
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Position of end-effector along outline of circle with random noises in real-world coordinates: (a) analytic RSAR model without noise and (b)–(d) inverse kinematics results using proposed method with random-noise radii (4 mm, 8 mm, and 12 mm).
Table 4 shows the root-mean-square error (RMSE) results of the accuracy experiment of the proposed kinematic control. The reference value for error determination is the position of the end-effector computed without random noise in the kinematic specification–based analytic RSAR model. First, we compared the proposed method without random noise. In addition, where random noise is present, we compared the results of a method using kinematic specifications with those of the proposed method. Our method was determined to have a lower RMSE than the method with kinematic specifications because we observed a noise smoothing effect owing to the use of B-spline surface fitting.
RMSE of position of end-effector between analytic RSAR model based on kinematic specifications and its model with random noise for modeling UCR-based RSAR with loose kinematic specifications.
Without noise With random noise
Proposed method Noise radii (mm) Kinematic specifications Proposed method
cx cy cx cy cx cy
0.0296 0.2585 4 1.8144 2.4387 0.9231 1.1977
8 3.3294 4.9929 1.9215 2.9191
12 5.1448 7.8924 2.6224 5.7513
V. Conclusion
The traditional control method for an RSAR system based on exact kinematic specifications is inappropriate in a UCR-based scenario in which such specifications are unavailable or invalidated. The proposed data-driven kinematic control method enables an RSAR system to be controlled through loose kinematic specifications.
The proposed method exploits the sample data acquired in an off-line process and represents them in a compact B-spline surface form, which replaces the analytic kinematic equations. During the on-line process, the relevant control parameters are computed by evaluating the B-spline surfaces using the measurable joint angles as parameters. To evaluate the accuracy of the proposed method, we built an analytic RSAR model with synthetic noises to simulate an assembly error. We were able to observe a smoothing effect that mitigates the simulated error during the processes of B-spline fitting and evaluation. We believe that our approach is a highly practical solution to a UCR-based RSAR system with loose kinematic specifications.
As future work, we need to integrate better computer vision techniques to minimize the calibration and registration errors. For example, coupled-line cameras and projectors are compact geometric approaches to calibrate a projector-camera system [24] , [35] . In addition, we will apply the proposed method in an RSAR system with more types of kinematic configurations and higher DOFs. We also plan to verify the feasibility of the data-driven kinematic control over a wide range of applications such as assembly guide [36] , product design [37] , human–vehicle interaction [38] , and gesture-based interaction [39] .
This work was supported by the MOTIE under the Robot R & D Program supervised by the KEIT, Rep. of Korea (10048920, Development of Modular Manipulation System Capable of Self-Reconfiguration of Control and Recognition System for Expansion of Robot Applicability).
Ahyun Lee received his MS degree in digital imaging from Chung-Ang University, Seoul, Rep. of Korea. From 2011 to 2012, he was an engineer at LG electronics Inc. Pyeongtaek, Rep. of Korea. He is currently working toward his PhD degree in computer software at the University of Science and Technology, Daejeon, Rep. of Korea. His research interests include computer vision, augmented reality, and robotics.
Corresponding Author
Joo-Haeng Lee received his BS, MS, and PhD degrees in computer science from Pohang University of Science and Technology, Rep. of Korea in 1994, 1996, and 1999, respectively. He joined ETRI in 1999 and is a principal research scientist with the Human–Robot Interaction Lab. He has also been teaching graduate students (as an associate professor) at the University of Science and Technology, Daejeon Rep. of Korea, since 2008. Based on geometric modeling and processing, his research interests include computer graphics, HCI, computer vision, robotics, and their convergence.
Jaehong Kim received his PhD degree in computer engineering from Kyungpook National University, Daegu, Rep. of Korea, in 2006. He has been a research scientist at ETRI since 2001. His research interests include socially assistive robotics for the elderly, human–robot interaction, and social HRI frameworks.
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