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`IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART B: CYBERNETICS, VOL. 29, NO. 2, APRIL 1999
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`Multisensory Visual Servoing by a Neural Network
`
`Guo-Qing Wei and G. Hirzinger
`
`Abstract— Conventional computer vision methods for determining a
`robot’s end-effector motion based on sensory data needs sensor cali-
`bration (e.g., camera calibration) and sensor-to-hand calibration (e.g.,
`hand–eye calibration). This involves many computations and even some
`difficulties, especially when different kinds of sensors are involved. In this
`correspondence, we present a neural network approach to the motion
`determination problem without any calibration. Two kinds of sensory
`data, namely, camera images and laser range data, are used as the input to
`a multilayer feedforward network to associate the direct transformation
`from the sensory data to the required motions. This provides a practical
`sensor fusion method. Using a recursive motion strategy and in terms of
`a network correction, we relax the requirement for the exactness of the
`learned transformation. Another important feature of our work is that
`the goal position can be changed without having to do network retraining.
`Experimental results show the effectiveness of our method.
`
`Index Terms— Cameras, laser range finders, neural networks, visual
`servoing.
`
`I. INTRODUCTION
`When we use robotic external sensors for object manipulation,
`e.g., grasping, the motion of the robot gripper needs to be deter-
`mined. Traditional computer vision methods for accomplishing such
`visual servoing tasks require both the sensors and their mounting
`parameters to be calibrated in advance [2], [3]. This involves a lot
`of computations and even some difficulties, especially when different
`kinds of sensors are used [16], [17]. In the case of multiple sensory
`visual servoing, an extra difficulty arises in determining the optimal
`relative weights (importance) of each sensor in the motion estimation
`procedure (e.g., in the minimization of an objective function [15]).
`On the contrary, a neural network approach for doing the same job
`can avoid all such calibrations and provides a convenient sensor
`fusion framework. The network learns the direct transformation from
`(multi-) sensory data to the required motions based on a set of
`examples. The effects of sensor calibration, geometric transformation,
`and the relative importance of each sensor are all absorbed in a single
`network.
`Kuperstein [7] first proposed to map stereo disparities of stationary
`cameras directly to the robot joint angles used to reach a single
`point in the three-dimensional (3-D) space by a nonlinear network.
`Martinetz et al. [9] addressed the same problem by adding a self-
`organization feature map to achieve a dynamic mapping resolution.
`Later, Kuperstein [8] considered more degrees of freedom by in-
`cluding orientation information in image features. Miller [10], [11]
`used an eye-on-hand configuration to track an object on a conveyor.
`This was done by learning the mapping from the differences between
`the current and the desired images to the joint angle displacements
`used to move the end-effector. Since the same relative hand-to-object
`position in different robot configurations would require different robot
`joint angle displacements to achieve the desired position, the robot’s
`current joint angles should be involved in the input space, leading
`to an increase in the dimension of the input space and thus in the
`
`Manuscript received October 14, 1998. This paper was recommended by
`Associate Editor M. S. Obaidat.
`G.-Q. Wei is with Siemens Corporate Research, Princeton, NJ 08540 USA.
`G. Hirzinger is with the Institute of Robotics and System Dynamics, German
`Aerospace Research Center (DLR), 82234 Oberpfaffenhofen, Germany.
`Publisher Item Identifier S 1083-4419(99)02299-2.
`
`computational complexity. Hashimoto et al. [4] simplified Miller’s
`method by considering the relative positioning with respect to a static
`object, without having to involve the current joint angle configuration
`in the input space. The case of static objects, however, is trivial since
`the desired joint angles are fixed.
`A common problem with all previous approaches is that the learned
`mapping is assumed to be exact in the recall stage, which is in practice
`either not the case or can only be achieved with increased complexity
`in learning [4]. Another problem with previous approaches (in the
`eye-on-hand case) is that the network has to be retrained if one wants
`to change the desired hand-to-object relative position, because of the
`change of the mapping.
`In this correspondence, we use a multilayer perceptron to learn
`the direct transformation from multisensory data to the end-effector’s
`Cartesian motion, assuming that the robot kinematics is known a
`priori [14]. The sensors we consider are stereo cameras and laser
`range finders mounted on a robot hand. We propose a method to relax
`the requirement for the exactness of the learned mapping by means
`of network modification and recursive motion. The same network can
`also be used to adapt to changed goal positions without the need for
`retraining.
`
`II. THE LEARNING AND CONTROL STRATEGY
`
`A. Learning the Sensor-Motion Transformation
`Suppose S 2 Rn is the vector of sensor values in the sensor space,
`where n is its dimension. The sensor value vector S is the input
`to the network. The general principle to choose the dimension is
`uniqueness and redundancy. Here uniqueness means that the sensory
`data should be able to uniquely determine the end-effector’s relative
`position with respect to the object, while redundancy requires that
`one use more than the minimum number of sensory data to achieve
`robustness in the pose determination. In our specific application to
`be presented in Section III, the sensor value vector contains two
`image points in each of a stereo pair and four laser ranges. Thus we
`have the input dimension at n = 12 (see Section III for uniqueness
`analysis). The network output M 2 Rm is the Cartesian motion
`parameters of the end-effector. It is well known that a rigid motion
`is fully described by a rotation matrix and a translation vector. For
`the sake of computational savings, it is useful to parameterize the
`rotation matrix by fewer parameters, e.g., by the representations in
`[1]. However, we showed [13] that most of those parameterizations
`are not appropriate to be used as the network output. The reason
`is that the singularities in the representations break the smoothness
`requirement for the input-output relationship of the network, which is
`a precondition for a correct learning and a meaningful generalization
`[14]. (The smoothness requirement says that smooth changes in the
`input space should also cause smooth changes in the output space.)
`We list in Table I the validity of the various parameterizations as the
`network output. It can be seen from the table that only the roll-pitch-
`yaw (or the X-Y-Z Euler angles) [1] can be used in a suitable range
`as the network output. Thus the universal representation of a rotation
`as the network output is the rotation matrix itself. (But in this case
`it is difficult to ensure orthonormality of the rotation matrix.) Since
`the range of motion in our case does not exceed 90 we choose
`the roll-pitch-yaw as our rotation parameterization for the network
`output. The output dimension is thus m = 6 (three for rotation and
`three translation).
`
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`
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`
`277
`
`TABLE I
`THE POSSIBILITY OF VARIOUS PARAMETERIZATIONS AS THE NETWORK OUTPUT
`
`Fig. 1. The exact and the learned mappings.
`
`the mapping f ( ); the inverse function g () is also smooth. That is,
`a small motion M will cause a small change S for the sensory
`data. Thus, at the nth step of motion, we have
`
` Sn 
`
` Mn
`
`@g(Mn)
`@Mn
`Sn+1  Sn + Sn
`@f (Sn)
`@Sn
`Mn+1  Mn + Mn+1
`
` Mn+1  n
`
` Sn
`
`(1)
`
`(2)
`
`(3)
`
`(4)
`
`To obtain the training data, we set the robot end-effector to the
`desired grasping position, which we call the reference position. Then
`we make random movement of the robot hand. The amount of
`motions fMi; i = 1; ; Kg with respect to the reference position
`and the sensory data fSi; i = 1; ; Kg after each motion are
`recorded, where K is the number of motions. The network is
`then trained by using the backpropagation algorithm [12] with the
`input–output examples fSi; Mi; i = 1; ; K g as the training data.
`
`B. Dealing with the Inexactness of the Mapping
`Theoretically, a feedforward network can approximate any contin-
`uous mapping up to any accuracy [6]. But due to the finite number of
`training samples available and the finite network size used in practice,
`the actually learned mapping is usually not exact, especially when a
`large motion range is involved.
`Under the assumptions made at the beginning of the last sec-
`tion, there is a one-to-one (bidirectional) correspondence between
`the sensory pattern and the motion parameters (uniqueness). The
`transformation from the sensory data to the robot motions is thus
`monotonic [18]. Therefore, there is only one sensory pattern which
`induces the zero motion: the sensory pattern Sref at the reference
`position. If we visualize the mapping in a simplified one-dimensional
`(1-D) case, there is only one point of intersection of the mapping-
`curve with the sensor axis S (see Fig. 1). If the learned mapping
`is accurate enough, the property that there is only one point of
`intersection with the S-axis in the learned mapping is maintained
`ref in Fig. 1). Suppose the exact and the learned mappings are
`(see S 0
`represented by M = f (S); and M = f 0(S); respectively. Then, it
`
`follows that f (Sref ) = 0 and f 0(S 0ref ) = 0: Based on this property,
`ref will be called stable sensory pattern since it
`the sensory data S 0
`does not trigger any motion; the corresponding robot end-effector
`position will be called the stable position.
`Now we analyze the behavior of an exact mapping under recursive
`motion. Suppose S1 is the sensory pattern at an initial gripper
`position. If the robot moves according to the exact mapping M1 =
`f (S1); the reference position will be reached in one step. With
`recursive motion (or sensory feedback), we send only a small portion
`of M1 to the robot. We denote the small portion by M1 = M1;
`where the constant  is used to scale the motion and is made
`dependent on the magnitude of M1: After the robot has moved by
` M1; we measure the sensory data to obtain, say S2; at the new
`position. Then, S2 is used to recall another small motion M2: This
`process repeats until convergence is reached at MN = f (SN ) = 0;
`where N is the number of motion steps. Since the exact mapping is
`used here, convergence is guaranteed to be reached at the reference
`position, that is, SN = Sref : (Since each step of motion reduces the
`difference between the current sensory pattern and Sref ; the process is
`convergent.) This procedure can be analyzed by a local linearization
`method as follows. Since M = f (S) is monotonic, its inverse exists,
`which will be denoted by S = g(M ): Because of the smoothness of
`
`where n indexes the motion step, n  1; Sn is the sensory data
`at the nth station (i.e., after the (n 1)th motion step), Mn is the
`total amount of movement from the initial position to the nth station;
`and n is a scale factor. Therefore, in the case of small motions,
`the sensor-motion loci are approximately along the mapping curve.
`It can be seen from the above equations that the dynamic behavior
`of the recursive motion is completely governed by the differential
`properties of the mapping, i.e., (1) and (3). Equations (2) and (4) here
`are only for understanding purposes: The exact value of Sn+1 should
`be read from the sensors after the motion Mn: The same applies to
`Mn+1: the total amount of robot motion should be computed from the
`difference between the actual robot position and the initial position.
`Based on (1) and (3), if the learned mapping (inexact) is differentially
`similar to the exact one, the system of the inexact mapping will
`
`converge at MN = f 0(SN ) = 0; with SN = S 0ref ; where N 0
`is the number motion steps. Here the differential similarity of the
`learned mapping to the exact one can be stated more concretely as
`the sign equality of the derivatives of the learned mapping to those
`of the exact mapping at every position. (It is the directions (signs)
`of the motions which determine the convergence of the system.) In
`this way, the requirement for the value exactness of the mapping is
`not necessary. Another important feature of recursive motion is that
`it ensures a smooth trajectory for an inexact mapping.
`
`C. Network Modification
`We have just established the convergence properties of the recur-
`sive motion for an inexact mapping. Since the converged position
`for an inexact mapping is different from the required one (i.e.,
`ref 6= Sref ); we have to modify the mapping such that the required
`S 0
`reference position be reached. This can be done in two ways. The
`first is to shift the sensory data in the input space of the network
`ref : The modified mapping reads as M =
`by the amount Sref S 0
`
`ref ): Since f 00(Sref ) = f 0(S 0ref ) = 0; we
`f 00(S) = f 0(S Sref + S 0
`now have the stable position at S = Sref ; i.e., the required reference
`
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`Fig. 2. The system diagram for learning the sensor-motion transformation.
`
`Fig. 3. The multisensory gripper used in the experiment.
`
`position; here, S 0ref should be first measured at the converged position
`
`by using M = f 00(S) in recursive motion. The second method is to
`shift the network output. We first compute M0 = f 0(Sref ) using the
`
`learned mapping, refer to Fig. 1. Then, the mapping is modified as
`M = f 00(S) = f 0(S)M0; which ensures the stable position to be at
`S = Sref ; since f 00(Sref ) = f 0(Sref ) M0 = 0: Since shift in either
`
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`279
`
`Fig. 4. The stereo image of the object superimposed with the detected centers of gravity and the region of interest in the tracking of the black blobs.
`
`the input or the output space do not change the shape (derivatives)
`of the mapping, the convergence property of the modified mapping
`in recursive motion is unaffected.
`The above methods can be extended to the case of a changed
`reference position. Suppose after network training, we want to change
`the reference position to a new one, which is specified by another
`sensory data vector Sg measured at that position. We can simply
`modify the learned mapping according to either of the following
`formulas:
`
`and
`
`M = f 00(S) = f 0(S Sg + S 0
`ref )
`
`M = f 00(S) = f 0(S) f 0(Sg):
`
`(5)
`
`(6)
`
`With the modified mapping as either (5) or (6), we have the converged
`position now at the new reference position S = Sg since f 00(Sg) =
`0: Therefore, we can use the existing network to achieve the new
`reference position without having to do retraining. Here, it is assumed
`that the new reference position is within the range where the training
`data were sampled. Otherwise there is no guarantee that the modified
`mapping curve has only one point of intersection with the sensor
`axis in the working range (refer to Fig. 1). Experiments indicate that
`the use of (5) needs fewer steps of recursive movements than using
`ref : Thus we use (6) in
`(6); but to use (5), one has to measure S 0
`our experiment. Fig. 2 shows the complete system-diagram of our
`method, where the training is done off-line, and the required reference
`position is used to modify either the network input or the network
`output.
`
`III. EXPERIMENTS
`Our method has been tested in a real robot environment. The
`robot we used is MANUTEC R2. The object we used is called
`ORU (the Orbital Replaceable Unit), and is chosen from the space
`robot technology experiment ROTEX in the 1993 German Spacelab-
`mission D2 [5]. This object is in octagonal shape and is to be
`grasped in a predefined position by a space robot using telesensor
`programming. The end-effector is mounted with multiple sensors
`including two hand cameras and nine range finders (cells) (see Fig. 3).
`In our experiments, we used 4 of the short range sensors (active range
`
`0–3 cm) mounted on the front side of the gripper and the stereo
`cameras for visual servoing. When the end-effector is far away from
`the object, the range finders are blind, and the camera images alone
`can be used for motion determination. The experiments have been
`reported in [13]. When the end-effector gets nearer to the object, the
`object is occluded by the end-effector, so that only two of the corner
`points on the object can be always seen by the cameras. In this case,
`the range finders are in work. But neither the camera images nor
`the range data alone can determine a unique end-effector position,
`while the use of them both can. The four range finders, hitting on
`the planar surface of the ORU, determine three degrees of freedom:
`one positional and two rotational. The camera images determine the
`other three degrees of freedom by using the two corner points. If we
`use analytic computer vision methods to solve the same problem, a
`lot of calibrations have to be involved [15]. The use of the neural
`network method avoids these computations.
`Fig. 4 shows the stereo view of the ORU object in the reference
`position, where the two black blobs were artificially marked on the
`object to ease real-time image processing for blob tracking. The center
`of gravity of the blobs were used as the image feature points. The blob
`tracking algorithm was realized on a Datacube MaxVideo 200 image
`processing system, see [15] for details. The detected blobs together
`with the region of interest for tracking are superimposed on the
`intensity image in Fig. 4. The absolute accuracy of blob localization
`by image processing is unfortunately unknown because of the difficult
`to obtain ground truth. We could only measure the variance of the
`localization; this is 0.23 pixels. Fortunately, the precision of blob
`localization is not important in our neural visual servoing method:
`Any localization error for the blobs can be learned by the network,
`as long as the error is systematic, e.g., a constant shift. This is not the
`case for conventional computer vision methods for doing the same
`job.
`A network of size 12  100  6 was chosen. A set of 250
`training samples was randomly generated to cover the work range
`and used to train the network. Note that due to the relaxation of
`the exactness of the learned mapping, we do not need to use huge
`amounts of training data. The conjugate gradient method is used for
`the training. After 280 cycles of iterations, which took about 5 min
`on a Indygo2 Silicon Graphics workstation, the training is stopped
`with a rms error being 4% of the maximum motion component (each
`
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`with some sensory data missing (as long as uniqueness is assured),
`and then switch between the different networks after identifying the
`type of sensory pattern.
`
`IV. CONCLUSIONS
`In this correspondence, we have presented a neural network
`approach to multisensory visual servoing. A multilayer perceptron
`network is used to learn the direct mapping from multisensory data
`to robot motions. We propose to deal with the inexactness of the
`learned mapping in terms of recursive motion and modification of
`the network input/output. In this way, an inexact network can be
`used to achieve the required mapping. This enables computational
`savings, in the sense that a smaller network can be applied, and
`fewer numbers of training samples can be used. Another feature of
`our method is that we do not need to retrain the network if we change
`the reference position; any position within the training range can be
`reached by modifying the existing network. Experiments have shown
`that satisfactory accuracy has been achieved.
`
`REFERENCES
`
`(a)
`
`(b)
`
`Fig. 5. The differences between the current sensor data and the reference
`sensor data during visual servoing (a) the image data error and (b) the range
`data error.
`
`TABLE II
`THE SENSOR VALUE DIFFERENCES AT THE
`STARTING POSITION AND THE CONVERGED POSITION
`
`motion component, i.e., the rotation angles and translation values,
`is normalized by its own maximum value). The trained network is
`then used for the visual servoing of the end-effector to any desirable
`position set within the range of training data without further need
`for learning. The scaling of motion used in the recursive scheme is
`done for rotation and translation components separately. For rotation
`part, we first represent the rotation matrix by the angle-axis form
`[1]. Then the rotation angle is scaled such that it does not exceed
`0.5. For the translation part, the magnitude of translation is scaled
`to be within 0.8 mm (if it is larger than this limit). Fig. 5 show the
`profiles of the differences between the current sensor data, with the
`gripper started from an arbitrary position, and the reference sensor
`data during visual servoing for a reference position. (Note that the
`starting position can be outside the range of the training data.) The
`sensory data differences at the starting position and the converged
`one are also listed in Table II, where X and Y represent the
`X and Y image coordinate errors, and d the range data error.
`It can be seen from the figures and from the table that after 50
`steps of motion, the average image error and the average range error
`have been reduced to 0.37 pixels and 0.08 mm, respectively. The
`result has been much more accurate than that reported in [4], where
`two networks, one for coarse motion and one for fine motion, were
`used, and the accuracy in [4] for noise-free (simulated) data was 4
`pixels.
`Concerning the stability of our procedure, occlusions in the sensory
`data are not allowed. That is, if an image point is out of track, or
`if a laser range sensor fails, the neural network may misguide the
`robot. This problem could be solved by training several networks
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