Multi-Finger Manipulation of Virtual Objects - CiteSeerX

Multi-Finger Manipulation of Virtual Objects* Ronan Boulic, Serge Rezzonico, Daniel Thalmann Computer Graphics Lab (LIG), Swiss Federal Institute of Technology (EPFL) CH-1015 Lausanne, Switzerland The manipulation of a virtual object by means of a digital glove is a tedious task for repetitive position and orientation adjustments. In this paper we try to overcome the lack of force feedback of general purpose digital gloves. We propose a solution based only on the interpretation of instantaneous hand posture variations. From this knowledge, a virtual contact model analog to the Coulomb law allows to evaluate the instantaneous nature of the contact, firm or sliding, between virtual sensors attached to the fingers and the virtual object. Although no force feedback is supplied, we are able to derive a visual restitution consistent with the user manipulative intentions while respecting the integrity of solid interaction with friction.

1

Introduction

Hand gestures form a rich and convenient channel to drive interactions in virtual environments and their interpretation is an established research topic [SZF89] [Sh92] [MS94]. Paradoxically the hand manipulative skill could not be reproduced in virtual environment with the first generation of digital glove due to high noise to signal ratio and missing degrees of freedom (e.g. no lateral opening in DataGloveTM). Although a digital glove can properly translate the posture of the user hand when calibrated [Sp92] [RH94] [MM95] it lacks bilateral force coupling. So, manipulating a virtual object with a virtual hand is generally accomplished by means of command coding through posture or gesture recognition [SZF89]. In such a context the user has to rely enormously on the visual feedback to assert the good or bad realization of the desired interaction. On the other hand systems providing force feedback involve additional mechanics which reduces the hand manipulation range (both in joint range and cartesian space accessibility). Moreover, it has been shown that a small delay in the application of the force feedback to the operator's hand was inducing instabilities [F66]. Finally, adding a force feedback specification for a hand interaction device increases its price significantly. For these reasons alternate approaches were proposed to overcome these limitations. A sensory substitution of the force feedback by vibrotactile and auditory modalities is proposed in [MS94]. These authors have demonstrated the feasibility of this substitution with and without time delay. The proposed sensory substitution is justified in the studied teleoperation context where the operator's visual system is not available because it is used for viewing the remote task environment on a television monitor. In [MM95], the authors propose a two-handed input based on the information of the position and orientation of both hands (with their custom ChordGlove associated with Polhemus Fastrack sensors). They demonstrated the ability to apply simple transformations to rigid objects (translate,rotate,scale, etc) In a recent article the fine manipulation of objects in virtual environment has been addressed kinematically [KH95]. The authors described an Impetus method to model the interaction between a fingertip and a virtual object. The virtual object can have a linear velocity. For each time step, they define the invasion vector, or impetus, of the fingertip as the fraction of the fingertip trajectory inside the virtual object (after integrating its current velocity). The impetus can be modified by factors as damping, dynamic and static friction, etc. Another method was dedicated to manipulation with three fingertips. In that context the object is included in a bounding sphere on which a specific manipulation operates. No approach was proposed to deal for general and dynamic interaction pattern. In our context of interaction with virtual objects, we prefer to enhance the operator’s visual feedback. We recently proposed an approach of interactive grasping where the hand posture is directly used to establish the grasp on the virtual object [RBHMTT95]. Its main interest is to reduce the cognitive gap between the intention and the action of grasping, i.e. there is no more need to know a specific posture to express a grasping command. Moreover, due to its fine interpretation of finger posture it reduces the time needed for complex positioning of virtual objects requiring multiple re-orientations (and so multiple grasp-release cycles). However the main limitation of this approach lies in the lack of finger manipulation of the object relatively to the hand coordinate system. Once the grasp is established, the object is rigidly linked to the hand coordinate system. The present paper defines a complementary approach to [RBHMTT95] in order to exploit the full mobility of the fingers. We first recall the interactive grasping approach. Then our analogy to the Coulomb law is developed in the so-called virtual contact model. Various examples illustrates the pertinence of our approach. *Published in Proc. of ACM Symposium on Virtual Reality Software and Technology VRST'96, ISBN 0-89791825-8, pp 67-74, Hong-Kong, July 96

2 2.1

Interactive Grasping Accurate Grasp Vs Symbolic Grasp

As the virtual environment is becoming more and more complex, hand-based interactions also evolve in complexity. The limitation of the symbolic grasp and release commands mostly comes from the rough relative positioning of the hand and the object which does not convey a clear understanding of the action to perform with the object [MM95]. More and more the interaction in a virtual environment requires greater manipulative skill than necessary for pick and place tasks which are easy to perform with grasprelease commands. In such context the hand associated with the digital glove device provides a high dimensional space as a direct operative space for precise manipulation or modification of virtual objects. Within this extended application context of the digital glove, it became crucial to display a posture of the hand consistent with the on-going manipulation of the virtual object. For this reason, we proposed a new approach for the interactive and consistent grasping of virtual entities with the interactive grasping automata [RBHMTT95]. The displayed grasping posture is established by correcting the hand posture according to the collision status of detection sensors.

2.2

Sensor-Based Grasp

Our approach is rooted in the use of proximity sensors in Robotics for the automatic adaptation to the environment [EB85]. The multifinger grasping [S85] and collision handling literature [M85][K93] also provided a clear grounding as developed later in this paper. More recently the sensor-actuator networks [VF93] and sensor-based automatic grasping approaches [MT94] demonstrated the interest of multiple spherical sensors with the evaluation of both touch and distance characteristics. In the approach described in [MT94], a set of spherical sensors is attached to the articulated figure with each sphere sensor fitted to its associated joint shape. An automatic "wrapping" grasp is performed by closing the joints and stopping them only when their immediately distal sensor is colliding or if they reach their limit (Figure 1).

a b Fig. 1. Virtual hand with sphere sensors (a); while grasping a sphere (b) [MT94] The interactive grasping automata uses the same type of sensors to drive an automatic "unfolding" correction. In this method we consider three different states of interactive grasping (figure 2): • FREE_HAND : the hand is freely moving in space without holding any object. The hand posture is displayed as measured with the digital glove. • GRASPING in progress : the touch property of the sensors is continuously evaluated to adjust the posture of colliding fingers with the object to grasp (the object is fixed or can move in a world coordinate system). If the simplified grasp condition is established, i.e. at least the thumb and one finger are maintaining a durable contact with the object, we enter the "SECURE_GRASP" state. • SECURE_GRASP : the touch property of the sensors is still used to continuously adjust the posture of colliding fingers with the grasped object (the object position is fixed in the hand coordinate system). FREE_HAND the hand and object bounding spheres intersect free object

The hand and object bounding spheres no more intersect

at least the thumb and GRASPING one finger establish a in progress durable grasp free object

SECURE_ GRASP not enough fingers to maintain a minimum grasp attached object

Fig. 2. The interactive grasping automata

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hand posture to correct finger base

corrected sensor

wrist corrected sensor

a b d c

corrected sensor

Fig. 3. An example of the opening adjustment loop for interactive grasping The interactive grasping procedure adjusts the hand posture by opening it rather than closing it. Without force feedback it is difficult to adjust the grasp precisely so that the fingers establish a permanent contact without penetrating into the virtual object. This is due to the fact that the approach is based on a visual feedback. So our working hypothesis is to rely on the operator to permanently close the grasping fingers slightly more than geometrically necessary. In such a way, the opening correction approach establishes a durable contact which overcomes the unavoidable small variations of hand posture and position (Figure 3). The correction algorithm is fully described in [RBHMTT95]. Figure 3 details all the stages of the opening algorithm for one colliding finger with an elliptic shape (in 2D for clarity). The algorithm begins by unfolding the finger base joint to release the first colliding sensor (fig. 3a,b). Then it unfolds the next joint to remove the following sensor (Fig 3b,c) and the same occurs for the last joint (Fig. 3c,d). In this case the final finger posture consistently wraps around the object. Figure 4 shows the hand posture as it is measured with the digital glove from Virtual Technologies (Fig. 4a) and the resulting correction and display for the grasp of a sphere (Fig. 4b).

a b Fig. 4. Example of application of the interactive grasping automata [RBHMTT95]

3

The Virtual Contact Model

We propose a new and complementary interpretation of the sensor interaction with the virtual object which aims to reflect the local manipulative intention of the user, i.e. moving and orienting the object from finger movement rather than from the hand motion. So, in the following sections we implicitly consider that the hand is static in a global coordinate system. The proposed method can handle small variations of the hand position and orientation but is not intended to manage large ones as for pick and place tasks. The interactive grasping automata presented in section 2 perfectly carries on that task with a simpler algorithm. Our proposal is to interpret the penetration of each colliding sensors in terms of desired normal and tangent displacements and a desired contact exertion. An analogy of the Coulomb law, the so-called virtual contact model, is established to drive the behavior of the sensor-object interaction from the combination of these desired displacements and contact exertion.

3.1

Representing the Local Manipulative Intentions

Three major characteristics have to be synthesized for each colliding sensor in order to reflect the desired manipulative intentions of the user. These are: • the nature of the contact with the object surface • a displacement along the normal of the object surface • depending on the contact nature, a displacement of either the object or the sensor in the tangent plane of the object surface.

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These three characteristics constitute the so-called virtual contact profile associated with the sensor. The virtual contact profile is presently used to control the object motion in a simple kinematic scheme ; it could also be integrated within a dynamic scheme. The derivation of the virtual contact profile from the interaction of the virtual sensor with the virtual object relies on the information of the normal sensor penetration within the virtual object (figure 5a). Now arises the fundamental question about how to derive three parameters out of the measured penetration. In the present approach, we construct them from the information of the normal sensor penetration and its instantaneous variations along the normal and the tangent plane (Cf. 3.2 for their exact evaluation).

Object Sensor Correction amplitude

Normal Correction

a Fig. 5. (a) normal penetration of a virtual sensor within a virtual object, (b) local normal penetration evaluated at the first correction

b

We adopt here the same working paradigm as in the interactive grasping automata. We rely on the operator to express a contact pattern by moving the sensors slightly within the object. At any time step we maintain two postures of the hand : the one measured by the digital glove (not displayed) and a corrected one which is consistent our real experience of non-penetrating bodies (displayed). The variation of sensor’s penetration defines the contact pattern and a corresponding variation of the object position and orientation. Finally a corrected hand is computed according to the new object situation for the operator's visual feedback. The resulting manipulation paradigm is the following . If the hand is still, there is no object motion even if some sensors are currently colliding. Otherwise, the instantaneous hand posture variation is interpreted in terms of normal and tangent displacements which may result in an object position and orientation variation. Furthermore, we don’t consider the normal collision variation as a desired displacement when the penetration is decreasing. In such a way, the user can freely readjust the contact profile without experiencing a gluing effect when reducing the sensor penetration. Using the derivative of the sensor penetration to drive the object motion is justified by the lack of real force feedback. With force feedback the user interaction naturally converges to an equilibrium state associated with the hand posture and pressure exertion pattern. In our case, we cannot exert any real contact with the fingers, so the real pressure exertion pattern is replaced by our penetration pattern. Then, if the penetration pattern is defined by the relative position of the hand posture and the object, we postulate that this information must not be used for another purpose (e.g. impulsing a motion to the object). This paradigm choice is what distinguishes our approach from the one described in [KH95].

3.2

Evaluating the Virtual Contact Profile

As two out of the three parameters of the virtual contact profile are derivatives, we need to distinguish the first penetration from the following ones. For the first one, no virtual contact profile is evaluated. The correction is performed along the local normal of the virtual object (Figure 6 time k). In the general case the correction process retains the previous penetration location, correction location, local normal direction and tangent plane. From the new sensor penetration location we can derive (Figure 6, time k+1) : • the absolute distance to the previous tangent plane along the previous normal direction (called the contact "force") • the variation of normal distance to the previous tangent plane (called the normal "force") • the variation of sensor location in the previous tangent plane (called the tangent "force" )

time k the first penetration is along the local normal time k+1

previous correction tangent force

normal force contact force Fig. 6. Evaluating the virtual contact profile of one sensor

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We now show how the contact force is used in conjunction with the tangent force to derive the nature of the sensor-object interaction.

3.3

Modeling the Sensor-Object Interaction

We propose an analogy of the Coulomb law on static friction to decide whether the sensor is sliding on the object surface or if it transmits the tangent force to the object. µ

the first penetration is corrected along the local normal vector

µ < µmax establishing a virtual contact

the object moves

following penetrations are corrected along the previous normal

correction location

µ

µ > µmax sliding

the sensor slides

Fig. 7. Analogy of Coulomb law for the management of a virtual contact with friction The Coulomb law states that the tangential force of friction during sliding is proportional to the normal force thus defining the coefficient of dynamic friction as this constant of proportionality. If there is no motion in progress a higher constant is used : the coefficient of static friction [M85]. In our approach we only consider the static friction case on a surface with a coefficient of static friction noted µmax. The motion of a point P on the surface is initiated only if the force applied to P presents a ratio of its tangent to normal components greater than µmax. In that case the applied force is said to be outside the friction cone defined by the friction angle : α = arctg µmax In our working paradigm, we discriminate the nature of the contact by evaluating the ratio of the tangent force to the contact force, noted µ. Whenever µ is smaller than µmax the contact is maintained and the sensor transmits the tangent force to the object as a desired displacement. Otherwise if µ is greater than µmax, the sensor slides on the object surface and does not transmit any tangent force to the object (Figure 7). Our original contribution comes from the use of the sensor corrected location as a reference to build the contact force information (Figure 6) while in [KH95] the instantaneous variation of the fingertip is used for that purpose. Whatever the contact nature, our so-called normal force is transmitted to the object as a desired displacement. We now describe the virtual contact automata required to manage the transitions between the various states of a sensor-object interaction.

3.4

The Virtual Contact Automata

We distinguish three different states of the sensor-object interaction (Figures 8 and 9) : • free : the sensor is not colliding the object • correction : the sensor is colliding with the object, sliding on the surface • contact : the sensor is colliding with the object, maintaining the contact According to these states, the correction process is different. Figure 8 highlights the whole set of transitions considered for the virtual contact automata. Figure 9 illustrates them in a general fashion with a spherical object and a sensor. E

B free

A

correction

contact

C

F

G

D H

Fig. 8. The Virtual Contact Automata

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µ

free B

correction

contact

E

C

G F

µ

D µ

H Fig. 9. Illustrating the states and transitions of the Virtual Contact Automata The free states does not induce any constraint on the sensor or on the object as long as they are not colliding (transition A). When a collision occurs, we enter the correction state where the sensor just slides on the object surface (transition B). From there we can return to the free state if the sensor is no more colliding with the object (transition D). We can also stay in that state if the penetration does not satisfy to the virtual contact condition (transition C) or, if it does, we enter the contact state (transition E). The contact state is special in the sense that the object should follow the sensor motion. So we cannot evaluate the transition the same way as for the correction state. Just imagine holding a thin cylinder with the thumb and another finger and wishing to examine it under various angles. The fingers usually impulse gentle rotations but in our VE context these bring the sensors far out of the object during the current time step. For this reason, we consider the collision with the half-space defined by the previous tangent plane rather than with the primitive itself. Then, the transition for the free state (transition H) requires no collision with that half-space. The state is stable if the virtual contact condition is still maintained (transition F). It can be lost if the friction cone angle is too wide ; in such a case it returns to the correction state if the sensor really collides with the object (transition G) or to the free state if it does not (another case of transition H not appearing on Figure 9). Put in a few words, each sensor transmits a desired normal displacement to the object only in case of increasing penetration, and a desired tangent displacement only if the contact is established. We now review the synthesis of the object motion and the final correction of the hand posture.

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4

Object Motion

As mentioned in section 3.1 we are interested in a local motion control of the object derived from the motion of the sensors attached to the fingers (Figure 11). The present study is limited to sphere, cylinder and parallelepiped objects without restraining the generality of the approach. Each sensor maintains its own state of interaction with the object. From the current sensor position and state we obtain a set of desired instantaneous displacements on the object. These displacement cannot be exactly realized for all the sensors as they may act in opposite directions. We choose to evaluate the kinematic torsor (v,ω ) applied to the object as the vectorial sum of all the desired instantaneous displacements (as v) and the vectorial sum of their moments at the center of the object (as ω). Then we solve the object motion at the first order by adding v to its current position and multiplying its orientation matrix by the rotation matrix corresponding to ω (using the Euler vector formalism). Two scaling factors allow to adjust the dynamics of the interaction especially if a low refresh rate induces large time steps and thus eventual large sensor motions.

5

Hand Posture Correction

The maintenance of two hand postures, measured and corrected for display, is one key concept of our working paradigm. The real measured posture defines a penetration pattern interpreted as a contact pattern. The corrected posture is necessary for the operator to obtain a visual feedback consistent with the experience we have from grasping real objects. In other words, the corrected posture must be close to the real posture while respecting the solid nature of the object. So, the finger sensors are corrected by acting on the knuckles joints both in lateral direction and in the current finger plane with the flexion-extensions. We also have to take into account the interactive refresh rate required to maintain the coherence of the operator performance. This issue raises the question of how should we perform the correction without degrading the overall interaction rate. The theoretical correction specified in section 3.2 supposes an individual cartesian control of all the colliding sensors. This could be realized with inverse kinematics in a multiple effector context [S86][BM96]. Although not as precise, we prefer to use the more efficient approach defined by the unfolding algorithm (Cf. section 2. and [RBHMTT95]) with an additional lateral correction. The algorithm proposed in [RBHMTT95] is only working in the finger current plane of motion (Figure 3). However, in the present context the correction should occur along the object normal. As the unfolding algorithm is working in the joint space we can only guarantee a partial achievement of that objective. So, the desired sensor correction is decomposed into a component belonging to the finger plane of motion and into an orthogonal lateral component. Besides the correction realization, the algorithm now takes into account the status of the sensor. If it is in the correction or the contact state, we constraint it to lie on the object surface. The new algorithm is valid for convex objects and becomes : (Figure 3 is still valid for the order of sensor correction) For each colliding finger For each sensor distal to the colliding one closest to the base (from base to tip side of the finger) If the sensor is currently colliding Extract the correction lateral component Realize it with the finger base lateral opening If the sensor is still colliding Unfold the closest proximal joint until the sensor is tangent to the object or the joint reaches its limit EndIf Else If the sensor is in correction or contact state Fold the closest proximal joint until the sensor is tangent to the object or the joint reaches its limit Endif EndIf EndFor EndFor

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The finger lateral opening is allowed only for some fingers in order to obtain a corrected posture close to the measured one (Figure 10).

lateral range of motion 4

2

1

3

5

lateral opening sensors Fig. 10. Allowing lateral finger motion for correction

6

Fig. 11. Sensors on palm and fingers

Experimental Results

We use a hand model with 15 active sensors (three sensors per fingers installed at the knuckles joints and the fingertips). Figure 11 shows them, displayed as cubes to enhance the display performance, within the CyberGloveTM hand model of Virtual Technology (The 2600 polygons hand model provided by Virtual Technologies comes from the 3-D Dataset of Viewpoint DataLabs). The position and orientation of the CyberGloveTM was acquired with one bird sensor from the "Flock of bird" device of Ascension Technologies. The multi-fingers manipulation experiments were realized at an average interactive rate of 20 images per second on an ONYX workstation. Figure 12 and 13 show images of various maneuvers both in rotation and translation of the object. Sensors in the collision or contact states appear here as darker grey than the ones in the free state. The direction of their normal is also displayed in black.

a

b

e

Fig. 12. Orienting maneuvers of a cylinder

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c

d

f

a

b

c

Fig. 13. Rolling a sphere on the fingers

7

Discussion

As far as the first experiments we made with simple volumic primitives (sphere, cylinder, cube), the virtual contact is a first step in the right direction for finer object manipulation in virtual environments. In the experimental context of objects without gravity the operator feeling resembles the one of wearing thick gloves for manipulation. The average frame rate of 17 to 23 frames/s can be improved but yet it allows to achieve a good perception-action control loop in order to push, pull, rotate locally the object. In our default setting the display is completed with color coding information as described now. Each state of the virtual contact automata is associated with a different color of the sensor: pale skin color for free, blue for correction and green for contact. This additional symbolic information especially enhances the operators feedback when they work with a 2D display. Our approach improves the manipulation of objects compared to the interactive grasping automata [RBHMTT95]. With the interactive grasping automata a large object reorientation is performed with multiple grasp-release cycles. Now with our virtual contact model we can handle the local manipulation of an object with the fingers. Significant reorientations can be achieved without repositioning the hand relatively to the object, as in a real hand manipulation. In fact, the finger and the hand motion are usually combined to obtain a desired effect on the object. This can be handled within the same framework as the virtual contact profile associated with each sensor leads to stable grasps. However, manipulations involving significant hand motions need at least a higher acquisition rate and processing bandwidth to be manageable within the same paradigm.

8

Conclusion

We have proposed a complementary approach to the interactive grasping automata where we exploit the full mobility of the fingers. We defined an analogy to the Coulomb law with the virtual contact model thus translating the manipulative intentions of the operator into effective motion of the virtual object. We are currently studying a coupling of the two approaches, interactive grasping automata and virtual contact model, to handle manipulations with significant hand motions in interactive context with restricted bandwidth (10 frames/s on medium range workstations).

Acknowledgments We would like to thank Manuel Bouvier for the implementation of a preliminary version of this approach. This research was partly supported by the Swiss National Research Foundation and OFES.

References [BM96] Boulic R., Mas R. (1996) “Hierarchical Kinematic Behaviors for Complex Articulated Figures”, in "Advanced Interactive Animation", Magnenat-Thalmann Edt, Prentice Hall, To Appear in Summer 1996. [EB85] Espiau B., Boulic R. (1986) “Collision avoidance for redundant robots with proximity sensors”, Robotics Research : the Third International Symposium, O.D. Faugeras and G. Giralt Edt., The MIT Press Series in Artificial Intelligence [F66] Ferrel W.R. (1966) “Delayed force Feedback”. Human Factors, 8(5), 449-455 [K93] Kamat V.V. (1993) “A Survey of Techniques for Simulation of Dynamic Collision Detection and Response”, Computers & Graphics, Vol 17(4)

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[KH95] Kijima R., Hirose S. (1995) “Fine Object Manipulation in Virtual Environment” , Proc. of the second EUROGRAPHICS Workshop on Virtual Environments, Monte-Carlo, january 1995 [MM95] Mapes D.P., Moshell J.M. (1995) “A Two-Handed Interface for Object Manipulation in Virtual Environments”, Presence 4(4), Fall 1995, pp403-416, The Massachusetts Institute of Technology. [MT94] Mas R., Thalmann D. (1994) “A Hand Control and Automatic Grasping System for Synthetic Actors”, Proceedings of Eurographic'94, pp.167-178. [M85] Mason T.M. (1985) “Manipulator Pushing and Grasping Operations, in "Robot Hands and the Mechanics of Manipulation", P.H.Winston and J.M.Brady Edt., The MIT Press Series in Artificial Intelligence, ISBN 0-62-13205-2. [MS94] Sheridan T.B. Massimo M.J. (1994) “Sensory substitution for Force Feedback in Teleoperation”, Presence 2(4), pp 344-35, The Massachusetts Institute of Technology. [RBHMTT95] Rezzonico S., Boulic R., Huang Z., Magnenat-Thalmann N., Thalmann D. (1995) “Consistent Grasping in Virtual Environments Based on the Interactive Grasping Automata”, in "Virtual Environment", M. Gobel Edt, Springer Verlag Wien. [RH94] Rohling R.N., Hollerbach J.M. (1994) “Calibrating The Human Hand for Haptic Interfaces” , Presence 2(4), pp81-296, The Massachusetts Institute of Technology. [S85] Salisbury J.K (1985) “Kinematic and Force Analysis of Articulated Hands”, in "Robot Hands and the Mechanics of Manipulation", P.H.Winston and J.M.Brady Edt., The MIT Press Series in Artificial Intelligence, ISBN 0-62-13205-2. [Sh92] Sheridan T.B. (1992) “Musing on Telepresence and Virtual Presence”, Presence 1(1), 120-125, The Massachusetts Institute of Technology. [Sp92] Speeter T.H. (1992) “Transforming Human Hand Motion For Telemanipulation”, Presence 1(1), pp 6379,The Massachusetts Institute of Technology. [SZF89] Sturman D.J., Zeltzer D., Feiner S.(1989) “Hands-on Interaction with Virtual Environments”, Proc. of ACM SIGGRAPH Symposium on User Interface Software and Technologies, pp 19-24 [VF93] van de Panne M., Fiume E. (1993) “Sensor-Actuator Network, Computer Graphics”, Annual Conference Series, 1993, pp.335-342.

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