Error-resilient Perceptual Haptic Data Communication ... - CiteSeerX

Error-resilient Perceptual Haptic Data Communication based on Probabilistic Receiver State Estimation Julius Kammerl, Fernanda Brandi, Florian Schweiger, and Eckehard Steinbach Technische Universit¨ at M¨ unchen, Institute for Media Technology, Munich, Germany {kammerl,fernanda.brandi,florian.schweiger,eckehard.steinbach}@tum.de

Abstract. We present an error-resilient perceptual haptic data compression scheme based on a probabilistic receiver model. While the previously proposed perceptual deadband approach successfully addresses the challenges of high packet and data rates in haptic real-time communication, packet loss in the network leads to perceivable distortion. To address this issue, a sender-driven transmission scheme for low-latency packet loss compensation is proposed. In this scheme, packet transmissions are adaptively triggered only if the reveicer state is likely to deviate from the error-free signal by more than the applied perception thresholds. Conducted experiments validate that the proposed haptic communication scheme successful compensates for packet loss with low computational complexity and without the need of acknowledgments. Keywords: Haptics, Communication, Compression, Error-resiliency

1

Introduction

Haptic data communication is an emerging research area in the context of telepresence and teleaction (TPTA) systems. These systems enable the execution of remote explorative and manipulative tasks by immersing a user into an environment that is distant, inaccessible, scaled to macro- or nano-dimensions or hazardous for a human being. A TPTA system can be decomposed into three main subcomponents: the human operator (OP) connected to a human system interface device (HSI), a teleoperator (TOP) which receives control commands for the execution of remote operations, and the communication link which bidirectionally transmits the multimodal information over a communication channel (see Fig. 1). In order to provide physical access to the remote environment, particularly the exchange of haptic velocity and force feedback signals plays a key role. In contrast to the transmission of audio and video signals, the haptic signals are bidirectionally transmitted and thereby close a global control loop between the human OP and the TOP. To maintain control loop stability and a high degree of system transparency, haptic real-time communication in TPTA systems is characterized by strict delay constraints. As the communication and processing latency must be kept at an absolute minimum, haptic samples are typically

2

J. Kammerl, F. Schweiger, E. Steinbach Visual Display

Local Control Loop

Local Control Loop

Operator

Network

Teleoperator Sensors & Actuators

Haptic Display

Fig. 1. Illustration of a telepresence and teleaction system and its main subcomponents: the human-system interface (HSI), the communication system and the teleoperator (TOP). Figure adopted from [1].

transmitted immediately upon their generation. In packet-switched networks, e.g., the Internet, this transmission behavior leads to high packet rates of up to the applied haptic sampling rates at the HSI and the TOP (typically 1000 Hz). Furthermore, modern TPTA systems deploy an increasing number of degrees of freedom (DoF) to provide intuitive and flexible remote manipulation. As every DoF is individually sampled and controlled, the bidirectional exchange of haptic signals leads to high data rates which are particularly challenging in large-distance or wireless TPTA scenarios. Several approaches addressing the challenges of haptic real-time communication have been presented in literature. Early work on haptic data compression can be found in [2, 3], where adaptive sampling and quantization techniques for haptic signals are discussed and compared with each other. In [4], predictive coding for haptic signals based on Differential Pulse Code Modulation (DPCM) and Adaptive Differential Pulse Code Modulation (ADPCM) combined with Huffman coding are used to reduce the load on the haptic channel. First research explicitely targeting the high packet rates in networked control loops can be found in [5]. Here, the concept of a deadband-based packet rate reduction is proposed where sensor readings are only transmitted if their magnitude changes by a fixed threshold. First work specifically exploiting limitations in human haptic perception can be found in [6, 7]. Here, the so-called ”perceptual deadband” (PD) compression approach (or in short ”deadband approach”) has been presented which is further investigated in terms of stability criteria in [8, 9]. It explicitly extends the deadband-based packet rate reduction scheme in [5] with a model of human haptic perception. It reduces the packet rate by detecting and transmitting only perceptually relevant haptic samples over the haptic communication channel. Consequently, as transmitted haptic samples are considered to describe perceivable information, packet loss in the network immediately leads to perceivable distortion in the haptic feedback. Research from the field of real-time video streaming [10, 11] proposes a technique for robust low-latency video streaming, which has been shown to also apply to the challenges of lossy haptic communication [12, 13]. It is based on a Markov decision tree which considers every triggered network transmission to either successfully arrive at the receiver or to be lost.

Error-resilient Perceptual Haptic Data Communication

3

In this way, it allows the consideration of all possible receiver states at any time. If possible signal disturbances become likely, additional redundancies can be added to the haptic channel for compensating the network errors. However, the exponential growth of the tree structure that occurs with every triggered network transmission limits the applicability due to its expensive memory and computation requirements. Brandi et. al address this issue [13] and show that the exponentially growing Markov tree can be significantly simplified to an adaptive Markov chain model which reduces the complexity to linear time. However, the constantly growing data structures require techniques to limit their size such as the transmission of acknowledgment feedback or the detection and removal of unlikely receiver states. In this work, a novel probabilistic receiver state model using a multivariate Gaussian distribution is presented. In contrast to previous approaches, it does not require any feedback information (ACKs or NACKs) and operates with low computational complexity. Conducted experiments validate that the proposed approach can successfully restore the perceived quality of haptic feedback when operating a TPTA system on a highly erroneous network channel. This paper is organized as follows. In Section 2, the perceptual deadband scheme for haptic real-time compression is explained. The novel error-resilient haptic communication scheme which is based on probabilistic receiver state estimation is introduced in Section 3 and experimentally evaluated in Section 4. Section 5 concludes the paper.

2

Perceptual haptic data compression

The challenges of high packet and high data rates in haptic real-time communication are successfully addressed by the perceptual deadband (PD) compression scheme proposed by Hinterseer et al. [6]. It allows a tremendous reduction in network transmissions, imperceptible to the human. To this end, two key components are used: a psychophysical model at the sender, and a signal predictor deployed both at the sender and the receiver (see Fig. 2). Hinterseer et al. further show that a simple yet effective psychophysical model of human haptic perception suitable for haptic real-time communication can be built based on Weber’s Law of Just Noticeable Differences (JND) [14]. Weber’s research revealed that over a large dynamic range, the perception of relative changes in stimulus is linearly proportional to the stimulus intensity itself. This implies a constant ratio between the intensity of a pending stimulus and the maximum change in intensity that is just not noticeable. Weber’s Law of the JND can be mathematically described in the following way: ∆I = k = const. or ∆I = kI (1) I where I is the stimulus intensity, ∆I is the so called Difference Threshold or the JND and k is the constant Weber fraction. Integrated into the proposed perceptual coding scheme, Weber’s Law of JND can be used to estimate haptic

4

J. Kammerl, F. Schweiger, E. Steinbach

Predictor

Predictor

Input/ Source

Network Perceptual Model

Output

Receiver

Sender

Fig. 2. Illustration of the perceptual predictive coding scheme for haptic real-time transmission introduced in [6].

discrimination bounds. As long as the difference between the incoming signal h and the predicted signal p stays within imperceptible bounds, no network transmissions are required and the predicted samples at the receiver can be output. If the difference between the incoming and the predicted haptic sample exceeds the applied perception thresholds at the sender, additional signal information is sent over the network which also updates the predictors. To this end, the haptic signals are perceptually downsampled while keeping the introduced compression distortion below human haptic perception thresholds. For the prediction of haptic signals, typically linear predictors of very low order (e.g. order one) are deployed to comply to the strict delay constraints which are required to maintain control loop stability. They successfully model the low frequency characteristics of haptic signals while still being able to quickly adapt to transients during contact events due to their low group delay. Fig. 3 visualizes the process of PD compression using a zeroth-order predictor (hold-last-sample algorithm) and with perceptual thresholds defined by Weber’s Law of JND. Samples illustrated with solid vertical lines are considered to be relevant for transmission. They also define the discrimination thresholds based on Weber’s Law of JND represented by PDs, illustrated as gray zones. Note that the size of the applied PD is a function of a deadband parameter k and the magnitude of the most recently predicted haptic sample value |pi−m |, where m samples back in time the last violation of the then applicable perception thresholds occurred. This can be described by ∆i = ∆i−1 = . . . = ∆i−m = k · |pi−m |.

(2)

Receiver:

Sender: Perceptual Deadband

t

t

Signal Updates Haptic Communication Channel

Fig. 3. Perceptual deadband compression using a zeroth-order prediction (hold-lastsample) algorithm.


5

Once the PD is violated by a new input sample, this input sample is transmitted and redefines the applied perception thresholds. Samples with dotted lines fall within the currently defined deadband and can be dropped as their change in signal is too small to be perceptible. Similarly, the first-order haptic prediction scheme proposed in [6] takes the two most recently transmitted haptic signal updates hi and hj at time i and j into account. This allows for the calculation of a gradient gj gj =

hi − hj i−j

with i > j > 0

(3)

Accordingly, the haptic signal prediction pi can be calculated by pi = hj + gj · (i − j)

3

(4)

Error-resilient perceptual haptic compression

As the perceptual haptic data compression approach transmits only perceptually relevant haptic samples, lost network packets consequently lead to noticeable disturbances. Furthermore, failed haptic data transmission leads to inconsistent predictor states which also results in disturbing artefacts in the decoded haptic signal. A common strategy for detecting and compensating for packet loss in a network is to acknowledge successfully transmitted packets to the sender. If the sender does not receive an acknowledgment message from the receiver within a fixed period of time, it assumes the packet was lost and triggers retransmissions until a successful transmission is achieved. In haptic real-time communication, however, the strict latency constraints prevent any acknowledgment-based waiting strategy. Furthermore, since the transmission of compressed haptic packets is temporally irregular, the receiver does not know when it is supposed to receive a network packet. This poses a serious challenge for the detection and corresponding concealment of network errors on the haptic channel. Brandi et al. [12, 13] address this challenge (inspired by [11]) and show that robust low-latency streaming of compressed haptic signals can be achieved with the help of a binary Markov decision tree, which reflects all possible receiver states after n packet transmissions. Whenever a network transmission is triggered, the corresponding data packet either successfully updates the receiver or it is lost due to packet loss. If the actual sender state and possible receiver states deviate by more than the applied perception thresholds, additional data transmissions can be adaptively triggered in order to compensate for the packet loss at the cost of increased packet rates on the haptic channel. As the Markov tree structure grows exponentially with every transmitted haptic packet, the corresponding computational complexity and memory requirements are limiting its application. To address this issue, acknowledgments with receiver state information are typically signaled from the receiver back to the sender (see [12, 13, 10, 11]).

6


In the following, a novel receiver state estimation technique is presented which does not require the transmission of acknowledgment feedback, and is characterized by low computational complexity. 3.1

Probabilistic receiver state estimation

Experiments reveal that the distribution of the signal error in the PD compression scheme originating from packet loss exhibits a Gaussian-like distribution (see Fig. 4). This motivates us to probabilistically model the uncertainty of the receiver state with a multivariate normal distribution (see Fig. 5). Initially, the sender and the receiver are initialized with state h0 . From then on, a successful transmission of packet hn+1 updates the receiver state ˆ n+1 = hn+1 ) with probability p. Otherwise, the receiver holds its most recently (h ˆ n+1 = h ˆ i with probability successfully received update at time i ≤ n, hence h (1 − p). Hence,

ˆ n+1 = hi } = Pr{h

( ˆ n = hi } · (1 − p) : 0 ≤ i ≤ n Pr{h p :i=n+1

(5)

By using (5), we can iteratively calculate the sample mean hn+1 of all possible receiver states after n + 1 transmissions which then serves as an estimate of the expected mean of the receiver state. hn+1 = =

n+1 X i=0 n X i=0

ˆ n+1 = hi } · hi Pr{h

(6)

ˆ n+1 = hi } · hi + Pr{h ˆ n+1 = hn+1 } · hn+1 Pr{h | {z } | {z } p ˆ n =hi } · (1−p) Pr{h

(7)

= (1 − p) · hn + p · hn+1 Zero Order Reconstruction

1

0.8

Normalized Histogram

Normalized Histogram

1

0.6 0.4 0.2 0 −0.5

(8)

0 Force Error on X axis (N)

0.5

(a) Force error when using a zerothorder PD compression.

First Order Reconstruction

0.8 0.6 0.4 0.2 0 −0.5

0 Force Error on X axis (N)

0.5

(b) Force error when using a firstorder PD compression.

Fig. 4. Distribution of haptic signal errors originating from packet loss. In this experiment, a uniform packet loss with probability 0.5 and PD compression with k = 10% is used.


7

Fig. 5. Illustration of a multivariate Gaussian distribution describing the receiver state.

Hence, the sample mean hn+1 can be successively updated by only taking the previous sample mean hn and the current haptic input sample hn+1 into account. Similarly, the sample mean of all vector products hi hi | can be iteratively updated with every triggered network transmission: hn+1 h|n+1 = =

n+1 X i=0 n X

ˆ n+1 = hi } · hi h| Pr{h i

(9)

ˆ n+1 = hi } · hi h| + Pr{h ˆ n+1 = hn+1 } · hn+1 h| (10) Pr{h n+1 i

i=0

= (1 − p) · hn h|n + p · hn+1 h|n+1

(11)

With the help of the sample mean values hn+1 and hn+1 h|n+1 , an estimate of ˆ n+1 can be determined which expresses the uncertainty the covariance matrix C of the current receiver state estimation. It is defined by: ˆ n+1 ) = hn+1 h| − hn+1 · hn+1 | C(h n+1 h i = (1 − p) · hn h|n + p · hn+1 h|n+1 − i h | (1 − p) · hn + p · hn+1 · (1 − p) · hn + p · h|n+1

(12) (13)

Hence, the receiver state can be statistically modeled with every network transmission by successively updating the mean and covariance estimates of ˆ n+1 . This iterative estimation procedure can be performed with low computah tional effort and at high update/transmission rates at the sender. 3.2

Error-resilient transmission scheme

ˆ incorporates correlations within the transThe estimated covariance matrix C mitted signal h. The principal axes of the recently transmitted haptic samples ˆ hi are reflected by the eigenvectors of the covariance matrix C(h). Hence, the uncertainty described by the covariance matrix increases towards the direction of current signal change and, consequently, stays within smaller bounds along

8


ˆ is nonsingular and an orthogonal direction to the current signal trajectory. If C positive definite (which is usually the case after a few iterations), its deterˆ can be used to obtain a measure of uncertainty of the current minant det(C) ˆ falls below a small threshold , the receiver state estimation process. If det(C) sample mean hn+1 can be considered to be a precise estimate of the current ˆ n+1 . Consequently, a perceptual evaluation of the sample mean receiver state h hn+1 at the sender allows a reliable decision over the transmission of additional ˆ exceeds the uncertainty threshold , packets (see Section 2). However, if det(C) additional steps are required to decide over possibly required redundancy on the haptic channel which are discussed in the following (see Fig. 6). As the exact receiver output is unknown at the sender at time i, the region ˆ in the receiver state space is of interest, within which haptic output samples h are in PD compliance with the current input sample hi at the sender. If hi falls into this region, the difference in signal between sender input hi and receiver ˆ i can be considered to be imperceptible and no additional network output h transmissions are required. Interestingly, this PD compliance assuring region is of circular/spherical shape with center s and radius r, as shown in the following equations: ˆ − h| ≤ k|h| ˆ |h ˆ x − hx )2 + (h ˆ y − hy )2 + (h ˆ z − hz )2 ≤ k 2 h ˆ 2 + k2 h ˆ 2 + k2 h ˆ2 (h x y z .. . 2 2 2 hy hz k2 hx ˆ ˆ ˆ + h − + h − ≤ (h2 + h2y + h2z ) hx − y z (k 2 −1)2 x 1−k 2 1−k 2 1−k 2 | {z } | {z } | {z } | {z } =: sx

=: sy

=: sz

=: r 2

ˆ − s| ≤ r |h

(14)

ˆ − s| ≤ r, the current haptic input h at the sender is PD comHence, if |h ˆ Consequently, the probability of being in PD pliant with the receiver output h. compliance can be calculated by integrating over the PD assuring spherical region within the probability density function fhˆ of the modeled receiver state distribution Z Pr[PD Compliance] =

fhˆ (x) dx

(15)

{x|r≥|x−s|}

using the probability density function fhˆ of a D-dimensional multivariate Gaussian distribution: D ˆ − 12 exp − 1 (x − x)| C ˆ −1 fhˆ (x) = (2π)− 2 det(C) (x − x) (16) x 2 As long as the probability of the signal error being in PD compliance with the input signal h stays below a target probability ψ, additional packet transmissions need to be triggered until the desired PD compliance probability ψ is retained.


9

Fig. 6. Flow diagram at the sender of the error-resilient transmission scheme.

3.3

Extension to first-order PD compression

In the first-order PD compression scheme (see Section 2), the prediction coefficient/gradient g is typically jointly transmitted together with the current absolute haptic sample value h [13]. This allows the separate modeling of not only the statistical distribution of the absolute signal h, but also of the prediction gradient g. However, transmission errors in predictive coding schemes propagate over time which requires updating of the sample mean and covariance estimates ˆ and g ˆ at every sampling instance (and not only when network transmissions of h are triggered). According to linear regression theory in statistics, the absolute sample amplitude and the corresponding gradient can be understood as independent random variables. As the sum of normally distributed independent random variables is again normally distributed, the signal prediction step can be easily applied to the probabilistic models during periods of network inactivity: hn+1 = hn + gn ˆ ˆ n ) + C(ˆ ˆ ˆ h ˆ gn ) C(hn+1 ) = C(

(17) (18)

Hence, the modeled receiver state and its covariance are linearly modified over time. However, each triggered update reduces again the uncertainty in the haptic communication system. Consequently, the presented approach does not require acknowledgments from the receiver. However, feedback can be optionally used to support the receiver state estimation process.

4

Experimental Evaluation

A psychophysical study has been conducted to investigate the performance of the proposed robust haptic data communication scheme. 16 test subjects participated in the experiment. The experimental setup consists of a Phantom Omni HSI device from SensAble and a simulated virtual TPTA environment. It contains a touchable virtual sphere with a smooth surface which can be approached and haptically touched from any direction. During contact with the remote environment, collision detection and contact force rendering are performed by the CHAI3D library at 1000 Hz. In the experiment, a simulation of a uniform packet loss is applied to the transmission of the force feedback signal. The position/velocity signals stay unmodified during the experimental study.

10


ˆ is set to 10−15 N2. The uncertainty threshold applied to the determinant of C The PD parameter k is kept at 10% during the experiment. The integral in (15) is numerically evaluated with a resolution of 0.01 N in every dimension. The experiment consists of two runs which investigate the performance of the proposed packet loss concealment scheme applied to zeroth-order and first-order PD compression, respectively. In each run, ten different system configurations with varying packet loss and deadband compliance probability ψ are evaluated which are randomly presented to the subjects. Specifically, the impact of network packet loss of 0%, 20%, 40%, 60% on PD compressed force feedback signals is investigated. In addition, for each of the test configurations with a packet loss probability > 0%, the influence of the proposed packet loss compensation scheme using the multivariate Gaussian receiver model on subjective quality and packet rates are observed. Here, three PD compliance probabilities ψ = 0%, 70%, 95% are used to configure the sender-driven transmission scheme. The subject can freely choose between the ten test configurations by pressing the numbers 0–9 on a keyboard. As soon as a different test configuration is selected, the corresponding feedback is immediately displayed to the subject which allows for pairwise comparison of the test items. In addition, a reference configuration is provided to the subject which deactivates the simulated packet loss on the haptic channel. This enables the direct comparison and subjective rating of the different test configurations against the presented reference. The subjects are asked to perceptually evaluate any perceived difference in the haptic feedback to the reference setting in accordance to a predefined subjective rating scale from 0 (strong difference) to 100 (no difference perceivable). The experimental results are shown in Fig. 7. They demonstrate the strong performance of the PD compression scheme. Here, the test configurations without applied packet loss achieve a packet rate reduction of > 90% while keeping introduced coding artefacts below haptic discrimination thresholds. The upper figures show the mean packet rates and mean subjective ratings for the zerothorder PD compression scheme. It can be observed that with increasing packet loss probability, the subjective quality of the haptic feedback becomes clearly impaired. The light and the dark gray bars illustrate the results with applied packet loss compensation using the multivariate Gaussian receiver model. In order to conceal the packet loss on the haptic channel, additional packet transmissions are triggered as soon as disturbing signal distortion at the receiver becomes likely, which can be seen in Fig. 7(b). The subjective ratings in Fig. 7(a) show that by adding redundancy to the haptic channel, the disturbing packet loss effects in the TPTA system can be successfully compensated. Even at a PD compliance probability of 70%, the transparency of the TPTA system is almost completely restored. The lower figures illustrate the mean packet rates and the mean subjective rating of the first-order PD compression scheme. The results clearly show that first-order PD compression is significantly more sensitive to data loss on the communication channel. Here, already a low packet loss probability significantly impairs the subjective quality of haptic feedback. This is mainly due to incorrect signal predictions which occur as soon as haptic predictor updates are lost

Error-resilient Perceptual Haptic Data Communication 120

350

Mean Subjective Rating

80 60 40 20

0% PD Compliance 70% PD Compliance 95% PD Compliance

300 Mean Packet Rate (pks/s)


100

0

11

250 200 150 100 50

0

20

40 Packet Loss (%)

0

60

0

20

40 Packet Loss (%)

60

(a) Subjective ratings (zeroth-order PD (b) Mean packet rates (zeroth-order PD compression). compression). 120

350

Mean Subjective Rating

80 60 40 20 0


300 Mean Packet Rate (pks/s)


100

250 200 150 100 50

0

20

40 Packet Loss (%)

60

0

0

20

40 Packet Loss (%)

60

(c) Subjective ratings (first-order PD (d) Mean packet rates (first-order PD compression). compression). Fig. 7. Experimental results of perceptually robust haptic communication based on the multivariate Gaussian receiver state model. In all test configurations, PD compression with a PD parameter of k = 10% is applied to the force feedback.

during transmission. However, the results in Fig. 7(c) demonstrate that also for the first-order PD compression scheme, the sender-driven transmission scheme successfully compensates for the network data loss. Interestingly, the additional packet rates required for error-resilient haptic communication are similar for the zeroth-order and first-order PD compression schemes.

5

Conclusion

In telepresence and teleaction systems, the communication of compressed haptic signals is sensitive to data loss on the communication channel. In this paper, a novel error-resilient perceptual communication scheme has been proposed which employs a probabilistic model of the perceptual deadband receiver. Whenever the actual sender state and the estimated receiver state are expected to deviate by more than the applied perception thresholds, additional data transmissions are adaptively triggered in order to compensate for the packet loss. Experimental results reveal that the novel multivariate Gaussian receiver model is able to compensate even high packet loss up to a loss probability of 60%. This can be achieved with low computational complexity and in real time, without the need of acknowledgment feedback.

12


Acknowledgment This work has been supported, in part, by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement no. 258941 and, in part, by the German Research Foundation (DFG) under the project STE 1093/4-1.

References 1. W. R. Ferrell and T. B. Sheridan, “Supervisory control of remote manipulation,” IEEE Spectrum, vol. 4, no. 10, pp. 81–88, Oct. 1967. 2. A. Ortega and Y. Liu, “Lossy compression of haptic data,” in Touch in Virtual Environments. Prentice Hall, 2002, ch. 6, pp. 119–136. 3. C. Shahabi, A. Ortega, and M. R. Kolahdouzan, “A comparison of different haptic compression techniques,” in Proc. of the Int. Conf. on Multimedia & Expo, Lausanne, Switzerland, Aug. 2002, pp. 657–660. 4. C. W. Borst, “Predictive coding for efficient host-device communication in a pneumatic force-feedback display,” in Proc. of the First Joint Eurohaptics Conf. and Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems, World Haptics, Pisa, Italy, March 2005, pp. 596–599. 5. P. G. Otanez, J. R. Moyne, and D. M. Tilbury, “Using deadbands to reduce communication in networked control systems,” in Proc. of the American Control Conf., Anchorage, Alaska, 2002. 6. P. Hinterseer, S. Hirche, S. Chaudhuri, E. Steinbach, and M. Buss, “Perceptionbased data reduction and transmission of haptic data in telepresence and teleaction systems,” IEEE Trans. on Signal Processing, vol. 56, no. 2, pp. 588–597, Feb. 2008. 7. P. Hinterseer, E. Steinbach, S. Hirche, and M. Buss, “A novel, psychophysically motivated transmission approach for haptic data streams in telepresence and teleaction systems,” in Proc. of the Int. Conf. on Acoustics, Speech, and Signal Processing, vol. 2, Philadelphia, PA, USA, March 2005. 8. S. Hirche, P. Hinterseer, E. Steinbach, and M. Buss, “Transparent data reduction in networked telepresence and teleaction systems. part i: Communication without time delay,” Presence: Teleoperators & Virtual Environments, vol. 16, no. 5, pp. 523–531, 2007. 9. ——, “Network traffic reduction in haptic telepresence systems by deadband control,” in Proc. of the IFAC World Congress, Int. Federation of Automatic Control, Prague, Czech Republic, 2005. 10. J. Chakareski and B. Girod, “Computing rate-distortion optimized policies for streaming media with rich acknowledgments,” in Proc. of the Data Compression Conf., Snowbird, Utah, USA, 2004, pp. 202–211. 11. P. Chou and Z. Miao, “Rate-distortion optimized streaming of packetized media,” IEEE Trans. on Multimedia, vol. 8, no. 2, pp. 390–404, April 2006. 12. F. Brandi, J. Kammerl, and E. Steinbach, “Error-resilient perceptual coding for networked haptic interaction,” in Proc. of the ACM Multimedia, Firenze, Italy, Oct. 2010. 13. F. Brandi and E. Steinbach, “Low-complexity error-resilient data reduction approach for networked haptic sessions,” in Proc. of the IEEE Int. Symposium on Haptic Audio-Visual Environments and Games, Nanchang, China, Oct. 2011. 14. E. Weber, “Die Lehre vom Tastsinn und Gemeingef¨ uhl, auf Versuche gegr¨ undet,” Vieweg: Braunschweig, Germany, 1851.