# FPGA Applied to Latency Reduction for the Tactile Internet
## 3 Discrete Model of the Tactile Internet  
A discrete model of the tactile internet system is proposed and presented in Figure 1. This model consists of seven subsystems: the Operator (OP), Master Device (MD), Hardware of the MD (HMD), Network (NW), Hardware of the SD (HSD), Slave Device (SD) and the Environment (ENV). It is assumed that the signals are sampled at time \(t_{s}\). The OP is an entity responsible for generating stimuli that can be in the form of position signals, speed, force, image, sound or any other. These stimuli are sent to the devices involved so that some kind of task can be performed in some kind of environment. The environment, the ENV subsystem, receives the stimuli from the OP and generates feedback signals associated with sensations such as reactive force information and tactile  
Figure 1: Proposed discrete model of the tactile internet system. information that are sent back to the OP. The interaction between the OP and the ENV is performed through the master and slave devices, MD and SD, respectively. Specifically in this work, MD is characterized as a local device, SD as remote one and both of them are responsible for transforming the stimuli and sensations associated with OP and ENV into signals to be processed. Tactile devices (MD and SD) can take the form of robotic manipulators, haptic devices, tactile gloves and others that may be developed in the future. In the coming years, the introduction of new types of sensors and actuators is expected that will form the basis for the development of new tactile devices. Although there are no tactile internet standards nor products yet, it can be affirmed that future tactile devices will be integrated with a hardware responsible for all operational metrics and calculations. Within this conjecture, this work adds a couple of modules to the discrete model (as per Figure 1), called HMD and HSD. HMD is responsible for performing all transformations and calculations associated with MD, and HSD performs the equivalent operations for the SD. Several algorithms associated with transformation, compression, control, prediction will be under the responsibility of these two modules. The authors from [36] present a few approaches focusing on the reduction of kinesthetic data and tactile signal compression, which can be applied to the model. Based on the model presented in Figure 1, the signals generated by the OP can be characterized by the array \(\mathbf{a}(n)\) expressed as  
\[\mathbf{a}(n)=\big{[}a_{1}(n),\ldots,a_{i}(n),\ldots,a_{N_{OP}}(n)\big{]}, \tag{1}\]  
where \(a_{i}(n)\) is the \(i\)-th stimulus at the \(n\)-th instant and \(N_{OP}\) is the total number of stimuli signals generated by the OP. At every \(n\)-th moment the stimulus array, \(\mathbf{a}(n)\), is received by the MD which transforms the stimuli into a set of \(N_{MD}\) signals expressed as  
\[\mathbf{b}(n)=\big{[}b_{1}(n),\ldots,b_{i}(n),\ldots,b_{N_{MD}}(n)\big{]}, \tag{2}\]  
where \(b_{i}(n)\) is the \(i\)-th signal generated by MD at the \(n\)-th instant. It can be stated that at each \(n\)-th moment a set of stimuli \(\mathbf{a}(n)\) generates a set of signals \(\mathbf{b}(n)\) that depend on the type of MD and the sensor set associated with the device. Especially important is the fact that the signals generated by MD, \(\mathbf{b}(n)\), have heterogeneous characteristics in which each \(i\)-th signal \(b_{i}(n)\) can represent an angle, spatial coordinate, pixel of an image, audio sample or any other information associated with a stimulus generated by OP. In practice, the signals grouped by the \(\mathbf{b}(n)\) array originate from sensors coupled to the MD and the amount of data may vary according to the amount of information to be sent, \(N_{MD}\). The set of signals, expressed by \(\mathbf{b}(n)\) are sent to the HMD (Figure 1) which has the function of processing this information before sending it to the NW subsystem. Calculations associated with calibration, linear and nonlinear transformations and signal compression are performed by the HMD.