# Conceptual Design of BCI for Mobile Robot Control
## 2 Materials and Methods
### Conceptual Model for BCI System Design
Figure 5a presents the mentioned linear velocities of both wheels. Vertical bold lines indicate two time moments (\(t_{1}\) = 2.49 s and \(t_{2}\) = 9.19 s). Figure 5b,c show pictures from the simulation showing the current position of the robot along with the trajectory of the point \(P\) (black) and the point \(Pp\) (blue) for \(t_{1}\) and \(t_{2}\) time moments respectively. The green lines represent linear velocity vectors with the beginnings in the center of each wheel. The lengths of the vectors represent the values of the current linear velocity shown in the upper right corners of the simulation Figure 5b,c. Additionally, the current values of the following parameters are shown: simulation time (\(t\)), current position of the \(P\) point, i.e., \(x\),\(y\) coordinates, and angle \(\varphi\) value. The current position of the ICC and radius \(R\) (red line) are also presented. Figure 4: Robot kinematics model created in Simulink: (**a**) general view, (**b**) simulink realization of kinematic equations describing robot location [12]. As for the robot dynamics, aggregated dynamic model \((\overline{\rho},\overline{\varphi})\) of the MR can be presented at the phase of the detailed design like in [13] or in the following form:  
\[\dot{\mathbf{x}}=\mathbf{A}\mathbf{x}+\mathbf{B}\mathbf{u},\mathbf{y}=\mathbf{C}\mathbf{x} \tag{9}\]  
State equation in (9) corresponds to the state transition function \(\overline{\varphi}\) in MR conceptual model (2) and the second output equation corresponds to the reaction \(\overline{\rho}\). Vectors \(\mathbf{x}\), \(\mathbf{y}\), \(\mathbf{u}\) and matrices \(\mathbf{A}\), \(\mathbf{B}\), \(\mathbf{C}\) must be predefined. In the case of the mobile robot motion, the elements of states vector \(\mathbf{x}=[x_{1}\ x_{2}]^{T}\) are the displacement \(x_{1}\) and velocity \(x_{2}\). Mobile robot kinematics and dynamics tasks, briefly described above, belong to analysis design task of the BCI subsystem being designed, i.e., mobile robot in our case. Concerning the man-operator subsystem, its model \(\alpha_{1}^{\ell-1}\) can be constructed on its inputs \(X_{1}^{\ell-1}\), i.e., visual stimuli signals, perceived by human eyes; its outputs \(Y_{1}^{\ell-1}\), i.e., EEG signals recorded by measuring system \(\alpha_{2}^{\ell-1}\), taking into consideration human's physiological state \(C_{1}^{\ell-1}\). Measuring subsystem \(\omega_{2}^{\ell-1}\) purpose is EEG signals registration, processing and data transmitting to BCI control system by TrueScan 24 subsystem. TruScan Acquisition program is used as software means to perform impedance measurements. The electroencephalographic (EEG) signal was recorded using the EEG cap of Deymed Diagnostic company (Figure 6a), containing 19 chlorine silver electrodes (Ag/AgCl) arranged according to the International System 10-20. In addition, the cap contained a reference electrode and a grounding electrode (Figure 6b). The cap is placed on the head of the subject, i.e., man-operator, being examined (Figure 6c). EEG gel application to the measuring electrodes allowed to maintain electrodes impedance at 2-5 k\(\Omega\) level during the conducted tests. Figure 5: Simulation results of robot’s motion: (**a**) values of linear velocities \(\upsilon\) and \(\upsilon\), (**b**) picture at \(t1\) time moment, (**c**) picture at \(t2\) time moment. The _BCI_ environment has its own structure and contains the following sub-systems: panel \(\omega_{1}^{\ell+1}\) which generates light stimuli perceived by man-operator's eyes; floor area \(\omega_{2}^{\ell+1}\) where the mobile robot moves; man-coordinator \(\omega_{3}^{\ell+1}\), which places electrodes on man-operator's \(\omega_{1}^{\ell-1}\) head and attaches the measuring system; the higher level \(l+1\) design and control system \(\omega_{4}^{\ell+1}\).