## 2 Materials and Methods
### Location Estimation Methods of Autonomous Driving Robot  
#### 2.2.1 Dynamic Model of the Autonomous Driving Robot  
Figure 2 shows the robot location on a 2D coordinate system and its dynamic model. The mobile robot used in this study is a four-wheel drive, four-wheel steering based type vehicle, which is driven using principles similar to those used for real cars. The mobile robot also has two DC motors for driving, and two DC servo motors for steering.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **Equipment** & **Model and Specification** \\ \hline \multirow{3}{*}{Sensor} & LiDAR Sensor & LMS-111 2D (SICK, Waldkirch, Germany) \\ \cline{2-3}  & IMU Sensor & EBIMU – 9 DOFV4 (E2 BOX, Hanam, Korea) \\ \cline{2-3}  & Encoder Sensor & IG-32 PGM 01 TYPE (YOUNGJIN B\&B, Seoul, Korea) \\ \hline \multirow{6}{*}{Controller} & & Intel Celeron(R) CPU 1007U 1.50 GHz, 4 GB \\  & & RAM, Intel(R) HD Graphics, (Intel, Santa Clara, CA, UAS) \\ \cline{2-3}  & High Level Controller & Windows10 (Microsoft Corporation, Redmond, WA, USA) \\ \cline{2-3}  & & NI LabVIEW software (National Instruments, Austin, TX, USA) \\ \cline{2-3}  & Low Level Controller & AVR Microcontroller ATMega128 Pro Kit (MICROCHIP, Chandler, Arizona, USA) \\ \cline{2-3}  & & C Language (Bell Labs, Murray Hill, NJ, USA) \\ \cline{2-3}  & Remote Controller & Intel Atom (TM) CPU N2600 1.60 GHz, 2 GB RAM, Intel(R) Graphics Media \\ \cline{2-3}  & & Accelerator 3600 Series, Windows 7 \\ \cline{2-3}  & & NI LabVIEW Software \\ \hline Driving Platform & Driving Robot & ERP-42(Unmanned Solution, Seoul, Korea) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Specification of sensors, controller, and driving platform used in this study.  
Figure 2: Two-dimensional coordinate system and dynamic model of the autonomous driving robot used in this study.  
The position of the robot in the two-dimensional coordinate system can be expressed using three variables [\(x(t_{k})\), \(y(t_{k})\), \(\alpha(t_{k})\)], where \(x(t_{k})\) and \(y(t_{k})\) are the \(x\) and \(y\) coordinates at time \(t_{k}\), and \(\alpha(t_{k})\) is the robot's heading angle. By defining the straight distance from [\(x(t_{k+1})\), \(y(t_{k+1})\)] to [\(x(t_{k})\), \(y(t_{k})\)] as \(d(t_{k})\), the robot's location at time \(t_{k+1}\) can be defined by Equations (1) and (2).  
\[x(t_{k+1})=x(t_{k})+d(t_{k})\cdot cos(\alpha(t_{k})) \tag{1}\]  
\[y(t_{k+1})=y(t_{k})+d(t_{k})\cdot sin(\alpha(t_{k})) \tag{2}\]  
Because the roads in underground mine environments are often sloped, the height (\(z\)) from the surface must be included to accurately estimate the location of the robot. If the angle of the z-y coordinate axis rotated about the x-axis is called \(\beta\) (Pitch), the robot's three-dimensional coordinates can be defined by Equations (3)-(5).  
\[x(t_{k+1})=x(t_{k})+d(t_{k})\cdot cos(\beta(t_{k}))\cdot cos(\alpha(t_{k})) \tag{3}\]  
\[y(t_{k+1})=y(t_{k})+d(t_{k})\cdot cos(\beta(t_{k}))\cdot sin(\alpha(t_{k})) \tag{4}\]  
\[z(t_{k})=z(t_{k})+d(t_{k})\cdot sin(\beta(t_{k})) \tag{5}\]  
Unlike Equations (1) and (2), \(cos(\beta(t_{k}))\) was multiplied with the variables in Equations (3) and (4) to convert the travel distance in the three-dimensional space to the travel distance projected in the x-y plane. This way, the location of the robot in three dimensions can be defined as variables [\(x(t_{k})\), \(y(t_{k})\), \(z(t_{k})\), \(\alpha(t_{k})\), \(\beta(t_{k})\)].