## 3 Proposed Washout Algorithm
### Subregion Scale Method  
In the case of vehicles, unlike aircraft, the angle of the roll and pitch direction is limited in motion within a specific angular range depending on road gradient and dynamic characteristics. Accordingly, the rotational motion sensation may be improved by directly reflecting the tilt angle of the vehicle to the simulator motion. Rotational motion sensation can be simulated by the tilt angle of the vehicle, but excessive application of the tilt angle of the vehicle rather leads to a decrease in translational motion sensation. Therefore, there is a need for a method of maintaining an improved translational motion sensation, improving a rotational motion sensation and appropriately scaling so as not to deviate from the motion area of the simulator.  
Although this method has been proposed in the past [4; 5], it simply presents the scale method and insufficient research on the method of selecting the scale parameter, so this paper presents the criteria for setting the scale value considering the operation area of the motion system through mathematical analysis. Figure 2 shows the structure of the proposed washout algorithm. SSM means the subregion scale method.  
Analysis of Parameter Used in Subregion Scale Method  
Figure 3 represents principle of the subregion scale method. \(N_{L}\) is the normal zone without signal scale. \(N_{L}\) is defined as  
\[N_{L}=kA_{max} \tag{6}\]  
where \(k\) is the scale constant and has a value between 0 and 1, and \(A_{max}\) represents the maximum vehicle tilt angle generated by the VDS. If \(k\) has 1, rotation angle value is not scaled and is reproduced on the simulator's motion platform.  
In the scaling region, it may be expressed by the following equation so as not to exceed the mechanical limit of the motion platform.  
\[A_{S}=(A-N_{L})S_{V}+N_{L} \tag{7}\]  
where \(A_{S}\) represents a scaled angle value, \(A\) is an original angle value and \(S_{V}\) is a scale constant having a value between 0 and 1. In order to maintain the shape of the angle value, \(S_{V}\) is replaced with \(k\), and Equation (7) can be summarized as follows using Equation (6).  
\[A_{S}=(A-kA_{max})k+kA_{max} \tag{8}\]  
To determine \(k\), it is necessary to consider \(A_{max}\) and the angular motion limit of the motion platform.  
\[M_{L}=\delta A_{max}\,\ \ if\ A_{max}\geq M_{L} \tag{9}\]  
Figure 3: Principle of the SSM.  
Figure 2: Structure of the proposed washout algorithm.  
where \(M_{L}\) is the kinematic limit of the motion platform, and \(\delta(0<\delta\leq 1)\) is a scale constant representing the ratio between \(A_{max}\) and \(M_{L}\). The constraint condition to restrict the rotational angle within \(M_{L}\) is defined as  
\[A_{S}=(A-kA_{max})k+kA_{max}\ \leq\ \delta A_{max} \tag{10}\]  
Equation (10) is rewritten as  
\[2k-k^{2}\leq\delta \tag{11}\]  
Equation (11) is the constraint condition to select scale parameter \(k\). Figure 4 shows relations between \(k\) and \(\delta\). If the user selects \(\delta\) in consideration of the maximum angle value of the vehicle and the mechanical limit value of the motion system, the user can select the scale variable \(k\), which the user can set to the maximum. For example, if \(A_{max}=10\) and \(\delta=0.7\), \(k\) that does not exceed the kinematic limit can be set to maximum 0.4523. Figure 5 shows the scaled tilt angle according to the change in the value of \(k\).  
Figure 4: Relation of \(k\) and \(\delta\).  
Figure 5: Example of rotational angle according to value of \(k\).