## 2 Methods
### Definition and Calculation of the Fitness
#### 2.3.2 Environment Fitness  
The concept of environment fitness refers to the ability of the robot to adapt to the lunar environment. \[EF(ro,te,mp,lt)=P(ro,te,mp,lt)[S(ro,te,mp,lt)+V(ro,te,mp,lt)] \tag{5}\]  
\(EF(ro,te,mp,lt)\) represents the terrain fitness of the robot \(ro\) in the environmrmt with the type \(te\) of terrain, with the map \(mp\) and light \(mp\). Where \(te\) represents the type of topography, it may be one of four types, including powdery, rocky, undulating, and unknown. \(mp\) represents the degree of unpredictability of the map of the task region, which may be of one of two types, including the case where only the coordinates are known but no detailed map is, and the case where the detailed map with the coordinates is known. \(lt\) is the intensity of the light \(lt\), divided into two types, dark and bright. The passability, stationarity, and speed of the robot \(ro\) in the environmrmt with the type \(te\) of terrain are denoted by \(P(ro,te,mp,lt)\), \(S(ro,te,mp,lt)\), and \(V(ro,te,mp,lt)\), respectively. It is worth noting that \(EF(ro,te,mp,lt)\) is calculated using (5) only if \(te\) is known. The parameters are defined and computed as follows. The passability \(P(ro,te,mp,lt)\) is defined as 1.0 when the robot \(ro\) is able to pass through the terrain \(te\) with the map \(mp\) and light \(mp\) successfully. \(P(ro,te,mp,lt)\) is defined as 0.0 when the robot \(ro\) is not able to pass through \(te\) at all. The stationarity \(S(ro,te,mp,lt)\) is calculated through the Sperling equation, which represents the stability when the robot is moving. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \begin{tabular}{c} **Astronaut** \\ **in the** \\ **Capsule** \\ \end{tabular} & \begin{tabular}{c} **Astronaut** \\ **Outside the** \\ **Capsule** \\ \end{tabular} & \begin{tabular}{c} **Small** \\ **Exploration** \\ **Robot** \\ \end{tabular} & \begin{tabular}{c} **Large Recue** \\ **Robot** \\ \end{tabular} & \begin{tabular}{c} **Material** \\ **Transport Robot** \\ \end{tabular} & \begin{tabular}{c} **Lunar** \\ **Rover** \\ \end{tabular} \\ \hline \multirow{3}{*}{\begin{tabular}{c} Ground \\ Exploration \\ \end{tabular} } & Terrain Detection & \(\surd\) & \(\times\) & \(\surd\) & \(\times\) & \(\times\) & \(\times\) \\  & Path Planning & \(\surd\) & \(\times\) & \(\surd\) & \(\times\) & \(\times\) & \(\surd\) \\  & Obstacle Avoidance & \(\times\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline \multirow{3}{*}{Robot Rescue} & Positioning Robot & \(\surd\) & \(\times\) & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) \\  & Trouble Shooting & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) & \(\times\) & \(\times\) \\  & Moving Robot & \(\times\) & \(\times\) & \(\times\) & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} Material \\ Transportation \\ \end{tabular} } & Lifting Material & \(\surd\) & \(\surd\) & \(\times\) & \(\times\) & \(\surd\) & \(\times\) \\  & Moving Material & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\surd\) & \(\surd\) \\  & Lowering Material & \(\surd\) & \(\surd\) & \(\times\) & \(\times\) & \(\surd\) & \(\times\) \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Lunar surface \\ samples \\ \end{tabular} } & Trajectory Planning & \(\surd\) & \(\surd\) & \(\times\) & \(\times\) & \(\times\) & \(\surd\) \\  & Cutting Operation & \(\times\) & \(\surd\) & \(\times\) & \(\times\) & \(\surd\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The agents’ ability in LSO tasks. Figure 4: Task fitness of different agents. \[S(ro,te,mp,lt)=2.7\sqrt[10]{a^{3}f^{5}Fc(f)}=0.896\sqrt[10]{\frac{3}{f}Fc(f)} \tag{6}\]  
where \(a\) is the amplitude of robot moving. \(j\) is the acceleration of amplitude, \(f\) is the frequency of vibration, and \(Fc(f)\) is the correction factor of frequency. \[Fc(f)= \begin{cases}0.8f^{2}&f=0.5\,\sim 5.4\;\mathrm{Hz}\\ \frac{650}{f^{2}}&f=5.4\,\sim 26\;\mathrm{Hz}\\ 1&f>26\;\mathrm{Hz}\end{cases}