## 3 Decomposition and Design of Basic Actions
### Basic Actions on Stairs  
As mentioned before, the stair-climbing motion is inspired by humans' alternating action. However, the alternating action is a combination of a series of basic actions. To realize stair-climbing, four cases of moving upstairs are illustrated in detail as examples, shown in Figure 4, and they are explained below. For the stairs, the width and the height of the step are indicated as \(w\) and \(h\), respectively.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Description of Scenes** & **Velocities** \\ \hline On the road: Car-like movement with longitudinal & \\ velocity and steering speed & \(v_{x}=0\), \(v_{y}=v\), \(\omega\propto\omega_{stearing}\) \\ \hline Indoors: Omnidirectional movement & No limit \\ \hline Spot steering: Rotation around the center of the & \(v_{x}=0\), \(v_{y}=0\), \(\omega\propto\omega_{stearing}\) \\ robot’s chassis until it is perpendicular to the stairs & \(v_{x}=0\), \(v_{y}=0\), \(\omega\propto\omega_{stearing}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Moving models in different scenes.  
Figure 4: The actions for stair-climbing. Case I: the actions when the front wheels are close to the step; Case II: the actions when the front wheels and/or the wheel-legs are close to the step; Case III: the actions when the EH A cannot touch the upper step; Case IV: the actions when only the wheel-legs are close to the step.  
**Case I:** The two front Mecanum wheels are close to the step, and the robot cannot go forward (see Case I(a)). Therefore, to continue the stair-climbing process, as shown in Case I(b), EH A and EH B on the tetrapod start stretching (action 1), lifting the robot up until the button of the front wheels and the wheel-legs is higher than the upper step. Then, the chassis frame slides forward until the front Mecanum wheels and the wheel-legs reach their new step (action 2). As shown in Case I(c), EH A and EH B start shortening (action 3), leaving the wheel-legs to keep the balance of the chassis frame (action 4).  
**Case II:** In this case, both front Mecanum wheels and/or the wheel-legs are close to the step. The actions are almost the same as those in Case I, except some preconditions are different. These preconditions are further discussed in the next section.  
**Case III:** The front Mecanum wheels still have space to move forward until they are close to the step (action 1). However, EH A cannot touch the upper step; thus, the tetrapod slides forward along the rails (action 2). Finally, EH A and EH B on the tetrapod start stretching (action 3).  
**Case IV:** In this case, only the wheel-legs are close to the step. Therefore, the wheel-legs (also EH C) are shortened by \(h\). If there is still a step in front of the wheel-legs, the robot needs to firstly deal with it as described for **Case II**. Then, after the tetrapod is ready, the wheel-legs start shortening (action I), and the chassis frame slides forward (action 2). Finally, EH A and EH B are shortened so that the four Mecanum wheels land.  
The process of moving downstairs is basically the inverse process of moving upstairs. In other words, the execution sequence of each case above starts from (c) and ends with (a), and the movement direction is also inversed. However, to avoid the risk of falling down, the detection of being \"close to the step\" when going upstairs is changed to the detection of being \"close to the edge of the step\". Every time the robot's front and rear ends are close to the edge of the step, the robot must stop moving using the wheels immediately. Then, the tetrapod helps the chassis frame to land on the lower step safely. In a similar manner, the basic actions of moving downstairs can also be established, which can be denoted as Case I', Case II', Case III', and Case IV'.  
By combining the aforementioned cases according to the different preconditions, the stairs with different steps can be dealt with. The preconditions and the combinations are discussed in the next section.