# Controllable Height Hopping of a Parallel Legged Robot
## 2 Robotic System Design  
This section depicts the design thought of the actuation, mechanism and control hardware system. The robot prototype is shown in Figure 1a. As in the figure, the robot was limited in vertical slide guides to realize vertical hopping, and a laser range finder was fixed on the top of the guides to measure the height of robot trunk. The two main requirements in actuator design are high output torque density and high transmission transparency. As introduced in Section 1, the actuator design schemes involving hydraulic and direct-drive motors both have weaknesses. Therefore, scheme of BLDC motor and reducer with appropriate ratio is an optimal approach. In the reducer selection, in contrast to both planetary and cycloidal gear reducers, the harmonic reducer has a lower weight while providing the same ratio. In terms of the actuator feedback system, two main methods are used to realize high-performance torque control on legged robots: torque sensor feedback and motor current feedback control. However, torque feedback such as SEA (series elastic actuator), which is used in many legged robot [24, 25], requires an extra elastic feedback unit that has a non-negligible mass and causes unavoidable vibration. Thus, we used motor current feedback as proprioceptive control in our design. In terms of our development target, the main aim of our actuation design is to realize output torque control directly with motor current feedback. Through numerical simulation, we found that a 5.5 kg robot jumping to 1.5 m height with a constant vertical acceleration needs maximum torque about 95 Nm and maximum rotational speed about 100 rpm (joint speed). According to such requirements, we selected a self-developed BLDC motor and a harmonic reducer with a ratio of 1:31 as our actuator. The actuator structure is shown in Figure 1b. Based on this design, the maximum output torque of the actuator can reach 124 Nm theoretically, maximal rotational speed over 4000 rpm, and power density 808.82 W/kg, which is sufficient output for robot's high jumping. Compared with MIT Cheetah's large-radius actuator, our design has smaller radius and higher torque-radius ratio of the whole module (details in Table 1), which is more compact for multi-joint robot system [8, 9]. To validate linearity and transparency of the actuator, a simple test facility was set as shown in Figure 2a. According to the input current-output torque relation in Figure 2b, we can conclude that the actuator has a certain transparency in action, while it is still different from the ideal condition. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Total Diameter** & **Reduction Ratio** & **Max. Output** & **Max. Torque-** \\  & **(mm)** & **Torque (Nm)** & **Radius Ratio** \\ \hline
**MIT Cheetah** & 125 & 1:5.8 & 174 & 2.8 \\
**This paper** & 70 & 1:31 & 124 & 3.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance parameters comparison of actuator between MIT Cheetah and our design. Figure 1: (**a**) Robot prototype; and (**b**) structural profile of actuation module. As for structural design, compared with the serial mechanism leg, the parallel leg offers several advantages. First, the knee joint actuator rotates relative to the trunk in the parallel case rather than relative to the thigh, which causes extra inertia for the hip joint. Second, on our robot, as identical thigh and shank lengths were selected for the maximum vertical movement range [23], we found that parallel mechanism has similar torque and speed requirements for the two active joints during the vertical jumping simulation. Thus, we could use two same actuators in active joints. The details of the structure comparison and jumping simulation results are shown in Figures 3 and 4. More comparative analyses of parallel and serial structure of legged robot are presented in another paper [26]. Previous research has shown that the ideal mass ratio of the leg involves a large trunk mass and a lower leg mass [27].