# Design and Experiment of a Novel Facade Cleaning Robot with a Biped Mechanism
## 2 Development of Biped Robot
### Biped Robot Design  
Our strategy consisting of the biped mechanism and its control system has been described. In this section, specifications of the biped robot are analyzed quantitatively, and the development of the biped robot is shown. Figure 3 is a CAD design of the biped robot. Each foot unit includes a cleaning unit, a suction cup, a vacuum pump, a seal mechanism, a valve to break vacuum, and servo motors for joint actuation. The morphology adopts a parallel linkage mechanism that keeps the foot unit of the robot and the glass surface parallel without any control system. That is, since the degree of freedom of the system is able to be decreased, the number of actuators for locomotion can also be decreased. Hence, adopting a parallel linkage mechanism provides an advantage in terms of weight saving. Weight saving is important because it allows one to decrease the amount of energy needed to maintain the robot's weight. The area of both the adhesion/sealing mechanism and the driving mechanism are separated. This separation provides two advantages: the driving range in the rotational direction is extended, and maintenance is easy. Since only one attachment is required between each part, hardware updates in the future will be easy. Support parts, such as legs, can be installed onto the adhesion component. The support parts are pushed to the glass surface when the suction cup is in vacuum mode. This makes the robot robust against glass surfaces. Figure 1: Two key points that need to be addressed. Figure 2: A biped robot adapts to distinct window frames. The process of our strategy is illustrated from (**1**) to (**5**). Figure 4 shows a schematic figure of the designed robot. The designed robotic system can be supposed as a simple two-link manipulator in a vertical plane on the arm. The origin is set on the center of the supporting leg, and the center of the idling leg \((x_{h},y_{h})\) is  
\[ \begin{cases}x_{h}=l(\cos\phi_{1}+\cos\phi_{2})+2d,\\ y_{h}=l(\sin\phi_{1}-\sin\phi_{2})\end{cases}  \tag{1}\]  
where \(l\) [cm] and \(d\) [cm] represent the length of the link and the distance between the center of the foot to the joint, respectively. The angles of each link \(\phi_{\{1,2\}}\) are limited within Equation (2) as a result of the installation of the parallel linkage mechanism:  
\[\frac{\pi}{4}\leq\phi_{\{1,2\}}\leq\frac{3\pi}{4}. \tag{2}\]  
Figure 4: A schematic figure of a vertical plane of the arm of the designed robot. Figure 3: CAD design of the robot. Each foot unit includes a cleaning unit, a suction cup, a vacuum pump, a seal mechanism, a valve to break vacuum, and servo motors for joint actuation. The robot installs a parallel linkage mechanism to keep the foot unit of the system and the glass surface parallel without any control system. From Equation (1) within Equation (2), the theoretical movement range of the model is shown in Figure 5, where the actual movement range is smaller than Figure 5 due to collisions between the foot units. On the basis of Figure 5 and Equation (1), the robot is capable of moving \(\pm 13.66\) cm along the \(z\) axis and \(22.54\) cm along the \(x\) axis. In the case of the X-Y stage type, its movement range depends on one of its actuators. On the other hand, biped type robots, like the designed robot, can obtain enough movement range, even though one of the actuators is limited, since it mainly depends on its mechanism and link lengths. The MX-106T and the RX-28 Dynamixel Robot Servo Actuator were adopted for driving actuators and were utilized as a base actuator and an arm actuator, respectively. Table 1 shows their specifications. Regarding the base actuator, the required torque \(\tau_{b\{1,2\}}\) [Nm] for driving is obtained by Equation (3), based on a simplified model shown in Figure 6.  
\[\tau_{b\{1,2\}}\geq m_{\{2,1\}}g(2d+l_{1}\cos\phi_{1}+l_{2}\cos\phi_{2})\cos \theta_{b\{1,2\}}. \tag{3}\]  
From Equation (3), if \(\theta_{b\{1,2\}}=\phi_{\{1,2\}}=0\) rad, the required torque becomes maximum.