## 2 Proposed System
### Environmental Disinfection  
The CONNOR UVC Disinfection Robot [29], Xenex Disinfection Services LightStrike [30], TmiRob [31], XDBOT [32], and Siemens and Aucma Co., Ltd's disinfection robots [33] represent existing commercial disinfection systems. In comparison to these systems, our solution offers several advantages. We utilize 3D cameras to create detailed maps of the environment. Beyond having UVC lights on the robot's body, our system is equipped with UVC lights on a six-axis robotic arm, allowing for flexible and precise surface coverage, especially in complex environments. Moreover, we introduce a dosage estimation method to achieve uniform and effective disinfection by spreading appropriate dosage to each area. The proposed system aims to achieve even disinfection for the entire environment, which is then validated via the assessment of UVC irradiation dose. The UVC lamps are equipped on both the mobile platform and robotic arm of the mobile robot manipulator, with the former used for disinfection in the open area and the latter for objects with complex surface contours that usually lead to blind spots. Therefore, the proposed system should enable the mobile robot manipulator to autonomously explore unknown environments and objects, build the corresponding maps for both the mobile platform and the robotic arm, and then segment them for path planning, obstacle avoidance, and object contour following. Figure 7 shows the system block diagram for environmental disinfection. As the navigation of the mobile platform is applied to the open area, the system utilizes the Lidar and the technique of 2D SLAM to obtain a 2D map of the environment, which is then sent to the developed navigation scheme for path planning [23]. The GMapping algorithm is adopted to serve for 2D SLAM, as it is effective and accurate enough for this application [34]. The robotic arm is activated when an object in the environment is detected. To let it be able to follow the contour of the object for disinfection, the system utilizes the depth camera and that of 3D SLAM to derive a 3D map. The Real-Time Appearance-Based Mapping (RTABMap) algorithm is adopted for 3D SLAM [35], which fits well with the 3D data acquired from the depth camera. Figure 8 illustrates the process of constructing a map for a laboratory environment using RTABMap. Specifically, Figure 8a displays the input captured using the depth camera, while Figure 8b exhibits the resulting point cloud map. With the 3D map available, the system then adopts the Probabilistic Roadmap (PRM) and Nearest Neighboring (NN) algorithms to determine an effective and collision-free disinfection path, among several possible choices [36; 37]. To ensure that the UVC irradiation is enough for the entire object, the robotic arm will stay on the same location of the path until the estimated intensity reaches the preset amount. We came up with a method for estimation based on that in [38], while further considering the pose of the UVC lamps so that the effect due to the incident angle of the irradiation can also be included in computing the received intensity on the surface, as  
Figure 7: System block diagram for environmental disinfection. described below. For each point light source along the UVC lamp, the generated irradiation d\(E\) can be derived as  
\[\text{d}E=\frac{\Phi_{E}}{4\pi L}\frac{1}{\left(x^{2}+y^{2}+\left(z-\ell\right)^ {2}\right)}\text{d}\ell\hat{r}\cdot\hat{n} \tag{6}\]  
where the center of the lamp is set to be the origin, its length and irradiation intensity are denoted as \(L\) and \(\Phi_{E}\), respectively, the point light source and its distance to the origin are denoted as d\(\ell\) and \(\ell\), the vector from the point light source to the point \(r(x,\,y,\,z)\) under estimation is denoted as \(\hat{r}\), and the unit normal vector of \(r\) is denoted as \(\hat{n}\). The lamp is placed along the \(z\)-axis, with the robotic arm moving along the \(x\) direction.