## Materials and Methods
### MRVF Tele-Welding System Overview  
In this study, we investigated the impact of an integrated visual/haptic perception in MR on a natural, 3D motion mapping, enhanced immersive, and intuitive tele-welding process. Figure 2 shows the MR-incorporated virtual fixture (MRVF) telerobotic system consisting of four main elements--(1) the welding robot and visualization system; (2) the haptic master robot; (3) the MR workspace implementation; (4) the robot and operator space communication implementation.  
The remote robotic welding platform consisted of a UR5 industrial manipulator with six degrees of freedom (DOF), gas metal arc welding (GMAW) equipment, welding camera, and auto-darkening filter. The UR5 industrial manipulator was equipped with an arc welding torch to perform the remote welding process, as shown in Figure 3. A monocular Logitech C615 webcam (Logitech International S.A, Lausanne, Switzerland) with an auto-darkening lens was mounted on the robot to observe the welding process and provide the operator with a direct view of the workpieces. A robot operating system (ROS) middleware-supported driver for the UR5 robot ran on a computer with an Ubuntu 16.04 operating system. The Ubuntu computer was equipped with an i7-10700 CPU, 64 GB RAM, and GeForce RTX 2060 graphics to command the UR5 robot controller through TCP/IP and process the on-site welding streams. The TCP/IP-based ROS communication protocol was capable of fast control rates at 125 Hz, which is sufficient for teleoperated robotic welding tasks, where real-time control is required.  
A PHANToM Omni haptic robot (SensAble Technologies Inc., Woburn, MA, USA) was utilized as the motion input device to remotely operate the welding robot in a manual welding manner. The MRVF system features velocity-centric motion mapping (VCMM) from the user's hand movements to the robot motions and enables spatial velocity-based control of the robot tool center point (TCP). The welder uses the stylus of the haptic robot with the same motion and manner as when performing manual welding. This approach enables intuitive and precise user control of the position and orientation of the UR5 end  
Figure 1: The hardware components of the GMAW motion tracking platform. (**a**) Welding motion-tracking platform, including welding shelter, welding torch, and the attached motion tracker; (**b**) an unskilled welder performing manual welding for motion data collection and analysis; (**c**) a professional welder performing on-site GMAW operation for expertise and skill extraction.  
effector to achieve the desired travel speed, and travel/work angles as if the user was directly present.  
The operator space for the MRVF tele-welding consisted of an HTC Vive HMD and 27-inch monitor connected to a desktop with an i7-8700k CPU, 32 GB RAM, and a GeForce GTX 1080 graphics processor. The immersive MRVF environment was generated in Unity 3D to display an integrated 3D visualization with overlaid monoscopic image streams and corresponding haptic feedback during the welding process. The ROS bridge provided a network intermediate, enabling the exchange of messages between nodes, and it was used to establish communication between the master and slave robot sides.