# Bi-Objective Function Optimization for Welding Robot Parameters to Improve Manipulability
## 1 Introduction  
The hull of a ship is an enclosed space composed of double bulkheads, known as a double hull [1]. The interior of the double hull consists of transverse plates (Trans) and longitudinal plates (Longi). By shortening the outer hull plate, the plates are perpendicular to each other, creating a U-shaped weld seam as shown in Figure 1. This is called a U-cell. Depending on the presence or absence of a collar plate, additional vertical welding lines may be created, which are divided into front and back sides and require new work motions. There are cases where a mobile platform-type robot [2] controlled by a wireless PDA (personal digital assistant) [3] has been applied to weld the U-cell section within such an enclosed area, or in an open block state that is not sealed or a gantry in a small member welding area. It was also applied by installing a vertical articulated robot on the structure [4; 5]. The robot's work commands are executed by an OLP (offline program) [6], or, if the system is connected online, tasks are created using CAD (computer-aided design) data and sensor data [7]. The welding automation solutions introduced earlier are applicable only in open blocks or fail to be applied because the equipment is too heavy to be used in enclosed areas. The welding robot introduced in this paper is a six DOF (degree of freedom) vertical articulated robot with a self-weight of 15 kg and a payload of 3 kg. This robot is carried by a person into an enclosed area, installed inside the U-cell, and performs welding work through the OLP of the teaching manipulator. When a person selects the shape of the work object on the OLP and enters the approximate dimensions and welding conditions, the robot moves near the weld line to find the weld line and then obtains accurate weld line information through touch sensing. On this work path, singular points occur dependingon the robot's posture. If the number of stops to avoid these increases, the overall work time increases and efficiency decreases. In this study, we wanted to calculate the robot's manipulability for the task motion and find design parameters that do not have outliers in the task path. Generally, research on robot operability analyzes the operability of joint robots [8,9], constraints on operability and trajectory for flat manipulators [10,11], path planning in a direction with good robot operability [12,13], and control to optimize the manipulability of a surgical serial vertical joint robot. Research cases include the optimal structure design of a serial joint robot based on posture manipulability [14,15]. Still, there are few papers on the optimal design of mechanisms to improve robot operability. In this paper, we establish a procedure for the optimal design of the robot parameters, simulate the PID (proportional-integral-derivative) position control environment with a CLIK (closed-loop inverse kinematics) algorithm [16,17] to which a WLN (weighted least norm) solution [18] is applied, and simulate the tracking error that may exist in the actual robot. The PID controller gain tuning discussed in this paper does not involve the use of an optimization algorithm [19,20]. In actual industrial settings, engineers manually tune the gains by individually manipulating each axis of the robot, similar to the approach adopted in this paper for gain tuning. In welding operations, there is minimal external force applied to the workpiece (non-contact), and the process is carried out at a slow speed of 15-30 CPM (centimeters per minute). Furthermore, due to the minimal disturbance factors in the external environment, this paper did not address dynamic models for path generation. As a constraint for optimal design, a geometric inverse kinematics solution exists in the posture conditions required for the robot along the work path, so that the solution to be derived can be meaningful in the position control area. In the case of the objective function, the bi-objective function is set to improve both linear velocity manipulability and angular velocity manipulability.