## 1 Introduction  
Pouring processes in the casting industry can be dangerous to workers because they perform the task of handling molten metal with extremely high temperatures. Accordingly, the need for automation of the pouring process has promoted improvements in the work environment in this context [1, 2, 3, 4]. A tilting-ladle-type automatic pouring machine, where molten metal is poured into the mold by tilting the ladle automatically, is employed as one such automated pouring process. It can be installed relatively easily as part of the pouring process because it essentially employs the same pouring method as a manual handling of this task [5]. As a control system for the tilting-ladle-type automatic pouring machine, the teaching-and-playback control approach has been practically applied [6, 7, 8]. The pouring process requires the precision pouring of molten metal into the pouring basin of the mold to improve productivity and user safety. However, doing so can be difficult because the pouring flow rate is indirectly changed by tilting the ladle [9, 10, 11]. Furthermore, the molten metal can spill from the mold due to the falling trajectory of the outflow liquid varying in accordance with the flow rate changes. To solve these problems, control technologies have been developed to improve pouring precision. The sloshing suppression controls of the liquid in the ladle were developed for suppressing the liquid vibration while the liquid is poured into the mold [12; 13]. For keeping the pouring mouth of the ladle in a fixed position, a forward-and-backward and an up-and-down motions of the ladle were controlled synchronously to the ladle tilting [12]. Moreover, the sloshing caused in the ladle's back-tilting-motion was suppressed by the input shaping approach in which the input command is shaped for generating the anti-phase sloshing in [12; 13]. The sloshing caused in the pouring motion was modeled simply by a pendulum model in [14; 15]. In addition, the sloshing was suppressed by combining the partial inverse dynamics approach and PID controller. The parameters of PID controller was designed using the metaheuristic search algorithm. The sloshing in the liquid container handled by a robotic manipulator was modeled by a spherical pendulum model in [16; 17]. For suppressing the sloshing, the reference trajectories with the container's position and orientation were shaped by an exponential filter, the parameters of which were designed using the spherical pendulum. The sloshing caused in the ladle's forward-tilting-motion was suppressed by making the angular velocity in the ladle's tilting motion smaller [18]. The control system for the liquid height in the pouring basin was constructed using the audio vibration sensing and the deep neural network [19]. The neural network in the pouring robot system was trained with a real-world pouring dataset with multi-modal sensing data, which contains more than 3000 recordings of audio, force feedback, video, and trajectory data of the human hand that performs the pouring task. The pouring skill of human was emulated by the robot with the haptic device using the parametric hidden Markov model [20]. In this approach, the human tele-operated the robot using a haptic device, and data from the demonstrations were statistically encoded by a parametric hidden Markov model. The Gaussian mixture regression was used at the reproduction in the robotic playback motion. The angular velocity of ladle tilting was optimized using the optimization approach with a Computational Fluid Dynamics (CFD) simulator for suppressing the casting defects [21]. The flow-rate feedforward control, based on the mathematical model of the pouring process, was developed in [22]. The falling position control of the liquid outflow from the ladle was developed to achieve precise pouring of the liquid into a steady position inside the pouring basin of the mold [23]. Additionally, a control method for positioning the ladle as low as possible while pouring the liquid was proposed in [24].