# Manipulator Control of the Robotized TMS System with Incurved TMS Coil Case
## 1 Introduction  
Transcranial magnetic stimulation (TMS) is a non-invasive and safe technique that induces a current in the brain by passing a brief and high-intensity magnetic field generated by a magnetic coil [1, 2, 3]. This technique is used in various areas such as brain mapping [4, 5, 6, 7], studying brain-behavior relationships [6, 8, 9], and medical therapeutic applications [3, 10, 11]. A professional operator usually manipulates the TMS coil manually. However, adjusting the TMS coil by hand is limited in for reducing the error between the coil position and the target stimulation point. This error affects significantly TMS responses like the motor-evoked potential (MEP) and the TMS-evoked potential (TEP). In other words, the subjects may receive weaker stimulation to their brain by a small error [12]. Meanwhile, because each TMS session progresses for tens of minutes [13, 14], it is difficult to compensate for the head movement of the subject by continuously holding the coil using a hand. Additional devices can be used [15, 16] to solve this problem. However, because these devices make subjects uncomfortable owing to their poor wearing sensation, they cause stress. Sincethis stress makes subjects secrete cortisol, which affects neuronal activity [17], it can cause variability in the efficacy of the TMS [18; 19]. To overcome these shortcomings, the robotic TMS system in which a robot manipulator controls the TMS coil has been proposed [18; 20; 21; 22; 23; 24; 25; 26; 27]. As robot manipulators have a high positioning accuracy and repeatability, they can improve the coil positioning accuracy. Furthermore, because the neuronavigation of the robot's TMS system can estimate the subject's head position and the target stimulation site, the operator does not have to continuously adjust the coil manually for a long time. Some studies used the force/torque control strategies of a robot manipulator, which are methods to regulate the contact force between the robot manipulator's end-effector and the environment, to improve robotized TMS systems. The first case is that of [PERSON] [26]. Using adaptive force control and a neuro-fuzzy algorithm, he composed a system that can track slight head movement and improve safety. In the same year, [PERSON] et al. [22] suggested a method for controlling the interaction force between the coil and the subject's head by moving the coil in the direction of the end-effector of the robot manipulator or in the opposite direction. [PERSON] et al. [27] used a hybrid position/force control to maintain a constant interaction force between the head and the coil while compensating to ensure the position error. [PERSON] et al. [21] used impedance control for the safe interaction between the coil and head. This study used hybrid position/force control and proportional torque control, which generates the torque proportional to the torque error between the current and desired torque, taking into account the shape of the TMS coil. The coil we used in this study has an incurred shape, as shown in Figure 1, and we will utilize that characteristic. As the coil is curved and the human head is round, the contact area between them increased. This increases friction and reduces the instability caused by oscillations generated from sensor measurement noise or control signal disturbances. It also causes greater surface friction between them, physically prohibiting the slight head movement. And, because the surface contact reduces the distance between the coil and head, the magnetic field for stimulation is less affected by the slight head motion. However, the larger surface contact area also makes it difficult for the coil to compensate for the error between its current and target treatments with small force because of the larger friction while changing the force direction commanded by the robot controller. This problem was solved by scheduling the magnitude of the force. Proportional torque control is also applied to create a contact area between the coil and the head near the center of the coil.