Development and validation of a novel calibration methodology and control approach for robot-aided Transcranial Magnetic Stimulation (TMS)

Abstract

Objective

This paper presents the development and validation of a new robotic system for Transcranial Magnetic Stimulation (TMS), characterized by a new control approach, and an ad-hoc calibration methodology, specifically devised for the TMS application.

Methods

The robotic TMS platform is composed of a 7 dof manipulator, controlled by an impedance control, and a camera-based neuronavigation system. The proposed calibration method was optimized on the workspace useful for the specific TMS application (spherical shell around the subject’s head), and tested on three different hand-eye and robot-world calibration algorithms. The platform functionality was tested on six healthy subjects during a real TMS procedure, over the left primary motor cortex.

Results

employing our method significantly decreases (p < 0.001) the calibration error by 34% for the position and 19% for the orientation. The robotic TMS platform achieved greater orientation accuracy than the expert operators, significantly reducing orientation errors by 46% (p < 0.001). No significant differences were found in the position errors and in the amplitude of the motor evoked potentials (MEPs) between the robot-aided TMS and the expert operators.

Conclusion

The proposed calibration represents a valid method to significantly reduce the calibration errors in robot-aided TMS applications. Results showed the efficacy of the proposed platform (including the control algorithm) in administering a real TMS procedure, achieving better coil positioning than expert operators, and similar results in terms of MEPs.

Significance

This work spotlights how to improve the performance of a robotic TMS platform, providing a reproducible and lowcost alternative to the few devices commercially available.

I. Introduction

The last decades have seen the increasing employment of Transcranial Magnetic Stimulation (TMS) to investigate and modulate human brain functions. TMS is a non-invasive and painless technique used to elicit a local stimulation in the cerebral cortex, through an electromagnetic field generated by a coil placed upon the scalp [1], [2]. Depending on the coil shape (e.g. figure of eight or circular), it can stimulate wider or more focal cortical surfaces [3], and it is used for both clinical assessment and research purposes [4], [5]. Usually the TMS is carried out manually by an expert operator who holds the coil on the subject’s head [6]. However, the coil position and orientation above the scalp hugely affect the intensity and the location of the induced current inside the stimulated area [7], [8], [9].

Many efforts have been made to improve the coil positioning, through the employment of neuronavigation systems that guide the operator in placing the coil over the scalp [10]. These neuronavigators are typically made of a stereotaxic system combined with a software for the estimation of 3D models of the scalp and the brain, based on the correlation of the geometrical data of the scalp with average or personal Magnetic Resonance Images. [11]. Despite the introduction of the neuronavigation, accuracy and reliability of the coil positioning are still strongly dependent on the operator skills [12]. Very recently, robot-aided TMS systems have been proposed to improve the accuracy and the repeatability of coil positioning, and to make the procedure more comfortable for both the participant and the operator, while potentially reducing the duration of the experimental session [13], [14], [15], [16], [17], [18]. Although a few systems for robot-aided TMS have been proposed [19], [20], [21], the research on robotic platforms for TMS is still an open topic to be investigated.

The aim of this paper is to develop and validate a new robot-aided TMS system, characterized by a new control approach and to propose a calibration procedure tailored on the specific application. The robot-aided TMS platform is based on the integration of a 7 degrees of freedom (dof) robotic manipulator and a stereotaxic neuronavigation system. The control approach is based on an impedance controller, which guarantees to achieve both high coil positioning accuracy and high safety of interaction.

The innovative approach relies on an ad-hoc method for system calibration, needed to align the data coming from the neuronavigation system to the robot base reference frame.

In robotics the calibration between a camera-based system and a robotic manipulator is a well-known problem, called toolflange and robot-world calibration [22], [23], [24], [25], [26], [27], [28]. From a mathematical point of view, the problem can be solved by finding a solution to a matrix equation of the type MX = YN, where all the matrices are 4x4 homogeneous transformations in the SE(3) space. In particular, M represents the robot end-effector pose expressed in the robot base frame, N is the coil pose expressed in the camera base frame, and X and Y are two unknown transformations between the endeffector and the coil frames, and the robot and camera base frames respectively [29], [30], [31].

Several approaches are effective to solve it for general robotic applications, but none of them takes into account the constraints imposed by our specific target application, i.e. the TMS (e.g. the specific shape and the limited dimension of the useful workspace) [32], [33], [34].

Conversely, the calibration strategy we developed is specifically devised for TMS application, by constraining the calibration points inside the useful TMS workspace. To validate the novel strategy, we tested three calibration algorithms proposed in literature in different contexts (e.g. aerial vehicle applications, etc.) [29], [30], [34].

The developed system, employing the novel control approach, was then validated in real TMS sessions on healthy subjects, assessing its performance in term of position and orientation error positioning the coil and the amplitude of the elicited Motor Evoked Potentials (MEPs) [35].

The paper is organized as follows: section II-A focuses on the twofold problem addressed in the manuscript, i.e. the calibration and the control approach; in section II-B and II-C the calibration algorithms and the new methodology are presented; section II-D describes the developed TMS robotic platform and the adopted control algorithm. Section III-A and section III-B depict the experimental setup and the experimental protocol, whereas in section III-C the data analysis is described. Results are presented in section IV and discussed in section V. Finally, section VI summarizes the main results of this work, outlining the research impact and the possible future developments and perspectives.

II. Materials and Methods

A. Problem statement

Robot-aided TMS platforms can be either ad-hoc designed or devised integrating built devices in a unique system; typically, the integration is made of: robotic manipulator, neuronavigation software with a stereotaxic system, TMS stimulator with coil and a workstation (Fig. 1). The aim of a robot-aided TMS platform is to hold and move the coil on the subject’s head, compensating for her/his movements to keep the stimulation point constant, with the correct coil orientation. To achieve this objective, we need to address two problems: i) calibrating the camera-based neuronavigation system (the gold standard to identify the stimulation point and to monitor the coil position so far) and the robot to obtain a common reference system; ii) controlling the robot to follow the stimulation point on the scalp, while guaranteeing subjects safety.

Fig. 1.

Scheme of the proposed robot-aided TMS system: on the left side the robot holds and moves the attached coil on the subject’s head; the head and the coil are tracked by the camera thanks to the markers placed on them. On the right side the camera is placed so that its volume of capture overlaps the robot workspace. In the center, the main control application receives data from the robot and from the camera, through the neuronavigation software, and sends to the robot the computed motor commands, to keep the coil in the right pose with respect to the head, according to the stimulation point set in the neuronavigator.

1. Hand-eye and robot-world calibration

The calibration of the robot-aided TMS system, composed of a robot holding the coil and a stereotaxic system for neuronavigation, can be addressed as a two-frame sensor calibration problem, also called hand-eye and robot-world calibration. The hand-eye and robot-world calibration results in a single reference system for all the devices integrated in the platform (i.e. robot, coil and camera). Thus, it allows to control the robot even when the coil is not visible by the camera: for example, when the target is located in posterior areas. The main disadvantage is the need to keep the camera and robot base fixed, conversely to alternative approaches (i.e. the one employed by Axilum) that simultaneously neuronavigate all the items, with the possibility to move the system’s elements without affecting the control. We selected the first approach to achieve better online control performance; the need to keep the items fixed is negligible since the robot base is usually already fixed and, thanks to the possibility to control the system even with the coil not visible, the camera movement is unnecessary during the stimulation session.

Referring to Fig. 2, the equation relating the coil pose measured in camera frame (^bCT_c) and the robot end-effector pose measured in robot frame (^bRT_EE), can be expressed as:

$${}^{bR}{T}_{EE}{}^{EE}{T}_c={}^{bR}{T}_{bC}{}^{bC}{T}_c$$ (1)

and it could be generalized in the aforementioned equation MX = YN, where M represents the end-effector pose with respect to the base frame (^bRT_EE); X is the transformation ^EET_c between the robot end-effector and the attached coil reference frames; Y represents the transformation ^bRT_bC between the robot base and camera base reference frames; N is the coil pose expressed with respect to the camera base frame (^bCT_c). All the aforementioned matrices are 4x4 homogeneous transformation matrices in the SE(3) space. Solving that problem means to compute the unknown transformation matrices X and Y.

Fig. 2.

Experimental setup and scheme of the system reference frames: on the left side the Panda robot (1) with the 3D printed flange and the coil (2) attached and connected to the coil item (3); on the right side the Polaris Vicra camera (4). The camera and the robot are connected to a PC (5) through an USB and an Ethernet cable, respectively. Subject’s head (6) with the head reference item attached and visible to the camera allows the SofTaxic Optic software to work. S_bR, S_EE, S_c, S_h and S_bC are the reference frames of the robot base, end-effector, coil, head and camera base, respectively. ^jT_i is a 4×4 homogeneous transformation matrix between the j and i reference frames. The equation representing the system could be synthetically expressed as an hand-eye and robot-world calibration problem: MX = YN.

2. Robot control

Regarding the robotic platform (scheme in Fig. 1), once the stimulation point is selected, the aim of the control is to move the coil keeping it on the target regardless to possible head movements, which means to keep the coil pose constant with respect to the head. The constant relative pose between head and coil in the target is mathematically defined as:

$${}^h{T}_c{|}_{target}=const$$ (2)

where T is a 4x4 homogeneous transformation in the SE(3) space between the head (h) and the coil (c) reference frames (see Fig. 2). To make the stimulation effective, the coil should be always tangent to the scalp upon the stimulation point [8], [36]. Moreover, the control approach needs to employ several constraints to guarantee the subject safety, e.g. to keep the contact force under the safety threshold [37].

B. Calibration Algorithms

A typical approach to solve the hand-eye and robot-world calibration problem is a mathematical regression to find the unknown homogeneous transformation matrices X and Y that best fit a set of equations of the type

$$M_{i}X=Y{N}_{i}i=1,\dots ,n.$$ (3)

acquired moving the robot with the attached coil on n different poses. We implemented and tested three algorithms -hereafter briefly described-available in literature to solve a similar problem in different contexts.

1. Stochastic Global Optimization (SGO)

The Stochastic Global Optimization (SGO) method [29], is a two-phase stochastic geometric optimization algorithm, based on the minimization of the last-squares criterion

$$\frac{1}{2}\sum _{i=1}^n{\Vert M_{i}X-Y{N}_i\Vert }^2,$$ (4)

where the || · ||² is defined as ${\Vert P-Q\Vert }^2={\Vert R_P-R_Q\Vert }_F^2+\zeta {\Vert p_P-p_Q\Vert }_C^2.$ P,Q ∈ SE(3) are 4x4 homogeneous transformation matrices, R_P, R_Q ∈ SO(3) are the rotation matrices representing the rotation part of P, Q and p_P, p_Q ∈ IR³ are the translations of the same transformations; the || · ||_F is the Frobenius norm, || · ||_C is the Cartesian norm, and ζ ∈ IR₊ is a weighting factor for the translation component.

This approach allows the localization of the optimal local minimum, achieving the best performance with noisy data. More details on implementation and characteristics of the SGO method can be found elsewhere [29]. In the present study we employ the algorithm with random initial guesses and set the termination criteria corresponding to $\frac{Er}{\omega }<1.05$ with $Er=\frac{\omega (Z-1)}{Z-\omega -2};\omega$ number of local minima; Z = kṡ number of acquired samples; k number of performed iterations and s number of samples per iteration.

2. Non-Orthogonal Method (QR24)

The QR24 method, based on a least-squares approach, let us to simultaneously compute the rotational and translational part, allowing for non-orthogonal calibration matrices in order to deal with real-world localization devices and imperfect robots [34]. Expressing the equation (3) as a system of linear equations:

$$A_{i}w=b_i,i=1,\dots n.$$ (5)

with A_i ∈ IR^12nX24, b_i ∈ IR¹²ⁿ and w ∈ IR²⁴ composed of the non-trivial elements of X, Y, M and N, the aforementioned system (eq. (5)) is solved minimizing the Frobenius norm, through a least-squares approach by means of QR-factorization. Because of the adopted approach and the number of unknown variables that have to be estimated, the method is also called QR24 calibration algorithm. Details on how to transform the eq. (3) into the system of equations in (5) are described in [34].

3. Quaternion approach (QUAT)

The quaternion approach addresses the problem decomposing the Eq. (3) in the rotation and position equations as follows:

$$R_M\cdot R_X=R_Y\cdot R_N$$ (6)

$$R_M\cdot t_X+t_M=R_Y\cdot t_N+t_Y$$ (7)

where R_j is the 3x3 rotation matrix and t_j is the 3x1 translational vector of the j_th 4x4 homogeneous transformation matrix. Since Eq. (6) could be expressed in a unit quaternion form

$$q_M\ast q_X=q_Y\ast q_N,$$ (8)

this method attempts to simultaneously solve for the rotation and translation parts through a Levenberg-Marquardt nonlinear constrained minimization. The error function to minimize is:

$$\begin{array}{r}\hfill f\left(R_X,R_Y,t_X,t_Y\right)={\mu }_1\sum _{i=1}^n{\Vert R_{Mi}{R}_X-R_{Ni}{R}_Y\Vert }^2\\ \hfill +{\mu }_2\sum _{i=1}^n{\Vert R_{Mi}{t}_X+t_{Mi}-R_Y{t}_{Ni}-t_Y\Vert }^2\\ \hfill +{\mu }_3{\Vert R_X{R}_X^T-I\Vert }^2+{\mu }_4{\Vert R_Y{R}_Y^T-I\Vert }^2\end{array}$$ (9)

where the four μ are real positive weight coefficients and ||·||² is an Euclidean norm. The last two terms of the equation represent the constraint for R_X and R_Y to be rotation matrices, i.e. matrices that verify RR^T = I, with I identity matrix. Deeper details on the implementation and features of the quaternion approach can be found in [30].

C. Selection of the Useful Workspace

Although some of those calibration methods have been employed in robotic TMS systems, no specific constraints have been set for their application, which is quite different from other generic robotic tasks.

Typically, in a TMS session, the subject is asked to stay still. Even though the use of a robot allows for small head movements, thanks to the motion compensation, they are still limited. Indeed, the subject is usually sat in the back seat, thus the possible movements are small rotation of the head and limited displacements of the neck. Furthermore, the coil is always placed over the scalp, thus we can assume that the effective workspace of robot movements for this specific application is restricted to a head-centered spherical shell (see Fig. 3a).

Fig. 3.

(a) Sphere workspace concentric to the head, with in yellow the spherical shell useful to the TMS, that takes into account physiological head movements. The bottom and inner parts of the sphere (in red) are excluded. (b) Seven concentric spheres with radii varying from r1=0.05 m and r7=0.2 m with 500 equally spaced-out points selected per sphere surface. All measures are referred to the robot base reference frame. (c) In red the 250 points that belong to the useful TMS workspace (spherical shell), picked among the entire sphere dataset (in blue). Coordinates are referred to the robot base reference frame.

Usually the calibration is performed moving the robot on different equally spaced-out points in a cube or a sphere, involving the specific workspace [34], [38].

The spherical shell constituting the useful TMS workspace can be identified as the volume between two concentric semispheres with radii of 0.1 m and 0.15 m (see Fig. 3c). These dimensions derive from the average size of the human head and its possible movements during the TMS [39], [40], [41]. On the other hand, a typical calibration workspace in a general application is the volume of an entire sphere with radius of 0.2 m [23], [34].

Thus, as shown in Fig. 3b, seven concentric spheres with radii varying between 0.05 m and 0.2 m, with 500 equally spaced-out points on each surface, were identified to create a discrete representation of the two workspaces (i.e. the entire sphere and the spherical shell). Among this pool of data, three datasets were selected:

• 1)Dataset for calibration in the entire sphere;
• 2)Dataset for calibration in the spherical shell;
• 3)Dataset for error assessment.

Each dataset was composed of 250 points randomly picked in the above mentioned pool of predefined points, considering only those into the spherical shell for the second and third dataset (i.e. for the assessment we only considered those points in the useful TMS workspace, since for this specific application a good accuracy is required only in that region). In particular, the first and second group of data were used to perform the calibration considering the two different workspaces, while the third set was used to assess the calibration performance. Each dataset was different from the others, being the points randomly selected.

We tested our proposed methodology with the three different calibration algorithms presented in section II-B, assessing the performance on the third dataset, in term of position and orientation error and duration. Thus, the overall dataset, acquired using the described platform, is composed by 3500 points, 500 on each sphere surface. Among this pool of data, the above mentioned 3 datasets were selected by randomly picking the points 5 times. The three algorithms were tested on the same data, with the translational part represented in meter, without using scaling factors. Preliminary tests were conducted to select the best weight coefficients (i.e. unitary values). Also, the same approach was implemented to assess the calibration errors for all the algorithms. Referring to Eq. (3), the 4x4 homogeneous transformation matrix E = (M_iX)^–1YN_i, i = 1,...,m was computed. From this matrix the position and orientation errors were obtained as the average of the norm of the E translational part and of the norm in the SO(3) space of the E rotational part, respectively.

D. Robot-aided TMS: platform and control approach

The developed robot-aided TMS platform (Fig. 1) is composed of a 7 dof robotic manipulator (Panda by Franka Emika GmbH), a Polaris Vicra infrared camera (by Northern Digital Inc.) and the SofTaxic Optic neuronavigation software (by E. M.S. srl).

The robot holds and moves the coil, which is attached to its end-effector by a custom-designed and 3D printed flange. Since the coil cable is usually heavy and it can affect the contact force estimation as well as the center of mass and the gravity compensation of the flange-coil system, we designed the flange to fix the coil cable on its side; then we estimated the coil-flange inertial parameters to set the payload of the robot. This solution allowed to avoid artifact perturbation in the contact force due to the coil cable, at least for stimulation protocols limited in one hemisphere. In case of protocols covering the whole scalp (i.e. extended cortical mapping) the force artifacts due to the cable could not be completely removed, but they still remain negligible with respect to the flange-coil contribute.

An infrared camera is placed in front of the robot and it is positioned in order to maximize the overlap between its working volume and the robot workspace. Two sets of passive reflective markers are fixed on the handle of the coil and on the subject’s head (using a headband), in order to allow the camera to track both head and coil pose during the TMS procedure.

The data streamed from the camera (i.e. the coil and head positions and orientations) are directly received by the neuronavigator, which reconstructs the 3D model of the subject’s scalp and brain, in order to select the stimulation point that allows to elicit a stimulation of a specific cortical area [42].

The main control application processes both the data acquired from the camera through the neuronavigator, and the data recorded from the robot sensors; then the application sends commands to the robot motors in order to keep the coil on the selected stimulation point.

Once the stimulation point is selected, the robot is controlled to move and hold the coil on the target according to the head pose tracked by the camera, keeping the transformation between the head and the coil constant (Eq. 2). Once the system is calibrated, the coil pose is directly acquired through the robot data regardless of the coil pose measured by the cameras. Indeed, since the coil is rigidly linked to the robot end-effector, and the end-effector pose referred to the robot base frame is computed using the forward kinematics, we can derive the coil pose even when the coil markers are not visible by the camera, as it could happen when stimulating posterior brain areas.

Adopting that solution, the equation (2) is expanded as follows:

$${}^h{T}_c{|}_{target}={}^h{T}_{bC}{}^{bC}{T}_{bR}{}^{bR}{T}_{EE}{}^{EE}{T}_c=const$$ (10)

where ^hT_bC is the transformation between the head and the camera base frame (bC), recorded by the camera-based tracking system; ^bCT_bR and ^EET_c are the two constant calibration matrices representing the robot base frame (bR) with respect to the camera base frame, and the coil pose with respect to the end-effector (EE) reference frame, respectively; ^bRT_EE is the end-effector pose with respect to the robot base frame that can be modified by the robot controller.

In order to set the target position for the robot controller (^bRT_EE|target), the following constant transformations, obtained through the calibration, are needed (see Fig. 2):

• ^EET_c: transformation between the robot end-effector and the coil

• ^bRT_bC: transformation between the robot and the camera base frames

so that the desired robot pose can be calculated as:

$${}^{bR}{T}_{EE}{|}_{target}={}^{bR}{T}_{bC}{}^{bC}{T}_h{}^h{T}_c{|}_{target}{}^c{T}_{EE}$$ (11)

In eq. (11), ^hT_c|target is the above mentioned stimulation target (see eq. (10)) and ^bCT_h is the head pose with respect to the camera base frame, acquired through the neuronavigator software. Since the desired pose is usually expressed in a vector representation, in the control law it is useful to express the target as:

$${}^{bR}{T}_{EE}{|}_{target}=\left[\begin{array}{cc}{R}_d& p_d\\ 0& 1\end{array}\right];x_d=\left[\begin{array}{l}{p}_d\hfill \\ {\varphi }_d\hfill \end{array}\right]$$ (12)

where x_d is the 6x1 vector representing the desired robot pose and it is composed of the 3x1 position vector p_d and the 3x1 vector of Euler angles ϕ_d computed from the rotation matrix R_d. Given a selected stimulation point, the robot moves the coil on the target 10 cm above the scalp (see Fig. 4a), then it proceeds slowly towards the head, keeping the correct orientation (i.e. if the head moves, the control adapts in real time to keep the stimulation face tangent to the scalp). Splitting the trajectory in this way is useful to reduce the risk to collide with the subject, especially when sequential stimulation points are on opposite sides of the head [43]. In this case, the coil first moves far from the head backward on the second path and then it starts the predefined 2-paths trajectory (Fig. 4a). Moreover, we ensure that the path is collision-free thanks to the head tracking. Any unexpected collision, both at the tip of the coil or along the robotic arm, can be detected trough the torques measured at the joints level and the forces estimated at the end-effector (coil), leading to emergency stop and improving the safety not only for the subject but also for the operators. The collision detection was implemented using the SDK libraries provided by the manufacturer (FCI libraries by Franka Emika available at https://frankaemika.github.io/libfranka/index.html), which includes a collision detection routine. In particular, we set separate torque and force boundaries for acceleration/deceleration and constant velocity movement phases. Forces or torques between lower and upper threshold are shown as contacts; forces or torques above the upper threshold are registered as collision and cause the robot to stop moving. Both the pathsegments are planned as minimum jerk trajectories on a linear path, to avoid acceleration discontinuities that badly affect the robot control resulting in emergency stop; when new data are available from the camera, the robot pose is updated according to the head’s current pose, as described by eq. (11).

Fig. 4.

(a) The robot moves on the stimulation point following a minimum jerk trajectory split in 2 paths: 1) to reach, with the right orientation, the point 10 cm above the scalp; 2) to slowly move on the head. The coil reference frame trajectory is highlighted on the two paths. (b) Marker items equipped with four passive reflective markers: stylus item used to point the scalp points and reconstruct the head 3D model; head item attached on a velcro band to be fixed on the subject’s forehead, coil item.

Given the mechanical interaction -between coil and head-required in this application, we implemented an impedance control to enhance safety. Indeed a system controlled in motion or force can become unstable when coupled to an environment that is itself stable [44]. The controller stiffness and damping values have been set to allow obtaining a good accuracy in coil positioning while minimizing interaction forces. To identify those values, preliminary tests have been conducted performing TMS sessions on the mock-up head (i.e. styrofoam head in Fig. 4b), moved by another Panda robot to simulate the subject’s movements. Tests have been conducted varying the control parameters and recording the performance in term of accuracy and interaction forces.

The impedance control (see Fig. 5 for a complete block diagram of the control algorithm) was implemented by commanding torques to each robot joint according to the following equation:

$$\tau =J^T\left(K\left(x_d-x\right)-D(J\cdot \dot{q})\right)+C\dot{q}+G$$ (13)

where τ is the 7x1 vector of the joint torques, J is the 6x7 robot Jacobian matrix, x_d and x are respectively the desired and actual robot pose in the cartesian space (i.e. the end-effector pose with respect to the base reference frame, expressed as 6x1 vectors as in eq. (12)), $\dot{q}$ is the 7x1 vector of the joint velocities, K and D are the stiffness and damping matrices; C represents the centrifugal and Coriolis forces contribute, whereas G is the 7x1 vector of the gravity forces [45]. The desired pose x_d is the vector representation of the end-effector desired pose, which depends on the coil target pose (^hT_c|target) and the head pose (^bCT_h), as computed in eq. (11) and eq. (12).

Fig. 5.

Block diagram of the robot control loop. Head and coil movements are tracked at 20 Hz by the camera and sent to the main application through the neuronavigator. Then the desired pose x_d is computed considering the calibration matrices estimated offline. The control loop running at 1kHz plans a minimum jerk trajectory to reach the target and calculates the torques to control the robot. A safety double control on the head’s velocity and on the collisions detected by the robot allows to stop the robot in possible dangerous situations.

In our implementation of the impedance control in eq. (13), the two matrices K and D are 6x6 diagonal matrices defined as:

$$K=diag(Kx,Ky,Kz,Krx,Kry,Krz)$$ (14)

$$D=diag(Dx,Dy,Dz,Drx,Dry,Drz)$$ (15)

The robot employed in our platform is a 7 dof manipulator with torque sensors at each joint, that allows to smoothly implement the torque-based impedance controller in eq. (13), allowing to safely regulate the interaction at the tip of the coil. Indeed the embedded torque sensors allow to estimate the interaction force and to adjust the cartesian impedance, using the libraries provided with the Franka Control Interface (FCI), through which the joint torques can be commanded. Moreover, the kinematic redundancy of the robot could be exploited in further applications such as a TMS session with two coils held by two manipulators. Indeed, in this case the redundant dof allows to avoid collision between two robot arms, keeping the desired end-effector poses.

Several safety constraints have been implemented in the control algorithm, so that the robot stops its movement, instead of carrying on with the tracking, when:

• the contact forces on the robot measured by the torque sensors (not only at the coil but also along the whole robotic arm) exceed safety thresholds [37].

• the participant moves the head too fast (as could happen for patients fainting out).

• the markers on the head becomes not visible for a long time, or the head moves too much while the markers are not visible to the camera.

This control aims to follow a target position, but it is implemented through an impedance control, which guarantees the stability during interaction tasks by setting a desired mechanical impedance at the interface. This means that, even though the controlled variable is the coil position, there is a constraint on the robot mechanical impedance. The proposed control allows indeed to reduce the position error, maintaining the contact on the scalp, without direct regulation of the contact force but regulating the impedance between the robot and the environment in order to not harm the subject during the interaction. While pressure helps to stabilize both the head and the coil in manual sessions or while using robot with force control, it does not affect the TMS effectiveness as long as the coil touches the scalp in the correct pose [36]; our impedance control makes the robot enough compliant to have low pressures -increasing the subject comfort-while maintaining the coil in the hot-spot, gently touching the head. After initial validation on a mock-up head, the procedure was performed on six healthy subjects. The assessment of the system with the proposed calibration methodology was performed considering both the accuracy in coil positioning and its usability in a real TMS procedure. As concerns the accuracy, the performance was evaluated in terms of error between the target and actual coil pose, using data acquired from the camera. Specifically, the evaluated errors are:

• the Cartesian norm of the position error, on the stimulation plane.

• the norm, in the SO(3) space, of the orientation error.

Additionally, during real sessions on healthy participants, we evaluated the amplitude of the MEPs, i.e. the peak-to-peak value of the EMG muscular activity evoked by a single pulse of TMS stimulation on the primary motor cortex [3], [35], and compared the results with a similar procedure performed by two expert operators - both with more than 3 years of experience in the use of single pulse TMS and rTMS, as well as SICI and LICI protocols.

The software application is available at https://github.com/ANoccaro/Robot-aidedTMS.

III. Experimental Validation

A. Experimental Setup

A set of passive reflective markers (named coil item) was attached to an eight-shaped coil (Alpha D40 by Magstim). The item had a peculiar geometry that can be recognized by the neuronavigation system. The coil was fixed to the robot end-effector using a 3D printed flange. The flange was printed with the Ultimaker2+ 3D printer using PLA material, with a filling percentage of 70%. More details about the flange design and the estimation of the flange maximum deformation can be found at https://github.com/ANoccaro/Robot-aidedTMS. The inertial parameters of the flange -together with the screws, the markers and the coil-were set as payload in the robot’s settings and considered in the robot control law (i.e. gravity compensation, etc.). The coil’s cable was fixed to the side of the flange in order to minimize variations in the center of mass, that was estimated, together with the inertia matrix, by means of a linear regression on the robot forces and torques at the end-effector in different configurations (with the flange-coil system attached).

The coil was registered in the system before starting the calibration; an additional stylus item (Fig. 4b), provided with the Polaris system, was used to point three points on the coil stimulation surface (focus, left wing and back point), collected by the neuronavigation software to align the predefined item reference frame to the actual coil reference frame, centered in the focus and aligned with the electric field (Fig. 4a). The coil registration was performed with the coil fixed on the robot, to avoid eventual marker displacements during its mounting.

The camera was roughly placed pointing towards the robot in order to have the camera capture volume maximally overlapping with the robot workspace, with the coil item visible to the camera (Fig. 1 and Fig. 2). After this first manual alignment the calibration procedures allows to properly transform data from the camera reference frame to the robot one.

The robot controller was connected to a pc running on the O.S. Ubuntu 16.04 with real-time kernel. A customized version of the neuronavigation software was employed to stream the camera data to the main control application developed in c++ language, using the Qt libraries. This customized version of the SofTaxic is equal to the commercial one except for the feature of streaming data of the coil and head marker to third-party software via UDP communication.

This application connects all the system’s components, elaborates data read from the camera and the robot, and sends commands to the robot in order to move the coil on the target point. The robot was controlled with a 1 kHz control rate by means of the Franka Control Interface (FCI), whereas the camera sampling rate was 20 Hz. The impedance value, defined with respect to the coil stimulation plane and not to the robot end-effector, was set after preliminary tests in order to find the best compromise between high accuracy and low contact force. Stiffness and damping values defined in section II-D were set as:

• $K_t=3000\frac{N}{m};D_t=80\frac{Ns}{m}$

• $K_r=80\frac{Nm}{rad};D_r=10\frac{Nms}{rad}$

with K_x = K_y = K_z = K_t, K_rx = K_ry = K_rz = K_r and D_x = D_y = D_z = D_t, D_rx D_ry = D_rz = D_r.

For safety reasons the interaction forces were continuously monitored and an emergency stop intervenes when the force rises above a security threshold, set to 2.5N. During the recorded procedures, the force emergency stop was never triggered, and the maximum recorded value of interaction force was 2.2N. The control torque vector (Eq. 13) was computed by the implemented control algorithm, using the FCI features to estimate the robot state only (i.e. J, $\dot{q}$, C and G) [46]. Then the torque vector was sent to the robot controller. More details about the impedance settings can be found at https://github.com/ANoccaro/Robot-aidedTMS.

B. Experimental Protocol

In order to test the performance of our calibration procedure, and to validate the whole system during real TMS operations, we ran two main experimental sessions:

1. Calibration session: to collect the points dataset and test the hand-eye and robot-world algorithms.

2. Stimulation session: to test healthy volunteers while recording coil position and orientation errors and MEP responses to TMS stimuli.

1. Calibration Session

In the calibration session the robot moved the attached coil to n different poses, while data from the robot and the camera were acquired at the camera frequency (i.e. 20 Hz); the acquired data were then processed off-line in Matlab 2017, through the three previously described calibration algorithms (see section II-B.1, II-B.2 and II-B.3). The calibration points were identified as the robot end-effector positions with respect to the robot base frame. The center of the sphere (Fig. 3a) was defined so as to roughly correspond to the center of the subject’s head, when he/she is seated on a chair at a distance of 60 cm from the robot base and considering an average subject height of 170 cm. Once the starting point was identified, the rest of the sphere was built in the robot base reference frame, moving the end-effector on the sphere surface as described in Fig 3.

The parameters that allow to achieve the best results (i.e. 150 calibration points on the spherical shell using the SGO approach, see section IV for details) were adopted to calibrate the system for the TMS procedure on healthy subjects, and to compute the calibration matrices used into the main control application.

2. Stimulation Session

The subject head was placed in the center of the two workspaces (Fig. 1 and Fig. 2). The head tracker -head reference item- was placed on the participant’s forehead using a velcro headband (Fig. 4b). The head tracker, as well as the coil one, is a rigid-body marker equipped with four passive markers, disposed with a peculiar geometry recognizable by the camera. The headband was placed in order to be as more fixed as possible, avoiding any degree of freedom with respect to the head.

The neuronavigation software was employed to build the 3D model of the brain and the scalp of the subjects, allowing to register the stimulation point. The latter was selected as the area of the left primary motor cortex (M1) that elicits the MEP in the contralateral First Dorsal Interosseus (FDI) muscle with the lowest stimulator intensity (FDI Hotspot) [47].

The target -motor hot-spot- was manually picked by an expert operator gradually moving the coil over the motor cortex to find the location that evokes the largest EMG responses, while applying a series of pulses at a relatively high intensity [48], [49].

The selected target of stimulation, characterized as a coil position and orientation (i.e. tangent to the scalp and rotated in order to induce a postero-anterior current perpendicular to the main dimension parallel to the Central Rolandic Sulcus) with respect to the head, was streamed to the main control application, together with the head and coil poses with respect to the camera base frame. Once the stimulation session started, the robot moved the coil on the stimulation point over the scalp.

The stimulation trigger was automatically provided after at least 5 seconds from the previous one, only if the error between the current coil pose and the hot-spot was under a threshold set by the experimenter (5 mm and 5 deg in the presented validation [14]). The error threshold constraint was present both during the robot-aided session and the manual session, with the trigger automatically provided by the implemented control interface (as done in the robot-aided session). To do this, the software controlling the robot sends a trigger to the magnetic stimulator (Magstim BiStim), via a dedicated electronic board connected through a serial port, only when the conditions on the errors are satisfied. The trigger consists in a 5 V square-wave signal with a 10 ms duration.

MEPs were collected by measuring the EMG response to a single TMS pulse delivered on M1 over the FDI hotspot. EMG was recorded from the FDI of the right hand, using surface Ag/Cl electrodes. Electromyographic signals were acquired and processed using the Digitimer D360 amplifier, the Power1401-3A interface (CED) and the Signal software. The resting Motor Threshold (rMT) was established as the lowest percentage of the Maximal Stimulator Output (MSO) required to produce at least 5 out of 10 MEPs greater than 50 μV in the right FDI. The FDI hotspot, i.e. the site over the left M1 scalp that has the lowest rMT in the FDI muscle was chosen as the stimulation point and selected in the neuronavigation software.

Six right-handed healthy participants were tested. Participants were enrolled after having signed a written informed consent and experimental procedures were approved by the Ethics Committee of the Università Campus Bio-Medico di Roma (EMBODY protocol) and carried out according to the Declaration of Helsinki. Each participant underwent four experimental sessions. In the first two, the experimenter manually administered over the FDI hotspot 30 TMS pulses with the intensity set at 100% of the rMT (session 1) and 30 pulses with the intensity set at 120% of the rMT (session 2), respectively. The minimum interstimuli interval was set to 5 s. The operators were instructed to obtain feedback exclusively from the neuronavigation system, while keeping the coil steady as best as they could. It is worth to notice that the trigger to the stimulator was provided automatically using the electronic board even during the manual session, relieving the operator from pressing a pedal or a button. This choice led to avoid the slight movements usually done by the operator to deliver the stimulation, intrinsically improving his performance. The third and the fourth sessions were administered using the robot-aided TMS platform, handing out the same number of stimuli as delivered in the first two sessions with the same parameters (i.e. 30 stimuli at 100% rMT in session 3 and at 120% rMT in session 4).

C. Data Analysis

We ran a statistical analysis both on the calibration data and on the comparison between robot and human experimenters performance. In particular, we run two Kruskal-Wallis tests on the calibration errors data, with two different factors, i.e. “method” and “workspace” (a non-parametric test was used due to the non-normality of the data, checked through Kolmogorov-Smirnov test). We run the analysis two times: the first time considering the entire dataset and the second time testing only the datasets with more than 70 calibration points. Considering the stability of the outcomes for these datasets, the number of calibration points was not treated as a factor in statistical analysis. Mann-Whitney tests were used as the post-hoc tests to compare the effect among the three algorithms, using Bonferroni correction.

The coil positioning errors during the robot-aided and manual TMS sessions were analyzed using a Mann-Whitney test. However, we want to underline that the Mann-Whitney test has low robustness with strongly skewed data, as in the present case, even though it remains the most suitable for that comparison. In the validation on healthy subjects we considered only the errors measured when the stimulation was provided (at the instant triggered by the TMS stimulator), since they are the only which matter for the efficacy of the stimulation.

The comparison between the MEPs elicited in the manual session and the ones elicited in the robot-aided session, was conducted using the Generalized Estimating Equation.

IV. Results

In Fig. 6 the position and orientation errors obtained using the SGO, QR24 and QUAT algorithm are shown, respectively. Each graphic depicts the median value and the 25^th and 75^th percentile of the position and orientation error obtained among the evaluation dataset, varying the number of points taken into account to estimate the calibration matrices. Points involved into the calibration were selected from two different workspaces, as explained in section II-C:

• w₁. the entire sphere (workspace for a general application)

• w₂: the spherical shell (specific workspace readapted for robot-aided TMS)

Fig. 6.

Position and orientation errors using the SGO, QR24 and QUAT calibration method. Errors are evaluated in the useful TMS workspace, selecting the calibration points in the whole sphere workspace (w₁) or in the useful one (w₂). The dots represent the median value and the extreme points of the bars represent the 25^th and 75^th percentile, computed on 5 different datasets.

As visible from the plots, both for the position and orientation, the error is higher for small values of the number of calibration points, whereas it settles when more than 70 calibration points are employed. Of note, employing less than 70 points, the QUAT method resulted in a lack of convergence of the algorithm in both w₁ and w₂, thus exhibiting errors some orders of magnitude bigger than other methods/number of points; for this reason these datapoints were not displayed in Fig. 6. We also report in Fig. 7 the distributions of the residual of M_iX – YN_i in one representative dataset with 250 calibration points. The figure represents the distribution of both positon and orientation errors, for the three methods and the two workspaces. More details and figures about the residual distribution for the entire dataset can be found at https://github.com/ANoccaro/Robot-aidedTMS.

Fig. 7. Distribution of the residual of M_iX – YN_i for the SGO, QR24 and QUAT algorithms, for the general workspace ws₁ and the customized workspace ws₂, employing 250 calibration points.

The general trend of the error as function of the number of calibration points confirmed the preliminary results obtained in the previous work [38]. The statistical analysis revealed a main effect of the workspace selection on both the position (p < 0.001) and orientation error (p < 0.001): all the calibration algorithms result in errors for the w₂ lower than the w₁ with a 34% reduction for the position errors and a 18% decrease for the orientation ones.

Conversely, the use of different calibration algorithms affects the position errors (p < 0.001) -using QUAT or SGO method further reduces the QR24 error by 43%-, but not the orientation ones (p = 0.995). Mann-Whitney test, corrected for three comparisons, revealed that the QR24 method is significantly worse (p < 0.001) than the SGO and QUAT ones, regardless of the workspace selection; conversely, there is no difference between the errors obtained with the SGO and QUAT methods considering more than 70 calibration points. However, the analysis on the entire dataset revealed significantly worse (p < 0.001) performance for the QUAT approach with respect to the SGO method in term of position errors and worse performance (p < 0.001) than the SGO and QR24 algorithm in term of orientation errors, confirming the convergence problem of the QUAT approach for small number of calibration points. Table I reports the duration of the calibration session depending on the number of collected points: from less than one minute for 10 points to 11 minutes for 250 points. The computational time needed to run the calibration algorithms is negligible with respect to the collecting data procedure (tens of seconds vs few minutes), therefore it was not reported.

Table I. Duration of calibration session.

Number of Calibration Points	10	25	40	55	70	85	100	115	130	145	160	175	190	205	220	235	250
Duration [min]	0.69	1.37	2.02	2.69	3.32	3.97	4.62	5.27	5.89	6.54	7.19	7.82	8.47	9.09	9.74	10.37	11.02

Summing up, among all the different configurations and parameters adopted, the calibration procedures that guarantees lower errors is the one taking more than 150 points on the spherical shell, using the SGO algorithm (average errors lower than 0.5 mm and 0.2 deg).

Concerning the assessment of the robot-aided TMS system on healthy participants, Fig. 8 shows the distribution of coil positioning errors during the TMS stimuli administration, comparing the manual (red) and robotic (blue) stimulation sessions. When the robot administered the stimuli, the coil position error is not significantly different (p = 0.982) compared to the manual session, even though the distribution is slightly less spread and the median value decreases by 6%. On the other hand, the robotic platform achieved significantly lower orientation errors than the expert operators (p < 0.001), reducing the median value by 46%.

Fig. 8. Coil positioning errors (position [m] and orientation [deg]) recorded during the stimuli administration provided by the robotic platform or manually by the expert operators.

The amplitudes of the MEPs elicited in the robot-aided and manual session at 100% and 120% of the rMT intensity, respectively, were compared using a Generalized Estimating Equation (GEE) through the SPSS Statistics software, with the experimenter (robot or human) and the intensity of stimulation (100% of rMT or 120% of rMT) as factors. No significant differences were found between the robotic and manual stimulations (p = 0.94).

V. Discussions

In this paper we aim to provide a novel strategy to calibrate and control a robot-aided TMS system, testing its functionality in a real TMS scenario on healthy subjects; our approach is employable to the scientific community working on TMS, even using different devices. Indeed the proposed control (as well as the calibration) can be adapted to any robotic manipulator with at least six degree of freedom and joint torque sensors; any neuronavigator -e.g. an open-source one [50]- able to provide to thirdy-parts software the pose of the coil, head and the hot-spot data. Likely, the stimulator can be replaced with any stimulator provided with an external triggering module, thanks to the electronic board integrated in our system.

While other systems previously developed used non-orthogonal or laser-based methods for calibrating the system [32], [51], we proposed three different algorithms (SGO, QR24 and QUAT), presented in [29], [34] and [30] for different applications, customizing the calibration workspace according to the one required by the TMS.

Experimental results showed an improvement of the calibration performance for all the tested algorithms, suggesting that constraining the calibration dataset to the TMS useful workspace is a good practice, regardless to the specific mathematical approach implemented. Compared to generic approaches, our TMS robotic platform decreases calibration errors by 34% and by 19% for the position and orientation, respectively. It is worth noting that while reducing the calibration workspace usually implies limitations in the effective use of the system (i.e. limited workspace), this is not the case for this specific application, since the excluded workspace can not be used anyway due to the presence of the subject’s head. Moreover, we found in the present scenario that a global optimization method (SGO) minimizes the positional calibration errors significantly better than non-orthogonal approaches (QR24) influenced by scaling factors [52]. Even though there are no differences between the SGO and QUAT algorithms in term of errors with more than 70 calibration points, the SGO algorithm shows significantly better performance also for small number of calibration points, revealing its potential for obtaining good results even with noisy data.

As regards the control of the robotic arm, we implemented an impedance controller that, exploiting the torque sensors embedded in robot joints, achieves high accuracy in keeping the coil on the hot-spot, limiting the interaction force between the coil and the head. We indeed convert motion errors into robot torque commands (via Jacobian transform) in order to compensate head movements while controlling interaction impedance (for safety reasons). Moreover, our control algorithm allows to adapt in real time the trajectory while approaching to the head, compensating the head movements occurred during the first phase of the planned movement, conversely to the systems previously proposed [53], that use position and/or force control [7], [33], dealing with stability issues during contact/non-contact transitions (thus reducing the safety of the subjects) [54].

Our torque control allows to efficiently follow the target both for slow and fast movements, not exceeding the maximum contact force between the coil and the head. Going beyond simulations and tests with mock-up, we tested the whole platform during a real TMS procedure involving six healthy volunteers, proving that it allows to elicit MEPs not different in amplitude to the ones evoked by two expert users during a manual TMS session that benefits of the neuronavigator. This is the first evidence that the system could be effectively employed in TMS studies. Furthermore, the presented platform -intended as the integration of the robot, the cameras and the neuronavigation software in a single system controlled through the presented control strategy-achieves a better rotational accuracy and a comparable positional one, with respect to the experimenters. Our platform guarantees a coil positioning accuracy lower than 2 mm, equivalent to the one declared by Axilum for his TMS-Cobot system [20] and lower than the one obtained by Matthaus and colleagues which is lower than 3 mm [43]. The dynamic errors were not analyzed in this study that, on the contrary, focused on the static positioning error, which can affect the stimulation effectiveness. Indeed, our control is implemented to avoid firing when the coil is not on the head and in general when the error between coil and target is higher than the set threshold. This allowed to limit the amount of error due to the coil repositioning after small head’s movements. The platform allows to achieve 1.5 ± 1.3 deg of accuracy, significantly reducing the orientation error by 46% (p < 0.001) with respect to the stimulation provided by the human operators. One operator reported to have partially ignored the visual orientation feedback during few stimulations on one subject, being confident on his long lasting experience in providing such kind of protocols. Nevertheless, the control on the maximum admissible error before triggering a TMS pulse prevented from delivering stimulation when the coil was far from the selected hotspot (see supplementary materials at https://github.com/ANoccaro/Robot-aidedTMS for more details). Although there is no clear evidence that 1 mm and 1 deg variations in the position and in the orientation hugely affect the efficacy of TMS procedures [55], de Goede and colleagues [9] showed that “at the subject level significant effects on MEP amplitude, TEP, and LICI were found for changes in coil location or orientation”. After testing position variations of 2-5 mm and 10 deg, author concludes that “This study indicates that a high accuracy in coil positioning is especially required to measure cortical excitability reliably in individual subjects using single or paired pulse TMS”. This is another evidence that providing a tool capable to constantly maintain errors below that thresholds can be beneficial for TMS-based protocols. Moreover, the robotic platform provides long-term stability and automated procedures, not achievable even with well experienced operators. The experimental session was carried out testing the lowest stiffness values allowing to have an effective stimulation, keeping the contact with the head as more comfortable as possible. Hence, the subjects referred to feel the coil less uncomfortable and to experience the whole robot-aided session more pleasant than the manual one. The use of an automatic stimulation trigger even in the manual session was to force the stimulation to be within the error margin set on the neuronavigation system; without this further control, the human operator could have triggered a stimulus even if the target was not in the correct spot (within the preset tolerance), and this could have strongly biased our results in favor of the robotic system. We think our experimental choice is more conservative and strengthens the obtained results.

As regards future perspectives, our research group is currently working on the integration of an open-source neuronavigation software into our robotic TMS system. In particular, we are working on integrating in our system the NeuRRonav [50] developed in unity 3D, and on substituting the Polaris Vicra camera with the Optitrack Prime cameras, that represent a much cheaper solution with higher performance. In fact, the use of an open-source software will further improve the value of our solution; its implementation and testing are currently ongoing and it will be the natural evolution of the present work.

VI. Conclusions

We presented a new robot-aided TMS system aiming to automatize the TMS procedure, typically administered manually by an expert operator, improving the accuracy in positioning the coil and the comfort for the subject. Together with the platform we proposed a calibration methodology tailored on the TMS application: we added TMS-related constraints (selecting a spherical shell centered in the subject’s head as calibration workspace) on three approaches used for different robotic applications.

Results showed that, using the presented approach rather than a general one, the position and orientation errors significantly decrease (p < 0.001) by 35% and 19% respectively, regardless to the implemented algorithm; the SGO algorithm showed significant better results than the QR24 method and more stable performance than the QUAT one, confirming its best performance, as assessed in the previous work. It is worth noting that the presented method, used here to optimize the overall error, can be employed in other techniques where a higher accuracy is needed, e.g. ultrasound stimulation.

The system was validated in a real TMS session on six healthy subjects, leading to higher accuracy than the experimenters - guided by the neuronavigation software-in term of orientation errors, that significantly decreased by 46%, while obtaining a slight 6% reduction for the position errors.

Furthermore, by adapting the workspace of the calibration methodology, the proposed system can extend the use of current TMS procedures to implement TMS protocols while the subjects are performing a functional task. Future perspectives would include dynamic error assessment during functional tasks and the involvement of two robots for a double-coil stimulation, fully exploiting the redundancy of the robotic manipulators in avoiding conflicts in the joint space while keeping the coil in the right hot-spot.