Paladyn Journal of Behavioral Robotics a Teleoperation System for Micro-invasive Brain Surgery

This paper deals with controller design issues for a neurosurgical teleoperator system. The specific application of interest consists of remotely inserting a linear-stage rigid endoscope into the patient's brain for microinvasive neurosurgery interventions. This work aims at evaluating advantages and drawbacks of using a general-purpose control architecture versus a simpler task-oriented architecture, from a point of view of stability and transparency. Experiments revealed that in spite of its simplicity, the task-oriented design allows an improvement in the trade-oo between performance, transparency and stability requirements.


Introduction
In recent years, the usage of robotic teleoperation systems in the operation room is increasing rapidly [1]. Among the large variety of applications dealing with teleoperation, in this paper attention is directed towards microinvasive neurosurgery. The scenario is the one presented in [2] where a master-slave telemanipulation system must be designed to drive the insertion of a linear-stage rigid endoscope into the brain of the patient for neurosurgery interventions. The endoscope insertion will be assisted by a haptic interface, which will extend and complement the surgeon's skills during the insertion process. The device will be responsible for the reproduction and the eventual amplification of the forces experienced by the end-e ector linear stage via a force feedback interface onto the surgeon's hand. This teleoperation architecture will enable the servo-assisted insertion of the probe into soft tissues without the loss of an eventually augmented kinesthetic perception.
Regarding transparency, the controller should be able to virtually reflect to the user the same real impedance of the operational environment, in addition to guaranteeing safety and stability as well. Several approaches can be found in the literature, in which the transparency has been quantitatively defined in di erent ways. In [3], the transparency has been defined as the perfect position and force matching between the master and slave manipulator. In [4], the transparency has been defined in terms of the ratio between the real and the rendered impedance. In [5], the fidelity metric is based on the ability of the system to render environmental compliance changes while taking into account some cognitive aspects of the operator perception. Although di erent point of views, all solutions are obviously subject to the same stability requirements, i.e. the system should not exhibit vibration or * E-mail: {manganelli, chinello, formaglio, prattichizzo}@dii.unisi.it divergent behavior, under any operating conditions and for any environments. However, as discussed in detail in [4], the stability is often achieved by adding damping elements in the control loop, eventually using nonlinear or switching techniques. For example, in [6] the reflected impedance is intentionally shaped by the bilateral controller in order to improve perception by the user and to achieve robust stability. In any case, any change of the rendered impedance results in a transparency degradation. In summary, transparency and stability may be conflicting design goals for a teleoperation controller, hence a suitable trade-o must achieved to guarantee realistic and stable operation in a wide range of environment impedance and in the presence of signal latency [7−11]. In addition to providing a comparison between di erent control architectures available in the literature, this paper evaluates and discusses the possibility of adapting existing control schemes to the application of interest, before undertaking the development of a new specific and task-oriented control architecture. The Time-Domain Passivity Control (PC) approach introduced in [12] is considered. Then, a task-oriented proportional-derivative (PD) control is proposed. The PD control is designed taking into account the slave maximum velocity during the needle insertion which is upper bounded at 5 mm/sec. The PD controller allows filtering out all surgeon motions exceeding a given bandwidth, thus preferring task accuracy and safety with respect to dynamic performances. Preliminary experimental results of this study were introduced in our previous contribution [13]. In this work, we improved the mathematical formalization of the two-port network model adopted for the Time-Domain Passivity Control, along with the analytical proof of stability for such a control architecture. Moreover, the stability analysis has been addressed also for the PD controller. The testbed setup consists of a master-slave system composed by an Omega Haptic Device (master) and a KUKA KR3 robot (slave). We qualitatively evaluated the system performance in three telemanipulation tasks: rigid contact with high sti ness objects, soft contact with a deformable object and finally the insertion of a needle into a soft ma-terial. The results stemming from this preliminary study show that in spite of its simplicity, the task-oriented design better satisfies the requirements for the application of interest. The remainder of this paper is structured as follows: in Section 2 we model the teleoperation system, the Section 3 discusses the adopted control strategies, the Section 4 reports experiments and results, and finally the Section 5 concludes this work.

The prototype system
The teleoperation system features a master-slave configuration. The master device is the Omega.3 haptic interface (ForceDimension). It is remotely handled by the operator to drive the endoscope insertion and it renders the interaction forces fed back by the controller. As already mentioned in the introduction, the application of interest consists of safely driving a linear-stage endoscope into the brain of the patient. Since the brain tissues are very soft and feature a jellylike dynamical behavior, the insertion is a high-risk task the contact forces measured by the endoscopic probe during the penetration are very small. In order to improve the safety and the precision, the master measured motion is scaled, using a constant factor to smooth the reference input signal for the slave robot. Also, the forces experienced by the end-e ector linear stage are amplified before being rendered to the surgeon's hand by the master haptic interface. The insertion task features a single translational degree of freedom (DoF). To that end, we mechanically customized the Omega in order to constrain the possible motion along only a single DoF, as shown in Fig. 1 (left). In addition, the end-e ector has been replaced with a stylus. The slave device is the anthropomorphic manipulator KUKA KR3 reported in Fig. 1 (right). Table 1 reports the main technical specifications of the slave robot. As for the master robot, the slave is also constrained along a single DoF to run the experiment. The KR3 robot is a discrete-time system featuring sampling time T s = 12 ms, its end-e ector motion can be controlled by applying force or velocity reference signals, defined in the joint space or in the operational space.
In order to measure the forces due to the interaction with the environment, the slave end-e ector was instrumented with a 1−DoF force sensor. The data acquisition setup, including the sensor power supply and a National Instrument 6014-PCI acquisition device, was tuned to measure forces ranging from −12 N to 12 N, with a resolution of 0.4 mN.

Control design
According to Passivity Control Theory [12], a master-slave teleoperator is stable if it is passive. In other terms, it should convey signals without increasing their energy. Modeling the system as a two-port electric network, the methods of electrical engineering can be easily used to evaluate the network energy and to check whether the control loop is passive or not. To that end, the teleoperator has been modeled as a two-port network (Fig. 2), where the master and slave forces f m and f s are the e orts, and the master and slave velocities v m are the flows, (Fig. 1). The system inputs are v m (n) and f s (n), while the outputs are the f m (n) and v s (n). As mentioned above, the operator's commanded motion and the measured force can be scaled by user-defined factors According to classic theory of electrical networks, the energy flow is computed for each port, and the amount of energy stored in the network is equal to the energy introduced through the master port minus the energy conveyed through the slave port. If the stored energy is negative, it means that the slave energy is greater than the master energy, i.e. the system is generating energy, it is not passive and the stability is no longer guaranteed. Hence, the passivity (and hence the stability) is guaranteed if the stored energy is non-negative.
The key idea of the Time-Domain Passivity Control consists of measuring the energy flows at the master and slave ports. If the system becomes active, the exceeding energy is dissipated by a Passivity Controller (PC) connected with each port.
The network is passive until W (n) ≥ 0, otherwise the system stability is no longer guaranteed. The classic approach consists of activating the PC only when W (n) ≥ 0 [12]. Given the high risk level of our application, we adopted a more conservative strategy, which consists of activating the PC as soon as the current energy becomes smaller than the predefined threshold W 0 = 2f max v max , where f max and v max are the maximum force and velocity allowed by the system. In the worst case W 0 is the maximum energy output that can occur in one time step.
This strategy guarantees that in the time instant the PC is activated, the energy is such that 0 < W (n) < W 0 . As it is shown in Fig. 2, we add one series PC α m (n) to the master port and a parallel PC α s (n) to the slave port, therefore the controlled network constitutive laws become: Slave PC: It can be easily demonstrated that using the master and slave controllers (2) and (3) the system passivity is always guaranteed: Hence, using equations (2) and (3), the energy stored in the controlled network is W (n) > 0 ∀ n, hence the stability is ensured in any condition.
The energy evaluation and the eventual dissipation is based on the measured signals, hence it is crucial to have reliable measurements and to filter out the noise without introducing the phase delay usually caused by low-pass filtering. To that end, the discrete-time First Order Adaptive Windowing (FOAW) filter introduced in [14] has been implemented to smooth the commanded velocity signal. It originates from common FIR filters, but the time window size is set as the maximum size such that the straight line joining the extreme samples passes through the uncertainty interval of each sample falling inside the window. Hence, as the size h is adapted, the velocity samplev (n) at time instant n is computed as:v where x(n) is the end-e ector position at time instant n, and T c is the sample time (for more details about the FOAW filter, please refer to [14]). Smoothing the insertion velocities will result in measuring smoother contact forces at the endoscope tip, reducing the noise in the force feedback profile rendered to the surgeon's hand.
The main drawback of this technique is that the control e ort determined by the PC can lead to actuator saturation. Generally, in order to prevent saturation, the PC signal is upper bounded, but this in turn can result in a drop in performance. In fact, in such a case the dissipation of the exceeding energy may require more than one time step, leading to transient vibration e ects. A simpler control strategy has been designed for this teleoperation system relying on the assumption that the user's commanded motions during microinvasive neurosurgery interventions will be slow and sharp, thus also the force reflection will be fed back with slow dynamics. Hence, we designed a simple proportional-derivative (PD) controller in order for the slave end-e ector to track the master end-e ector motion, filtering out all frequency contents exceeding a predefined bandwidth.
Hence, the PD transfer function C (s) is defined as: The block scheme for the teleoperation system can be simply represented as: Figure 3. The master-slave teleoperator system with the PD controller.
The slave device has been simply modeled as an integrator, yielding the transfer function 1 s . The proportional and derivative factors have been designed using classical control theory [15], according to the desired closed-loop performance. As regards stability, we chose again the approach of passivity. A system composed by passive subsystems is passive as well [12]. In the literature, the human model and the Omega Haptic Device have been demonstrated to be passive [16,17], hence only the passivity of the controlled slave transfer function must be studied [18]. The PD parameters we tuned according to closed-loop performance specifications resulted as passive. Again, the FOAW filter was adopted in order to filter out the noise from the velocity signals.
In addition to the e ects of the control law, the haptic transparency of the teleoperator can also be a ected by the gravitational force. While using the master device, the mass perceived by the surgeon at the haptic handle is due to gravity acting on the whole mechanical structure of the master device. Compensating these e ects of gravity is not straightforward, since generally they depend on the end-e ector position in the workspace through a non-linear relationship. We adopted the Autocalibrated Gravity Compensation technique [19]. The strategy consists of performing an o -line recursive estimation of the apparent gravity force acting at a certain set of positions inside the workspace. Secondly, the on-line gravity compensation at an arbitrary position is computed by interpolating the estimated data. The stability of the Autocalibrated Gravity Compensation has been analytically proved in [20]. The compensation algorithm has been adopted with both the PC and the PD controller. Anyway, we remark that this control stage is applied directly to the master device low-level control, it is not correlated with the control signals involved in the teleoperator, hence it has not been included in the two-port network.

Experiments
Several experiments have been carried out to evaluate the performance of the teleoperation system using passivity control (PC) and low-pass proportional-derivative (PD) control. The threshold energy for the PC was W 0 = 120J, stemming from f max = 12N and v max = 0.005m/s, while the PD parameters were k P = 3 and k D = 0.35, designed according to the model of the KR3. In the following, we report the results achieved in three teleoperation tasks: rigid contact, soft contact and needle insertion. For each task, we recorded position, velocity and force of both master and slave end-e ectors. In the first task, the contact with a rigid wall was performed, as shown in Fig. 4. The experimental data acquired using PC control and PD control are shown in Fig. 5 and Fig. 6 respectively. The second task consisted in remotely touching the foam rubber dice depicted in Fig. 7, whose sti ness has been estimated as approximately 100 N m . Figs. 8 and 9 show the data recorded during the contact, using PC control and PD control. Finally, the third task consisted in remotely inserting a syringe needle into an organic material. To this end, the needle was rigidly attached to the slave end-e ector, as shown in Fig. 10. We were interested in experiencing the e ects of penetration and of viscous dumping due to the perforation of the skin and of the internal pulp. In this experiment,  as a target object we chose a kiwi fruit. As expected, the forces stemming from this type of interaction were very di cult to be perceived by the user, hence it was necessary to amplify the measured forces. Fig. 11 and Fig. 12 show the trajectories recorded during the contact, using PC control and PD control, and amplifying the forces with a gain k f = 10. The PC was able to restore the system passivity every time it was required during all tasks, thus guaranteeing the system stability. Using the PD controller, the system was always stable. In terms of master-slave position tracking, in the case of rigid contact the PC performance was slightly higher than that of PD, while in the other tasks there were no significant di erences. On the other hand, considering the haptic feedback, the PD was always able to render smooth contact forces, while the PC generally delivered noisy force profiles. This can be ascribed to the PC e orts required to restore the system passivity. Recall that as soon as the passivity observer reveals that the energy is lower than the threshold, the controller attempts to instantly dissipate the energy flow from each active port in a single step. Hence the PC impulsive control e orts can a ect the haptic feedback, providing a noisy force profile.

Conclusion
This paper addresses design issues characterizing a teleoperation control system targeted at driving the insertion of a linear-stage rigid endoscope into the brain of a patient for neurosurgery interventions. We present preliminary results of our current research, addressed towards evaluating the applicability of a general-purpose control scheme compared to a specific and task-oriented architecture. The general-purpose control scheme we chose was the timedomain passivity control. Meanwhile, the task-oriented scheme was a proportional-derivative control, based on the assumption that during microsurgery interventions the user's commanded motions and the reflected forces will be characterized by slow dynamics. Hence, the PD was designed in order to filter out all surgeons motions exceeding a predefined bandwidth, thus privileging task accuracy and safety in spite of a loss of dynamical performance. The experimental setup was a master-slave system composed by a Omega Haptic Device (master) and a KUKA KR3 robot (slave). Three tasks were performed to qualitatively evaluate the system performance: rigid contact with high sti ness objects, soft contact with a deformable object and finally the insertion of a needle into a perforable material. The results stemming from this preliminary study show that even if the task-oriented design provides lower dynamical performance than the    general-purpose one, it revealed to be stable and was able to render smoother forces in any situation, improving the user's kinesthetic perception during the task remote control.