Force-based control strategy for a collaborative robotic camera holder in laparoscopic surgery using pivoting motion

Force-based control strategy for a collaborative robotic camera holder in laparoscopic surgery using pivoting motion Carlos Fontúrbel*, Ana Cisnal, Juan Carlos Fraile-Marinero and Javier Pérez-Turiel Escuela de Ingenierías Industriales, Medical Robotics Group, Instituto de las Tecnologías Avanzadas de la Producción (ITAP), Universidad de Valladolid, Valladolid, Spain Introduction: Laparoscopic surgery often relies on a fixed Remote Center of Motion (RCM) for robot mobility control, which assumes that the patient’s abdominal walls are immobile. However, this assumption is inaccurate, especially in collaborative surgical environments. In this paper, we present a force-based strategy for the mobility of a robotic camera-holder system for laparoscopic surgery based on a pivoting motion. This strategy reconceptualizes the conventional mobility control paradigm of surgical robotics. Methods: The proposed strategy involves direct control of the Tool Center Point’s (TCP) position and orientation without any constraints associated with the spatial position of the incision. It is based on pivoting motions to minimize contact forces between the abdominal walls and the laparoscope. The control directly relates the measured force and angular velocity of the laparoscope, resulting in the reallocation of the trocar, whose position becomes a consequence of the natural accommodation allowed by this pivoting. Results: The effectiveness and safety of the proposed control were evaluated through a series of experiments. The experiments showed that the control was able to minimize an external force of 9 N to ±0.2 N in 0.7 s and reduce it to 2 N in just 0.3 s. Furthermore, the camera was able to track a region of interest by displacing the TCP as desired, leveraging the strategy’s property that dynamically constrains its orientation. Discussion: The proposed control strategy has proven to be effective minimizing the risk caused by sudden high forces resulting from accidents and maintaining the field of view despite any movements in the surgical environment, such as physiological movements of the patient or undesired movements of other surgical instruments. This control strategy can be implemented for laparoscopic robots without mechanical RCMs, as well as commercial collaborative robots, thereby improving the safety of surgical interventions in collaborative environments. KEYWORDS robotic surgery, laparoscopy, force control, collaborative robotics, admittance control OPEN ACCESS EDITED BY Anzhu Gao, Shanghai Jiao Tong University, China REVIEWED BY Gianni Borghesan, Faculty of Engineering Sciences, KU Leuven, Belgium Hunter Gilbert, Louisiana State University, United States *CORRESPONDENCE Carlos Fontúrbel, [email protected] SPECIALTY SECTION This article was submitted to Biomedical Robotics, a section of the journal Frontiers in Robotics and AI RECEIVED 15 January 2023 ACCEPTED 29 March 2023 PUBLISHED 17 April 2023 CITATION Fontúrbel C, Cisnal A, Fraile-Marinero JC and Pérez-Turiel J (2023), Force-based control strategy for a collaborative robotic camera holder in laparoscopic surgery using pivoting motion. Front. Robot. AI 10:1145265. doi: 10.3389/frobt.2023.1145265 COPYRIGHT © 2023 Fontúrbel, Cisnal, Fraile-Marinero and Pérez-Turiel. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. Frontiers in Robotics and AI frontiersin.org01 TYPE Original Research PUBLISHED 17 April 2023 DOI 10.3389/frobt.2023.1145265 1 Introduction Laparoscopic surgery is a widely accepted and extended technique in the current medical context. In this type of interventions, small incisions are made in the patient’s abdominal area. Through these open orifices, laparoscopic forceps, needle holders, laparoscope, and any other surgical tools are introduced. This minimally invasive surgical technique is beneficial for both surgeons and patients, leading to a postoperative recovery with fewer complications (Rau and Hünerbein, 2005). The da Vinci is the market leader in robotic surgery. This robotic system is capable of performing complete laparoscopic surgeries under surgeon’s control. However, the large investment required in infrastructure and its high cost make it unaffordable for a large number of hospitals (Crew, 2020). One cost-effective solution is to integrate partially automated surgical systems, such as robotic assistants for performing individual tasks (Voros et al., 2010). For example, the laparoscope handling could be automated, mitigating human errors and saving resources, since it is currently handled by a medical assistant. Robotic solutions for assistance in laparoscopy surgery, such as laparoscope handling, have been proposed in the literature since the end of the 20th century (Hurteau et al., 1994), (Taylor et al., 1995). However, their integration into such collaborative systems remains a challenge due to the complexity of the human–robot interaction (Haddadin, 2014). In addition to the price, another limitation of the da Vinci is its absence of force feedback, which makes it difficult to control the contact forces at the incision. Nowadays, the most widespread mobility method of robotic systems in the context of laparoscopy surgery is based on a remote centre of motion (RCM), coinciding with the entry point of the tool through the incision. It simplifies the development and control of robotic laparoscopic assistants (Voros et al., 2010;Kuo et al., 2012; Voros et al., 2010). There are strategies for the RCM implementation based on the mechanical design, as in the da Vinci (Freschi et al., 2013)orinAksungur (2015) and Zhou et al. (2018), or based on control (Sandoval et al., 2021), where a virtual RCM is defined at the start of the surgery. These robots that include the RCM as a central feature of their design are based on the immobility of the entry point, thus defining the mobility constraints of the robot. The premise of the staticity of the RCM approach omits the actual movement due to the physiological activity of the patient, such as the patient’s abdomen ventilation, which causes movement at the incision point (Valenza et al., 2010). Additionally, the trocar’s rest position varies for each patient. It is mainly affected by the patient’s abdominal elasticity coefficient, which depends on fat and other body parameters. This cannot be taken lightly in collaborative environments, where accidents can occur, or larger forces can be exerted by the surgical instruments that displace the patient’s abdomen. Control strategies have been proposed to reduce the force exerted at the contact point between the trocar and the patient by measuring this force. This approach was tested in the early 21st century by Krupa et al. (2000), implementing what is now considered a mobile RCM (Marinho et al., 2016). The results were not fully satisfactory due to the low frequency of the force sensor, which made a truly effective control infeasible. This may be the reason why these force-based control strategies which ensures low contact forces are not widely extended in real surgical settings nowadays. Due to the improvement in technology, some hands-on robot approaches have appeared (Kastritsi and Doulgeri, 2021;Kim et al., 2021). They use a force sensor to move the robot to the desired position but always using the RCM as a fundamental mobility restriction. In contrast to the traditional or mobile RCM-based solutions, this paper presents a mobility strategy based on pivoting the laparoscope to minimize the efforts measured by a force/torque sensor located in the coupling of the tool. The measured force is used to pivot the camera, minimizing the contact force without losing control of the camera’s TCP. This approach allows to perform an automatic control of the orientation of the tool, thus releasing the TCP control position. In this way, a pivoting motion is achieved, similar to the proposal made by Muñoz et al. (2005), with the advantages of having rigid joints and the use of a commercial robot. It allows to keep the desired field of view (FoV) using modern mobility and camera tracking strategies as proposed by Sandoval et al. (2021), with a greater degree of security since the contact forces are minimized in the background. The proposed control strategy has been tested for the handling of a laparoscope using a 6-DoF Universal Robots UR3e robot and a pelvitrainer. Trainee surgeons often use pelvitrainersastheyallowthemtopractice individual aspects of minimally invasive surgical procedures, such as camera navigation or instrument handling, on a model rather than the patient (Ackermann et al., 2022). Tests have been carried out with different contact forces caused by the movement of a pelvitrainer or the laparoscope’s tip, thus simulating the patient’s physiological movement, or sudden accidental movements. In general terms, the control is able to minimize accidents in the operating room through rotations of the tool; it reduces the exerted forces at the trocar without losing the control of the laparoscope’stip. FIGURE 1 Four DoFs available using the RCM approach, which is coincident with the trocar position. Frontiers in Robotics and AI frontiersin.org02 Fontúrbel et al. 10.3389/frobt.2023.1145265 2 Materials and methods 2.1 Traditional RCM approach The traditional RCM approach considers the incision as a static point characterized by four DoFs: a translation along the axis of the instrument and three rotations around this axis (Figure 1). The surgical instrument penetrates the patient’s body through the incision point. The 4-DoF mobility constraints featured by the RCM generate a spherical working space for the TCP and can be mechanically imposed or virtually defined (Dombre et al., 2013). However, considering the incision as a fixed point that coincides with the RCM has some disadvantages. It requires a very precise positioning of the RCM with the incision point during surgery to avoid tissue damage (Dong and Morel, 2016) and also causes the Cartesian position of the TCP to be controlled indirectly. Marinho et al. (2016) reported that it was possible to generate TCP linear movements through the implementation of a RCM by controlling the 4 available DoFs without an error in the RCM positioning. The primary goal of this approach is to keep the tool static at the RCM, preventing the occurrence of contact forces. Consequently, the TCP positioning is left as a secondary role in RCM-based implementations (Kim et al., 2021). The popularity of the RCM approach, which considers the incision a static point, has limited the development of methods for minimizing the forces exerted at the trocar due to physiological movements of the patient or collaborative environments. Some methods that dynamically modify the position of the RCM by estimating the trocar position have been developed (Riviere et al., 2006;Dong and Morel, 2016;Richa et al., 2011). This approach, known as mobile RCM, causes difficulties in the camera repositioning as a result of the trocar’s movement during the intervention. If the exact application point of the force is unknown, the entire camera must perform a Cartesian motion in order to reduce the contact force of the trocar (Marinho et al., 2016). The RCM must coincide with the trocar to ensure that no force is exerted on the patient, since the position of the TCP is conditioned by the position of the RCM. To avoid this continuous movement, relatively high force thresholds must be applied, which limits the performance of this strategy. Hence, we considered that the mobile RCM is not an ideal solution once the non-staticity of the trocar is considered. If the incision point is not considered static, the use of the RCM approach is no longer justified. If it is possible to measure the contact forces between the trocar and the patient, these forces should be able to be controlled independently of the TCP position, allowing precise independent control at the trocar and at the tip of the camera. 2.2 Proposed pivoting motion control To overcome the disadvantages of the traditional approach based on a static RCM, a mobility strategy based on pivoting motion is presented. It consists of varying the orientation of the camera so as to minimize the contact forces with the abdominal walls of the patient. It adapts the laparoscope’s orientation to the real location of the incision, or in other words, to the trocar position at each moment. Since the laparoscope must keep track of the scenario and should not interfere with other instruments or tissues, we can infer that no other contact forces should affect the camera’s navigation. Therefore, an admittance control can determine the angular velocity (pivoting movement) of the camera required to minimize the contact forces, which are measured by a force/torque (F/T) sensor located in the coupling of the tool. In this way, the position of the TCP remains under direct control, while the pivoting motion minimizes the forces on the trocar, which always tends to a resting position. This motion strategy is a restatement of the strategy proposed by Krupa et al. (2000), which considered that the position of the trocar varies over time. Although this control strategy was too complex to implement at the time, it is a valid approach today due to the improvements in sensorization in the last years. In this article, the absolute tool velocity was determined at the height of the trocar, displacing this pointhorizontallyasaresultofthe force at the trocar. Krupa’s strategy was directly related to those that implement a mobile RCM, which have not been particularly fruitful in the literature. We consider that this approach, although it could not be widely extended due to technological deficiencies, as mentioned in the article itself, can be simplified by displacing the controlled point to the tip. This force-based strategy allows to control the pivoting motion without the need of the passive joint. Multiple advantages associated with pivoting motion control have been previously reported in the literature (Muñoz et al., 2005). These advantages include, above all, repositioning the tool, in this case the camera, without losing control of its tip. Thus, it is possible to track the image even during the pivoting that may occur due to contact between the camera and patient. This allows lowering the threshold of admitted force before starting the reorientation, as well as solving the problem with a less aggressive movement, avoiding displacement of the entire camera and also through low magnitude turns. FIGURE 2 Pivoting movement as a consequence of forces exerted in the direction of the Y-axis of {B}. Frontiers in Robotics and AI frontiersin.org03 Fontúrbel et al. 10.3389/frobt.2023.1145265 In the following section, the admittance control will be introduced. It generates the pivoting motion of the tool to minimize the forces produced at the trocar. Second, the feedforward control is described, which avoids the occurrence of exerting forces due to the movement of the laparoscope. Third, the mobility constraints associated with the proposed control are addressed. 2.2.1 Admittance control The mechanical admittance (Y) of a system is defined as the ratio of its velocity (v) to its force (F), as expressed in Equation 1. This definition is related to the second-order differential equation which describes a mass, spring, and dumping serial system and hence, it is characterized by a mass (m), a stiffness (k), and a viscous damping (b) (Mihelj and Podobnik, 2012). Ys ()v F1 ms +b+k s .(1) Theobjectiveofanadmittancecontrolistoshapethe mechanical admittance of a device such that it possesses desired characteristics. In this proposal, it is used to determine the angular velocity that minimizes the interaction forces. Figure 2 shows that the rotational velocity of the TCP that characterizes the pivoting motion is related to the forces exerted at the trocar. The exerted force FB ywould be avoided by a negative rotation in the X-axis of {B}. Analogously, if the force is exerted in the X-axis, FB x, it can be avoided by a rotation around the Y-axis of {B}. The mechanical admittance can be simplified so that it consists of only one damping. Eq. 2describes this simplified admittance, which provides good results in terms of robustness and control accuracy despite its simplicity. Ys ()v F1 b.(2) By this model, we can determine a relationship between force and angular velocity that constrains the working space of the camera around the Xand Y-axes, defined as ωB Ax and ωB Ax at Eqs 3,4, respectively, where the sub-index A stands for admittance. The gains applied to relate force and angular velocity, kAx and kAy, are experimentally calculated and are dependent on the environmental stiffness (Zeng and Hemami, 1997). ωB Ax kAxFB y,(3) ωB Ay kAyFB x.(4) For its implementation, a F/T sensor placed at the laparoscope’s coupling is used to determine the applied force at the trocar, taking {S} as a reference system (Figure 2). Note that to relate this force to the velocity using the admittance control, both variables must refer to the same system. The absolute reference system, which corresponds to the base of the robot {B} (Figure 2), is used. Hence, it is necessary to transform the force measurements to the absolute reference system {B}. The aforementioned angular velocities allow the parameterization of the twist vector, (sB A), which represents the linear and angular velocity of the TCP as shown in Eq. 5. This vector characterizes the pivoting motion of the tool that minimizes the interaction forces at the trocar, constraining the tool orientation and thus freeing the Cartesian control of the TCP. sB AvA,ωA () B  T0,0,0,ωB Ax,ωB Ay,0  T.(5) Forces are used to calculate the pivoting motion of the camera. Forces close to zero causes low pivoting speed, while higher order forces provoke higher response speeds. This strategy favours that the camera always tends to a resting position without aggressive movements, and consequently the forces exerted on the patient are minimized. 2.2.2 Feedforward orientation control The vector calculated at the TCP by the admittance control (sB A) allows to minimize the forces exerted when the Cartesian velocity at the tool’s tip is zero. However, it is also convenient to maintain low contact forces once the camera is in motion to change the field of view. When there is a movement of the camera, the exclusive use of the admittance control would require a too elevated velocity or a high gain, causing oscillations and abrupt changes of direction, and therefore high forces on the trocar. This problem has been previously reported by Calanca et al. (2016) and may be solved with the addition of a position control loop that prevents large forces from being exerted, so a lower gain can be applied to the admittance control, avoiding an oscillatory behaviour. This position control loop can be implemented as a feedforward (ff). Figure 3 shows that it is possible to geometrically determine which rotation the tool should perform against the future Cartesian velocity of the TCP. The objective of this control is to limit the Cartesian velocity of the camera when Cartesian movement occur in the immediate future. The ff predictive action complements the admittance control, which minimizes the forces exerted in the present by pivoting, displacing the tool to a rest position as a consequence of the forces measured. Hence, this control ensures FIGURE 3 An adequate rotation related to the Cartesian velocity vB c prevents exerting forces when the TCP of the laparoscope, or point pB TCP, is displaced. Frontiers in Robotics and AI frontiersin.org04 Fontúrbel et al. 10.3389/frobt.2023.1145265 that the forces exerted are minimized without giving up the direct control of the TCP position. For the calculation of the angular velocity, the ff controller needs to know the position of the camera point whose Cartesian velocity would be reduced due to this control. This point will be referred to hereinafter as the fulcrum position (pB f), and it is the projection of the contact point between the laparoscope and the trocar at the laparoscope’s longitudinal axis. Eqs 6,7allow the calculation of the tool’s angular velocity at pB TCP that keeps the camera immobile at the point pB f.dB tisthedistancetravelled between pB TCP and pB finthetimeperiodΔt.Intheexampleof Figure 3,whendisplacingpB TCP at a speed vB y,theangleαof rotation that prevents forces around the X-axisisthedifference between the angle formed by the vector dB tintheYZplaneatthe current and future instances. Thiscalculationisperformedinthe YZ and XZ planes to determine the rotation using the X-and Y-axes, respectively, allowing to create the velocity vector of the ff control sB f,asshowninEq.8. ωB fx α ΔtdB ty +vB y·Δt dB tz +vB z·Δt−dB ty dB tz  ·1 Δt,(6) ωB fy − dB tx +vB x·Δt dB tz +vB z·Δt−dB tx dB tz  ·1 Δt,(7) sB fvf,ωf  B  T 0,0,0,ωB fx,ωB fy,0  T.(8) While the admittance control pivots the camera in response to the contact force, the ff control calculates the angle that the laparoscope must pivot in advance to maintain the fulcrum point at a low speed. In this way, the ff controller reduces the contact forces and ensures that the admittance control maintains its corrective functionality. The angular velocity vector calculated by the ff is added to the provided by the admittance control, thus allowing both preventive and reactive orientation controls even if the TCP is moving. 2.2.3 Movement in the released degrees of freedom The proposed force-based pivoting motion control liberates the TCP movement, characterized by velocity vB ix,v B iy,v B iz. Movement is also released around the longitudinal axis of the laparoscope es z characterized by the rotation velocity wz, since this will not cause any contact forces with the patient. This allows to transform the four DoFs available in the RCM approach (Figure 1) into 3 DoFs of Cartesian motion and 1 DoF of rotation (Figure 4). The twist velocity vector sB i, which defines the four DoFs released at the TCP referred to the robot base{B}, is described in Eq. 7a.sB iis referred to the system {B}, and consequently, the Cartesian velocities and the angular velocity must be also referred to{B}. Hence, the angular velocity wzof the tool through its longitudinal axis eS zis transformed to the system {B} using the rotation matrix RB S. sB ivi,ωi () B  TvB ix,v B iy,v B iz,w zeS zRB S  T. (7a) The reference velocity, considering the four DoFs of the TCP, can be defined without worrying about the exerted forces since they would be minimized by the control. 2.3 Complete force-based pivoting motion control strategy The complete force-based pivoting motion control is shown in Figure 5. This control strategy is the result of the sum of the admittance and ff controls described previously. A PI controller is also included, although it could be omitted in case the exact position of the fulcrum point pB fis known. The PI and the ff controllers, shown with dashed lines in Figure 5, should only act when the camera is in motion. PI complements the predictive action of the ff when the position of the fulcrum point pB fis not accurate, since the ff control would not completely eliminate the forces exerted on the trocar during the movement. This would cause a stationary error during Cartesian pB TCP movement that the admittance control could not correct. Therefore, the inclusion of the PI integral action compensates the imperfection of the ff controller associated with a poor fulcrum point estimation. Due to the dynamic nature of the system, where continuous trocar displacements may occur due to physiological and camera movements, we proposed an operation mode for this PI control since an over-action would affect the quality of the control strategy. The PI control is only active when the camera is in motion, and therefore, it is configured to reset after each change of direction or stop of pB TCP. In addition, the PI control must be adjusted with a low gain and an appropriate control frequency in such a way that past states do not affect the present control, or in other words, so that it can be determined whether the stationary error is still present and to prevent past forces already compensated to affect the control. In the experimental results, control parameters and its performance are analysed. To sum up, interaction forces are reduced due to the pivoting motion provided by the admittance control. Additionally, the ff control anticipates the laparoscope’s motion to prevent the appearance of forces due to this motion, and the PI control eliminates errors that have not been corrected in the immediate past. For this purpose, the forces exerted at the trocar point, once FIGURE 4 Four DoFs released at the TCP by the proposed force-based pivoting motion control. Frontiers in Robotics and AI frontiersin.org05 Fontúrbel et al. 10.3389/frobt.2023.1145265 gravity has been compensated, are inputted to the admittance control and the PI, while the ff control requires the current and desired (future) positions of the TCP (pB TCP) and the current position of the fulcrum (pB f). Additionally, not only the force measurements and orientation of the tool but also the weight of the tool is needed to calculate the gravity-compensated force. As previously mentioned, all control variables are expressed in the same reference system associated with the robot base {B}. Hence, the gravity can be directly compensated (Figure 6). 2.4 Setup platform The setup platform used to test the performance of the presented force-based control strategy is shown in Figure 7. The experimental platform mainly consists of a 6-DoF UR3e robot (Universal Robots, Denmark), a Hex-H F/T sensor (OnRobot A/S, Denmark), and a SZABO-BERCI-SACKIER pelvitrainer (KARL STORZ SE & Co. KG, Germany). The reference systems which are required by the theoretical proposal {B} and {S} are located at the base of the UR3e Robot and the F/T sensor, respectively. A new reference system {P} is attached to the pelvitrainer (Figure 7). The pelvitrainer recreates the mobility restrictions in laparoscopic surgeries, due to the rigidity of its orifices, which FIGURE 5 Diagram of the force-based angular velocity control for the laparoscope. The dashed lines connect elements that are only activated by moving the laparoscope’s tip. FIGURE 6 Forces measured on the trocar and their reference systems. FIGURE 7 Experimental setup mainly consisting of the robot, F/T sensor, and pelvitrainer. Frontiers in Robotics and AI frontiersin.org06 Fontúrbel et al. 10.3389/frobt.2023.1145265 mimic those of a real abdomen. To test the safety of the proposed control, a 3D-printed PLA rails were arranged for the pelvitrainer to move along ^ pB xaxes. In this way, it is possible to test the control response to small movements that mimic the patient’s physiological movement, as well as larger movements, which simulates accidents that might happen in collaborative environments. The F/T sensor, used to measure the interaction forces at the trocar, has an accuracy of 0.2 N in the XY plane of {S}, and its maximum frequency sample is 500 Hz. The surgical instrument is introduced inside the abdomen through 10-mm and 12-mm ENDOPATH XCEL ® trocars. A Storz Telecam One-Chip Camera Head 20212030 is used which is integrated in a HOPKINS telescope 0°with 10 mm diameter. This cylindrical device is inserted into the trocar and in turn into the interior of the pelvitrainer. It has been coupled to the robot by means of a rigid resin coupling tool of our own manufacture, in order to avoid unwanted plastic deformation and inaccuracy in the positioning of the TCP. 2.5 Control system implementation The proposed control architecture is implemented using ROS (Robot Operating System) and is illustrated in Figure 8. The green blocks correspond to ROS nodes, being three main blocks: the navigationcontrol,theUR3erobot,andtheHEXF/Tsensor.The navigation control is subdivided into three specific tasks. The Cartesian velocity control and the fulcrum point estimation (white blocks in Figure 8) can be freely implemented and are not detailed in this manuscript. For the experimental tests, the reference Cartesian velocity has been defined according to the experimental goals. Additionally, experimental results showed that it is not necessary to provide the precise fulcrum location for the control strategy to work correctly. In fact, a 5 cm height error provides an appropriate response, which improves if the point is determined accurately. The angular velocity control (orange block in Figure 8)istheone responsible of controlling the TCP’sangularvelocityunderthe principles presented in this paper. A 4-point average filter is applied to the force measurements to reduce the noise, resulting in afiltered force with a frequency of 125 Hz. This filtered force combined with the reference Cartesian velocity of the TCP, fulcrum position, and tool orientation is used to calculate the reference angular velocity by the angular velocity control. The communication between the ROS nodes is carried out by means of ROS topics, through the subscriber–publisher relationship that they maintain. The SpeedL command, provided by Universal Robots on 0F 1 URScript, is sent to the UR3e robot with the desired velocity vector of the pB TCP point, generated on the navigation control block, as shown in Figure 8. This command requests the robot every 8 ms to control the absolute velocity of a point in real time in a fluent way. 3 Results The proposed force-based pivoting motion control has been tested using the experimental setup shown in Figure 7. First, the pivoting motion generated by the admittance control has been evaluated as a method to control the forces exerted on the trocar. Second, the effectiveness of the ff and PI together with the admittance control has also been tested to avoid exerting forces on the patient due to the Cartesian motion of the TCP. Third, the performance of the proposed control has been tested against errors in the estimation of the fulcrum position, to validate the robustness of the control in real environments. The detection and minimization of risks in the event of accidents have been tested. Finally, the ability of the control to maintain the FoV of the camera at a fixed point during pelvitrainer movements has also been evaluated. FIGURE 8 ROS implementation diagram of the robot control. Frontiers in Robotics and AI frontiersin.org07 Fontúrbel et al. 10.3389/frobt.2023.1145265 3.1 Admittance control The first experiment aimed to determinate the gain of the admittance control by evaluating its response to the contact forces produced between the laparoscope and the patient. The patient’s abdomen was simulated by a pelvitrainer characterized by a radial stiffness of 3 N/mm, which is a representative value of the human tissue. In this experiment, the pelvitrainer was moved in the ^ pB xdirection (Figure 7), resulting in a movement of 3 mm in the Xand Y-axes of {B}. This displacement caused a constant force of 9 N in each axis. The response of the system to this external force is shown in Figure 9. The force on the X-axis is shown as a solid line, while the force on the Y-axis is represented with a dashed line. The figure shows that once the admittance control is activated, the contact forces of 9 N are minimized by the pivoting motion of the TCP. The gains kAx and kAy of the admittance control are experimentally determined. Both gains are equal since the system should respond in the same manner on both axes. Therefore, three experimental tests were carried out with the following gain values: 0.03, 0.06 and 0.075 radN -1 s -1 . There is also a clear need to avoid high or low gains since the system loses efficiency in both cases. A high gain (blue line in Figure 9) provokes undesired and unsafe oscillations, while a low gain (green line in Figure 9) causes an overdamped response, which increases the time response of the system. In the case of a gain of 0.03 radN -1 s -1 (orange line in Figure 9), the system stabilizes quickly, not exceeding ±0.2 N again at 0.2 s after the over-peak and 0.7 s after the start of the pivoting. It is noteworthy that, with this gain, the system takes 0.32 s to reduce the exerted forces of 2 N, a threshold at which the risk can be considered avoided. It has been proved that the system provides an adequate response to high forces and has therefore been validated to be FIGURE 9 Response of the admittance control to a contact force of 9 N between the laparoscope and the pelvitrainer, characterized by a radial stiffness of 3 N/mm. FIGURE 10 Linear movement performed to test the ff pivoting control for the Cartesian movement of the TCP. Frontiers in Robotics and AI frontiersin.org08 Fontúrbel et al. 10.3389/frobt.2023.1145265 effective in minimizing the contact forces produced by any movement of the patient, including slight physiological movements. The following experimental tests are carried out with an admittance control determined in this experiment at 0.03 radN -1 s - 1. Note that the mechanical characteristics of the pelvitrainer, such as the stiffness, may slightly differ from a patient’s abdominal wall, so the gain might require some finetuning. 3.2 Force-based pivoting motion control The performance of the complete force-based pivoting control to minimize the forces exerted by the camera during its movement has also been evaluated. The admittance control in combination with the action of the PI and ff controls is tested against repetitive linear movements of the TCP between pB TCP1 and pB TCP2, producing the motion shown in Figure 10.The displacement of the TCP is 3 cm in the X-andY-axes of {B}, without height variation, introducing the laparoscope to a depth of 15 cm inside the pelvitrainer. In the following experiments, the reference Cartesian velocity is 8mm/sinbothaxes,decreasing linearly as the TCP approaches the target zone, to observe if there were any changes in the behaviour at lower speeds. Figure 11 represents the reference Cartesian velocity in Y (black dashed line) to show the relationship between the TCP velocity in Y-axis andtheforceappearinginthisaxisinthedifferenttests.TheX Cartesian velocity of the TCP has been omitted to simplify the graph, as it is opposite to the Y velocity, producing an X force also opposite to the Y force. The first test (green line in Figure 11) aimed to evaluate the performance of the admittance control during these linear movements of the TCP. Although the admittance controller operates alone (neither ff nor PI has been implemented), the system response is closed to be considered safe, narrowly exceeding ±1 N as the maximum force. The contact force decreases during deceleration of the TCP displacement, indicating that once the ff is implemented, it will effectively reduce the force exerted at the contact point, even if its position is not accurately estimated. The second test (orange line in Figure 11) evaluated the response of the system to the TCP displacement, when the system is composed of the admittance control and the PI control. The PI, which requires current and past force measurements, is characterized by a low integral gain of 0.00015 rad/(s·N) and a frequency of 100 Hz. Note that the PI control has been activated only during the TCP point. A low value of this gain allows to reduce part of the stationary error during the Cartesian motion of the TCP, while a high value produces oscillations. The inclusion of the PI controller improves the response of the system without implementing yet any kind of position control. Figure 11 (orange line) shows that the forces exerted during the TCP displacement never surpass ±0.9 N, and therefore, the control can be already considered safe. The last test (red line in Figure 11) was performed with the complete angular velocity control, which consisted of the FIGURE 11 Force at the trocar during Cartesian movement of the TCP by the combination of the different control algorithms. Green, admittance control; orange, admittance control and PI; red, complete control strategy: admittance control, PI, and ff. Continuous lines represent forces at the X-axis, while dashed lines show forces at the Y-axis. The dashed black line represents the TCP Cartesian speed at the Y-axis. Frontiers in Robotics and AI frontiersin.org09 Fontúrbel et al. 10.3389/frobt.2023.1145265