A High-Precision Robotic System Design for Microsurgical Applications ^†

Abstract

The introduction of robotic systems in medical surgery has achieved the goal of decreasing procedures’ invasiveness, positively impacting the patient’s prognosis by reducing the incision size, surgical infections, and hospitalization time. Nowadays, robotic surgery is used as an integral part of urology, gynecology, abdominal, and cardiac interventions. Despite its adoption in several surgical specialties, robotic technology remains limited in the area of microsurgery. In this paper, we present the development of a robotic system providing sub-millimeter motion resolution for the potential manipulation of fine structures. The design is based on linear delta robotic geometry. The motion, resolution, and repeatability of the developed system were simulated, followed by proof-of-concept experimental testing. The developed system achieved a motion resolution of 3.37 ± 0.17 µm in both the X- and Y-axes and 1.32 ± 0.2 µm in the Z-axis. We evaluated the system navigation, setting a zigzag trajectory with dimensions below those found in blood vessels (300 to 800 µm), and found that the system is capable of achieving a maximum resolution of 3.06 ± 0.03 µm. These results demonstrate the potential application of the here-presented robotic system for its use in microsurgical applications such as neurosurgery, plastic, and breast cancer surgeries.

1. Introduction

Within the last two decades, multiple efforts have been focused on introducing robotic surgeries in routine procedures within multiple surgical disciplines [1] spanning from ophthalmology, urology, gynecology, cardiology, etc. The benefits of such technology compared to open surgery include the reduction of incisions from centimeters to tens of millimeters, resulting in minimized patient trauma, reduction in surgical site infections, and shorter hospitalization time, providing benefits to the patient’s recovery. Current commercial robotic systems allow the surgeon to manipulate the laparoscopic tools using a set of controls that translate the surgeon’s natural hand and wrist movements into corresponding surgical tool movements, providing the millimetric precision required for general surgical procedures.

However, specialized procedures requiring sub-millimeter precision manipulation such as reconstructive microsurgeries, surgical anastomosis, vitreoretinal eye surgery, and neurosurgery have not yet benefited from robotic surgery [2,3], posing the need for the development of robotic systems specially designed for such applications. Surgical anastomosis is a surgical technique used to make a connection between tubular body structures such as blood vessels, with diameters ranging between 300 and 800 µm. The reconnection of such structures is key to the re-establishment of lymphatic flow required in vascularized tissue transplantation [4]. Commercial platforms such as the da Vinci robot have been used to attempt procedures requiring high-precision manipulation such as microsurgical anastomosis. However, the design specifications of such systems are best suited to perform key-hole surgeries that deal with structures having dimensions in the centimeters range [5], making challenging the provision of sufficient motion resolution to accomplish tasks at a micro-scale level. State-of-the-art examples of robotic systems capable of achieving high-precision actuation are limited. These have been mainly evaluated in research laboratories trialing microsurgical applications including blood vessels nerve tracts and other soft tissue structure reconnection. Initial first-in-human surgeries reported in the literature include lymph venous anastomosis required for breast cancer-related lymphedema treatment [6]. Here, the surgeon’s movements can be downscaled down to ~70 µm motion precisions well beyond key-hole surgical robots. Other robotic systems developed for microsurgical applications include the MUSA robot [7] and MMI’s Symani System with NanoWrist (Italy) [8]. These systems provide magnification of the surgical area allowing simplified implementations in the operating room to perform micro-surgical procedures. Such robots are based on serial link geometries designed to cover larger workspaces. This, however, possesses the challenge of cumulative backlash errors that are often compensated using pre-loaded differential gears impacting the robot complexity, often associated with price [9].

In this paper, we present the design and simulation of a surgical robotic system based on a parallel geometry aiming to reduce the design complexity while providing sub-millimeter motion resolution. Using this type of geometry, the robot link dimensions were tailored for a defined workspace and resolution suited for microsurgical tasks. The motion, resolution, and repeatability of the developed system were assessed using simulations followed by an experimental proof-of-concept high precision, mimicking a stitching task to validate its potential to be used for microsurgical procedures.

2. Materials and Methods

In a parallel robot geometry, the end-effector is connected to the base using multiple link sequences, forming a closed-loop system. This has been widely used in industrial pick-and-place applications [8]. The implementation of parallel structures can be used to simplify the robot design while achieving high precisions [9].

The design of the proposed surgical robotic system is based on a linear delta robotic geometry consisting of three linear actuators, three pairs of parallel legs, and twelve spherical joints, enabling high stability, low inertia, and high motion precision all required for microsurgical tasks. Thus, in this paper, we describe the robot design methodology consisting of three stages: geometrical structure design, robot simulation and validation, and robot proof-of-concept testing.

2.1. Geometrical Structure Design

The simplified geometrical model of the linear delta robot design is shown in Figure 1.

Here, the ball joints are fixed to linear sliders (B1, B2, B3) and the end-effector (P1, P2, P3). The coordinate of the base plane O is (0, 0, 0), the coordinate of the end-effector O’ is (x, y, z), and the displacement of the linear sliders are z1, z2, z3. This implies that the coordinates of the B1, B2, B3 are (0, √3/2, z1), (−√3/2, z2), and (√3/2, 0, z3), respectively. The geometrical relationship between arm length L, the radius of the based platform R, and the radius of the moving platform are obtained using Equations (1)–(4).

Equation (1) shows the spatial relationship between robotic arms and the center of the mobile platform using vector arithmetic, to express the arm length L.

Equations (2)–(4) are related to the robotic arm length L, which is obtained using end-effector coordinates (x, y, z), r, R, and the vertical motion of the three linear sliders z1, z2, and z3 respectively. Using mathematical simplifications, the equations of x, y, z or z1, z2, z3 can be obtained.

$$\overrightarrow{O{O}^{\prime }}=\overrightarrow{OBi}+\overrightarrow{BiPi}+\overrightarrow{Pi{O}^{\prime }}$$

(1)

$$x^2+{\left(y+r-R\right)}^2+{\left(z-z1\right)}^2=L^2$$

(2)

$${\left(x-\frac{\sqrt{3}}{2}\left(r-R\right)\right)}^2+{\left(y-\frac{1}{2}\left(r-R\right)\right)}^2+{\left(z-z2\right)}^2=L^2$$

(3)

$${\left(x-\frac{\sqrt{3}}{2}\left(r-R\right)\right)}^2+{\left(y-\frac{1}{2}\left(R-r\right)\right)}^2+{\left(z-z3\right)}^2=L^2$$

(4)

2.2. Kinematic Simulation

Using Equations (1)–(4) while defining the motion limits of B1, B2, and B3, the motion state of the end-effector O’ was represented dynamically using simulations. The robot design and the kinematics modeling were simulated using MATLAB 2020 (Math Works, Natick, MA, USA) and CATIA V5-6R2018 (Dassault Systems, Vélizy-Villacoublay, France).

Following the geometric solution of forward kinematics, simulation results showed that the motion resolution considering the final arm length and the base platform radius (L = 250 mm, R = 235 mm, r = 20 mm) ranges between 0.24–0.625 μm. Thus, the minimum single-step motion resolution of a single motor is 0.625 µm considering micro-stepping of 1/8. Figure 2 presents an example trace resulting from the simulations outlining the temporal evolution of the XYZ-axis coordinates of the end-effector. Figure 2a shows the displacement of the X-axis and Y-axis coordinates over time, and Figure 2b shows the Z-axis coordinate displacement over time. From these results, it can be observed that the maximum achieved motion resolution under the final dimension parameters is ~0.24 µm.

To assess the robotic workspace considering the obtained dimensions (L, R, and r), all simulated trajectory points of the end-effector O’ were traced. Figure 2c shows the front view of the simulated full workspace having a pyramid-like structure with dimensions of ~114.2 mm × 114.2 mm × 110 mm and 130 mm depth.

The forward kinematic simulation shows that the end-effector resolution of the linear delta robot can reach a maximum of 0.36 µm/pulse considering 1/8 micro-stepping and 1.75 µm/pulse considering 1/2 micro-stepping. By integrating both the workspace and motion resolution, it can be concluded that using the design parameters obtained (R = 250 mm, L = 235 mm, r = 20 mm), it is possible to reach the required precision for microsurgical applications dealing with structures having dimensions between 300 to 800 µm [10].

The inverse kinematic (IK) simulation was used to determine the accuracy of the stepper actuator setting and to guarantee, using simulations, that the system configuration will match the sub-millimeter level performance required for microsurgical applications. The IK expressions are represented in a similar fashion to the forward kinematics. Here, the positions B1, B2, and B3 were expressed as the positions of end-effector (x, y, z). Following the geometrical construction of the linear delta robot shown in Figure 1, the coordinates of the linear sliders on the XY plane were considered to be fixed, then the change in the coordinates is reflected in the displacement of the z-axis coordinates relative to the initial position (z1, z2, z3). The real-time z-axis coordinates of B1, B2, and B3 can be obtained using Equations (5)–(7):

$$z1=\pm \sqrt{L^2-x^2-{\left(y+r-R\right)}^2}+z$$

(5)

$$z2=\pm \sqrt{L^2-{\left(x-\frac{\sqrt{3}}{2}\left(r-R\right)\right)}^2-{\left(y-\frac{r-R}{2}\right)}^2}+z$$

(6)

$$z3=\pm \sqrt{L^2-{\left(x-\frac{\sqrt{3}}{2}\left(R-r\right)\right)}^2-{\left(y-\frac{r-R}{2}\right)}^2}+z$$

(7)

Note that Equations (5)–(7) show the vertical motion of the linear sliders z1, z2, and z3, expressed by the parameters L, R, and r, which are affected by the end-effector’s position (x, y, z). The notation ± corresponds to the robotic motion direction, where a positive sign indicates a downward movement of the end-effector’s position.

Figure 3 shows the IK simulation results of a zigzag trajectory. Figure 3a shows the zigzag trajectory in the XY-plane, consisting of horizontal and vertical displacements set to describe 150 µm and 15 µm segments, respectively. Figure 3b shows the coordinate changes in the end-effector in the XY-plane, while Figure 3c shows the changes in three robot sliders (Z1, Z2, Z3). In this case, a 15–150 µm displacement of the end-effector produces a displacement of 25.4–218.7 µm of the three linear sliders of the robot.

3. Results and Discussion

Robot Proof-of-Concept Trajectory Testing

Considering the geometric design and simulation results described in Section 2, the proposed robotic system was built employing metallic beams (MakerBeam B.V., Utrecht, The Netherlands) and custom-made 3D-printed components. Figure 4a shows the physical prototype (top view) of the robotic platform. The drive system uses three 35 mm SH3533-12U40 stepper motors (Sanyo Denki, Tokyo, Japan) and a BSD 02.V motor driver (RTA Pavia, Marcignago, Italy). The robotic system is controlled with a custom-made GUI controlled though a MyRIO 1900 FPGA (National Instruments, Austin, TX, USA).

For the evaluation of the precision and kinematic performance of the linear delta robot manipulator, a noncontact metrology approach based on a bright field microscopy system was used. To reach the required micron-level resolution, the linear slider displacement was set to 20 microns/pulse, corresponding to an angular movement of 0.225°. This resulted in a motion resolution of 1.32 ± 0.02 µm for the Z-axis and 3.37 ± 0.17μm for the X- and Y-axes, indicating the system’s potential to be used for microsurgical tasks [11]. The motion performance of the proposed robotic system was set up in a laboratory environment and evaluated using a proof-of-concept experimental evaluation shown in Figure 4. We define a zigzag/raster trajectory, which consists of five 180 µm horizontal lines and four 15 µm vertical lines. For each test, three forward trajectories and three backward trajectories were carried out.

The representative zigzag trajectory test was set up in LabVIEW software (v2021 National Instruments, Austin, TX, USA) considering the dimensions of fine structures such as skin cells with an average size of 50 µm [11]. For data analysis, the videos of the executed trajectory were recorded. By tracing a zigzag 2D trajectory, we aim to simulate a simplified stitching procedure, where the end-effector is to be moved from side to side to join the adjacent portions of tissue. The zigzag 2D trajectory is shown in Figure 4. Figure 4b is the executed zigzag trajectory without compensation, as can be observed in the resulting differences between the trajectory segments and figure. This is to be expected as the robot operates in an open-loop configuration.

However, further analysis of the traces indicated repeatable offset errors within the trajectory which can be further compensated. The results after trajectory compensation are presented in Figure 4c.

Table 1. Test results of the compensated zigzag trajectory.

No.	Resolution [μm]	Angle Error [°]	Trajectory Error [μm]
Zigzag 1	3.17 ± 0.03	−2.52 ± 0.85	9.59 ± 0.91
Zigzag 2	3.08 ± 0.04	−2.30 ± 0.25	3.47 ± 0.65
Zigzag 3	2.94 ± 0.02	−3.28 ± 0.53	3.85 ± 0.34
Average	3.06 ± 0.03	2.7 ± 0.54	5.64 ± 0.63

shows the detailed results of the compensated zigzag trajectory. It can be observed that the average trajectory error is improved from 40 ± 2.13 µm (uncompensated trajectory) to 5.64 ± 0.63 µm (compensated trajectory) with an average angular error reduction of 2.7 ± 0.54°. Assessing the resolution obtained within this proof-of-concept test resulted in an average motion resolution of 3.06 ± 0.03 µm.

Comparing the results obtained from the simulations and experiments, it can be concluded that the built system dynamics and the open-loop control affect the obtained motion accuracy. This is expected as the built system elements’ specifications and tolerances differ for the ideal conditions set in the simulations. Nonetheless, the motion resolution was found to be less than 5 microns, indicating that the system offers a performance that goes well beyond that required for performing microsurgical operations.

4. Conclusions

In this paper, the design, simulation, and proof-of-concept evaluation of a linear delta robot device to be used for microsurgical applications has been presented. The robot design was focused on achieving high motion precision tasks considering the dimensions of structures such as blood vessels ranging between 300 to 800 µm.

This developed system had dimensions of R = 250 mm, L = 235 mm, r = 20 mm, and a pyramid-like workspace with dimensions of ~114.2 mm × 114.2 mm × 110 mm and 130 mm depth. This resulted in a motion resolution of 3.37 ± 0.17 µm in both the X- and Y-axes and 1.32 ± 0.2 µm in the Z-axis considering individual steps. The system was evaluated considering a zigzag trajectory with dimensions similar to those found in blood vessels. We found that performing the zigzag trajectory in a series of three experiments resulted in a displacement between these, resulting in an error of 40 ± 2.13 µm. With the addition of displacement and angle compensation, these errors were reduced by 85.9%. These results demonstrate the potential application of the here-presented robotic system for its use in microsurgical procedures.