2.1. Robotic tendon-driven active needle

The design of the tendon-driven active needle is shown in Fig. 2a. The active needle was developed by carving a series of six small notches on each side of a superelastic nitinol tube (Johnson Matthey, London, UK). Schematic dimensions of each notch are shown in Fig. 2b with the corresponding values listed in Table 1.

The notches produce a FS, shown in Fig. 2a, that allows for improved flexibility of the active needle. Two holes (0.25 mm in diameter) were made near the distal end of the FS for two tendons (0.10 mm diameter SMA wires) to get attached to. The tendons were looped in and out of the holes and completely fixed to drive needle bending when pulled.

Two active needles were developed in this work, with two different FSs, using the following manufacturing methods (i) ultraviolet (UV) laser cutter machine (Confluent Medical, Scottsdale, AZ) on the nitinol tube with 1.49 mm inner diameter (ID) and 2.00 mm outer diameter (OD) shown in Fig. 2c, henceforth called FS I, and (ii) typical machining methods in lab on the nitinol tube with an ID of 1.60 mm and OD of 2.00 mm shown in Fig. 2d, henceforth called FS II.

The notches on the FS I were developed with a width of 0.46 mm and a depth of 1.68 mm, achieving enhanced flexibility through increased precision, however at higher manufacturing cost. The notches on the FS II were created in the laboratory using a Dremel, with dimensions of around 0.42 mm in width and 1.33 mm in depth, all achieved at a relatively low production cost. In contrast, FS I demonstrates superior fatigue properties when compared to FS II.

The FS of the active needle was sealed to prevent tissue penetration into the needle tube and avoid tissue rupture. Shown in Fig. 2c, the FS was covered (tight fit) with a polyethylene terephthalate (PET) heat shrink tube (13 μm thickness). The PET material is biocompatible and sterilizable with ethylene oxide. We have tested the heat shrink tube on the active needle when bent and inserted into phantom tissues to ensure that it does not rip off during an insertion task [Reference Padasdao, Lafreniere, Rabiei, Batsaikhan and Konh68]. The active needle including the covered FS is sterilizable.

The utmost expected angular deflection of the active needle to realize a curved trajectory inside prostate gland was estimated using Fig. 1b, where a small radius of curvature is desired inside a deformed prostate. The bending angles were marked in the figure with small triangles on the curved trajectory, and the largest overall angular deflection of 50 degrees was measured. Methods to estimate the bending angles of the two active needles, developed in this work, are explained below.

Table I. The dimensions of the notches for the two active needles developed in this work. Units are in mm.

Figure 2. Schematic design of (a) Tendon-driven active needle with (b) The notch dimensions that are fabricated on a nitinol tube using UV laser cutter and typical machining in our laboratory to develop two flexure sections (FSs) shown in (c) FS I and (d) FS II, respectively.

The following equations are used to estimate the bending angle of the FS. For the notches schematically shown in Fig. 2b, the neutral bending axis is estimated using the following equation [Reference Eastwood, Francis, Azimian, Swarup, Looi, Drake and Naguib69]:

(1) \begin{equation}\overline{y}=\frac{4({r_{o}}^{3}\mathit{\sin }^{3} (\phi _{o})-{r_{i}}^{3}\mathit{\sin }^{3} (\phi _{i}))}{3\left({r_{o}}^{2}\left(2\phi _{o}-\mathit{\sin } 2\phi _{o}\right)-{r_{i}}^{2}\left(2\phi _{i}-\mathit{\sin } 2\phi _{i}\right)\right)}\end{equation}

where $\overline{y}$ is the distance moved from the center of the tube, $r_{o}$ and $r_{i}$ are the outer and inner radii of the tube, respectively, and $\phi _{o}$ and $\phi _{i}$ are found by the following equations:

(2) \begin{equation}\phi _{o}=\mathit{\arccos } (\frac{d-r_{o}}{r_{o}})\end{equation}

(3) \begin{equation}\phi _{i}=\mathit{\arccos } (\frac{d-r_{o}}{r_{i}})\end{equation}

where d is the notch depth. The bending angle for each notch can be estimated as:

(4) \begin{equation}\theta _{i}=\frac{h}{r_{o}+\overline{y}}\end{equation}

where h is the height of the neutral axis for each, which in this work is equal to the height of the cut (t). Assuming that the total deflection is distributed equally among the six notches, the bending angle of the whole flexible section could be found by multiplying the bending angle of each notch by the number of notches.

Dimensions of each notch for the two FSs are listed in Table 1. Using the equations above, the angular deflections of each notch were 14.48 and 14.13 degrees for the FS I and FS II, respectively. The overall angular deflections of the FSs (six notches) were 86.88 and 84.78 degrees for the FS I and FS II, respectively, which both surpass the expected angular deflection of 50 degrees for the active needle.

2.2. Actuation and ultrasound tracking system

The actuation system designed in this work consists of a motor, gear box, and lead screw. The tendon pulling force (F) to realize a specific bending on the FS when bending inside tissue should be estimated experimentally. The following equation is used to calculate the amount of torque (T) required to pull the tendon and consequently bend the active needle, similar to lowering a load on a lead screw:

(5) \begin{equation}T=\frac{Fd_{m}}{2}\left(\frac{l+\pi fd_{m}\mathit{\sec } \alpha }{\pi d_{m}-fl\mathit{\sec } \alpha }\right)\end{equation}

where d _m , l, f, and $\alpha$ are the mean diameter of a single thread, tendon displacement, coefficient of friction, and thread angle, respectively. To provide an example of calculations for the active needle (shown in Fig. 1b), we estimated that a maximum of 22N of force (tendon pulling force) is sufficient to bend the needle inside the tissue. This was estimated through needle insertion experiments in tissue phantoms with different Young’s modulus [Reference Datla, Konh, Koo, Choi, Yu, Dicker, Podder, Darvish and Hutapea70] resembling prostate tissue. With this tension, an 8 mm diameter lead screw, friction coefficient of 0.25 for threaded pairs of a steel and dry screw, and thread angle of zero for square threads, the maximum torque was estimated as 0.41 N.m. Upon torque estimation, a DC motor, gear, and a lead screw combination were selected and purchased to develop a pulling actuation mechanism. To realize bidirectional bending on the active needle, two similar tendon actuation mechanisms were developed and installed to have full control over needle bending.

The experimental setup to actuate the active needle at a desired bending angle and real-time US tracking in water medium is shown in Fig. 3a. The position of the tip is tracked using the US machine, processed through a series of image processing commands, and provided to the controller for appropriate control actions (explained later).

Figure 3. Experimental setup to evaluate performance of the tendon-driven active needle in water medium consisting of (a) US tracking, (b) Tendon actuation system to bend the flexure section in two directions, (c) Active needle and US probe submerged in water bath, and (d) 2D US plane for tracking bidirectional movement of the active needle tip.

The actuation system to pull the internal tendons of the FS I to realize a desired bidirectional bending at the tip (shown in Fig. 3b) consists of two motors, each consisting of a 0.5W (Maxon Group, Sachseln, Switzerland) DC motor RE 8 Ø8 mm, Precious Metal Brushes with an 8 mm diameter lead screw drive (GP 8 S Ø8 mm, Metric spindle, M3 x 0.5), and an encoder (MR, Type S, 100CPT).

An L7 Linear Array US probe (CHISON Medical Technologies Co., Ltd., Jiangsu, China) was used to track the tip of the active needle in real time in water medium. The active needle was submerged in water with the US lying on the surface of the medium. For proper sealing, the inner walls of the 3D-printed box (made by Prusa i3 MK3 printer), shown in Fig. 3c, were coated with a silicone sealant (Gorilla Glue Co., Cincinnati, OH). To prevent water from entering the needle tube, wood putty (Minwax, Cleveland, OH) was used at the distal end surrounding the entry point of the needle.

Figure 3d shows the 2D plane of the US for tip tracking. The cross section of the needle appears as a circular shape in the US images. The US images are obtained in real time with a frame grabber, Epiphan Av.io HD. (Epiphan Systems, Ottawa, Canada) from the ECO 5 (CHISON Medical Technologies Co., Ltd., Jiangsu, China) through the US probe.

Due to the artifacts observed in the US images while tracking the needle movement in the water medium, a series of image processing techniques (Fig. 4a) were performed to obtain the 3D coordinates of the active needle tip in real time. Fig. 4b shows an unprocessed US image, while Fig. 4c shows the processed image where region of interest is designated by the white box with the needle tip being marked with a red circle. The script assigned a coordinate system for the y-z plane over the US image being generated, using the pixel count as a basis for converting to millimeter scaling.

Figure 4. (a) Image processing method showing (b) Unprocessed US images with sources of noise, and (c) Processed US images in real time. The tip is marked with a red circle.

2.3. Actuation and electromagnetic tracking system

Another method of tracking the needle tip position was developed in this work using two 3D Guidance Model 55 EM tracking sensors (Northern Digital Inc., Waterloo, Canada), shown in Fig. 5. The EM tracking system includes two sensors. The first and second sensors were installed inside the needle tube at the tip and the proximal end of the needle, respectively. The EM tracker reports displacement and rotation data, so the bending angle at the FS of the active needle is measured directly by measuring the rotation of the distal sensor compared to the stationary proximal sensor. A similar actuation system, using Maxon motors as explained above, was used to manipulate the active needle. Manipulation and control were performed in the air.

Figure 5. Actuation and electromagnetic (EM) tracking system consists of (a) Active needle, (b) EM sensors, (c) EM transmitter, (d) EPOS4 positioning control boards, (e) Two Maxon motors, and (f) Power supply.

2.4. Closed-loop control

This section presents our controller to manipulate the tip of the active needle to follow a desired trajectory and reach a target point in water medium and air. Fig. 6 shows a schematic block diagram of our closed-loop control algorithm for US-based or EM-based tracking methods to realize a desired bending angle at the active needle’s FS. The controller communicates with the actuation system to realize appropriate tendon displacements via actuation of the Maxon motors and consequently realizes an angular deflection at the FS of the active needle. The controller was programed to force the FS to follow an input desired bending angle function. The needle tip position obtained by the US tracking system, or the tip and distal positions of FS obtained by the EM tracking system, was recorded in real time and used to estimate the angular bending of the FS. The PID controller (explained below) compares the input desired function with the bending angle estimated obtained in real time from the US or the EM tracking system to adopt appropriate control actions.

Figure 6. Scheme of closed-loop control method to realize a desired bending angle at the flexure section of the active needle.

To properly control the actuators to pull the internal tendons and consequently realize a desired bending angle at active needle tip, kinematic analysis of the FS is needed. The kinematic analysis provides a relationship between the tendon displacement and the bending angle. For the active needle, presented in this work, the kinematic analysis is as follows:

(6) \begin{equation}\Delta L=f\left(\theta,N,d\right)+\epsilon (\theta,d,t,N)\end{equation}

where $\Delta L$ is the tendon displacement, $\theta$ is the bending angle, $N$ is the number of notches, $d$ is the notch depth, and $t$ is the gap between two consecutive notches. The first and second terms refer to the kinematic and the tendon elongation, respectively. The kinematic term is:

(7) \begin{equation}f\left(\theta,N,d\right)=N.r_{t}.\sin (\delta \theta )\end{equation}

where $\delta \theta$ is the bending angle of each notch, which is part of the total bending angle ( $\theta =N.\delta \theta$ ), and $r_{t}$ can be found by:

(8) \begin{equation}r_{t}=d-\frac{\left(OD-ID\right)}{2}-\frac{t_{d}}{2}\end{equation}

where $OD$ is the outer diameter of the tube, $ID$ is the inner diameter of the tube, and $t_{d}$ is the diameter of the tendon. The tendon elongation term is approximated by:

(9) \begin{equation}\epsilon \left(\theta,d,t,N\right)=E_{\textit{tendon}}.F_{\textit{tendon}}(\theta,d,t,N)\end{equation}

where $F_{\textit{tendon}}$ is the tendon tension measured experimentally, and $E_{\textit{tendon}}$ is the tendon compliance approximated by the relationship between the tendon length ( $L_{\textit{tendon}})$ , and the Young’s modulus of the nitinol tendon ( $E_{\textit{tendon}}$ ) as:

(10) \begin{equation}E_{\textit{tendon}}=\frac{L_{\textit{tendon}}}{A.E_{\textit{tendon}}}\end{equation}

For the active needles presented in this work, the parameters listed in Table 1 are fed into the equations. The relationship between the force and the bending angle, $F_{\textit{tendon}}(\theta,d,t,N)$ , is obtained experimentally as:

(11) \begin{equation}F_{\textit{tendon}}\left(\theta,d,t,N\right)=0.2743\theta\end{equation}

To realize a desired bending angle at the tip of the active needle, a closed-loop PID controller (shown in Fig. 7a) was designed and implemented.

Figure 7. (a) Closed-loop PID controller to realize a desired bending angle on the compliant flexure section, (b) Comparison between the reference (desired) and output bending angles, and (c) Tendon displacement simulated for the system input.

In the system diagram, $\Delta \theta$ is the bending angle output of the active needle that is provided as a feedback in the closed-loop system, $\Delta \theta _{ref}$ is the reference (desired) bending angle with respect to the measured angle ( $\Delta \theta$ ), $e$ is the error of the system ( $e=\Delta \theta _{ref}-\Delta \theta$ ), and $\Delta L$ is the tendon displacement. The transfer functions, shown in the system diagram, are K _i , G ₁ (s), G ₂ (s), and G ₃ (s), that describe relationships between control input (u) vs. current (i), current (i) vs. actuator torque (τ), actuator torque (τ) vs. actuator stroke (ΔL), and actuator stroke (ΔL) vs. $\Delta \theta$ , respectively. Since the electrical response of the actuator based on the current input is faster compared to other mechanical responses in the diagram, G ₁ (s) is assumed as a constant value. G ₂ (s) is designed as a second-order system. The linear stroke of the actuator ( $\Delta L$ ) is measured experimentally to build dynamics with respect to the actuator torque. The control error, e, is used as the input of the PID controller, producing the PID control input ( $u$ ). G ₃ (s) represents the kinematic model of the active needle (described above). The relationship (and the transfer function) between $\Delta L$ and $u$ could be found as:

(12) \begin{equation}\Delta L=\left(K_{i}\right) G_{1}\left(s\right) G_{2}(s)\left(u\right)\end{equation}

The system is subject to a disturbance torque (τ _d ) imposed by the stiffness of the FS of the active needle on the motor, and thereby cannot have a consistent response. To avoid undesired responses (e.g., overshoot or non-consistent steady-state error) and to develop a precise and robust position controller, a disturbance observer was added to the PID controller. The disturbance observer loop estimates τ _d in form of a control input ( $\hat{u}_{d}$ ) as:

(13) \begin{equation}\hat{u}_{d}=\left(u-\Delta L.K_{in}^{-1}.G_{1n}^{-1}. G_{2n}^{-1}\right)Q\end{equation}

where $K_{in}^{-1}$ , $G_{1n}^{-1}$ , and $G_{2n}^{-1}$ are nominal forms of the functions, K _i , G ₁ , and G ₂ , respectively, which are estimated with the system identification toolbox (MATLAB R2022b, The Mathworks Inc.) from the measured response of these functions with respect to a chirp signal input, and Q is a second-order low-pass filter as $Q(s)=w_{c}^{2}/(s^{2}+2w_{c}s+w_{c}^{2})$ , where w _c is cutoff frequency. Then, $\hat{u}_{d}$ is added to u _c resulting in the control input, u:

(14) \begin{equation}u=u_{c}+u_{d}\end{equation}

The control algorithm was implemented in Simulink (The Mathworks Inc.) to tune the PID coefficients. The controller’s capability to match the output angle to the reference (desired) angle was evaluated when the reference bending angle changed between −60° and + 60°. The simulation tuned the PID coefficients as P:1.2, I:5, and D:0.02. Fig. 7b compares the output angle ( $\Delta \theta$ ) and the reference bending angle ( $\Delta \theta _{ref}$ ), showing that the output follows the reference angle. Fig. 7c shows the tendon displacement that is set by the controller to reach the reference angle. Additional experimental tuning was required when implementing the closed-loop control on the active needles. This was done by careful observation of the effects of each coefficient on the overall performance of the system. The proportional gain affects the speed of reaching the desired angle, the integral gain reduces the steady-state error, and the derivative gain reduces the overshoots. The experimentally tuned PID coefficients are P:0.45, I:0.0075, and D:0.5. The system oscillates between two close values (with ± 2° error from the desired angle). Bending experiments were performed with the active needles and the actuation system to evaluate the controller.