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Abstract

Objective

Traditional computed tomography (CT)-guided tumor ablation procedures are often hampered by the need for repeated scans and significant radiation exposure, primarily due to challenges in manual needle insertion and the iterative realignment process. This research introduces an advanced intraoperative CT (iCT)-guided robotic system. The core aim is to enhance procedural accuracy and efficiency by implementing precise, real-time remote-center-of-motion (RCM) control for needle interventions.

Methods

This study develops an integrated iCT-guided robotic needle biopsy/ablation system. A key distinction from conventional iterative navigation systems is their capability for surgeons to dynamically adjust the intervention line in situ. Real-time visualization of relative positioning is achieved using 3D (three-dimensional) Slicer software. This is coupled with a novel and robust RCM control strategy, meticulously engineered based on screw axis theory and velocity twist, and further optimized with interpolation and feedforward control laws. This framework enables precise, surgeon-guided adjustments of the guiding catheter's posture throughout the procedure.

Results

The RCM control system effectively and reliably governed the motion of the robotic guidance arm. This ensured that the catheter tube consistently maintained its accurate orientation relative to the target even after multiple surgeon-adjusted posture modifications. Experimental validation demonstrated the system's high performance, achieving exceptionally low RCM errors as 2×10⁻⁴ m. Consequently, any deliberate pause during the robotic arm's movement could be utilized to define a precisely targeted and safe puncture path.

Conclusion and significance

Comprehensive numerical modeling and experimental evaluations using a TM5-700 robotic arm with phantoms have provided validation for the proposed screw axis-based RCM control concept. Integrating iCT guidance with this RCM system indicates increased precision, operational flexibility, and overall safety of robotic needle-based interventions. This work presents a noteworthy contribution with potential for clinical adoption in various minimally invasive procedures.

Keywords

intraoperative computed tomography navigation percutaneous puncture remote center of motion surgical robot velocity twist

Introduction

Image-guided percutaneous puncture biopsy/ablation is a treatment method in which an imaging method, such as ultrasound, computed tomography (CT), or magnetic resonance imaging (MRI), is used to aid the insertion of a thin ablation needle into deep-seated tumor lesions to extract a tissue sample or to apply energy to ablate the tumor tissue. Compared with the traditional surgical removal of tumors, percutaneous ablation surgery has the advantages of less bleeding, faster postoperative recovery, shorter surgery time, and the ability to preserve most organs; thus, the use of percutaneous ablation surgery is becoming popular in various procedures.^1–4

In percutaneous ablation, the surgeon places a needle through the skin into the tumor. In contrast to minimally invasive surgery, percutaneous ablation does not involve the use of a camera for observation, and the surgeon often relies on a CT scan or an ultrasound for guidance. Ultrasound and MRI are less suitable for imaging lung tumors because of the shielding effect of lung gas, and only CT can provide clear images of these tumors.⁴ In contrast to ultrasound, which has real-time imaging ability, traditional CT is time-consuming. Patient movement during CT may result in inaccurate tumor localization. Moreover, manual puncture may cause deviation from the planned needle path. Therefore, repeated scanning is required in CT, and the iterative process can take several hours.

To address the unmet needs encountered in the clinical CT and puncture biopsy/ablation settings above, robot-assisted methods can be used to reduce the uncertainty involved in the puncture process. Robot-assisted percutaneous ablation is a stable and accurate process, and commercial systems are available for this process. A robot is fixed to a scanning bed for the robot and patient to be scanned simultaneously. For instance, Siemens introduced a C-arm system based on cone-beam CT (CBCT) that enables the surgeon to plan the puncture path on an imaging interface. The advantage of these systems is that they have a fixed coordinate relationship with the scanning bed; however, their bulky setup makes it highly difficult to recalibrate the patient's position. Other similar products include Innomotion (developed by Innovedic), Micromate (developed by ISYS), and DEMCON.^5–8

The above system has certain drawbacks. First, the equipment in the operating room might obstruct the robotic-arm's movement, and the puncture posture might need to be changed. Second, the patient's other organs might lie on the puncture path, thereby necessitating a change in the puncture path. Moreover, the surgeon may wish to adjust the puncture path during the operation after observing the relative position between the path and the tumor. Ideally, the catheter should always point toward the tumor. This represents another unmet need for percutaneous ablation operations for the medical staff.

To overcome the limitations commonly encountered in percutaneous ablation procedures—where clinicians often face challenges in accurately targeting lesions, as reported in various research studies and observed in commercial systems—the integration of remote-center-of-motion (RCM) control technology offers a promising solution. A comparative summary of the relevant CBCT technologies is presented in Table 1.^9–13

Table 1.

Systematic comparison of the CBCT technology.^9–13

	BENEFITS	DRAWBACKS
FIXED CBCT	Real-time high-resolution 3D imaging Immediate complication detection Minimized patient transfers Complete fluoroscopy capabilities Versatile clinical applications Superior tissue differentiation	Fixed installation space limitation High capital expenditure Patient breath-hold requirement Contrast interpretation challenges Motion artifact vulnerability
ROBOTIC-ARM CBCT	Expanded procedural application spectrum Dual-mode 2D/3D imaging functionality Procedure time reduction Workflow optimization High correlation with postoperative CT	Specific region scanning limitations Specialized training requirement CT-equivalent radiation exposure
MOBILE CBCT	Inter-operation room mobility advantage Dual-mode imaging capability Simplified operational protocol Cost efficiency versus fixed/robotic systems	CT-inferior image quality Field-of-view limitation Staff-dependent positioning requirement Motion artifact susceptibility
RCM CONTROL WITH ROBOTIC-CBCT (THIS STUDY)	Combines robotic precision with enhanced control Potential for reduced procedure variability Optimization of the target acquisition	Currently under investigation System complexity Additional implementation costs

2D: two-dimensional; 3D: three-dimensional; CBCT: cone-beam computed tomography; CT: computed tomography; RCM: remote-center-of-motion.

RCM control has emerged as a critical technology for addressing the above limitations in percutaneous ablation procedures. By enabling instruments to pivot around a fixed point—typically the incision site—RCM control effectively mitigates the issues of needle path deviation, improves targeting accuracy, and minimizes trauma while enhancing precision. This technology directly addresses the challenge of maintaining consistent catheter orientation toward the tumor throughout the procedure. As presented in Table 1, when integrated with robotic-CBCT, RCM control offers significant advantages, including robotic precision, improved control, and optimized target acquisition. For example, in both clinical applications and research, AcuBot—developed by Stoianovici et al.¹⁴—is a robotic arm equipped with an RCM mechanism that can be remotely controlled by a surgeon.

Research on constrained kinematic control in minimally invasive robotic surgery under RCM constraints¹⁵ has significantly advanced the field of robot-assisted minimally invasive surgery. Although Table 1 highlights that robotic-arm CBCT systems already contribute to workflow optimization and reduced procedure time, the integration of RCM control further enhances these advantages by reducing procedural variability. Some studies on RCM control also incorporate gravity compensation and the development of specialized end-effector design. For example, investigations into partial gravity compensation of surgical robots¹⁶ demonstrated that counteracting gravitational forces improves system performance by minimizing undesired forces at insertion points. Furthermore, research on innovative end-effectors for robotic needle insertion systems¹⁷ illustrates how targeted mechanical design addresses the specific requirements of percutaneous interventions. These innovations also help mitigate the specialized training requirement—one of the key drawbacks associated with robotic-CBCT systems, as noted in Table 1.

The limiting distal motion center can be achieved primarily through two approaches: mechanism design (mechanism-based RCM control)^18,19 or appropriate control laws (programable RCM control).^20–22 The present study mainly focused on programable RCM control as it offers greater flexibility during surgical operation compared to mechanism-based approaches and does not require additional mechanism design and installation. This approach effectively addresses the “fixed installation space limitation” associated with fixed CBCT systems, as noted in Table 1, while still ensuring precise control.

Some studies have proposed a dual-quaternion-based velocity controller with trajectory interpolation capabilities to satisfy RCM constraints.²³ The Jacobian matrix of the RCM point is combined with the Jacobian matrix of the robotic arm's linear velocity to form an extended Jacobian matrix.²⁴ Based on the constrained Jacobian matrix, the lateral velocity at the RCM point can be set as zero.²⁵ Additionally, the velocity term of the directional error toward the RCM can be constrained using null-space control.²⁶ Motion constraints are achieved by solving a constrained quadratic programming optimization problem.²⁷

As evident from the comparative analysis presented in Table 1, our integration of RCM control with robotic CBCT is designed to synergize the benefits of various systems while addressing their limitations. Although this integration introduces challenges, such as system complexity and additional implementation costs, the potential advantages—combining robotic precision with enhanced control and optimizing target acquisition—represent significant advancements for percutaneous ablation procedures. The comparative evaluation of fixed CBCT, robotic-arm CBCT, mobile CBCT, and our RCM-controlled robotic CBCT approach offers a comprehensive framework for understanding the evolution of image-guided intervention technologies. However, to date, limited research has proposed a control law based on the screw axis theory and velocity twist for controlling the RCM and end-effector attitude. Addressing this gap remains a promising direction for future work in our study.

Our approach aims to integrate the benefits of multiple technologies while addressing their limitations. In this study, we aim to develop an intraoperative CT (iCT)-guided robotic needle biopsy system with RCM control to overcome the limitations of existing methods. The primary objectives of this research are as follows:

To investigate and implement an effective RCM control strategy for percutaneous procedures.

To implement a novel screw axis and velocity twist approach for the RCM control.

To establish a precise spatial relationship between the robot workspace and the CT image space.

To ensure consistent and accurate needle targeting throughout the positioning process.

To develop an intuitive user interface for real-time visualization and procedure planning.

The proposed system establishes a precise spatial relationship between the robot workspace and the CT image space, enabling surgeons to accurately determine the distance between the puncture line and the target lesion. The proposed system features two complementary operation modes: a manual dragging mode for initial positioning and a computer-controlled mode for precise alignment. Surgeons can easily guide the robotic arm near the desired puncture path through manual dragging and then switch to the computer-controlled mode to achieve precise positioning under the RCM constraint. This ensures that the annular guide consistently maintains its orientation toward the target lesion.

We implemented RCM control using a screw axis and velocity twist approach, enabling the surgeon to plan needle position and orientation through the imaging interface. The novelty of the proposed system is that the cannula maintains its orientation toward the lesion throughout the positioning process, providing enhanced operational flexibility while maintaining precise control. This ensures that even if the surgeon pauses the robotic arm during its movement, the annulus remains correctly aligned with the intended puncture path. By maintaining this consistent orientation, our approach effectively overcomes several limitations of existing percutaneous ablation systems, offering a more accurate and efficient solution for clinical applications.

Control methods and experiments

Screw axis theorem and motion control

The screw axis theorem of finite motion, also known as the Mozzi–Chasles theorem, states that the finite or instantaneous motion of a rigid body in space can be represented as a rotation about an axis and a translation along the rotation axis. As illustrated in Figure 1, a movement from coordinate system {A} to coordinate system {B} can be interpreted as a rotation by angle θ from {A} to {A^’} about the screw axis, followed by a translation d in the direction of the unit vector ω ^ to reach coordinate system {B}.²⁸

Figure 1.

Screw axis with limited motion.²⁸

If a 6 × 1 vector X is used to represent the screw axis, equation (1) is valid. The 4 × 4 matrix representation of this vector is expressed in equation (2).

\begin{matrix} X = [\begin{matrix} v \\ \hat{ω} \end{matrix}] \end{matrix}

(1)

\begin{matrix} \hat{S} (X) = [\begin{matrix} S {(\hat{ω})}_{3 \times 3} & v_{3 \times 1} \\ 0_{1 \times 3} & 0 \end{matrix}] \end{matrix}

(2)

where

\hat{ω}

denotes the unit vector of the screw axis,

S (\hat{ω})

the skew-symmetric matrix of

\hat{ω}

, and v the moving tangential vector of the coordinate system around the start of the screw axis. The matrix logarithm for the screw axis theorem can then be expressed as follows:

\begin{matrix} l o g (T) = \hat{S} (X) \end{matrix}

(3)

where T represents the homogeneous transformation matrix (i.e.

T =_{B}^{A} T s . t_{B}^{0} T =_{A}^{0} T T

). From Figure 1, the homogeneous transformation matrix can be expressed geometrically as

\begin{matrix} T = [\begin{matrix} e^{S (\hat{ω}) θ} & (I_{3} - e^{S (\hat{ω}) θ}) q + h θ \hat{ω} \\ 0 & 1 \end{matrix}] \end{matrix}

(4)

where q represents the vector formed from the origin of the reference coordinate system

{A}

to any point on the screw axis, h the ratio of the translation of the screw axis to the angle of rotation to the screw axis, that is,

h = \frac{∥ d ∥}{θ} {q, \hat{ω}, h}

and

θ

can be used as a set of parameters to describe the screw axis with limited motion. Geometrically, represents the moving tangent direction vector of the coordinate system around the start of the screw axis. Therefore,

{v, \hat{ω}}

and

θ

can also be used to describe the screw axis of the finite motion, and equation (4) can be rewritten as

\begin{matrix} T = [\begin{matrix} e^{S (\hat{ω}) θ} & G (θ) v \\ 0 & 1 \end{matrix}] \end{matrix}

(5)

where

G (θ) = (I_{3} θ + (1 - \cos θ) S (\hat{ω}) + (θ - \sin θ) S {(\hat{ω})}^{2})

On the other hand, if the instantaneous rotational velocity $\dot{θ}$ is considered, the screw axis of equation (1) and the rotation speed can also be represented with a new notation $_{B}^{V}$ . This is called the velocity twist, a vector composed of linear and angular velocities and expressed in a moving coordinate system as follows:

\begin{matrix} X \dot{θ} = [\begin{matrix} v \\ \hat{ω} \end{matrix}] \dot{θ} =_{B}^{V} \end{matrix}

(6)

Figure 2 shows the conversion of velocity twist between different coordinate systems. The object velocity twist $^{b} V$ and $^{d} V$ and the two coordinate systems have the following relationship:

\begin{matrix} ^{b} V = [A d_{_{d}^{b} T}]^{d} V, [A d_{_{d}^{b} T}] = [\begin{matrix} _{d}^{b} R & S (_{d}^{b} P_{o r g})_{d}^{b} R \\ 0_{3 \times 3} & _{d}^{b} R \end{matrix}] \end{matrix}

(7)

Figure 2.

Speed screw conversion.

Equation (7) is the adjoint representation of the homogeneous transformation matrix $_{d}^{b} T = [\begin{matrix} _{d}^{b} R & _{d}^{b} P_{o r g} \\ 0 & 1 \end{matrix}]$ of the coordinate system ${d}$ relative to the coordinate system ${b}$ . According to equation (7), the ideal velocity rotation can be transferred to the current coordinate system $[A d_{_{d}^{b} T}]$ .using.

To implement a closed-loop control law²⁹ based on the screw axis theorem, let $_{b}^{0} T (t)$ represent the current coordinate system, ${b}$ , and $_{d}^{0} T (t)$ represent the ideal coordinate system, ${d}$ , on the task. The control objective is to ensure that converges to $_{d}^{0} T (t)$ . To achieve this, a control scheme combining feedforward control and proportional–integral feedback control is employed. The resulting control equation is given as follows:

\begin{matrix} u_{b} (t) = [A d_{_{d}^{b} T}] V_{d} (t) + K_{p} X_{e} (t) + K_{i} \int_{0}^{t} X_{e} (t) d t \end{matrix}

(8)

where

u_{b} (t)

denotes the input object velocity twist,

[A d_{_{d}^{b} T}] V_{d} (t)

the feedforward control item, and

V_{d} (t)

the object velocity twist in the ideal coordinate system. The last two terms on the right side of equation (8) are the proportional error and integral error terms, respectively.

X_{e} (t)

denotes the error between

_{b}^{0} T (t)

and

_{d}^{0} T (t)

. This error is not directly computed by subtracting the two matrices, as subtracting rotation matrices is meaningless. Instead, the error is determined using the screw axis parameters and the rotation angle

θ

, as described in equation (3), by expressing the transformation from

_{b}^{0} T

_{d}^{0} T

as the bihomogeneous transformation matrix.

\begin{matrix} \hat{S} (X_{e} (t)) = \log (_{b}^{0} T {(t)}^{- 1}_{d}^{0} T (t)) \end{matrix}

(9)

Derivation of RCM motion control

Based on equation (8), $_{i}^{0} T$ is assumed to be the initial coordinate system of the cannula at the end of the robotic arm, and $_{f}^{0} T$ assumed to be the final position and attitude ${f}$ to be achieved (Figure 3). To reach the final state, the ideal coordinate system is set as the final coordinate to be reached, that is, T $_{d}^{0} T (t) =_{f}^{0} T {d} = {f}$ ; thus, only the proportional control item of equation (8) is reserved. Equations (8) and (9) are, respectively, simplified as follows:

\begin{matrix} u_{b} (t) = K_{p} X_{e} (t) \end{matrix}

(10)

\begin{matrix} \hat{S} (X_{e} (t)) = \log (_{b}^{0} T {(t)}^{- 1}_{f}^{0} T) \end{matrix}

(11)

Figure 3.

Starting and final coordinate systems.

Although the robotic arm can be moved from the initial coordinate system $_{i}^{0} T$ to the final coordinate system $_{f}^{0} T$ on the basis of equation (10), it cannot be guaranteed that the cannula would always point toward a fixed point during this process. In Figure 4, $P (t)$ represents the origin of the coordinate system of the cannula at the end of the robotic arm at time $t; v (t)$ , denotes the linear velocity at the origin of the coordinate system at time $t; z (t)$ , denotes the $z$ -axis unit vector of the coordinate system at time t, and $ω (t)$ the angular velocity at time t. Moreover, $P_{R C M}$ is the fixed point, and $P (t + d t)$ and $z (t + d t)$ represent the origins of the coordinate system and the unit vector of the $z$ -axis at time $t + d t$ , respectively.

Figure 4.

Velocity relationship of the RCM in a continuous condition. RCM: remote-center-of-motion.

Based on Figure 4, with a simplification for the nonlinear system, the equation is as follows:

\begin{matrix} S (ω (t)) z (t) = \underset{d t \to 0}{l i m} \frac{z (t + d t) - z (t)}{d t} = \dot{z} (t), \\ z (t) = \frac{P_{R C M} - P (t)}{‖ P_{R C M} - P (t) ‖} \end{matrix}

(12)

By differentiating the two sides of equation (12) with respect to time and then simplifying the resultant equation, we obtain

\begin{matrix} (- I_{3} + z (t) z {(t)}^{T}) \frac{v (t)}{‖ P_{R C M} - P (t) ‖} = S (ω (t)) z (t) \end{matrix}

(13)

Equation (14) describes the relationship between the linear and angular velocities of the object velocity twist, which must satisfy the RCM limit in the continuous condition.

\begin{matrix} (\frac{[\begin{matrix} - 1 & 0 & 0 \\ 0 & - 1 & 0 \\ 0 & 0 & 0 \end{matrix}]}{‖ P_{R C M} - P (t) ‖})^{b} v (t) = S (^{b} ω (t)) [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \end{matrix}

(14)

To ensure that the object velocity twist $K_{p} X_{e} (t)$ obtained using equation (10) satisfies the velocity limit in equation (14) in the continuous RCM case, the premultiplied matrix A is obtained $A K_{p} X_{e} (t)$ so that it satisfies the RCM motion limit. The matrix A is expressed as follows:

\begin{matrix} A = [\begin{matrix} 0 & 0 & 0 & 0 & ‖ - P_{R C M} - P (t) ‖ & 0 \\ 0 & 0 & 0 & ‖ P_{R C M} - P (t) ‖ & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \end{matrix}] \end{matrix}

(15)

The relationship between velocity twist and RCM limit

In equation (12), $d t \to 0$ is used as a condition to ignore high-order terms; thus, in simulations, the sampling time is fixed, or in practical discrete cases, the error accumulates and does not always point to a fixed point. This study derives the velocity term that allows the orientation error to converge.

Based on Figure 5 and the previous research,²⁶ the differentiated term of the orientation error can be defined as follows:

\begin{matrix} \dot{e} = S (^{b} z) (\frac{I_{3 \times 3}}{‖^{b} r_{b, l} ‖} - \frac{(^{b} r_{b, l}) (^{b} r_{b, l})^{T}}{‖^{b} r_{b, l} ‖^{3}}) \frac{d}{d t} (^{b} r_{b, l}) \end{matrix}

(16)

where

^{b} r_{b, l}

denotes the vector directed from the origin of

{b}

to a fixed point. This vector is expressed in

{b}

. Moreover,

^{b} z

is the

z

-axis of

{b}

Figure 5.

Schematic representation of the orientation error.

From Figure 6, the following differentiating expression with respect to time and rearranging the terms (with $\frac{d}{d t} (^{0} r_{0, l}) = 0_{3 \times 1}$ ) is obtained:

\begin{matrix} \frac{d}{d t} (^{b} r_{b, l}) = [\begin{matrix} - I_{3 \times 3} & S (^{b} r_{b, l}) \end{matrix}] [\begin{matrix} ^{b} v \\ ^{b} ω \end{matrix}] \end{matrix}

(17)

Figure 6.

Schematic representation of the vector relationship in {b}.

Using equation (17), the relationship between $\frac{d}{d t} (^{b} r_{b, l})$ and the object velocity twist in ${b}$ can be established. This relationship can be expressed as follows (when $\dot{e} = - λ e$ and $λ > 0$ ):

\begin{matrix} \dot{e} = L [\begin{matrix} ^{b} v \\ ^{b} ω \end{matrix}] = - λ e \end{matrix}

(18)

\begin{matrix} [\begin{matrix} ^{b} v \\ ^{b} ω \end{matrix}] = - λ L^{+} e \end{matrix}

(19)

Equation (19) describes the object velocity spinor (in ${b}$ ) that allows the direction error to converge, where $L^{+}$ denotes the pseudoinverse matrix of L. The object velocity twist that the controller sends to the robotic arm is also obtained with $A K_{p} X_{e} (t)$ addition of.

\begin{matrix} u_{b} (t) = \underset{\begin{matrix} satisfy RCM velocity \\ constraint \end{matrix}}{\underset{⏟}{A (K_{p} X_{e} (t))}} - \underset{\begin{matrix} let the error \\ converge \end{matrix}}{\underset{⏟}{λ L^{+} e}} \end{matrix}

(20)

The term $A (K_{p} X_{e} (t))$ enables the RCM speed limit to be satisfied in continuous conditions, and $(- λ L^{+} e)$ enables the convergence of the remaining small cumulative error. The corresponding joint speed $\dot{q}$ can be obtained from the pseudoinverse matrix of the Jacobian matrix.

Control algorithm of the robotic-arm system based on the RCM control

According to equation (20), the differences between the starting and final positions and postures affect the movement speed, making it difficult to determine the movement time and causing a high initial error in pointing toward the fixed point. In practice, excessive torque can be easily caused by the robotic-arm's joints.

To avoid the above situation, suppose that the interpolation in the “The relationship between velocity twist and RCM limit” section is performed between the initial coordinate system {i} and the final coordinate system {f}. In that case, the ideal coordinate system {d} in the control law is not only simply set as {f}, the interpolation coordinates at different times system, it is hoped that the casing coordinate system can start from {i} and follow the interpolation coordinate system to {f}.²³

As shown in Figure 7, postural change is initiated from the green coordinate system ${R C M}$ , followed by translation to obtain the interpolated coordinate system at different times. The attitude transformation and translation settings change linearly with time. The attitude transformation is used to calculate the corresponding axial-angle transformation according to the rotation matrix of {i} and {f} to obtain the rotation axis and rotation angle.

Figure 7.

Interpolation coordinate system.

Therefore, the interpolated coordinate system $_{d}^{0} T (t)$ at t s can be expressed as follows:

\begin{matrix} _{d}^{0} T (t) =_{R C M}^{0} T_{d}^{R} o t (t)_{d}^{T} r a n s (t) \end{matrix}

(21)

where

_{R C M}^{0} T

denotes the homogeneous transformation matrix of coordinate system relative to the fixed reference coordinate system.

_{d}^{R} o t (t)_{d}^{T} r a n s (t)

represent the rotation and translation matrices of the interpolation coordinate system, respectively.

As mentioned above, the original control law in equation (20) can be expressed as follows, as the main control law based on the RCM control in this study:

\begin{matrix} u_{b} (t) = \underset{\begin{matrix} satisfy RCM velocity \\ constraint \end{matrix}}{\underset{⏟}{A ([A d_{_{d}^{b} T}] V_{d} (t) + K_{p} X_{e} (t))}} - \underset{\begin{matrix} let the error \\ converge \end{matrix}}{\underset{⏟}{λ L^{+} e}}, \dot{q} = J^{+} u_{b} (t) \end{matrix}

(22)

The term $A ([A d_{_{d}^{b} T}] V_{d} (t) + K_{p} X_{e} (t))$ satisfies the RCM speed limit in the continuous case, and $- λ L^{+} e$ enables the convergence of the remaining small cumulative error. The control law of this study is illustrated in Figure 8.

Figure 8.

Block diagram of the system developed in this study.

Error characteristics used in RCM control practice

In this RCM control algorithm, two types of errors were examined through simulation and experimentation: (a) RCM errors and (b) position and attitude errors.

RCM error

The RCM error is defined as the components $e_{R C M, x}$ and $e_{R C M, y}$ of the vector projection from the cannula's end point to the lesion point in the $x y$ plane of the current coordinate system of the cannula and their magnitude. This error is expressed as follows:

\begin{matrix} e_{R C M} = \sqrt{e_{R C M, x}^{2} + e_{R C M, y}^{2}} \end{matrix}

(23)

Position and attitude errors

Assuming that the current coordinate system of the casing is $T_{b} = [\begin{matrix} R_{b} & t_{b} \\ 0 & 1 \end{matrix}]$ and the ideal coordinate system is $T_{d} = [\begin{matrix} R_{d} & t_{d} \\ 0 & 1 \end{matrix}]$ , the position error is expressed as follows:

\begin{matrix} e_{p o s} =∥ t_{b} - t_{d} ∥ \end{matrix}

(24)

The attitude error is expressed in the axial-angle corresponding to the rotation matrix, that is, the magnitude of the product of the unit vector W of the rotation axis and the rotation angle around this axis.

\begin{matrix} e_{o r i} =∥ \hat{ω} \cdot θ ∥, \hat{ω} = {[\begin{matrix} ω_{x} & ω_{y} & ω_{z} \end{matrix}]}^{T}, \\ l o g (R_{b}^{- 1} R_{d}) = [\begin{matrix} 0 & - ω_{z} & ω_{y} \\ ω_{z} & 0 & - ω_{x} \\ - ω_{y} & ω_{x} & 0 \end{matrix}] θ \end{matrix}

(25)

Constant maintenance of RCM points

In the control law, it is important to check whether the related limit point of the distal motion center remains constant in the real robot arm application. In Figure 9, $P_{6}$ represents the end point of the sixth-axis of the robotic arm; $P_{t r o c a r}$ represents the insertion point of the endoscope; $P_{R C M}$ represents the limit point of the distal motion center; $P_{t o o l}$ represents the end point of the endoscope. It denotes the ratio of the distance from $P_{R C M}$ to $P_{6}$ to the distance from $P_{t o o l}$ to $P_{6}$ :

\begin{matrix} γ = \frac{| P_{R C M} - P_{6} |}{| P_{t o o l} - P_{6} |} \end{matrix}

(26)

Figure 9.

Schematic representation of an endoscope's RCM. RCM: remote-center-of-motion.

Experimentally, to measure the control law performance, $γ$ is obtained through a first-order approximation. The ratio $γ$ would be assumed:

\begin{matrix} γ_{k + 1} = γ_{k} + {\dot{γ}}_{k} Δ t \end{matrix}

(27)

where

{\dot{γ}}_{k + 1}

is the joint velocity at time

k + 1

Experimental and simulation architecture

Figure 10 shows our experimental and verification architecture of the proposed system, which facilitates seamless data flow through control signals and feedback loops, enabling precise needle positioning under continuous CT guidance. The real-time CT-guided robotic needle system with RCM control has the following components, and the following provides a detailed explanation:

Intraoperative CT system: Provides CT imaging data as input to the processing pipeline.

3D Slicer interface: Processes CT image data while enabling the following:

Image registration and path planning;

Real-time visualization;

Target identification.

MATLAB control system: Functions as the computational and research core by

Executing the RCM control algorithms;

Processing the trajectory data;

Managing bidirectional communication between the imaging and robotic components.

TM5-700 robot: Performs the mechanical intervention through

Receive control comments from the MATLAB system;

Providing position feedback signals;

Manipulating the needle assembly for precise insertion.

Phantom with silicone markers: Fiducial markers serve as the experimental target for validation.

Figure 10.

System architecture in this study.

TM5-700 robot and phantom

In this study, we used the TM5-700 six-axis collaborative robotic arm from Techman Robot (Figure 11(a)). This robotic arm features a maximum allowable load of 6 kg, a movement range of 700 mm, and a repeatability of ±0.05 mm. For safety purposes, the TM5-700 can immediately halt operations when it detects external forces or collisions exceeding a predetermined threshold. It also includes a key for releasing the motor brake, allowing manual guidance and movement of the robotic arm. Table 2 presents the basic specifications of the TM5-700 robot.

Figure 11.

Experimental equipment: (a) TM5-700 six-axis collaborative robotic arm and (b) adopted phantom.

Table 2.

Specifications of the TM5-700 six-axis collaborative robotic arm.

Arm weight		22.1 kg
Max payload		6 kg
End tool speed		1.1 m/s
Repeatability		±0.05 mm
Degrees of freedom		6 axes
Axis limits	Axis 1 (J1) Axis 6 (J6)	$\pm 270 \circ$
	Axis 2 (J2) Axis 4 (J4) Axis 5 (J5)	$\pm 180 \circ$
	Axis 3 (J3)	$\pm 155 \circ$
Max axis speed	Axes 1, 2, 3 (J1–J3)	$180 \circ / s$
	Axes 4, 5, 6 (J4–J6)	$225 \circ / s$

For our experimental evaluations, we employed a phantom constructed from transparent silicone containing yellow silicone balls (Figure 11 (b)). Based on consultations with medical specialists, we designed the phantom with silicone components measuring 10, 15, and 20 mm to accurately reflect the lesion sizes typically found in human lung or liver pathologies. This carefully selected size range enables the effective assessment of the imaging system performance across clinically relevant scenarios.

Needle trajectory planning using the 3D Slicer software

In this study, we used the 3D Slicer software, an open-source platform developed by the Slicer Community, for medical imaging analysis. The extensible architecture of this software supports modular enhancement. The software enables CT visualization and three-dimensional (3D) reconstruction from two-dimensional (2D) slices. By leveraging its compatibility, we achieved comprehensive data and initial trajectory planning integration between the robotic system, RCM control comment using MATLAB, and the imaging interface, thereby enabling synchronized operational workflows across all components.

The captured CT images were imported into the 3D Slicer software, after which at least three noncollinear points were selected (Figure 12). As a result, the coordinates of these points in the robotic-arm and images spaces were obtained. Then, the Kabushi algorithm^30,31 was used for the conversion between the image and robotic-arm spaces.

Figure 12.

Reference points for the space transformation.

In the process of the 3D Slicer, the location of the lesion can be marked (Figure 13(a)) and the coordinates of the lesion in the image space are configured. The coordinate system of the casing before arrival was selected in the 3D Slicer according to the relevant requirements (Figure 13(b)). In addition to the conversion relationship between the two spaces obtained, it can also be used to obtain the angles of each joint of the robotic arm in real time using the Modbus TCP function in MATLAB software.

Figure 13.

(a) Marked lesions and (b) needle position and posture.

Data transmission and RCM algorithm implementation using MATLAB tools

In this study, we used the MATLAB 2021b integrated development environment, developed by MathWorks Corporation, for data transmission and implementing the RCM core control algorithms. It was used to calculate the coordinates of the two ends of the casing in the robotic-arm space according to the forward kinematics.

The coordinates were calculated using MATLAB, and the transmitted data were then sent to the 3D Slicer through the communication network protocol for subsequent display. This data was then converted into a cannula object representing the casing body. The detailed transmission and display process is shown in Figure 14.

Figure 14.

Detailed transmission and display process.

As shown in Figure 15, the upper right section of the matrix in the transmitted data computed from MATLAB is extracted and assigned to one of the markup point coordinates named “Points” through the communication network protocol, which represents the coordinates of one end point of the cannula in the image. In doing so, the data transmitted from MATLAB to the 3D Slicer can automatically update the coordinate values of the two end points. Therefore, when the robotic arm moved, the cannula was displayed on the interface of the 3D Slicer in real time.

Figure 15.

Schematic representation of coordinate values updation with communication protocol.

The control law in this study was simulated using the RVC toolbox (a robot module library) and Simulink model with MATLAB 2021b. The system modeling diagram is shown in Figure 16. In this study, two types of errors were examined: (a) RCM errors and (b) position and attitude errors, through simulation and experimentation, respectively.

Figure 16.

Diagram of the system modeling in the MATLAB simulation.

Results

Numerical simulation using the MATLAB software

The robotic arm used in the numerical simulation was the TM5-700 six-axis collaborative robotic arm. An extended sleeve processing part was added to the end of the arm. The axis defined by the tool coordinate system was the same as that of the sixth-axis coordinate system. The origin of the tool coordinate system was positioned relative to the sixth-axis coordinate system by translating −122.2 mm along the x-axis and 113.4 mm along the z-axis. The sampling time was set to 0.01 s, and the total simulation time was 20 s. The initial joint angles of the robotic arm, target joint angles, and tumor coordinates used during the simulation are, respectively, expressed as follows:

q_{i} = [- 7 8.04 2 \circ 5 .04 7 \circ 74 .55 2 \circ 5 .01 8 \circ 106 .39 6 \circ - 1.65 3 \circ]^{T}

q_{f} = [- 5 7.78 4 \circ 21 .73 6 \circ 60 .92 3 \circ 25 .18 1 \circ 72 .24 5 \circ 34 .05 1 \circ]^{T}

P_{l e s i o n} = [- 0.04 7 - 0.49 4 0.231]^{T} (m)

The movement time T was set to 15 s, and the errors of and in the control law equation (22) varied accordingly. Figure 17(a) shows the simulated RCM errors obtained under a fixed $K_{p}$ value $K_{p} = 5$ and different $λ$ values $λ = 0.1, 1, 10$ . When the arm moved (from 0 to 15 s) and $λ$ was greater than 1, the error increased to its peak value, remained at a certain value until 15 s, and then began to converge to 0. At higher $λ$ values, the RCM error increased more rapidly to its maximum value, the overall error was smaller, and the model converged more rapidly after the arm stopped for 15 s. Figure 17(b) shows the simulated RCM errors obtained under a fixed $λ$ value ( $λ = 1$ ) and different $K_{p}$ values ( $K_{p} = 0.1, 1, 10$ ). The parameter influences the speed of convergence to the interpolation trajectory, and the arm movement speed is determined by $t_{m a x}$ instead of $K_{p}$ ; thus, variations in $K_{p}$ have little effect on the RCM error.

Figure 17.

RCM error simulation results (a) under a fixed $K_{p}$ value and different $λ$ values and (b) under a fixed $λ$ value and different $K_{p}$ values. RCM: remote-center-of-motion.

Figure 18 shows the simulated position and attitude errors. As shown in Figure 18(b), under the situation of a fixed $λ$ value ( $λ = 1$ ) and different $K_{p}$ values $K_{p} = 0.1, 1, 10$ , with higher $K_{p}$ values, the error within 0 to 15 s was smaller, and the model converged faster to the interpolation trajectory. In contrast, with different $λ$ values (Figure 18(a)), the position and attitude errors increased more rapidly to their maximum values, and the model converged more rapidly after the arm stopped for 15 s. When $λ > 1$ , the changes in the attitude error and posture were relatively small, and the contraction speed of the arm after stopping was relatively low. Moreover, the convergence speed increased as $λ$ increased beyond 10 s.

Figure 18.

Position and attitude errors result: (a) under a fixed $K_{p}$ value and different $λ$ values and (b) under a fixed $λ$ value and different $K_{p}$ values.

Experimental verification

This section focuses on the experimental verification, and at least two repeated experiments were conducted and representative experimental results are shown. The initial position ( $T_{i}$ ) and desired final position ( $T_{f}$ ) in the robotic-arm space are expressed as follows:

\begin{aligned} T_{i n i} = [\begin{matrix} 0.9267 & 0.2331 & 0.2948 & - 0.065 \\ 0.2527 & - 0.9671 & - 0.0295 & - 0.4917 \\ 0.2782 & 0.1019 & - 0.9551 & 0.2902 \\ 0 & 0 & 0 & 1 \end{matrix}]; \\ T_{f i n a l} = [\begin{matrix} 0.9105 & - 0.0028 & - 0.4135 & - 0.0163 \\ 0.0352 & - 0.9958 & 0.0843 & - 0.4997 \\ - 0.4120 & - 0.0913 & - 0.9066 & 0.2978 \\ 0 & 0 & 0 & 1 \end{matrix}] \end{aligned}

With real clinical need, the threshold of the RCM error was set to $1 \times 1 0^{- 3} m$ , which was considered for the lung tumor stage and size. As shown in Figure 19, when $K_{p}$ was fixed, the higher was $λ$ , the faster the RCM error converged to 0 after 15 s; however, an excessively high $λ$ value caused the robotic arm to shake. Additionally, the curves of the position and attitude errors suddenly increased and then converged at the 15th second. A possible reason for this phenomenon was that the ideal coordinate system reached the desired coordinate system because of the sudden stop in the constant-velocity movement of the robotic arm. However, the above errors converged to 0 soon after the 15th second. While $λ$ was fixed, variations in $K_{p}$ had little influence on the RCM error, and the RCM error caused by different $K_{p}$ values was below $2 \times 1 0^{- 4} m$ , which was within the threshold and could be omitted in the real medical operation. This experimental result was consistent with its simulation counterpart. As shown in Figure 20, the higher the $K_{p}$ value, the faster the position and attitude errors converge to 0 after the 15th second.

Figure 19.

Experimental (a) RCM error (orange: $e r r o r_{x}$ ; yellow: $e r r o r_{y}$ ) and (b) position and attitude errors under a fixed $K_{p}$ and different λ values. RCM: remote-center-of-motion.

Figure 20.

Experimental (a) RCM error (orange: $e r r o r_{x}$ ; yellow: $e r r o r_{y}$ ) and (b) position and attitude errors under a fixed $λ$ value and different $K_{p}$ . RCM: remote-center-of-motion.

Figure 21(a) to (d) sequentially illustrate that the cannula is pointed toward the RCM point during the movement of the robotic arm. The left side of Figure 21(a) to (d) shows the photo of the above scenario, and the right side displays the corresponding rendering in the 3D Slicer. The yellow lines point toward the lesion. Figure 21 shows that when the robotic arm was moving, it could be stopped at any location, and its needle could be lowered to poke the upper edge of a yellow ball used as a lesion (Figure 21(e)). This lesion was different from the previous setting on the upper edge of the ball, and the tip of the needle was stained with red ink for ease of visual identification.

Figure 21.

(a)–(d) Cannula pointed toward the RCM point (left: actual image; right: 3D Slicer representation); (e) poking of a yellow ball with the needle of the robotic arm (the tip of the needle was stained using red ink). RCM: remote-center-of-motion.

Discussions

For applications, distal-center-of-motion restriction is implemented in minimally invasive endoscopic surgery.³² Minimally invasive surgery involves opening several small holes in the patient's body and inserting the required medical equipment, such as endoscopes, into the patient's body through the opened holes. When an endoscope is used in a patient, its movement is limited to the center of motion of its distal end to avoid enlarging the small hole on the patient's body surface to causing wound expansion.

In this section, an analysis and discussion will be conducted comparing the two RCM control algorithms based on the work of reference³² with the RCM control algorithm proposed in the present study. This comparative evaluation will also consider the behavior and impact of the γ parameter (introduced in the “Control algorithm of the robotic-arm system based on the RCM control” section) under these control strategies. Table 3 presents a comparative overview of these three control algorithms, which will be followed by a more detailed discussion.

Table 3.

Comparative performance of RCM control strategies.

	Prior work³²	Prior work,³² with feedforward	This research
Governing equation	Equation (28)	Equation (29)	Equation (22)
Characteristics	Basic RCM; direct γ update	RCM; feedforward	RCM, interpolation; feedforward
γ Calculation	Equation (27) (1st order approx.)	Equation (26) (geometric)	Equation (26) (geometric)
Risk of system halt (improper γ)	High (γ out of bounds)	Low (γ constrained)	Low (γ constrained)
RCM error (post-15 s stability)
Jitter	Persistent & significant	Minimal	Significantly reduced
Magnitude	High	Low	Low/very low
Attitude error (post-15 s convergence)
Convergence	Low/incomplete	Reliable	Reliable
Steady-state	High/fluctuating	Low & stable	Low & stable
Jitter	Moderate	Minimal	Significantly reduced

RCM: remote-center-of-motion.

In Figure 22, $P_{l e s i o n}$ represents the tumor location, $P_{R C M}$ is the limit point of the distal motion center, $P_{t u b e}$ is the origin of the cannula's coordinate system, $P_{e x t}$ is the distant point on the casing's extension line. The papameter γ represents the ratio of the distance from $P_{R C M}$ to $P_{t u b e}$ to the distance from $P_{e x t}$ to $P_{t u b e}$ . The distance from $P_{e x t}$ to $P_{t u b e}$ is fixed. The corresponding control law is expressed as follows:

\begin{matrix} [\begin{matrix} \dot{q} \\ \dot{γ} \end{matrix}] = {[\begin{matrix} \begin{matrix} J_{t u b e} & 0_{3 \times 1} \end{matrix} \\ J_{R C M} \end{matrix}]}^{+} [\begin{matrix} K_{t a s k} & 0_{3 \times 3} \\ 0_{3 \times 3} & K_{R C M} \end{matrix}] [\begin{matrix} e_{t a s k} \\ e_{R C M} \end{matrix}] \end{matrix}

(28)

Figure 22.

Schematic of a cannula's RCM. RCM: remote-center-of-motion.

Besides, if the control law is applied and added as the feedforward control term of the ideal trajectory, the following equation is obtained:

\begin{matrix} [\begin{matrix} \dot{q} \\ \dot{γ} \end{matrix}] = {[\begin{matrix} \begin{matrix} J_{t u b e} & 0_{3 \times 1} \end{matrix} \\ J_{R C M} \end{matrix}]}^{+} ([\begin{matrix} K_{t a s k} & 0_{3 \times 3} \\ 0_{3 \times 3} & K_{R C M} \end{matrix}] [\begin{matrix} e_{t a s k} \\ e_{R C M} \end{matrix}] + [\begin{matrix} {\dot{P}}_{t a s k} \\ 0_{3 \times 1} \end{matrix}]) \end{matrix}

(29)

where

J_{R C M} = [\begin{matrix} J_{t u b e} + γ (J_{e x t} - J_{t u b e}) & P_{e x t} - P_{t u b e} \end{matrix}]

Figure 23(a) illustrates the control performance using the law defined in equation (28), showing the experimental error results with γ according to equation (27). The data revealed persistent oscillations in the RCM error even after the robotic arm stopped at the 15s mark. The position error also fluctuates beyond this time point.

Figure 23.

Experimental error: (a) RCM error and position error results of updated according to Supplemental equation (S1) ( $K_{t a s k}$ = 5, $K_{R C M}$ = 1, orange: $e r r o r_{x}$ ; yellow: $e r r o r_{y}$ ), (b) RCM error and position error results for γ were updated according to Supplemental equation (S1) ( $K_{t a s k}$ = 5, $K_{R C M}$ = 1, and the feedforward control term was added to the control law). RCM: remote-center-of-motion.

Figure 23(b) shows the enhanced control law expressed in equation (29), with γ updated according to equation (26). The incorporation of the feedforward control terms yielded the same changes in the RCM error above, confirming that the primary RCM mechanism effectively dominates and is maintained after the addition of the feedforward control terms. Notably, the position error magnitude decreased significantly due to the trajectory-tracking-specific feedforward addition. The system stability with feedforward control demonstrates robustness, as evidenced by the smooth RCM error convergence, despite the high-frequency position error oscillations before 15 s that interact with the continuous-time model assumptions. As described in the above and Supplemental material, when $γ$ was updated to $γ < 0$ or $γ > 1$ according to equation (27), which caused the robotic arm to stop because of excessive torque. To solve this problem, in the following experiments, the suitable parameter $γ$ was updated to the form with equation (26).

Figures 24 and 25 show the errors obtained with the control law expressed in equation (29) under a fixed $K_{t a s k}$ value and different $K_{R C M}$ values and under a fixed $K_{R C M}$ value and different $K_{t a s k}$ values, respectively, indicating how the results changed when the feedforward control term was added to the control law, as depicted in Figures S3 and S4 in the Supplemental material. A comparison of Figure 24(a) and Supplemental Figure S3(a) show that after adding the feedforward control term to the control law, the RCM error under a fixed $K_{t a s k}$ value ( $K_{t a s k} = 5$ ) and different $K_{R C M}$ values ( $K_{R C M} = 1, 10$ ) increased, and the jitter remained high. The increased jitter of the RCM error with feedforward (especially for lower $K_{R C M}$ ) might suggest that the feedforward command, while improving the tip position tracking, introduces volatility dynamics or the controller whose greater flexibility. This could be one of the sources of the error.

Figure 24.

(a) RCM error (orange: $e r r o r_{x}$ ; yellow: $e r r o r_{y}$ ) and (b) position error under a fixed $K_{t a s k}$ value and different $K_{R C M}$ values after adding the feedforward control term to the control law. RCM: remote-center-of-motion.

Figure 25.

(a) RCM error (orange: $e r r o r_{x}$ ; yellow: $e r r o r_{y}$ ) and (b) position error under a fixed $K_{R C M}$ value and different $K_{t a s k}$ values after adding the feedforward control term to the control law. RCM: remote-center-of-motion.

A comparison of the position errors shown in Figure 24(b) and Supplemental Figure S3(b) shows that an excessively low $K_{R C M}$ value caused jitter in the position error after 15 s; however, after adding the feedforward control term to the control law, the order of the position error reduced. A comparison of Figure 25(a) and Supplemental Figure S4(a) shows that the RCM error under a fixed $K_{R C M}$ value ( $K_{R C M} = 10$ ) and different $K_{t a s k}$ values ( $K_{t a s k} = 1, 5, 10$ ) was almost the same with and without the addition of the feedforward control term to the control law. Figure 25(b) and Supplemental Figure S4(b) show that the addition of the feedforward control term to the control law reduced the position error; however, if $K_{t a s k}$ it was too low, jitter was observed in the position error after 15 s.

Figure 26 depicts the result of taking several Figures 19(b) and 20(b), and only displaying the position error. First, the control law used in this study was compared with the control laws expressed in equations (28) and (29) using the updated results obtained for $γ$ according to equation (27). Figures 20(a), 23(a), and 24(a) show that the RCM error did not exhibit jitter after 15 s. When the control law of this study was used, different parameter adjustments had a low likelihood of causing the arm torque to be excessive and the operation to stop. Figures 23(b), 24(b), and 26(a) show that the position error did not exhibit jitter after 15 s when the control law of this study was used. The results further confirm that the integration of the feedforward control, interpolation, and RCM algorithm enhances the system stability.

Figure 26.

Position errors under (a) a fixed $K_{p}$ value and different $λ$ values and (b) a fixed $λ$ value and different $K_{p}$ values.

Second, the control law used in this study was compared with those expressed in equations (28) and (29) using the updated $γ$ values according to equation (26). When the RCM error gain ( $λ$ or $K_{R C M}$ ) was fixed and the task trajectory error gain ( $K_{p}$ or $K_{t a s k}$ ) was varied, the RCM error obtained with the control law of this study did not exhibit jitter after the robotic arm stopped in the 15th second (Figures 20(a) and 25(a) and Supplemental Figure S4(a)).

Figures 25(b) and 26(b) and Supplemental Figure S4(b) show that the position error obtained with the control law of this study was smaller than those obtained with the control laws expressed in equations (28) and (29). The addition of the feedforward control term reduced the jitter after 15 s. When the RCM error gain ( $λ$ or $K_{R C M}$ ) was varied, the task trajectory error gain ( $K_{p}$ or $K_{t a s k}$ ) was fixed, and the RCM error gain was relatively small. The RCM error obtained with the control law of this study exhibited low jitter after 15 s (Figures 23(a) and 26(a), and Supplemental Figure S3(a)). Figures 23 (b) and 26(a) and Supplemental Figure S3(b) show that the position error obtained with the control law of this study (Figure 26) was lower than that obtained with the control law expressed in equation (28) (Supplemental Figure S3(b)). Moreover, the jitter in the position error after 15 s was lower when using the control law of this study than when using the control law expressed in equation (29) (Figure 23(b)) with the feedforward control term. Considering the position error results presented in Figure 26, it is worth exploring the possibility of employing distinct control strategies for different surgical phases. For instance, during the precision positioning phase, a higher $K_{t a s k}$ value could be adopted to enhance the positional precision. In contrast, during the stable observation phase, a higher $K_{R C M}$ value could be used to minimize the jitter at the RCM point.

In addition to the analysis with the two specific control algorithms mentioned above, regarding the integration of RCM within existing CT-guided robotic devices, several analogous studies have focused on optimizing RCM manipulator control. For instance, one investigation³³ demonstrated a maximum end-effector tracking error of 5.1 × 10⁻³ m under optimal RCM configurations. Similarly, another study³⁴ reported positioning deviations of 1.78 × 10⁻³ m under RCM control, while additional research³⁵ indicated RCM point deviation errors not exceeding 2 × 10⁻³ m. In contrast to these findings from studies with comparable applications, the results presented in the “Experimental verification” section demonstrate that through strategic parameter configuration ( $K_{p}$ , λ) within the proposed system, RCM error was effectively reduced to 2 × 10⁻⁴ m. This represents an effective and substantial improvement compared to existing methodologies, substantially enhancing RCM control precision in surgical needle guidance applications.

In this study, an initial phase of clinical operational validation was incorporated beyond the RCM control design, MATLAB numerical simulations, and real-time laboratory validation of the TM5-700 six-axis collaborative robotic arm employing the RCM control. This phase used an anthropomorphic model with the robotic arm directly in a clinical setting (Figure 27). It demonstrated the system's fundamental operational feasibility within a clinical context. Figure 27(a) illustrates the flexible deployment of the TM5-700 robotic arm in an operating room, independent of the fixed CBCT system. Figure 27(b) shows the system's use of a cannula for targeting lesions in the anthropomorphic model. Figure 27(c) shows the successful lesion localization and puncture, achieved using the 3D Slicer integrated with MATLAB to implement the RCM algorithm with feedforward control.

Figure 27.

Initial clinical validation of the RCM control algorithm in this study with TM5-700 six-axis collaborative robotic arm. RCM: remote-center-of-motion.

In essence, control system inaccuracies—which significantly compromise precision—arise from the intricate interplay of algorithmic limitations and mechanical nonidealities (e.g. robotic arm compliance, joint friction, and actuator dead zones). While previous studies have explored RCM implementations to address these issues, our experimental approach combining RCM, interpolation techniques, and feedforward control has yielded superior results. Our research demonstrates that this comprehensive integration produces performance enhancements that surpass those achievable through either conventional RCM-only or RCM with feedforward control approaches. This improvement was achieved through careful calibration of parameters within the RCM constraint framework, such as $K_{R C M}$ and $K_{t a s k}$ . Specifically, judicious adjustment of the interpolation methodology, feedforward control intensity, and RCM stiffness (the $K_{t a s k}$ value) was shown to effectively suppress system jitter to levels unattainable by previous control methods. The preliminary operational feasibility was also validated in this study using an anthropomorphic model within a clinical environment, thereby establishing a foundational basis for the system's application in actual medical settings with significant precision advantages over existing approaches.

Conclusions

This study details the development and validation of an iCT-guided robotic needle biopsy system, distinguished by its real-time imaging capabilities and a novel RCM control. The system's core contribution is an RCM control method, founded on screw axis theory, that innovatively integrates interpolation and feedforward control. This integrated architecture demonstrably maintains continuous, precise RCM-constrained cannula trajectory toward targeted tumors during complex robotic-assisted interventions, while responsively adapting in real time to clinician-issued posture adjustments via the 3D Slicer imaging interface. This significantly enhances both RCM dynamic accuracy and operational flexibility. Consistently, simulation and experimental data confirm RCM error below $2 \times 1 0^{- 4} m$ , outperforming prior other control strategies.^32–35 Furthermore, seamless bidirectional communication between MATLAB and 3D Slicer, facilitated by the Kabushi algorithm, provides precise intraoperative visual guidance.

While demonstrating significant advances in precise RCM control and real-time image guidance, opportunities for future enhancement exist. The current system could be updated and benefit from artificial intelligence algorithms for intelligent target localization and adaptive path planning to further optimize robotic percutaneous intervention efficiency and accuracy. Moreover, while initial validation occurred in simulated environments, comprehensive case testing and statistical analysis across diverse conditions and subsequent clinical implementation with systematic data collection are crucial for thoroughly evaluating and refining the robustness and clinical efficacy of this integrated control framework within actual intraoperative CT settings.

In summary, this research offers a clinically promising solution for efficient and precise intraoperative CT-guided robotic interventions. Its unique RCM control methodology, synergized with real-time imaging integration, represents a notable contribution to the field of robotic-assisted interventional radiology.

Supplemental Material

sj-pdf-1-arx-10.1177_17298806251352059 - Supplemental material

Supplemental material, sj-pdf-1-arx-10.1177_17298806251352059

Footnotes

Acknowledgement

This research was supported in part by the Ministry of Education, Taiwan R.O.C. under the Higher Education Sprout Project and in part by the National Science and Technology Foundation under project no. NSTC 111-2811-E-011-014-MY3.

ORCID iDs

Chun-Ting Kuo

Jia-Yush Yen

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data availability statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

Supplemental material

Supplemental material for this article is available online.

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Supplementary Material

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Intraoperative computed tomography-guided robotic needle biopsy system with real-time imaging ability and remote-center-of-motion control

Abstract

Objective

Methods

Results

Conclusion and significance

Keywords

Introduction

Control methods and experiments

Screw axis theorem and motion control

Derivation of RCM motion control

The relationship between velocity twist and RCM limit

Control algorithm of the robotic-arm system based on the RCM control

Error characteristics used in RCM control practice

Constant maintenance of RCM points

Experimental and simulation architecture

TM5-700 robot and phantom

Needle trajectory planning using the 3D Slicer software

Data transmission and RCM algorithm implementation using MATLAB tools

Results

Numerical simulation using the MATLAB software

Experimental verification

Discussions

Conclusions

Supplemental Material

sj-pdf-1-arx-10.1177_17298806251352059 - Supplemental material

Footnotes

Acknowledgement

ORCID iDs

Funding

Declaration of conflicting interests

Data availability statement

Supplemental material

References

Supplementary Material