Design and Experimental Study of a Robotic System for Target Point Manipulation in Breast Procedures

Abstract

To achieve obstacle-avoiding puncture in breast interventional surgery, a robotics system based on three-fingered breast target-point manipulation is proposed and designed. Firstly, based on the minimum number of control points required for three-dimensional breast deformation control and the bionic structure of the human hand, the structure and control scheme of the robotics system based on breast target-point manipulation are proposed. Additionally, the workspace of the robotics system is analyzed. Then, an optimal control point selection method based on the minimum resultant force principle is proposed to achieve precise manipulation of the breast target point. Concurrently, a breast soft tissue manipulation framework incorporating a Model Reference Adaptive Control (MRAC) system is developed to enhance operational accuracy. A dynamic model of breast soft tissue is developed by using the manipulative force–displacement data obtained during the process of manipulating breast soft tissue with mechanical fingers to realize the manipulative force control of breast tissue. Finally, through simulation and experiments on breast target-point manipulation tasks, the results show that this robotic system can achieve spatial control of breast positioning at arbitrary points. Meanwhile, the robotic system proposed in this study demonstrates high-precision control with an accuracy of approximately 1.158 mm (standard deviation: 0.119 mm), fulfilling the requirements for clinical interventional surgery in target point manipulation.

1. Introduction

According to global cancer statistics released by the International Agency for Research on Cancer (IARC), a branch of the World Health Organization (WHO), breast cancer accounts for 2.3 million new cases annually [1], surpassing lung cancer as the world’s most prevalent cancer [2]. Breast cancer has been shown to be the leading cause of harm to women’s physical and mental health [3,4]. For breast cancer patients, early treatment can effectively preserve physical function and ensure postoperative quality of life [5,6].

Minimally invasive interventional surgery is the most common method for treating breast cancer [7,8,9,10]. This minimally invasive surgical intervention, with its significant advantages of less intraoperative trauma, faster postoperative recovery, and reduced burden on the medical system, has been widely accepted as the optimal choice for both doctors and patients [11,12]. In fact, needle insertion into soft tissue is a complex, minimally invasive surgical procedure [13,14,15,16]. In addition, the boundary effect on the breast (which is a layered soft tissue) makes needle insertion more challenging [17]. In interventional surgery, whether the puncture needle can be accurately and stably placed in the patient’s diseased area (requiring diagnosis or treatment) is crucial to the success of the procedure [18]. Meanwhile, under gravitational force, the breast hangs downward along the chest wall, and because the breast tissue is very soft, when the needle punctures the breast tissue, the breast tissue is deformed, and this deformation leads to the displacement of the tumor lesions. Therefore, achieving accurate puncture requires solving the problem of breast tissue deformation and target displacement.

At present, as puncture surgery remains primarily a manual operation, surgeons typically employ various methods to minimize target point displacement risks. The two most common clinical approaches are (1) freehand stabilization of breast soft tissue and (2) compression of the breast between two parallel plates [19]. The freehand stabilization method of breast lesions requires the doctor to have a certain accumulation of experience and the patient’s active cooperation, and the puncture accuracy is difficult to guarantee. Breast stabilization using breast soft tissue compression between two parallel plates/grids also has the following disadvantages: (1)excessive breast compression may impair vascular perfusion in breast tissues; (2) poor fit for different breast shapes; (3) in some cases, anatomical limitations prevent a straight path from reaching the surgical site; (4) patients experience severe compression pain during surgery, and studies have shown that women with smaller breasts suffer from increased pressure-related pain [20]. In clinical practice, cases also occur where surgeries have to be terminated due to pain caused by excessive breast compression [21,22]. Additionally, achieving successful punctures under compression remains particularly challenging [23]. For patients with smaller breast volumes, reaching the minimum required thickness (25 mm) for needle puncture after parallel-plate compression proves especially difficult [24]. These conditions are more prevalent among Asian women, rendering many breast fixation devices unsuitable for a significant patient population. Current medical approaches predominantly rely on excessive breast compression, and while this stabilizes the glandular tissue, it simultaneously elevates the risks of patient injury.

To solve these problems, many researchers have conducted studies on breast deformation and internal target point displacement, and they are committed to developing more comfortable, accurate, and efficient techniques for breast fixation and manipulation. Kobayashi et al. [25,26,27] proposed using a concave semicircular preloaded pressure rod to compress flexible tissue, aiming to reduce breast tissue displacement during interventional surgery; however, they neither proposed nor employed relevant soft tissue deformation manipulation methodologies. Patriciu et al. [23] developed an MRI-guided breast tissue stabilization device for biopsy procedures, incorporating two geometrically adjustable support plates. This design was optimized to exert lower compression forces compared to conventional parallel plate systems, thereby minimizing target point site migration during the procedure. To improve patient comfort, the team upgraded the device to incorporate two pneumatically driven stabilization plates, and these plates position the breast between them, achieving better stabilization. Meanwhile, during needle puncture, breast soft tissue is dynamically adjusted based on real-time image feedback to compensate for target displacement [28]. Mallapragada et al. [29] controlled the tumor’s position by applying force at four fixed locations on the breast surface, ensuring continuous alignment between the tumor and the needle. Liu et al. [30] proposed a palm-shaped breast morphing robot for MRI-guided breast biopsy. Driven by a piezoelectric motor and multiple airbags, the mechanism has multiple degrees of freedom to hold the breast in place while adjusting the shape of the breast tissue by controlling the amount of air charged by the different airbags. In addition, the team proposed a flexible breast fixation system based on palm bionics and controlled the compression force by optimizing the flexible clamping mechanism to ensure the reliability of compression and reduce the pain of patients [20]. Yongde Zhang et al. [31] proposed an embracing-style breast fixation device. The device consists of four identical, circumferentially distributed finger-plate mechanisms that can slide along their axes, adjust positions, and self-lock to achieve stable morphological fixation of breast soft tissue.

In summary, the fixation and manipulation of breast soft tissue constitute critical components in interventional surgical procedures. It is feasible and helpful for surgery to apply controllable external force in an automated way to make appropriate compression adjustments of the breast and real-time manipulation of breast tumor targets. However, most of the current studies are qualitative control of breast soft tissue deformation, unable to give accurate adjustment and judgment results, and it can only achieve the overall compression of the breast tissue and cannot effectively control the internal target position so as to meet the obstacle avoidance planning requirements of interventional surgery, which will greatly limit the flexibility and efficiency of interventional surgery, especially in breast interventional surgery involving precise positioning and puncture.

To address the limitations in breast interventional procedures discussed above, this paper focuses on the interaction mechanism between mechanical fingers and breast soft tissues. In Section 2, the manipulation force and deformation displacement of breast soft tissues under the control of mechanical fingers are analyzed, and the breast soft tissue internal target point manipulation strategy is proposed. In Section 3, the breast soft tissue dynamics model is established based on the data of force–displacement in the operation process of mechanical fingers, and the control method of manipulation force in the process of mechanical finger manipulation of breast soft tissue is studied. In Section 4, the simulation and experiment of the breast target point manipulation task is conducted to verify the validity of the robotic system and breast target point manipulation strategy proposed in this paper. This study provides a design reference for achieving high-precision obstacle avoidance puncture in breast interventional surgery and meeting the demand for precise manipulation of breast targets in clinical surgery.

2. Design Method for Breast Target Manipulative Robot System

In clinical breast puncture surgeries, to avoid potential obstacles and improve the safety of the operation, the surgeon needs to implement measures that make the position of the target point in the patient’s body change relative to the surface rather than altering the insertion point of the puncture needle tip. This is because (1) breast characteristics of different patients, the location, size, and depth of each lesion are predetermined, and arbitrarily adjusting the puncture point will cause deviation from the target lesion point, making it impossible to obtain effective samples or therapeutic drug cannot effectively act on the lesion area, leading to diagnostic errors or treatment failure; (2) the needle insertion puncture point should be preoperatively optimized through precise calculations considering multiple factors (related factors such as the dose diffusion range of therapeutic drugs, the minimum damage caused to breast soft tissues during puncture treatment or sampling, etc.) under the concept of “precision medicine (minimal trauma, maximal benefit)”, and the unique target point and needle insertion point are fixed via medical imaging marking to avoid the increased risk of multi-point punctures. This requires doctors to overcome obstacles through precise, standardized operations and technical adjustments. However, we cannot directly manipulate the target point inside the breast; it needs to be adjusted externally. Therefore, a robotics system of breast target point manipulative is proposed in this study; the robot controlled and adjusted the movement of its internal target point by controlling a limited number of driving points on the breast surface, and the core idea is shown in Figure 1.

The objectives of the breast soft tissue internal target point manipulation strategy are as follows: N(N ≥ 1) external manipulators are proposed to directly exert control force on the soft tissue surface of the breast, and a control system is studied to be applied to control force. According to the position of the breast target and the information of obstacles (blood vessels/nerves/suspensive ligaments of the breast/lactation tube), the size and direction of the control force are adjusted so that the breast puncture path can be “turned straight” to bypass obstacles and ensure precise implementation of piercing tasks.

3. Implementation of Control Strategy for Target Point Within Breast Soft Tissue

A reasonable control strategy can effectively improve control efficiency and accuracy. When using external manipulators to implement the control strategy for target points within breast soft tissue, the following key factors need to be considered:

(1)

The minimum number of control points is determined:

A control point refers to the point where the external manipulator directly contacts the breast surface. The selection of control point quantity is a critical design decision that must balance actual control requirements against system complexity. To ensure the system can accurately manipulate the internal target point position and maintain its stability and reliability, selecting the minimum number of control points simplifies the design and control complexity of mechanical systems. Meanwhile, it can also retain the choice space of more puncture points.

(2)

Selection of optimal control point location:

After the minimum number of control points is determined, these control points should be reasonably distributed on the breast surface to cover the target area that needs to be controlled, and the position of control points will directly affect the accurate control of the breast target point. This requires selecting the appropriate control points based on the anatomy of the breast, the actual location, and the target location of the target point.

(3)

Force control during soft tissue manipulation:

The external mechanical finger manipulation needs to exert appropriate control force to manipulate the breast target point and achieve accurate target position control. The size of the control force should be reasonably adjusted according to the characteristics of the breast soft tissue and the needs of the target operation so as to ensure the accuracy of the control and avoid damage to the breast soft tissue. The magnitude of force should be sufficient for accurate manipulation of the breast soft tissue while avoiding exceeding the safe range and reducing operational risks.

3.1. Determination of the Minimum Number of Control Points for Breast Three-Dimensional Deformation Control

In the breast soft tissue, determining the optimal location of lesion point movement usually requires medical imaging analysis and computer simulation. For the active deformation process of soft tissue controlled by the manipulation of the mechanical finger, if all points on the breast surface can be effectively controlled for position and deformation, then it can also accurately control the movement of a certain point inside the breast. In practical clinical applications, this method of controlling all points on the breast surface is difficult to achieve and extremely complex. In order to achieve a specific motion of points inside a deformable object, the number of manipulated points must be greater than or equal to the number of fixed points. In actual breast puncture surgery, the doctor needs to locate the puncture needle to the lump; that is, the number of fixed points is usually one, and ideally, the number of control points should also be one. However, in the actual clinical operation, it is also necessary to consider the need for tumor localization and adjustment. In addition, in order to successfully shift the target lump into a position conducive to puncture, it is important to reverse-derive the task strategy by analyzing the manipulation process. According to the principle of force closure in modern robotics, it is assumed that there are n mechanical fingers in contact with the breast surface to adjust and control the position of any point inside the breast. Considering that when a force/moment P is applied to any point on the breast, if the force/moment P is balanced with the reaction force of the finger at the operating point on the breast surface, the force closure condition for the stable grasping of the deformable object can be satisfied [32]. The force closure condition can be described as Equation (1):

$$\left\{\begin{array}{l}\forall P,\hspace{0.33em}\exists F_1,\hspace{0.33em}{F}_2,\hspace{0.33em}\cdots \hspace{0.33em}{F}_n\ge 0;\hspace{0.33em}\\ Such\hspace{0.33em}that:\hspace{0.33em}P+F_{body}+{\displaystyle \sum _{i=1}^n{F}_i{w}_i=0}\end{array}\right.$$

(1)

where F_body is the volume force, which can be determined by the mass of the deformed object itself. F_i is the size of the operating force of the i finger, and w_i is the direction of the operating force of the i finger contact point.

In a stable control state, the i mechanical finger exerts a constant control force on the i contact point. If the coefficient of friction force at the contact point is zero, then the contact friction is exactly along the normal direction at the contact point. However, as long as there is non-zero friction at the contact point, the force closure condition can be satisfied when there are only two contact points on the plane or three contact points in space, which is also the simplest and most effective rule for studying mechanical grasping.

In addition, an object in three-dimensional space has six degrees of freedom (three translational and three rotational degrees of freedom). By controlling the position of the three points and applying force (F₁, F₂, F₃), the movement of the soft tissue on the three translational degrees of freedom can be fixed, and its rotation on the three rotational degrees of freedom can be restricted so as to achieve the control of the position of the target point. Because, at the mathematical level, three-dimensional space is a three-degree-of-freedom linear space, and its position is uniquely determined by three independent coordinates, satisfying the uniqueness of coordinate transformation; at the physical level, since attitude and displacement are decoupled, it does not require rotational degrees of freedom, which conforms to the particle model and the principle of superposition. Meanwhile, fully considering the performance of the robot in terms of accuracy, computational cost, and flexibility, this paper finally selected three finger manipulators to coordinate and manipulate the breast target position so as to achieve comprehensive and stable breast control, as shown in Figure 2.

3.2. Optimal Control Point Location Selection Based on the Principle of Minimum Resultant Force

In the process of interventional surgery for breast cancer, in order to achieve target point puncture more accurately, the deformation characteristics of breast soft tissue are used to control the position of the target point inside the breast soft tissue and make it locate the desired target position. Therefore, this section discusses the problem of determining the optimal control point position given the three breast surface control points, the initial position of the internal target, and the target point position. As an optimization problem, its optimization goal is to minimize the required resultant force. The basic idea is to minimize the external force required by selecting the position of the optimal control point so as to achieve accurate control of the position of the internal point. The optimal control point location selection based on the principle of least resultant force should take into account the following factors:

(1)

Puncture feasibility: Considering the characteristics of breast soft tissue and the limitations of the working space and carrying capacity of the manipulator, appropriate constraints should be designed to ensure that the position of the control point and the target shift are within the feasible range.

(2)

Puncture stability: the position selection of the control point should make the manipulator maintain stability during the control process to avoid increasing the error caused by unstable control.

(3)

Minimizing the resultant force: minimizing the resultant force of the required control force, that is, reducing the external force applied to the breast soft tissue, thereby reducing the degree of deformation and damage to the breast tissue and improving the safety of the operation.

As shown in Figure 3, the breast is simulated as a half sphere, where the plane O-ABCD is the bottom surface of the breast, and U is the apex of the top surface (the position of the nipple). Three different control point positions, M₁(θ₁), M₂(θ₂), and M₃(θ₃), are arranged on the boundary of the breast soft tissue. θ₁, θ₂, and θ₃ are the three angular values corresponding to the positions of the three control points. By applying force/displacement on the three control points by the external manipulator, the layered soft tissue of the breast can be deformed accordingly so that the internal target P of the soft tissue of the breast can be shifted to the desired target position point T.

If three non-collinear control points are arranged around the soft tissue of the breast surface, a plane containing the initial and target positions of the target point can be uniquely determined, and this plane can be defined as the control plane. Therefore, the selection of the control surface should be regarded as the precursor task of optimal control point location selection. Taking the requirements of the shortest puncture path into consideration, the coordinate point of the target position is taken as the center (T) of the sphere, the radius (R) is gradually increased, and the sphere is extended outward. The point (E) at which the sphere first intersects with the breast surface is the point at the shortest distance from the target position to the breast surface, and the three points of the shortest distance, the target position, and the target position can uniquely determine a control surface. If the above three points happen to be collinear, the horizontal plane containing the line where the three points are located is selected as the control plane. Reasonable selection of the position of the three control points is very important to improve the accuracy and stability of the puncture and achieve the optimal performance of the system.

In consideration of puncture stability, the manipulator should avoid sliding at the control point. Even if the tangential force is generated due to the deformation of the soft tissue of the breast during the operation, due to the existence of friction, it is assumed that the tangential force will never cause the manipulator to slip at the control point, and the control force will always be perpendicular to the breast surface. Meanwhile, angles θ₁, θ₂ and θ₃ need to satisfy the constraints of Equation (2) [33] in order to achieve physically stable clamping and manipulation:

$$\left\{\begin{array}{l}{\theta }_{\min }\le \left|{\theta }_i-{\theta }_j\right|\le {\theta }_{\max }\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}i,\hspace{0.33em}j=1,\hspace{0.33em}2,\hspace{0.33em}3,\hspace{0.33em}i\ne j\\ 0^{\circ }\le {\theta }_i\le {360}^{\circ }\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}i=1,\hspace{0.33em}2,\hspace{0.33em}3\end{array}\right.$$

(2)

Suppose that the displacement vector from the target position T to the target point P can be achieved by applying three external forces vector [f_in_i(M_i), (1 ≤ i ≤ 3)], which satisfies the interventional surgery requirements and achieves its optimal control. The resultant force of the three operating fingers at the control point is expressed as W, as shown in Equation (3):

$$W={\displaystyle {\sum }_{i=1}^3{f}_i{n}_i(M_i),\hspace{0.33em}(\forall W\in R^2)(\exists f_i\ge 0,\hspace{0.33em}1\le i\le 3)}$$

(3)

In the equation, f_i represents the amount of control force exerted by the i-th control finger, n_i(M_i) represents the unit internal normal at the i-th control point, the length of the vector is “1”, its direction is perpendicular to the tangent direction of the curve surface, and points to the inside of the curve. In order to minimize the norm of the three contact forces, the optimization equation minf^Tf is established, and the constraint conditions on the angle of the contact position of the three control fingers are determined by combining the constraint Equation (2) and the optimization objective function (3). In the process of solving, the software package for solving optimization model problems in Python3.7.9 is used to build the objective function and constraint model in this environment, and then the IPOPT (Interior Point OPTimizer) solver for solving nonlinear optimization problems is called. Finally, the optimal contact position of the three control fingers was obtained θ_i, i = 1, 2, 3. The purpose of this study is to guide the position of the internal target from point P to point T. Define point P as the actual location of the target:

$$P={[x_P\hspace{0.33em}\hspace{0.33em}{y}_P]}^T$$

(4)

where x_P and y_P are the position coordinates of point P in the global reference frame, and point T is the target position, expressed as the following:

$$T={[x_t\hspace{0.33em}\hspace{0.33em}{y}_t]}^T$$

(5)

where x_t and y_t are the coordinates of the target position. The displacement vector e of the target position is as follows:

$$e=T-P$$

(6)

The optimization goal of the minimum resultant force principle is to minimize the resultant force W so that the resultant force W is in the same direction as the displacement vector e. After the optimal contact position is determined by Equation (3), the target position point P and the error between the target position point T is processed:

$$e_i^{\ast }=e\cdot n_i$$

(7)

$$n_i={[n_{xi}\hspace{0.33em}\hspace{0.33em}{n}_{yi}]}^T$$

(8)

where n_xi and n_yi are the coordinates of the unit normal vector. In the process of controlling and selecting the optimal control point, the above steps are repeated several times until the desired position of the contact point achieves satisfactory system control accuracy.

3.3. Structural Design of Manipulation Mechanical Finger for Breast Target Point

3.3.1. Design Requirements

During breast interventional surgery, three common patient positions are typically used: supine, prone, and lateral positions, as shown in Figure 4a, b, and c, respectively. The choice of patient’s position can be determined according to the nature and needs of the surgery.

Figure 4d,e represent the breast morphology of the patient in the supine position and prone position, respectively. By comparing the two breast morphologies, it is found that the breast naturally hangs downward when the patient is in the prone position, which enables the doctor to better observe the shape and structure of the breast and help to visit some specific breast areas. Meanwhile, the prone position facilitates breast manipulation, enabling more accurate imaging and sampling. The prone position is more conducive to robot-assisted breast interventional surgery, so this study chose to carry out surgical research on the breast morphology of patients in the prone position. Based on the patient’s position selection and the implementation of target manipulation strategies within the soft tissue of the breast, in order to control the position of the breast target and achieve more accurate breast interventional surgery, the following key requirements should be considered when designing the mechanical finger for manipulating breast target point:

(1)

The position of three points can be controlled simultaneously: the minimum number of control points according to the determined three-dimensional deformation of the breast is three. Therefore, the manipulation mechanical finger for the breast target point is required to be able to control the position of three points on the surface of the breast at the same time. When the robot interacts with the breast soft tissue, the breast deforms so as to control the position of the breast target point in the three-dimensional space.

(2)

Full coverage of workspace: according to the breast size data of clinical patients obtained by the PLA Air Force General Hospital for reference in this study, the bottom surface diameter should be between 8.46 cm and 14.38 cm, and the breast height in the prone position should be between 4.15 cm and 7.53 cm. The working space of the mechanical finger for manipulating the breast target point should cover the entire breast surface of the patient.

(3)

Sufficient compactness: when the patient is in the prone position, the surgical space becomes limited; therefore, the manipulative mechanical finger for targeting breast lesions must feature a compact structural design, mechanical flexibility, and sufficient degrees of freedom.

(4)

Structural adjustability: it is necessary for the manipulative mechanical finger for the breast target point to have sufficient adjustability and scalability to adapt to different sizes (sizes) of the breast.

(5)

Patient comfort: one of the design goals of the manipulative mechanical finger for the breast target point is to reduce patient discomfort due to higher soft tissue compression forces in conventional parallel plates. Patient comfort and safety are considered to ensure that the impact of robotic operation on patients is minimized and pain and discomfort are reduced.

Taken together, these key requirements will help ensure that the manipulative mechanical finger for the breast target point maximizes the benefits of breast puncture surgery, improving accuracy, safety, and comfort while reducing postoperative recovery time and patient discomfort.

3.3.2. Structural Scheme of Robot of Breast Target Point Manipulation

The method of artificial manipulation of breast soft tissue in clinics benefits from the flexible grasp and manipulation of the human hand. The structural design of the bionic hand has been adopted in the field of surgery with obvious advantages: the structure of the bionic hand can provide better flexibility and control. Meanwhile, because its structure and movement are more similar to that of doctors in routine clinical operations, robots with bionic hands can more easily work with human operators. Considering the design requirements and actual operation conditions of the mechanical finger for manipulating the breast target point, the overall design of the mechanical finger for manipulating the breast target point is based on the three-finger structure of the bionic human hand, which can imitate the three-point grasping ability of the human hand and can better adapt to different shapes and sizes of the breast. According to the actual operation needs, the three control fingers can be changed in different positions on the breast surface to achieve the target control function. Meanwhile, this open structure also provides more space and freedom for the choice of puncture needlepoint and puncture path. Figure 5 shows the example of the clinician’s operation of breast interventional surgery with three-finger manipulation.

Human finger joints have two degrees of freedom: pitch (the direction points to the back of the hand and the palm) and side swing (to open and close the fingers), as shown in Figure 6. Based on the physiological structure of human hands, each finger of the breast manipulation robot hand is equipped with three joints, including a lateral swing joint and two pitch joints, which allows the fingers to mimic the natural movements of human hands, enabling the robot fingers to operate flexibly in three-dimensional space. The flexible finger design enables the robot fingers to make soft contact with the breast surface, thereby reducing the discomfort of the patient. The overall structure and the distribution of freedom degrees of the mechanical finger for manipulating the breast target point are shown in Figure 7, where 1, 4, and 7 are the freedom degrees of side swing, and 2, 3, 5, 6, 8, and 9 are the degrees of freedom of pitching.

The freedom configuration of the mechanical finger takes into account the specific needs of the breast manipulation task, enabling precise manipulation of the target point for sampling examination or treatment, which may involve holding, pressing, pinching, or lifting the breast to expose the lesion/target point area and make it easier to perform interventional surgery. During target manipulation procedures, the disc-shaped base of the mechanical finger for manipulating the breast target point is typically secured to the workbench, which can provide support and positioning for the entire robot. A center bracket is attached to the disc base to connect three operating fingers. The diameter of the disc base is 120 mm, the cross-section of the central support is an equilateral triangle, its side length is 60 mm, the thickness is 3.5 mm, the central support is 50 mm high, and the interior is hollow. During the experiment, a camera can be placed in the center of the central support so as to facilitate the acquisition of image information of the breast and the internal target point. Based on the shape and size of the human finger, the terminal of the mechanical finger is 3D-printed to make a spherical contact surface with a diameter of 15 mm. The control fingers of the mechanical finger for manipulating the breast target point are mainly formed by the combination of a U-shaped bracket, single-line bracket, steering engine bracket, steering engine, and steering wheel. The mechanical design and dimensions of the mechanical fingers are shown in Figure 8.

The lateral swing and pitching joints in the mechanical finger structure are driven by the steering engine, and the number of steering engines required for each mechanical finger is three. The connecting parts are made of aluminum alloy material to ensure the light weight and rigidity of the overall structure of the mechanical finger for manipulating the breast target point. The steering engine bracket provides a support structure, and the steering engine bracket has a fixed hole or groove, which can be matched with the bolts or threaded rods of the steering engine so that the steering engine is firmly fixed on the bracket, ensuring that the steering engine is firmly connected to the entire system so as to effectively transmit the control movement. The steering engine bracket needs to have sufficient strength and stability to support the weight of the steering engine and withstand its movement and load. The steering wheel is a round metal component that is combined with the steering engine to control steering. The U-shaped bracket is used to connect the steering wheel to the steering gear, and the U-shaped bracket needs to bear a certain load to ensure that the supported object will not sag or move. The line bracket is used for support and fixing between the U-shaped bracket and the steering engine bracket, and its total length is 63 mm.

3.3.3. Workspace Analysis of Mechanical Finger for Manipulating Breast Target Point

This study analyzed and solved the working space of the mechanical finger for manipulating the breast target point through the analysis of accessible posture and workspace simulation of the mechanical fingers of the mechanical finger for manipulating the breast target point. The accessible posture analysis of a single manipulative finger is shown in Figure 9.

As shown in Figure 9a,b, the maximum horizontal length of a single manipulative finger can reach 185 mm, and the limit position of inward propulsion is 60 mm; as shown in Figure 9c,d, the height of the upper limit position can reach 170 mm, the height of the lower limit position is 90 mm, and the upper and lower limit position is 80 mm. The normal angle range of the human finger lateral joint is usually small, generally between 10° and 20°, while the more special thumb can achieve only about −30° to 60°. To achieve comprehensive coverage of the breast surface position, the lateral swing angle of a single control finger is fully increased, as shown in Figure 9e,f. The limit angle of unilateral swing α can reach −45°, and the limit angle of unilateral swing β can reach 80°, which can reach a total range of 125°, and the three manipulative fingers can fully cover the entire circumference of 360°, reaching any point around the breast.

According to the joint length and number of the mechanical fingers for manipulating the breast target point, the robot toolbox of MATLAB2017a is applied to calculate the effective working space that could be covered by a single manipulative finger, and the results are shown in Figure 10.

As mentioned earlier, the base of the breast is between 8.46 cm and 14.38 cm in diameter, and the height of the breast in the prone position is between 4.15 cm and 7.53 cm. According to the reachable posture and working space simulation analysis of a single manipulative finger, the working space of the mechanical finger for manipulating the breast target point meets the requirements of breast interventional surgery. Meanwhile, the different working positions that the mechanical finger for manipulating the breast target point can achieve are shown in Figure 11.

3.4. Design of Control System for Manipulating Breast Target Point

3.4.1. Dynamic Modeling of Mechanical Finger for Manipulating Breast Target Point

The interaction between the mechanical finger and the breast soft tissue can directly affect breast deformation. Therefore, in this section, considering the specificity of breast soft tissue in different patients, a dynamic model of breast soft tissue based on the MRAC system is established, and MRAC can be used as a control strategy to control breast deformation. This paper intends to use the self-defined control rate to control the mechanical finger and achieve accurate control of the mechanical finger control force based on the MRAC algorithm,. In this paper, the manipulative force–displacement data of the square sample of breast layered soft tissue obtained by the experiment will be used to model the dynamics of mechanical fingers for manipulating the breast target point.

First, a transfer function is used to express the relationship between the handling force and the displacement, as shown in Equation (9):

$$G(z,k)={\displaystyle \frac{F(k)}{d(k)}}$$

(9)

In this paper, linear discrete transfer function is selected because it has the advantages of simple processing and fast operation speed in the process of analyzing soft tissue deformation response [34], as shown in Equation (10):

$$\widehat{G}(z,k)={\displaystyle \frac{F(k)}{d(k)}}={\displaystyle \frac{{\widehat{b}}_1(k)z^{-1}+{\widehat{b}}_2(k)z^{-2}+\cdots +{\widehat{b}}_n(k)z^{-n}}{1+{\widehat{a}}_1(k)z^{-1}+{\widehat{a}}_2(k)z^{-2}+\cdots +{\widehat{a}}_n(k)z^{-n}}}$$

(10)

where $\widehat{G}(z,k)$ represents the transfer function after k iteration optimization in discrete space; F and d are, respectively, the control force and displacement variables; a_i(k) and b_i(k) are the model parameters, that is, the coefficients of the transfer function after the k iteration optimization; n is the order of the transfer function; and z represents the complex variables of the system. To conduct dynamic modeling of breast soft tissue, the second-order linear model is considered to modify the data based on the experimental acquisition of manipulative force–displacement data through MRAC technology; that is, the quadratic polynomial is used for modeling. In the second-order linear model, the square of the independent variable is also one of the predictor variables, and the regression equation is built together with the first-order term. The second-order linear model can be used to model the nonlinear relationship:

$$\widehat{G}(z,k)={\displaystyle \frac{F(k)}{d(k)}}={\displaystyle \frac{{\widehat{b}}_1(k)z^{-1}+{\widehat{b}}_2(k)z^{-2}}{1+{\widehat{a}}_1(k)z^{-1}+{\widehat{a}}_2(k)z^{-2}}}$$

(11)

The model can estimate the dynamic behavior of the soft tissue of the breast; however, the model parameters a₁(k), a₂(k), b₁(k), and b₂(k) still need to be calculated. In this paper, a series–parallel model reference adaptive system is used to identify parameters of the breast soft tissue dynamic model. The schematic diagram of MRAC is shown in Figure 12.

The application of the MRAC system requires fitting the experimental data set to the transfer function to estimate the model parameters. In discrete space, the control force and displacement values after the k-m-th iterations are defined as follows:

$$F(k-m)=z^{-m}F(k)$$

(12)

$$d(k-m)=z^{-m}d(k)$$

(13)

A simpler model expression can be derived from Equations (12) and (13):

$$F(k)=-{\widehat{a}}_1(k)F(k-1)-{\widehat{a}}_2(k)F(k-2)+{\widehat{b}}_1(k)d(k-1)+{\widehat{b}}_2(k)d(k-2)$$

(14)

In the process of parameter identification of the breast soft tissue MRAC model, based on the Lyapunov stability theorem, an adaptive mechanism is used to calculate the model parameters. The model parameters are modified and converge to constant values after each iteration, and the following adaptive structure is selected:

$${\widehat{a}}_i(k)={\widehat{a}}_i(k-1)-k_{ai}e(k)F(k-i),\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}i=1,\hspace{0.33em}2$$

(15)

$${\widehat{b}}_j(k)={\widehat{b}}_j(k-1)-k_{bj}e(k)d(k-i),\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}j=1,\hspace{0.33em}2$$

(16)

where k_ai and k_bj are the self-defined coefficients affecting the convergence speed, and e(k) is the error signal of the k-th iteration. The error signal is extracted to obtain Equation (17):

$$\begin{array}{l}e(k)=Z_a-b_b\\ \hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}=F_k+{\displaystyle \sum _{i=1}^2{\widehat{a}}_i(k)F(k-i)-}{\displaystyle \sum _{j=1}^2{\widehat{b}}_j(k)d(k-j)}\end{array}$$

(17)

By substituting the model parameters obtained by Equations (15) and (16) of the k-th iteration into the error function Equation (17), the error signal of the k-th iteration can be obtained as shown in Equation (18):

$$e(k)={\displaystyle \frac{F(k)+{\displaystyle \sum _{i=1}^2{\widehat{a}}_i(k-1)F(k-i)-{\displaystyle \sum _{j=1}^2{\widehat{b}}_j(k-1)d(k-j)}}}{1+{\displaystyle \sum _{i=1}^2{k}_{ai}{F}^2(k-i)+{\displaystyle \sum _{j=1}^2{k}_{bj}{d}^2(k-j)}}}}$$

(18)

In order to obtain the linear dynamic model of Laplacian space/continuous space, the Tustin transform, namely bilinear transform, is implemented to convert the transfer function of the continuous time system into the difference equation of the discrete time system. The Tustin transform is shown in Equation (19):

$$z\approx {\displaystyle \frac{1+s\frac{T}{2}}{1-s\frac{T}{2}}}$$

(19)

where s is the Laplacian variable, and T is the time increment. A dynamic model can be obtained in Laplacian space by applying Equation (19) in the discrete model, such as Equation (20) through Equation (26):

$$\widehat{G}(s)={\displaystyle \frac{F(s)}{d(s)}}={\displaystyle \frac{B_1{s}^2+B_{2}s+B_3}{A_1{s}^2+A_{2}s+A_3}}$$

(20)

$$B_1={\displaystyle \frac{T^2}{4}}({\widehat{b}}_2-{\widehat{b}}_1)$$

(21)

$$B_2=-T{\widehat{b}}_2$$

(22)

$$B_3={\widehat{b}}_1+{\widehat{b}}_2$$

(23)

$$A_1={\displaystyle \frac{T^2}{4}}(1+{\widehat{a}}_2-{\widehat{a}}_1)$$

(24)

$$A_2=T(1-{\widehat{a}}_2)$$

(25)

$$A_3={\widehat{a}}_2+{\widehat{a}}_1+1$$

(26)

where A_i and B_i are the parameters of the Laplacian model. Assuming that both soft tissue displacement and manipulation force are 0 at the beginning, the differential equation for the dynamic behavior of breast tissue can be derived as follows:

$$A_1{\displaystyle \frac{d^{2}F(t)}{d{t}^2}}+A_2{\displaystyle \frac{dF(t)}{dt}}+A_{3}F(t)=B_1{\displaystyle \frac{d^2(d(t))}{d{t}^2}}+B_2{\displaystyle \frac{d(d(t))}{dt}}+B_{3}d(t)$$

(27)

3.4.2. Parameter Identification Results of Breast Soft Tissue Dynamics Model

Breast soft tissue manipulation requires the MRAC system to adjust the parameters of the breast soft tissue dynamics model to ensure accurate tracking or control of breast soft tissue manipulation. This approach can help overcome the nonlinearity and parametric uncertainty of breast tissue and enable the manipulation system to better adapt to the specific anatomy and physiological characteristics of the patient. Therefore, it is necessary to experimentally identify the parameters of the breast soft tissue dynamics model. The experimental equipment is shown in Figure 13. The feed speed of the mechanical finger during the experiment is 1 mm/s, and the time–handling force and displacement–handling force are 2 mm/s and 4 mm/s. In addition, the contact angles between the mechanical finger and the soft tissue are different, and the contact force and contact displacement change linearly; combined with Equation (20), it can be known that it will not affect the experimental results. For the convenience of the experiment, this paper selects the angle shown in Figure 13 for the experimental analysis. The experimental results are shown in Figure 14a,b.

According to the experimental results, there is little correlation between the displacement–handling force and the feed speed. Therefore, the influence of the feed speed of the mechanical finger can be ignored, and the control force can be directly controlled by controlling the feed displacement of the mechanical finger. Meanwhile, the experimental results show that when the mechanical finger reaches the designated position and stops the movement, the soft tissue will experience a relaxation phenomenon after the movement stops.

Take the experimental data with a mechanical finger feed speed of 1 mm/s as an example, time increment as T = 0.25 s, the real-time measured control force–displacement data are applied, the coefficients ${\widehat{a}}_1$, ${\widehat{a}}_2$, ${\widehat{b}}_1$, and ${\widehat{b}}_2$ of the transfer function are calculated, and finally, the coefficient convergence diagram of the transfer function is obtained, as shown in Figure 15. Among them, the horizontal axis is the number of iterations, and the vertical axis is the value of the coefficient. As can be seen from the figure, the coefficient convergence of the transfer function occurs around the 45th iteration.

According to the coefficient convergence values of the transfer function, ${\widehat{a}}_1$ = −0.0383, ${\widehat{a}}_2$ = −0.521, ${\widehat{b}}_1$ = 0.195, ${\widehat{b}}_2$ = 0.094 are inserted into Equations (21) to (26), and the model parameter values based on MRAC can be obtained. According to the solution results, the model parameter values at different feed speeds are also very similar.

The final obtained model parameter values based on MRAC are as follows:

A₁ = 0.0081; A₂ = 0.3803; A₃ = 0.4407; B₁ = −0.0016; B₂ = −0.0235; B₃ = 0.289

The parameter values of the model based on MRAC are brought into Equation (27) to obtain the final differential equation of the dynamic behavior of breast tissue; that is, the expression of the dynamic model of breast soft tissue, as shown in Equation (28).

$$\begin{array}{l}0.0081{\displaystyle \frac{d^{2}F(t)}{d{t}^2}}+0.3803{\displaystyle \frac{dF(t)}{dt}}+0.4407F(t)\\ =-0.0016{\displaystyle \frac{d^{2}d(t)}{d{t}^2}}-0.0235{\displaystyle \frac{d(d(t))}{dt}}+0.289d(t)\end{array}$$

(28)

In the process of manipulating breast soft tissue with mechanical fingers, the relationship between the manipulative force of mechanical fingers and the displacement of breast soft tissue can be obtained based on the dynamics model of breast soft tissue. Therefore, the control force exerted by the mechanical finger can be adjusted by controlling the feed displacement of the mechanical finger according to the soft tissue dynamics model of the breast and based on the MRAC system so as to achieve the desired control effect.

3.4.3. Structural Design of Control System

Figure 16 shows the structural design of the robotics system based on breast target-point manipulation. Among them, the DC power supply converts 220 V AC to 6 V DC and supplies power to both the servo and the controller. The driving mode of the servo is Pulse Width Modification (PWM). The pulse width of the PWM signal determines the rotation angle of the servo. The controller generates the appropriate PWM signal to drive the servor to achieve the desired movement, and the controller is STM32F103RC8T6 MCU. The instruction is issued by the demonstrator, and the controller analyzes the motion instruction, performs the kinematics solution, and drives the motor to reach the target position. The demonstrator selects the TJC4832T035 serial screen, which allows the operator to visually interact with the mechanical finger to manipulate breast target point, demonstrate the movement and tasks, and monitor the robot’s status.

The robotic system has a total of nine degrees of freedom, each of which is independently driven by a servo. Selection of high precision, low noise digital servo, model DS3218, steering gear size is 40 mm × 20 mm × 37.2 mm, weight is 60 g, torque is 20 kg·cm, operating voltage is 4.8~6.8 V, and control accuracy is 3μs. It can meet the driving and control requirements of mechanical finger for manipulating breast target points.

4. Simulation and Experiment of Breast Target Point Manipulation Task

4.1. Target Position and Optimal Control Point Selection Task Simulation

According to the structural characteristics of the breast soft tissue, there are skin layers, fat layers, and gland layers from the outside to the inside, and the breast soft tissue has characteristics such as non-uniformity, nonlinearity, anisotropy, and viscoelasticity, so the modeling of breast soft tissue is very complex [35]. Therefore, the Maxwell model is adopted in this paper to create a (particle-spring) model of breast layered soft tissue for numerical simulation [36]. The advantages of numerical simulation using the Maxwell model are mainly reflected in its effective characterization of the mechanical behavior of viscoelastic materials and computational efficiency, and it is particularly suitable for simulating biological soft tissues (such as human breast soft tissues). In addition to the central particle, the three outer tissue layers are divided into particles at 10° intervals; that is, 109 particles are shared to discretize the layered soft tissue of the breast. The particle m_i (i = 1, 2, 3... 109) indicates the mass. There is a Maxwell element between adjacent particles, as shown in Figure 17.

Relevant studies have shown that the average mass of the female breast is about 0.5 kg, and the mass m_i per particle is set at 0.005 kg. Meanwhile, according to the literature [37], the elastic coefficient of skin soft tissue is k₀ = k₁ = 87.7 N/m, the viscosity of skin soft tissue is η₁ = 0.6267 MPa·s, the elastic coefficient of fatty soft tissue is k₂ = 27 N/m, the viscosity of fatty soft tissue is η₂ = 82.9 MPa·s, the elastic coefficient of glandular soft tissue is k₃ = 107 N/m, and the viscosity of glandular soft tissue is η₃ = 468.6 MPa·s.

If the radius of the breast model is r, in the control plane, the polar coordinates of the control point M on the outer surface of the breast are (r, 40°). The initial length value of the spring is given according to the thickness between various soft tissue layers. As mentioned above, the thickness of each soft tissue layer can be determined by clinical ultrasound imaging and other image methods [38]. Therefore, each soft tissue layer thickness can be treated as a known constant during modeling.

To more reasonably simulate the real pathological conditions of breast cancer, reference is made to the real MR sections of four female patients in the clinic [39]. In addition, according to medical knowledge and treatment requirements, the target position, direction, and distance to which the four small targets in the soft tissue should be moved are specified within the control surface, and the target position is specified, as shown in

Table 1. Specified lesion location and target location.

	Task 1: Target 1	Task 2: Target 2	Task 3: Target 3	Task 4: Target 4
①
②	(0.11 r, 140°)	(0.41 r, 317°)	(0.70 r, 30°)	(0.30 r, 110°)
③	(0.30 r, 63°)	(0.33 r, 0°)	(0.49 r, 50°)	(0.59 r, 120°)

Note: ① Patient real MR slice images: as a reference for target location selection; ② define the target position coordinate point P within the control plane; ③ specify the target position coordinate point T within the control plane.

.

Based on the principle of minimum resultant force, and considering the minimum angle constraint between any two control fingers, the internal target point position P is positioned to the target position T with the least force. The position θ_i, i = 1, 2, 3 of the optimal control point M_i of the three control fingers is shown in Figure 18. In the figure, the bottom of the red arrow represents the actual target point position P, the head of the arrow represents the target position T, and the optimal control point position is represented by the bold red dot on the surface of the breast soft tissue control surface.

According to the solution results, when the optimal control point position based on the principle of minimum resultant force is determined, the control forces exerted by the three mechanical fingers, respectively, are shown in

Table 2. Control force values of three mechanical fingers in Figure 18 (unit: N).

	Task 1	Task 2	Task 3	Task 4
F1	0.73	0.92	2.03	1.14
F2	1.25	3.23	1.43	2.43
F3	2.28	1.50	3.85	2.16
Value of the minimum resultant force	4.26	5.65	7.31	5.73

.

In order to verify the effectiveness of the optimal control point selection, the three mechanical fingers are placed at 120° apart; that is, the three mechanical points are located at 0°, 120°, and 240° on the breast surface, and the manipulation task for focal point 1 is repeated, as shown in Figure 19.

The calculation results show that for task 1, compared with the optimal control point position, when the three mechanical fingers are placed 120° apart, the control force is F₁ = 1.21 N, F₂ = 1.44 N, F₃ = 3.75 N, and the resultant force is 6.4 N, which is greater than the minimum resultant force of 4.26 N at the optimal control point position. Therefore, the optimal control point location selection method based on the principle of minimum force can help doctors determine the optimal control point location so as to minimize the deformation energy inside the soft tissue of the breast layer and reduce the damage to the soft tissue.

4.2. Manipulation Experiment of Breast Target Point

The breast target point manipulation experiment platform mainly consists of the mechanical finger for manipulating the breast target point and its control system (power supply + controller + demonstrator), breast layered soft tissue model, PC (upper computer), and camera, as shown in Figure 20; among them, in order to ensure the stability of the robot’s movement, this paper adopts the scheme proposed in the literature [40] to control the servo motor. The mechanical finger for manipulating the breast target point is fixed on the adjustable fixed bracket, which can hover freely, and the overall height and posture of the mechanical finger for manipulating the breast target point can be adjusted. The breast model suspension connector is connected to the layered soft tissue model of the breast and is stably fixed to the model suspension bracket through a threaded connection, thus simulating the breast morphology of the patient in the prone position in clinical practice. Both the adjustable fixed bracket and the model suspension bracket can stably load 9 kg and can stably support and fix the mechanical finger for manipulating the breast target point and the layered soft tissue model to meet the needs of control stability. Camera 1 is placed on the camera mounting frame to record the image information of the breast layered soft tissue model in the vertical plane, and camera 2 is placed in the central support of the mechanical finger for manipulating the breast target point to record the image information in the horizontal plane. Therefore, the squeezing and deformation of the tissue generated by the mechanical finger for manipulating the breast target point, as well as the position changes of the breast target point, are visible in the image. The terminal of the mechanical finger is wrapped in a silicone protective sleeve, which can effectively improve the comfort of the patient when it comes into contact with the skin tissue on the surface of the breast.

In the process of the experiment, in order to obtain detailed position information of target point movement, it is necessary to establish the coordinate system of the breast model. Due to the fixed position of the breast model suspension connector, a stable reference point can be provided. Therefore, this study chose a corner point in the suspension connector of the breast model as the coordinate origin o and established the coordinate system o-xyz of the breast model, as shown in Figure 21.

Due to the different compression degrees of different control points, the outer contour of the breast model surface has certain shape differences, but real breast tissue is softer than silicone material, and the target point displacement phenomenon will be more significant. The changes in breast morphology and target position in the xoy plane and the xoz plane during manipulation are shown in Figure 22 and Figure 23, respectively. Figure 22 shows the position changes of the breast target point before, during, and after manipulation control, respectively. The displacement in the x direction is 3.7 mm, and the displacement in the y direction is 10.9 mm. As a practical matter, the force exerted by the mechanical finger for manipulating the breast target point on the breast model affects the position of the target in the xoy plane more than the xoz plane.

According to the established coordinate system of the breast model, the actual target point position coordinates in the layered soft tissue model of the breast can be expressed as P (73, 50, 44). To evaluate the consistency and accuracy of the mechanical finger for manipulating breast target point in repeatedly performing the same task, this paper focuses on three distinct target positions (except for point P, select two coordinate points near it, where the coordinate selection range is within the coordinate region established by the spatial image coordinate software, covering the coordinate points where the soft tissue images are located), denoted by the coordinates T₁ (65, 50, 43), T₂ (70, 40, 44), and T₃ (80, 60, 40), and multiple repeatability experiments are conducted for each target position. The experimental results of breast target point manipulation are shown in

Table 3. Breast target manipulation experimental results (mm).

	Target Point Position Coordinate	Target Point Position After Manipulation	Error	Mean Error	Standard Deviation
Group one	(65, 50, 43)	(64.7, 48.9, 43.4)	1.208	1.142	0.127
	(65, 50, 43)	(63.8, 49.7, 43.2)	1.253
	(65, 50, 43)	(64.2, 49.8, 42.5)	0.964
Group two	(70, 40, 44)	(69.3, 39.1, 44.3)	1.179	1.160	0.088
	(70, 40, 44)	(69.4, 39.2, 44.7)	1.044
	(70, 40, 44)	(68.9, 39.4, 44.1)	1.257
Group three	(80, 60, 40)	(79.2, 59.2, 39.8)	1.149	1.173	0.144
	(80, 60, 40)	(78.8, 59.5, 39.6)	1.360
	(80, 60, 40)	(79.3, 59.3, 40.2)	1.009
Mean value				1.158	0.119

.

From the experimental results presented in Table 3, it is evident that the breast target manipulation robotic arm achieves a high manipulation precision of approximately 1.158 mm for target points at different coordinate locations, with a standard deviation of about 0.119 mm, and this level of precision meets the requirements for soft tissue manipulation in clinical experiments.

5. Discussion

In biomechanical modeling or medical simulation, simplifying the breast into a hemispherical shape is a common idealization approach, which provides researchers with a simplified method to balance computational efficiency and geometric authenticity. The hemispherical model abstracts complex geometry into symmetrical regular forms by ignoring the local anatomical details of the breast, facilitating the rapid establishment of mechanical equations and the allocation of boundary conditions. It is suitable for the verification of basic mechanisms (such as the stress conduction path during breast compression). Therefore, the selection of the optimal control point position based on the principle of minimum resultant force is not affected by the hemispherical model. In the prone position, this model may be partially applicable due to morphological symmetry. However, the research of this paper is related to the external force on breast fixation and target manipulation. Therefore, the adoption of this model is applicable to the effective selection of the external optimal manipulation point without being affected by the prone position and other body positions.

The core limitation of using synthetic breast models (such as silicone prostheses) in this article lies in the inability to fully reproduce the biological complexity of human breast soft tissues, especially the inability to fully replicate the heterogeneity of the tissues and the real deformation behavior. However, the breast target-point manipulation method and the manipulation robot studied in this paper need to take the synthetic silicone breast model as the experimental object, mainly to verify the movement of the target point within the breast, which belongs to qualitative analysis. When the research objective is qualitative analysis, the limitations of the synthesized silica gel model have a relatively small impact on the conclusion. Meanwhile, low-hardness silicone was used to simulate adipose tissue, but the hardness of glandular tissue is usually slightly higher than that of silicone. In the experiment, the synthetic soft tissue was enhanced in terms of heterogeneity through a multi-layer structure (outer layer of silicone + inner layer of elastic resin), approximately simulating the deformation behavior of the human mammary gland. This can greatly ensure the validity of the experimental conclusion.

6. Conclusions

The design and experimental study of a robotic system for target point manipulation in breast procedures are presented in this paper. The following conclusions are drawn: firstly, a breast target control system based on three mechanical fingers is proposed, and the position of the optimal control point is determined according to the principle of minimum force. Secondly, a robot for breast target-point manipulation based on three fingers is designed. Through the analysis of this robot’s working space, it is demonstrated that the designed robotics system is capable of achieving precise control of the breast at any point in space. Third, based on the mechanical parameters of soft tissues, the position of the target point, and the target location, the position selection of the optimal control point is simulated. The results showed that the target could be moved to the target point based on the principle of minimum resultant force. Fourth, based on the MRAC system, a dynamic model of breast layered soft tissue under mechanical finger control is established, and the parameters of the MRAC model are obtained through the experimental collection of manipulative force–displacement data so as to realize the manipulative force control of breast layered soft tissue. Finally, the experimental results of breast soft tissue manipulation by this robot show that it has a high control accuracy of 1.158 mm with a standard deviation of 0.119 mm, which can meet the precision requirements for clinical breast interventional puncture procedures.

The problems faced by the current methods and approaches mentioned in the introduction can all be effectively solved by the robot system for target point operation in breast surgery proposed in this study, except for causing mild pain to the patients. In addition, after the mechanical hand has fixed the breast soft tissue, during the puncture process, the needle tip driving the soft tissue will cause the target point to move slightly along the needle axis direction, and the result will lead to a minimal positional error between the needle tip and the target point; this is an irresistible factor unless a very strong clamping force is applied, but this will also cause greater harm to the patient. Although it will not have an impact on the research of this article, future work will focus on developing compensation algorithms and control mechanisms to tackle this problem during the process of puncturing the soft tissue of the breast.