Flexible needle three-dimensional path planning method for multi-target puncture

Abstract

The invention relates to a flexible needle three-dimensional path planning method for multi-target puncture, and the method comprises the steps: obtaining a preoperative image, building a three-dimensional environment model through the preoperative image, and enabling the three-dimensional environment model to be used for recognizing target coordinates and marking obstacles; establishing a three-dimensional flexible needle kinematics model under the puncture base coordinates for determining the reachable domain section circle radius in the projection depth of the target spot along the needle axis; performing attitude judgment on the target spot by using the reachable domain cross section circle radius, defining a center deviation ratio, obtaining an average target spot centrality screening cost, and generating an effective candidate attitude in combination with an obstacle intrusion screening cost; screening effective candidate attitudes, determining a local coordinate system based on a unit needle inserting direction vector in the screened effective candidate attitudes in combination with a first target spot in the target spot access sequence, and performing path planning on a two-dimensional plane of the local coordinate system by adopting a fast extension random tree path planning algorithm to obtain a first path; and executing a retraction-rotation-repropulsion strategy to generate an optimal scheme.

Description

Technical Field

[0001] This invention relates to the field of path planning technology, and in particular to a three-dimensional path planning method for flexible needles used in multi-target puncture. Background Technology

[0002] Flexible needle puncture plays a crucial role in the diagnosis and treatment of minimally invasive surgery. It is highly favored due to its minimal trauma and rapid recovery, and is widely used in clinical procedures, especially in biopsy, brachytherapy, precise radiofrequency ablation, and targeted drug delivery. Due to tissue interaction forces, the flexible needle can utilize the force applied to its beveled tip to form different arcs during puncture, thus allowing for more flexible avoidance of various obstacles.

[0003] In traditional puncture procedures, doctors often plan the puncture route based on preoperative images (such as CT and MRI) combined with intraoperative two-dimensional ultrasound images, relying on their personal experience. This method demands extremely high levels of professional skill and spatial imagination from the doctor, and it is difficult to guarantee optimality and repeatability. With the development of modern smart healthcare, robot-assisted punctures have gained popularity, and the most important initial step is the proper planning of the puncture path. Currently, there are three main methods for puncture path planning: Path planning methods based on inverse geometry: These methods attempt to directly calculate the path from the starting point to the target point using an analytical kinematic or geometric model of the flexible needle. They typically simplify the movement path of the flexible needle into a combination of basic geometric shapes (such as straight line segments and arc segments). The core of this method lies in solving the inverse kinematics of the model, given the position and orientation of a target point, to deduce or directly calculate the parameters necessary for the needle to reach the target point, such as the required insertion depth, rotation angle, and curvature.

[0004] Multi-objective optimization path planning methods: These methods transform the path planning problem of flexible needle puncture into a multi-objective optimization problem. Examples include intelligent optimization algorithms such as Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), or Genetic Algorithm (GA). They typically construct a complex cost function that comprehensively considers multiple performance metrics, such as minimizing path length, smoothing the path, and maximizing the safe distance for obstacle avoidance. The algorithm iteratively searches the configuration space to find one or a set of Pareto optimal solutions.

[0005] Path planning methods based on post-processing of sampled paths: These methods are currently mainstream in the field of medical robot path planning because they can efficiently handle high-dimensional configuration spaces. Examples include Rapidly-exploring RandomTrees (RRT) and its various variants (such as RRT-Connect). RRT (Research-Based Traceability) rapidly explores high-dimensional spaces by randomly sampling from the starting point and expanding a tree. Another example is the Artificial Potential Field (APF) method, which guides the movement of a needle tip by constructing a virtual force field (the target point generates attraction, and obstacles generate repulsion). These methods typically generate a feasible path quickly first, and then perform smoothing or optimization.

[0006] The disadvantages of the above-mentioned prior art: The planned 3D path is incompatible with clinical ultrasound image workflow feedback: The aforementioned multi-objective optimization algorithms and sampling-based algorithms primarily focus on solving obstacle avoidance paths within a fully configured 3D space, often generating non-coplanar 3D curves with complex spatial structures. However, in actual clinical practice, doctors or robots rely most heavily on 2D ultrasound slice images for workflow feedback. If the 3D path frequently enters and exits the ultrasound plane, the operator finds it difficult to correlate this 3D curve with real-time 2D ultrasound images, leading to a disconnect between planning and execution. The operator cannot determine the accuracy of the needle tip position based on the planned path in real time, nor can they make effective adjustments when deviations occur.

[0007] Planning for a Single Needle Insertion Posture: Current inverse geometry methods and most sampling-based methods typically treat the needle insertion point and angle as fixed conditions, meaning the algorithm only attempts to plan a path under a single, pre-defined needle insertion posture. This method uses a pre-defined, fixed needle insertion posture and then attempts to plan a path to the target point from that posture. The success rate of this method heavily depends on the choice of the initial posture. If this pre-defined posture is unfavorable—for example, if there are unavoidable obstacles along the path, or if the kinematic constraints of the flexible needle prevent it from reaching the target point—the planning algorithm may fail or generate an extremely costly path.

[0008] For puncture planning involving multiple targets, repeated needle insertions are necessary: ​​The three mainstream planning methods mentioned above are mainly for puncture tasks involving multiple targets from a single starting point to a single target. However, when faced with the common clinical need for biopsies or treatments to cover multiple lesions (multi-target), current technologies cannot plan a smooth path that continuously runs through all targets. This necessitates multiple punctures, increasing patient trauma, operation time, and potential complications such as increased bleeding and infection risk. Summary of the Invention

[0009] In order to solve the problems existing in the prior art, the purpose of this invention is to provide a three-dimensional path planning method for flexible needles for multi-target puncture, so as to better assist the operator in completing complex minimally invasive surgery, and significantly reduce surgical risks, shorten operation time, and alleviate patient pain.

[0010] To achieve the above objectives, the present invention provides the following solution: A three-dimensional path planning method for flexible needles used in multi-target puncture includes: Acquire preoperative images, and use the preoperative images to build a three-dimensional environment model for identifying target coordinates and marking obstacles; The distance from each target point to the needle insertion point is calculated and sorted to obtain the target point access sequence. At the same time, a three-dimensional flexible needle kinematic model under the puncture base coordinates is established. A three-dimensional reachable domain is established based on the three-dimensional flexible needle kinematic model to determine the radius of the reachable domain cross-section circle in the projection depth of the target point along the needle axis. The target point is used to determine its attitude by using the radius of the reachable domain cross-section circle, which is used to define the center deviation ratio, obtain the average target point centrality screening cost, and combine it with the obstacle intrusion screening cost to generate effective candidate attitudes. The effective candidate postures are screened, and a local coordinate system is established based on the unit needle direction vector corresponding to the screened effective candidate postures and the first target point in the target point access sequence. A fast extended random tree path planning algorithm is used to plan the path in the two-dimensional plane of the local coordinate system to obtain the first path. The shrink-rotate-re-advance strategy is then executed to generate the optimal solution.

[0011] Optionally, establishing a three-dimensional kinematic model of the flexible needle in the puncture base coordinates includes: ; in, , , This represents the position in the corresponding coordinate system. , , for , , The corresponding derivative, , , Let be the rotation angle about the corresponding coordinate system. , , for , , The corresponding derivative, , These are the control inputs for needle insertion and rotation, respectively, acting on the base of the needle. During puncture, the needle tip travels along the radius The curvature formed by motion.

[0012] Optionally, determining the radius of the reachable domain section circle in the projected depth of the target point along the needle axis includes: On a unit sphere centered at the needle insertion point, the polar angle and azimuth angle are sampled at equal intervals to generate the unit needle insertion direction vector. A local coordinate system is established based on the needle insertion point and the unit needle insertion direction vector. The coordinates of each target point in the world coordinate system are transformed to the local coordinate system. The projection depth of the target point along the needle axis and the radial distance from the target point to the center line of the needle axis are calculated. The radius of the reachable cross-section circle of the projection depth is further calculated.

[0013] Optionally, the cost of obtaining the average target centrality screening includes: The target point's attitude is determined using the radius of the reachable domain cross-section circle. If the radial distance is greater than the radius of the reachable domain cross-section circle, or the projected depth exceeds the effective depth range, it is proven that the target point is not within the reachable domain, and the unit needle direction vector is deleted. If the radial distance is less than the radius of the reachable domain cross-section circle, it is proven that the target point is within the reachable domain, and the center deviation ratio is defined to obtain the average target point centerness screening cost.

[0014] Optionally, the cost of obtaining the obstacle intrusion screening includes: Discrete slice inspection is performed along the needle axis using a probe circle to assess the area ratio of obstacles in the reachable cross section. That is, multiple discrete depth points are selected along the needle axis at fixed step sizes, and the reachable cross section circle with the target radius at each depth point is determined. Calculate the ratio of the area occupied by obstacles within the reachable cross-section circle to the total area of ​​the detection cross-section circle to obtain the obstacle area ratio of the slice, and sum the obstacle area ratios of all slices to calculate the obstacle intrusion screening cost.

[0015] Optionally, establishing the local coordinate system includes: The unit needle entry direction vector corresponding to the selected valid candidate postures, combined with the first target point in the target point access sequence, geometrically defines a unique plane. That is, with the needle entry point as the origin of the coordinate system, the unit needle entry direction vector corresponding to the selected valid candidate postures is used as the local coordinate system. The positive direction of the axis is used to calculate the needle insertion direction vector and the first target point in the target point access sequence based on the plane normal vector, thereby obtaining the local coordinate system. shaft and axis.

[0016] Optionally, obtaining the first path includes: The fast extended random tree path planning algorithm is used to plan the path in the two-dimensional plane of the local coordinate system. That is, the node state in the RRT tree is defined, and during the iterative expansion of the RRT tree, the newly generated nodes are all generated on the plane projection of the reachable domain formed by the tangent direction vector in the node state. New nodes are repeatedly generated, and after each new node is connected, a new reachable domain projection is obtained based on the new tangent direction vector. This projection is used to guide the generated trajectory tree toward the target and around obstacles under the guidance of a heuristic function, while adhering to kinematic constraints, until the end node meets the reach condition. Finally, the first path is connected and output.

[0017] Optionally, the heuristic function includes: ; in, The nearest neighbor node, The coefficient is used to adjust the weights.

[0018] Optionally, generating a preferred solution includes: In the first path, backtrack to search for the hub point. That is, based on the position coordinate vector and tangent direction vector in the node state of each node, a new reachable domain is established. Then, the attitude of the remaining target points is determined by the radius of the cross-sectional circle of the new reachable domain. That is, it is determined whether the remaining target points are within the reachable domain and close to the central axis, and whether the obstacle intrusion is too high. Each backtracked node is evaluated, and the node with the smallest evaluation is taken as the best hub point for the first switch. A new plane is defined based on the coordinates of the pivot point and the second target point. The fast extended random tree path planning algorithm is used again to plan the path on the new plane to obtain the second path. This process is repeated until the paths for all target points are planned, resulting in a set of pivot points, a set of all planes, and a set of paths. A global evaluation function is established to calculate the global cost of all paths in the path set, and the minimum path planning is selected as the preferred solution.

[0019] Optionally, establishing the global evaluation function includes: ; in, The length of each path segment, This represents the minimum safe distance from each path segment to the obstacle. , These are the corresponding weighting coefficients.

[0020] The beneficial effects of this invention are as follows: Transforming 3D path planning into planning across multiple 2D planes: This invention decomposes the complex 3D path planning problem into path planning and connection on multiple key 2D planes. This allows the planned path to be naturally monitored and verified by 2D ultrasound imaging, facilitating real-time feedback and fine-tuning by doctors during surgery, achieving seamless integration of planning with clinical workflow. Simultaneously, it simplifies the computational load of the planning algorithm and reduces its convergence time. The invention considers needle insertion posture during path planning: Addressing the limitation of single needle insertion posture in traditional planning methods, a key objective of this invention is to incorporate the needle insertion posture itself into the planning considerations. This method is no longer limited to a fixed initial posture; by evaluating a wider variety of needle insertion options, it significantly increases the probability of finding a feasible path and is more likely to select an optimal puncture path from among many feasible options. Multi-target path planning during a single needle insertion: This invention aims to plan a continuous and efficient path that starts from a single needle insertion point and takes into account the kinematic constraints of the flexible needle. Following a series of actions such as advancement, partial retraction, rotation, and re-advancement of the flexible needle, it sequentially visits all target points in a predetermined order. This combines the complex task of multiple independent punctures into a single surgical procedure, thereby minimizing overall damage to healthy tissue, significantly shortening surgical time, and reducing the risk of complications.

[0021] In summary, this invention allows the planned path to be naturally composed of multiple arc segments on a two-dimensional plane, which can keep the ultrasound probe aligned with the current planned plane. As a result, the planned path and the real-time position of the needle tip can be clearly seen in the ultrasound two-dimensional image workflow.

[0022] This invention treats the needle insertion posture as an optimizable variable, actively searching for the optimal needle insertion posture. With more initial choices, it is easier to select an optimal puncture path, thus providing a higher planning success rate and better path quality.

[0023] This invention, by planning a continuous path that includes retraction and rotation, can stably generate an optimal path that continuously passes through all target points, achieving the ideal effect of multiple points reached with a single puncture, and reducing the overall trauma and infection risk to the patient. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a schematic diagram of the kinematic model of a three-dimensional flexible needle according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a funnel-shaped reachable region that gradually expands along the needle insertion direction, with the needle insertion point as the vertex, according to an embodiment of the present invention. Figure 3 This is a schematic diagram of the unit needle insertion direction vector according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the reachability domain screening cost function according to an embodiment of the present invention; Figure 5 This is a flowchart of a three-dimensional path planning method for flexible needles used in multi-target puncture according to an embodiment of the present invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0028] like Figure 5 As shown, this embodiment discloses a three-dimensional path planning method for flexible needles used in multi-target puncture, including: acquiring preoperative images; establishing a three-dimensional environment model using the preoperative images to identify target coordinates and mark obstacles; calculating the distance from each target point to the needle insertion point and sorting them to obtain a target access sequence; simultaneously establishing a three-dimensional flexible needle kinematic model under the puncture base coordinates; establishing a three-dimensional reachable domain based on the three-dimensional flexible needle kinematic model to determine the radius of the reachable domain cross-section circle in the projection depth of the target point along the needle axis; using the radius of the reachable domain cross-section circle to determine the attitude of the target point, defining the center deviation ratio, obtaining the average target centerness screening cost, and combining it with the obstacle intrusion screening cost to generate effective candidate attitudes; screening effective candidate attitudes; establishing a local coordinate system based on the unit needle insertion direction vector corresponding to the screened effective candidate attitudes and the first target point in the target access sequence; using a fast extended random tree path planning algorithm to perform path planning in the two-dimensional plane of the local coordinate system to obtain the first path; and further executing a shrink-rotate-re-advance strategy to generate an optimal solution.

[0029] Specifically, this embodiment discloses a three-dimensional path planning method for flexible needles used in multi-target puncture, including: Step 1: Using preoperative imaging data, establish a three-dimensional environment model, identify all target points, and obtain the set of three-dimensional coordinates of the target points. Mark all obstacles that need to be avoided to obtain the obstacle list. geometric boundary Determine the needle insertion point. .

[0030] Step 2, calculate each target point Distance to needle insertion point The target access sequence is obtained by sorting the values ​​from smallest to largest. .

[0031] Step 3: Establish a kinematic model of the flexible needle. The flexible needle possesses a certain degree of elasticity; the reaction force experienced by its obliquely cut tip within the tissue causes the needle body to continuously bend, thus forming a natural arc-shaped channel during the puncture procedure. Based on this nonholonomic constraint model, the motion state of the needle tip is determined by the coupling of the insertion speed and rotational speed. This means that in three-dimensional space, the trajectory of the needle tip is not a straight line, but a continuously changing spatial arc. For example... Figure 1 As shown, the three-dimensional kinematic model of the flexible needle under the puncture base coordinates {A} is defined as follows: ; Where x, y, and z represent the positions in the corresponding coordinate system. , , Corresponding to its derivative; , , The rotation angle about the corresponding coordinate system , , Corresponding to its derivative; , These are the control inputs acting on the needle base for needle insertion and rotation; among which... The curvature formed by the movement of the needle tip along radius r during puncture. When inserted at speed v, a high-speed rotation for a certain period of time results in a perfectly straight trajectory. Returning to the original needle axis angle results in a curved trajectory again. This method can be used to adjust the curvature. The size of the needle tip is limited by its physical material and mechanical properties, resulting in a physical upper limit to its bending ability; that is, there is a maximum curvature. Corresponding to the minimum bending radius According to the model, and the maximum curvature Due to constraints, the flexible needle cannot reach any arbitrary location in space; the set of all possible points reachable by its tip constitutes a three-dimensional reachable domain. For example... Figure 2As shown, at the same insertion depth, the reachable region geometrically resembles a funnel shape with the insertion point as its vertex, gradually expanding along the insertion direction. Let the insertion depth be... The radius of the plane at this point can then be derived from geometric relationships. Size: ; Step 4, at the needle insertion point Generated at location Discrete unit needle direction vectors .like Figure 3 As shown, a uniform mesh discretization strategy in a local spherical coordinate system is adopted, and the maximum safe needle insertion cone angle relative to the skin normal is set. and angle search step size In the On a unit sphere with center at the polar angle and azimuth Perform equal-interval sampling to generate Discrete unit needle direction vectors .

[0032] Step 5, establish the reachability domain screening cost function, such as Figure 4 As shown. Specifically, the total cost function is defined as a weighted sum of two parts. The first part is used to evaluate the target set within the reachable domain formed by the current direction vector. The location of each target point within the reachable region and its proximity to the central axis is considered. Closer proximity to the central axis results in lower costs and greater tolerance for errors in subsequent planning. At the needle entry point... The current candidate unit's needle direction vector Establish a local coordinate system and map each target point in the world coordinate system. Transform to this local coordinate system and use vector operations to calculate the projected depth of the target point along the needle axis: ; And the radial distance from the target point to the center line of the needle axis is: ; Subsequently, the radius of the reachable domain cross-section circle at this depth is calculated based on the third step: ; like Beyond the effective depth range (i.e.) or )or If the target point is unreachable, the unit needle insertion direction vector is directly deleted; if the target point is within the reachable domain ( Then define the center deviation ratio. and take its square. As a penalty for single points near the edge, the final average target centrality screening cost is: ; The second part is the obstacle intrusion screening cost, which uses discrete slice inspection along the needle axis using a probe circle to evaluate the area ratio of obstacles in the reachable cross-section. M discrete depth points are selected along the needle axis at fixed step sizes. Determine the radius at each depth point as... Given an accessible circular cross-section, calculate the area of ​​the region occupied by obstacles within that cross-section. With the total area of ​​the probe's circular cross-section The ratio of the two values ​​gives the percentage of the obstacle area in the slice. The final cost of calculating the area percentage of all slices is as follows: ; For cases where the obstacle in a certain detection circular cross-section is too large, the cost loss is exponentially amplified, whereby... A coefficient greater than 0 is used to adjust the sensitivity. Effective candidate poses are calculated and compared. for: ; The K ranked postures are selected for subsequent planning, among which... , This is the weighting factor.

[0033] Step 6, for each of the selected direction vectors Perform path planning and establish a local coordinate system. This is based on the determined entry point and first target point. Together with the needle insertion direction vector, they geometrically define a unique plane. The original three-dimensional planning task is simplified into a two-dimensional deterministic planning problem within this specific plane. (Setting the entry point...) The origin is the coordinate system, and the direction of the current direction vector is in the local coordinate system. Positive direction of the axis, according to the plane normal vector Determine the local coordinate system shaft and axis.

[0034] Step 7: Perform path planning in the defined two-dimensional plane by executing an improved Rapid Expanding Random Tree (RRT) path planning algorithm. First, define the node states in the RRT tree as follows: ,in Let be the position coordinate vector in the plane. Let be the unit tangent direction vector at that point. During the iterative expansion of the tree, all newly generated nodes have a reachable domain formed by the tangent direction vector in the plane. Generate on the projection. To guide the tree to grow toward the target point and actively avoid obstacles, based on the target point... and the obstacles collected in the first step Geometric boundaries, design heuristic functions Defined as a weighted sum of the target attraction potential and the obstacle repulsion potential: ; in The nearest neighbor node, The coefficients are used to adjust the weights. Each time a new node is connected, the weights are adjusted based on the new tangent direction vector. Generate a new reachable region projection. This process is repeated iteratively to ensure that the generated trajectory tree, guided by a heuristic function, efficiently approaches the target and bypasses obstacles while strictly adhering to kinematic constraints, until the terminal node. Meeting arrival conditions ,in The value is small enough. The final connection output is obtained. .

[0035] Step 8: After obtaining the first path, execute the "retract-rotate-advance" strategy, within the planned path. The search for good pivot points is performed by backtracking, based on the coordinate vector of each node's position. and position tangent direction vector Based on the information, establish the reachability domain, and use the same discrimination method as in step five to determine whether the remaining target points are within the reachability domain and close to the central axis, and whether the obstacle intrusion is too high. Evaluate each retreating node and find the node with the smallest value as the optimal hub point for the first switch. Based on the pivot point and the target point The information defines a unique plane. Repeat steps six and seven to obtain... This process continues until the paths to all target points have been planned, resulting in a complete set of all pivot points. All plane sets and all path sets .

[0036] Step 9: Finally, establish the global evaluation function. for: ; in, The length of each path segment, This represents the minimum safe distance from each path segment to the obstacle. , These are the corresponding weighting coefficients. Calculate the global cost of all paths in the path set, and select the one with the minimum cost as the optimal solution.

[0037] In summary, this invention employs a three-dimensional decomposition planning strategy, which intelligently decomposes and constrains complex three-dimensional spatial search problems to a series of key two-dimensional planes. This allows the planning algorithm to retain the flexibility of the three-dimensional path while ensuring that the generated path segments are naturally compatible with two-dimensional ultrasound images. This enables doctors to monitor and verify the path in real time during surgery using two-dimensional ultrasound images, achieving a seamless integration of three-dimensional planning and clinical two-dimensional ultrasound image workflow.

[0038] This invention achieves multi-target sequence planning for a single needle insertion. By planning a continuous three-dimensional path that includes advancement, partial retraction, rotation, and re-advancement, it enables sequential access to all target points from a single needle insertion point in an optimized order. This method combines multiple independent puncture tasks into a single surgical operation. Its core advantage lies in minimizing overall path damage to healthy tissue and significantly shortening surgical time.

[0039] This invention incorporates needle insertion posture into the global optimization process, treating it as an optimizable variable. By searching and evaluating diverse needle insertion postures within permissible limits, it significantly increases the probability of finding feasible paths and is more likely to select an optimal puncture path from among many feasible options.

[0040] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A three-dimensional path planning method for flexible needles used in multi-target puncture, characterized in that, include: Acquire preoperative images, and use the preoperative images to build a three-dimensional environment model for identifying target coordinates and marking obstacles; The distance from each target point to the needle insertion point is calculated and sorted to obtain the target point access sequence. At the same time, a three-dimensional flexible needle kinematic model under the puncture base coordinates is established. A three-dimensional reachable domain is established based on the three-dimensional flexible needle kinematic model to determine the radius of the reachable domain cross-section circle in the projection depth of the target point along the needle axis. The target point is used to determine its attitude by using the radius of the reachable domain cross-section circle, which is used to define the center deviation ratio, obtain the average target point centrality screening cost, and combine it with the obstacle intrusion screening cost to generate effective candidate attitudes. The effective candidate postures are screened, and a local coordinate system is established based on the unit needle direction vector corresponding to the screened effective candidate postures and the first target point in the target point access sequence. A fast extended random tree path planning algorithm is used to plan the path in the two-dimensional plane of the local coordinate system to obtain the first path. The shrink-rotate-re-advance strategy is then executed to generate the optimal solution.

2. The three-dimensional path planning method for flexible needles used for multi-target puncture according to claim 1, characterized in that, Establishing a three-dimensional kinematic model of the flexible needle in the aforementioned puncture base coordinates includes: ； in, , , This represents the position in the corresponding coordinate system. , , for , , The corresponding derivative, , , Let be the rotation angle about the corresponding coordinate system. , , for , , The corresponding derivative, , These are the control inputs for needle insertion and rotation, respectively, acting on the base of the needle. During puncture, the needle tip travels along the radius The curvature formed by motion.

3. The three-dimensional path planning method for flexible needles used for multi-target puncture according to claim 1, characterized in that, Determining the radius of the reachable cross-sectional circle in the projected depth of the target point along the needle axis includes: On a unit sphere centered at the needle insertion point, the polar angle and azimuth angle are sampled at equal intervals to generate the unit needle insertion direction vector. A local coordinate system is established based on the needle insertion point and the unit needle insertion direction vector. The coordinates of each target point in the world coordinate system are transformed to the local coordinate system. The projection depth of the target point along the needle axis and the radial distance from the target point to the center line of the needle axis are calculated. The radius of the reachable cross-section circle of the projection depth is further calculated.

4. The three-dimensional path planning method for flexible needles used in multi-target puncture according to claim 3, characterized in that, The cost of obtaining the average target centrality screening includes: The target point's attitude is determined using the radius of the reachable domain cross-section circle. If the radial distance is greater than the radius of the reachable domain cross-section circle, or the projected depth exceeds the effective depth range, it is proven that the target point is not within the reachable domain, and the unit needle direction vector is deleted. If the radial distance is less than the radius of the reachable domain cross-section circle, it is proven that the target point is within the reachable domain, and the center deviation ratio is defined to obtain the average target point centerness screening cost.

5. The three-dimensional path planning method for flexible needles used in multi-target puncture according to claim 1, characterized in that, The cost of obtaining the obstacle intrusion screening includes: Discrete slice inspection is performed along the needle axis using a probe circle to assess the area ratio of obstacles in the reachable cross section. That is, multiple discrete depth points are selected along the needle axis at fixed step sizes, and the reachable cross section circle with the target radius at each depth point is determined. Calculate the ratio of the area occupied by obstacles within the reachable cross-section circle to the total area of ​​the detection cross-section circle to obtain the obstacle area ratio of the slice, and sum the obstacle area ratios of all slices to calculate the obstacle intrusion screening cost.

6. The three-dimensional path planning method for flexible needles used in multi-target puncture according to claim 4, characterized in that, Establishing the local coordinate system includes: The unit needle entry direction vector corresponding to the selected valid candidate postures, combined with the first target point in the target point access sequence, geometrically defines a unique plane. That is, with the needle entry point as the origin of the coordinate system, the unit needle entry direction vector corresponding to the selected valid candidate postures is used as the local coordinate system. The positive direction of the axis is used to calculate the needle insertion direction vector and the first target point in the target point access sequence based on the plane normal vector, thereby obtaining the local coordinate system. shaft and axis.

7. The three-dimensional path planning method for flexible needles used in multi-target puncture according to claim 1, characterized in that, The first path is obtained by: The fast extended random tree path planning algorithm is used to plan the path in the two-dimensional plane of the local coordinate system. That is, the node state in the RRT tree is defined, and during the iterative expansion of the RRT tree, the newly generated nodes are all generated on the plane projection of the reachable domain formed by the tangent direction vector in the node state. New nodes are repeatedly generated, and after each new node is connected, a new reachable domain projection is obtained based on the new tangent direction vector. This projection is used to guide the generated trajectory tree toward the target and around obstacles under the guidance of a heuristic function, while adhering to kinematic constraints, until the end node meets the reach condition. Finally, the first path is connected and output.

8. The three-dimensional path planning method for flexible needles used in multi-target puncture according to claim 7, characterized in that, The heuristic functions include: ； in, The nearest neighbor node, The coefficient is used to adjust the weights.

9. The three-dimensional path planning method for flexible needles used for multi-target puncture according to claim 1, characterized in that, The preferred solution includes: In the first path, backtrack to search for the hub point. That is, based on the position coordinate vector and tangent direction vector in the node state of each node, a new reachable domain is established. Then, the attitude of the remaining target points is determined by the radius of the cross-sectional circle of the new reachable domain. That is, it is determined whether the remaining target points are within the reachable domain and close to the central axis, and whether the obstacle intrusion is too high. Each backtracked node is evaluated, and the node with the smallest evaluation is taken as the best hub point for the first switch. A new plane is defined based on the coordinates of the pivot point and the second target point. The fast extended random tree path planning algorithm is used again to plan the path on the new plane to obtain the second path. This process is repeated until the paths for all target points are planned, resulting in a set of pivot points, a set of all planes, and a set of paths. A global evaluation function is established to calculate the global cost of all paths in the path set, and the minimum path planning is selected as the preferred solution.

10. The three-dimensional path planning method for flexible needles used in multi-target puncture according to claim 9, characterized in that, Establishing the global evaluation function includes: ； in, The length of each path segment, This represents the minimum safe distance from each path segment to the obstacle. , These are the corresponding weighting coefficients.

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