Medical robot autonomous path planning method based on convex optimization and related device

Abstract

The invention discloses a medical robot autonomous path planning method based on convex optimization and a related device. The method comprises the following steps: acquiring an environment point cloud to construct a three-dimensional working space; performing alpha-shape segmentation on a collision-free region to obtain a convex set sequence; constructing a convex set graph by taking the convex set as a vertex and the intersection as an edge; shortest path mixed integer programming is established on the graph, and convex set coverage, continuity and acceleration constraint are added by taking the Bessel control point distance and the trajectory duration as targets; executing a convex set graph shortest path algorithm to obtain a discrete sequence, and then running mixed integer quadratic cone programming to output Bessel parameters; and circulating until the robot reaches the target. According to the method, the complex non-convex space is converted into the convex set sequence, efficient solving is achieved through convex optimization, the planning time is remarkably shortened, and the real-time performance and safety are improved.

Description

Technical Field

[0001] The present invention relates to the fields of medical devices, artificial intelligence and robots, and in particular to a medical robot autonomous path planning method based on convex optimization and related devices. Background Art

[0002] Medical robots are increasingly used in scenarios such as thoracic and abdominal interventions, biopsies, and radiotherapy. However, due to respiratory motion, soft tissue deformation, and complex cavity environments, traditional grid-based or sampling-based path planning struggles to balance real-time performance and safety. First, the non-convex space requires a large number of discrete nodes, resulting in high computational complexity and difficulty in updating within milliseconds. Second, rigid paths cannot dynamically compensate for respiratory rhythms, leading to puncture deviations and even instrument collisions. Furthermore, existing systems often rely on manually pre-set safety corridors and lack automated modeling for online fusion of ultrasound and CT multimodal information, resulting in lengthy preoperative preparation times and a steep learning curve for physicians. Clinically, there is an urgent need for an autonomous planning technology that can rapidly generate smooth, steerable, and collision-avoiding trajectories in dynamic soft tissue environments and adjust in real time to respiratory motion. Summary of the Invention

[0003] In order to solve the above technical problems, the present invention relates to a medical robot autonomous path planning method based on convex optimization and related devices, which include but are not limited to a medical robot autonomous path planning redundant device based on convex optimization, an electronic device, a computer-readable storage medium and a computer program product.

[0004] In a first aspect, a method for autonomous path planning of a medical robot based on convex optimization is provided, comprising the following steps: S1. Acquire environmental information, construct a three-dimensional model of the workspace based on the environmental information, and decompose the collision-free area of ​​the three-dimensional model into a convex set sequence; S2. constructing a convex set graph by taking each convex set in the convex set sequence as a vertex and establishing edges when adjacent convex sets have intersections; S3. Establish a shortest path mixed integer programming model on the convex set graph, where the path length is represented by the sum of the distances of the Bezier control points, and a binary variable is introduced to indicate the convex set to which the path segment belongs; S4. Using the convex set graph shortest path algorithm to obtain a discrete path sequence, performing mixed integer quadratic cone programming on the discrete path sequence, and outputting Bezier curve parameters; S5. Sending the Bezier curve parameters to the robot controller; S6. Repeat S1-S5 until the robot reaches the target position.

[0005] In conjunction with any embodiment of the present application, the three-dimensional model is processed by the alpha-shape algorithm to divide the collision-free area into convex sets represented by half-spaces, and each convex set is recorded as a half-space inequality: , Where k is the index of the convex set, A is Matrix, describing the half-space normal vector corresponding to the k-th convex set, b is Vector describing the offset of the kth half-space.

[0006] In combination with any embodiment of the present application, the convex set sequence is updated according to the respiratory motion compensation factor at the corresponding moment; the respiratory motion compensation factor is the product of the ultrasonic deformation matrix and the respiratory period function.

[0007] In combination with any embodiment of the present application, the convex set graph The vertex set V corresponds to a convex set sequence, and the edge set E consists of vertex pairs that meet the intersection condition. The intersection is defined as the existence of at least one point in the convex set With convex sets .

[0008] In conjunction with any embodiment of the present application, the objective function formula of the shortest path mixed integer programming model is: , in is the sum of the distances between the control points of the Bezier curve, is the trajectory duration; 、 is a preset parameter, and its value is a non-negative real number; The constraints of the objective function include: Convex set covering constraint, all control points are located in the corresponding convex set; Continuity constraints: adjacent Bezier segments must be continuous in position and derivative at their connection points. Acceleration constraints and the norm of the second-order derivative of the trajectory are bounded.

[0009] In combination with any embodiment of the present application, the discrete path sequence is obtained by a convex set graph shortest path algorithm; the degree of the Bezier curve is d, where , is the desired differentiable order of the Bezier curve.

[0010] In a second aspect, a medical robot autonomous path planning device based on convex optimization is provided, comprising: A perception processing unit is configured to obtain environmental information, construct a three-dimensional model of the workspace based on the environmental information, and decompose the collision-free region of the three-dimensional model into a sequence of convex sets; Convex set graph construction unit: taking each convex set in the convex set sequence as a vertex and establishing edges when adjacent convex sets have intersections, thereby constructing a convex set graph; A path planning unit is configured to establish a shortest path mixed integer programming model on the convex set graph, wherein the path length is represented by the sum of the distances between Bezier control points, and a binary variable is introduced to indicate the convex set to which the path segment belongs. The unit is also configured to obtain a discrete path sequence using a convex set graph shortest path algorithm, perform mixed integer quadratic cone programming on the discrete path sequence, and output Bezier curve parameters. Control and communication unit: used to send the Bezier curve parameters to the robot controller; also used to cycle the tasks of the perception processing unit, the convex set graph construction unit and the path planning unit until the robot reaches the target position.

[0011] In a third aspect, an electronic device is provided, comprising: a processor, a communication module, a sensor, a user interface, and a storage unit, wherein the storage unit is configured to store computer program code, wherein the program code comprises computer instructions. When the processor executes these instructions, the electronic device performs the method described in the second aspect and any embodiment thereof.

[0012] In a fourth aspect, another electronic device is provided, comprising: a processor, a wireless communication module, a touch screen, a speaker, and a storage unit, wherein the storage unit is configured to store computer program code, wherein the program code comprises computer instructions. When the processor executes these instructions, the electronic device performs the method described in the second aspect and any embodiment thereof.

[0013] In a fifth aspect, a computer-readable storage medium is provided, wherein a computer program is stored, wherein the program includes program instructions. When these instructions are executed by a processor, the processor will perform the method described in the second aspect and any embodiment thereof.

[0014] In a sixth aspect, a computer program product is provided, wherein the computer program product comprises a computer program or instructions. When the computer program or instructions are run on a computer, the computer will execute the method described in the second aspect and any embodiment thereof.

[0015] Compared with the prior art, the present invention provides a method and related device for autonomous path planning for a medical robot based on convex optimization. A depth camera is used to collect environmental point clouds in real time. The alpha-shape algorithm is used to segment the collision-free region into a sequence of convex sets in a half-space. A convex graph is constructed with the convex sets as vertices and the intersections as edges. A shortest path mixed integer programming model is established on the graph, with the weighted sum of the distance between Bezier control points and the trajectory duration as the goal. Convex set coverage, continuity, and acceleration constraints are introduced. After obtaining a discrete sequence using the convex graph shortest path algorithm, mixed integer quadratic cone programming is run to output Bezier curve parameters. The parameters are cyclically transmitted to the robot controller via a control and communication unit until the target is reached. The present invention transforms a non-convex space into a convex set sequence and uses convex optimization to globally solve the problem, avoiding the exponential expansion of traditional grid or sampling methods in high-dimensional space. The convex set is updated in real time using a respiratory motion compensation factor to ensure trajectory safety under soft tissue deformation. The device modularly integrates perception, graph construction, planning, and control functions, enabling seamless integration with multimodal imaging systems. This significantly reduces preoperative preparation time and the degree of manual intervention, improving the automation and reliability of surgical procedures. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the background technology, the drawings required for use in the embodiments of the present application or the background technology will be described below.

[0017] The drawings herein are incorporated into the specification and constitute a part of this specification. These drawings illustrate embodiments consistent with the present application and, together with the specification, are used to illustrate the technical solutions of the present application.

[0018] Figure 1 This is a flow chart of a real-time control method for a cavity robot based on a dynamic safety boundary proposed in an embodiment of the present application.

[0019] Figure 2 This is a schematic diagram of a real-time control device for a cavity robot based on a dynamic safety boundary proposed in an embodiment of the present application.

[0020] Figure 3 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0021] In order to allow professionals in this technical field to more fully understand the technical solution of the present application, the technical solution of the present application will be explained in detail and clearly with the help of the accompanying drawings. It should be noted that the described embodiments are only some examples of the present application and do not represent all. Based on these embodiments, those skilled in the art can directly deduce all other possible implementation plans without engaging in creative thinking, and these are also included in the scope of protection of the present application.

[0022] In the specification, claims, and related drawings of this application, the terms "first," "second," and the like are used solely to distinguish between different elements and do not imply any particular order. Furthermore, the use of "including," "having," and their variations denotes non-exclusive inclusion. This means that if a process, method, system, product, or apparatus includes a series of steps or components, the process, method, system, product, or apparatus is not limited to the enumerated steps or components and may include other steps or components not listed, or other steps or units inherent to the process, method, system, product, or apparatus.

[0023] The “embodiment” mentioned in this document refers to any instance in which a particular feature, structure or characteristic is combined, and these instances may belong to at least one embodiment of the present application. The “embodiment” mentioned in this document does not necessarily refer to the same specific case, nor does it mean that they are independent or exclusive alternatives. It should be understood by those skilled in the art that the embodiments described herein can be used in conjunction with other embodiments. It should be understood that in this application, “at least one” includes one or more instances, “a plurality” means two or more instances, and “at least two” means two or more instances.

[0024] It should be understood that the method embodiment of the present application can also be implemented by a processor executing computer program code. The embodiment of the present application is described below in conjunction with the drawings in the embodiment of the present application.

[0025] See also Figure 1 , Figure 1 This is a flow chart of a method for autonomous path planning of a medical robot based on convex optimization proposed in an embodiment of the present application.

[0026] 102. Convex set establishment: Acquire environmental information, construct a three-dimensional model of the workspace based on the environmental information, and decompose the collision-free area of ​​the three-dimensional model into a convex set sequence.

[0027] In this embodiment, the environmental information is multimodal information, including at least two of CT, MRI, ultrasound, and touch.

[0028] In this embodiment, the collision-free region is decomposed into a convex set sequence represented by a half-space using an alpha-shape algorithm. Each convex set in the sequence is expressed as a half-space inequality: , Where k is the index of the convex set, A is Matrix, describing the half-space normal vector corresponding to the k-th convex set, b is Vector describing the offset of the kth half-space.

[0029] In this embodiment, the convex set sequence is updated according to the respiratory motion compensation factor at the corresponding moment; the respiratory motion compensation factor is the product of the ultrasonic deformation matrix and the respiratory period function.

[0030] In this embodiment, a speckle tracking algorithm is used to extract surface feature points of the patient's organs from the environmental information, the displacement of the feature points is calculated through the inter-frame optical flow field, and a sparse displacement field is constructed. The sparse displacement field is then interpolated using thin plate spline interpolation to obtain a dense displacement field, which is discretized using B-spline basis functions to obtain the ultrasonic deformation matrix.

[0031] In this embodiment, band-pass filtering is used to remove heart rate interference from the displacement of the characteristic points, and then Hilbert transform is used to extract the instantaneous phase, and the respiratory cycle function is obtained by fitting.

[0032] In this embodiment, since the patient's breathing, heartbeat and other behaviors may cause displacement of organs, the three-dimensional model and the convex set sequence are dynamically updated as the environment changes.

[0033] In another possible implementation, the collision-free area may also adopt a Voronoi diagram-convex hull cascade decomposition strategy, first generating Voronoi cells and then solving the convex hull for each cell to obtain a finer-grained convex set partition in the narrow cavity.

[0034] In another possible implementation, the dynamic update can be driven by the displacement of organ surface markers collected in real time by the intraoperative electromagnetic tracking system, and the deformation trend of the next 2-3 respiratory cycles can be predicted through bidirectional LSTM to adjust the convex set boundary in advance.

[0035] In another possible implementation, the environmental information may also include electromagnetic information, tactile information, thermal sensing information, etc.

[0036] 103. Convex set graph construction: Construct a convex set graph by taking each convex set in the convex set sequence as a vertex and establishing edges when adjacent convex sets have intersections.

[0037] In this embodiment, the convex set graph The vertex set V corresponds to a convex set sequence, and the edge set E consists of vertex pairs that meet the intersection condition. The intersection is defined as the existence of at least one point in the convex set With convex sets .

[0038] In this embodiment, first, for each convex set Calculate the radius and center coordinates of the circumscribed sphere. If the distance between the two circumscribed sphere centers is less than the sum of the radii and the half-space inequality group has a feasible solution, then the intersection is determined to exist, thereby avoiding the high-dimensional calculation of direct intersection. In this embodiment, to reduce the amount of storage, the edge set E adopts a sparse adjacency list structure, which only stores the vertex pairs that meet the intersection condition. and the normal information of their shared faces for subsequent quick retrieval of coplanar constraints.

[0039] In another possible implementation, the generation of vertices and edges can be constructed incrementally: whenever a convex set is added, it is only necessary to detect its intersection with the adjacent convex sets, avoiding the reconstruction of the entire graph.

[0040] In another possible implementation, the intersection determination can also use the separating axis theorem to quickly eliminate non-intersecting pairs through the overlap of intervals projected onto the potential separating axis.

[0041] In another possible implementation, the sparse adjacency list may be further compressed, such as using the CSR format or the shared face normal vectors in the coefficient adjacency list, to reduce memory usage and improve cache hit rate.

[0042] 104. Path planning: A shortest path mixed integer programming model is established on the convex set graph, where the path length is represented by the sum of the distances between Bezier control points, and a binary variable is introduced to indicate the convex set to which the path segment belongs.

[0043] In this embodiment, the objective function formula of the shortest path mixed integer programming model is: , in is the sum of the distances between the control points of the Bezier curve, is the trajectory duration; 、 is a preset parameter, and its value is a non-negative real number;

[0044] In this embodiment, the objective function has constraints, including at least: Convex set covering constraint, all control points are located in the corresponding convex set; Continuity constraints: adjacent Bezier segments must be continuous in position and derivative at their connection points. Acceleration constraints and the norm of the second-order derivative of the trajectory are bounded.

[0045] In this embodiment, the continuity constraint achieves a smooth transition of curvature by forcing the difference in first-order derivative direction cosines between two adjacent Bezier curves at the connection point to be smaller than a preset threshold.

[0046] In this embodiment, the acceleration constraint limits the L2 norm of the second-order derivative of the trajectory to a preset upper bound and is converted into a second-order cone constraint to ensure that the robot joint torque does not exceed the limit.

[0047] In another possible implementation, the shortest path mixed integer programming model may introduce a soft constraint penalty term, quantify the convex set violation into an exponential cost, and add it to the objective function to allow for short-term minor violations in emergency situations.

[0048] In another possible implementation, when a flexible needle tip is used, the continuity constraint can be extended to higher-order derivatives, and the residual vibration of the flexible needle tip can be suppressed by imposing bounded restrictions on the rate of change of third-order and higher derivatives.

[0049] In another possible implementation, the acceleration constraint may also be in the form of an L1 norm, and piecewise linearization technology may be used to convert the non-smooth constraint into a set of linear inequalities to reduce the complexity of the solution.

[0050] 105. Path post-processing: A convex set graph shortest path algorithm is used to obtain a discrete path sequence, mixed integer quadratic cone programming is performed on the discrete path sequence, and Bezier curve parameters are output.

[0051] In this embodiment, the degree of the Bezier curve is d, where , is the desired differentiable order of the Bezier curve.

[0052] In this embodiment, the convex set graph shortest path algorithm is based on the D* algorithm, and the heuristic cost is set to the weighted sum of the Euclidean distance from the current node to the center of the target convex set and the number of convex sets crossed, so as to take into account both the path length and the number of convex set switches.

[0053] In this embodiment, the mixed integer quadratic cone programming is executed in the Gurobi solver to output the coordinates of the Bezier curve control points; wherein the Gurobi solver turns on multithreading and enables the Presolve and CutPass two-stage preprocessing to shorten the solution time of the mixed integer quadratic cone programming.

[0054] In another possible implementation, the convex set graph shortest path algorithm may be replaced by other path planning algorithms.

[0055] In another possible implementation, the mixed integer quadratic cone programming may call other solvers, such as CPLEX or Mosek solver.

[0056] In another possible implementation, after the Bezier curve parameters are output, B-spline post-fitting may be further performed to even out the curvature distribution and reduce the number of control points.

[0057] 106. Path execution: Send the Bezier curve parameters to the robot controller.

[0058] In this embodiment, the sending method includes but is not limited to wired transmission and wireless network transmission.

[0059] In another possible implementation, the Bezier curve parameters can be first cached in the edge computing node, and the node can make micro-corrections based on the speed error fed back by the robot in real time before sending them down to improve the trajectory tracking accuracy.

[0060] In some embodiments, the functions or modules included in the device provided in the embodiments of the present application can be used to execute the method described in the above method embodiments. The specific implementation can refer to the description of the above method embodiments. For the sake of brevity, it will not be repeated here.

[0061] The above describes in detail the method of the embodiment of the present application, and the following provides an apparatus of the embodiment of the present application.

[0062] See also Figure 2 , Figure 2 This is a schematic diagram of a medical robot autonomous path planning device based on convex optimization proposed in an embodiment of the present application. The path planning device 1 includes: a perception processing unit 11, a convex set graph construction unit 12, a path planning unit 13, and a control and communication unit 14. Specifically: Perception processing unit 11: used to obtain environmental information, build a three-dimensional model of the workspace based on the environmental information, and decompose the collision-free area of ​​the three-dimensional model into a convex set sequence; Convex set graph construction unit 12: constructing a convex set graph by taking each convex set in the convex set sequence as a vertex and establishing edges when adjacent convex sets have intersections; A path planning unit 13 is configured to establish a shortest path mixed integer programming model on the convex set graph, wherein the path length is represented by the sum of the distances between Bezier control points, and a binary variable is introduced to indicate the convex set to which the path segment belongs; the unit is further configured to use a convex set graph shortest path algorithm to obtain a discrete path sequence, perform mixed integer quadratic cone programming on the discrete path sequence, and output Bezier curve parameters; The control and communication unit 14 is used to send the Bezier curve parameters to the robot controller; and is also used to cycle the tasks of the perception processing unit, the convex set graph construction unit, and the path planning unit until the robot reaches the target position.

[0063] In some embodiments, the functions or modules included in the device provided in the embodiments of the present application can be used to execute the method described in the above method embodiments. The specific implementation can refer to the description of the above method embodiments. For the sake of brevity, it will not be repeated here.

[0064] See also Figure 3 , Figure 3The following is a schematic diagram of the hardware architecture of an electronic device described in an embodiment of the present application. The electronic device 2 is primarily composed of a processor 21 and a memory 22. In addition, the device may also include an input device 23 and an output device 24. The processor 21, memory 22, input device 23, and output device 24 are interconnected via connecting components, which may be various interfaces, data cables, or communication buses, and are not specifically specified in the present embodiment.

[0065] Processor 21 may be one or more graphics processing units (GPUs). If processor 21 is a GPU, the GPU may be single-core or multi-core. Optionally, processor 21 may comprise a processor group consisting of multiple GPUs, interconnected via one or more buses. Furthermore, the processor may be other types of processors, which are not specifically limited in this embodiment of the present application.

[0066] Memory 22 is designed to store computer program instructions and various program codes required to execute the present invention. Optionally, the memory may include, but is not limited to, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), or compact disc read-only memory (CD-ROM), which are used to store relevant instructions and data.

[0067] The input device 23 is used to input data and / or signals, and the output device 24 is used to output data and / or signals. The input device 23 and the output device 24 can be independent devices or an integrated device.

[0068] It should be appreciated that in the embodiment of the present application, the memory 22 can store not only relevant instructions but also relevant data. The embodiment of the present application does not specify the specific data content stored in the memory.

[0069] You should understand that Figure 3 Only a simplified design of an electronic device is shown. In actual use, the electronic device may also include other necessary components, such as different numbers of input / output devices, processors, memories, etc. All electronic devices that can implement the embodiments of this application are within the scope of protection of this application.

[0070] Those skilled in the art will recognize that, according to the components and algorithm steps of each example described in the embodiments disclosed herein, these functions can be implemented by electronic hardware or by combining computer software and electronic hardware. Whether these functions are performed by hardware or software will be determined based on the specific application requirements and design limitations of the technical solution. Technicians can adopt different implementation methods according to the requirements of each specific application, but such implementation methods should not be considered to exceed the scope of protection of this application.

[0071] Professionals should understand that, for the sake of ease of description and simplification, the specific operating procedures of the above-mentioned systems, devices, and components can refer to the corresponding steps in the previous method embodiments and will not be repeated here. At the same time, professionals should also understand that each embodiment in this application has its own focus. For the sake of ease of description and simplification, the same or similar content may not be repeated in different embodiments. Therefore, if a part is not mentioned or not explained in detail in a certain embodiment, reference can be made to the relevant description of other embodiments.

[0072] In the several embodiments provided in this application, it should be recognized that the disclosed systems, devices and methods can also be implemented in other ways. For example, the device embodiments described are only exemplary, in which the division of the units is only a division of logical functions, and there may be different division methods in actual implementation. For example, multiple units or components may be merged or integrated into another system, or certain features may be omitted, or certain steps may not be performed. In addition, the connections between each other shown or discussed, whether direct or indirect, whether coupling or communication connection, may be implemented in electrical, mechanical or other forms through interfaces, devices or units.

[0073] Units described as independent components may or may not actually be physically separate; parts presented as units may or may not be physical entities; that is, they may be centralized in one location or distributed across multiple network nodes. Depending on actual needs, some or all of these units may be selected to achieve the objectives of this embodiment.

[0074] Furthermore, in the various embodiments of the present application, the various functional units may be integrated into a single processing unit, physically exist independently, or two or more units may be combined into a single unit. In the aforementioned embodiments, the relevant functions may be implemented in whole or in part through software, hardware, firmware, or any combination thereof. If software implementation is chosen, it may be implemented in whole or in part in the form of a computer program product. This computer program product comprises one or more computer instructions. When these instructions are loaded and executed on a computer, they will generate, in whole or in part, the processes or functions described in the embodiments of this application. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. These computer instructions may be stored in a computer-readable storage medium or transmitted via such a medium. The computer instructions may be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic cable, DSL) or wireless (e.g., infrared, wireless, microwave, etc.) means. A computer-readable storage medium may be any computer-accessible, usable medium, or a data storage facility such as a server or data center that integrates one or more usable media. These available media may include magnetic media (e.g., floppy disks, hard disks, tapes), optical media (e.g., DVDs), semiconductor media (e.g., SSDs), etc. Those skilled in the art will appreciate that all or part of the process steps for implementing the above-described method embodiments can be accomplished through hardware associated with computer program instructions. These programs can be stored on computer-readable storage media. When executed, these programs will contain the processes for each of the above-described method embodiments. These storage media include, but are not limited to, various media capable of storing program code, such as read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

Claims

1. A medical robot autonomous path planning method based on convex optimization, characterized in that: The steps include: S1. Acquire environmental information, construct a three-dimensional model of the workspace based on the environmental information, and decompose the collision-free area of ​​the three-dimensional model into a convex set sequence; S2. constructing a convex set graph by taking each convex set in the convex set sequence as a vertex and establishing edges when adjacent convex sets have intersections; S3. Establish a shortest path mixed integer programming model on the convex set graph, where the path length is represented by the sum of the distances of the Bezier control points, and a binary variable is introduced to indicate the convex set to which the path segment belongs; S4. Using the convex set graph shortest path algorithm to obtain a discrete path sequence, performing mixed integer quadratic cone programming on the discrete path sequence, and outputting Bezier curve parameters; S5. Sending the Bezier curve parameters to the robot controller; S6. Repeat S1-S5 until the robot reaches the target position.

2. The method according to claim 1, characterized in that The three-dimensional model is processed by the alpha-shape algorithm to divide the collision-free area into convex sets represented by half-spaces. Each convex set is expressed as a half-space inequality: ， Where k is the index of the convex set, A is Matrix, describing the half-space normal vector corresponding to the k-th convex set, b is Vector describing the offset of the kth half-space.

3. The method according to claim 2, characterized in that The convex set sequence is updated according to the respiratory motion compensation factor at the corresponding moment; the respiratory motion compensation factor is the product of the ultrasonic deformation matrix and the respiratory period function.

4. The method according to claim 1, wherein The convex set graph The vertex set V corresponds to a convex set sequence, and the edge set E consists of vertex pairs that meet the intersection condition. The intersection is defined as the existence of at least one point in the convex set With convex sets .

5. The method according to claim 1, wherein The objective function formula of the shortest path mixed integer programming model is: , in is the sum of the distances between the control points of the Bezier curve, is the trajectory duration; 、 is a preset parameter, and its value is a non-negative real number; The constraints of the objective function include: Convex set covering constraint, all control points are located in the corresponding convex set; Continuity constraints: adjacent Bezier segments must be continuous in position and derivative at their connection points. Acceleration constraints and the norm of the second-order derivative of the trajectory are bounded.

6. The method according to claim 1, characterized in that The discrete path sequence is obtained by the convex set graph shortest path algorithm; the degree of the Bezier curve is d, where , is the desired differentiable order of the Bezier curve.

7. A medical robot autonomous path planning device based on convex optimization, characterized in that: include: A perception processing unit is configured to obtain environmental information, construct a three-dimensional model of the workspace based on the environmental information, and decompose the collision-free region of the three-dimensional model into a sequence of convex sets; Convex set graph construction unit: taking each convex set in the convex set sequence as a vertex and establishing edges when adjacent convex sets have intersections, thereby constructing a convex set graph; Path planning unit: establishing a shortest path mixed integer programming model on the convex set graph, where the path length is represented by the sum of the distances of Bezier control points, and a binary variable is introduced to indicate the convex set to which the path segment belongs; It is also used to obtain a discrete path sequence using a convex set graph shortest path algorithm, perform mixed integer quadratic cone programming on the discrete path sequence, and output Bezier curve parameters; Control and communication unit: used to send the Bezier curve parameters to the robot controller; also used to cycle the tasks of the perception processing unit, the convex set graph construction unit and the path planning unit until the robot reaches the target position.

8. An electronic device, characterized in that: include: A processor and a storage unit, the storage unit is used to store computer program code, the code includes computer instructions, when the processor executes these instructions, the electronic device performs the method according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, wherein the computer program includes program instructions. When the program instructions are executed by a processor, the processor is caused to execute the method according to any one of claims 1 to 6.

10. A computer program product, characterized in that The computer program product comprises a computer program or instructions, and when the computer program or instructions are run on a computer, the computer is caused to perform the method according to any one of claims 1 to 6.

Images