Pedicle orthopedic robot trajectory planning method and system

Abstract

The application provides a kind of pedicle orthopedic robot trajectory planning method and system, method includes: obtaining the planning entry point and target point of pedicle screw, generates initial three-dimensional path using triangular Bezier curve;Based on triangular Bezier curve and its analytical derivative, the screw rotation propulsion process is uniformly modeled as the screw motion of the form of spinor exponential product, the direct mapping of path parameter to end pose is obtained;With intermediate control point coordinates as optimization variables, construct a comprehensive cost function that combines smoothness, safety and biomechanical performance, and use adaptive differential evolution algorithm for global optimization;The optimal path is adaptively S-shaped velocity planned for safety distance, and robot executable instructions are generated.The application eliminates the disconnection between path planning and motion control, and takes into account path smoothness, safety margin and bone density through multi-objective optimization, making joint movement more stable, safety distance more adequate and screw biomechanical performance more optimal.

Description

Technical Field

[0001] This invention relates to the field of surgical robot technology, specifically providing a method and system for trajectory planning of a pedicle screw orthopedic robot. Background Technology

[0002] Pedicle screw fixation is a classic surgical procedure for treating spinal fractures, spondylolisthesis, scoliosis, and tumors. Its core lies in the precise planning of the screw implantation path: the ideal path must be entirely within the pedicle cortical bone boundary to avoid damage to adjacent spinal cord, nerve roots, and major blood vessels; simultaneously, under safe conditions, the screw length should be maximized to maintain contact with bone density, thereby improving pull-out resistance and long-term stability. Traditional freehand screw placement relies on the surgeon's experience and intraoperative X-ray fluoroscopy. In segments with significant anatomical variations, such as the thoracic spine, cortical penetration can reach 10%–30%, and it also has inherent drawbacks such as high radiation exposure and a long learning curve.

[0003] In recent years, the clinical application of orthopedic surgical robot systems such as Mazor X, ROSA ONE Spine, and ExcelsiusGPS has significantly improved screw placement accuracy. Multiple meta-analyses have confirmed that robot-assisted screw placement in Gertzbein-Robbins Class A cases achieves an accuracy rate exceeding 94%, reduces cortical penetration to below 3.8%, and significantly lowers the risk of facet joint invasion and major complications. However, existing robot systems still generally face the following technical bottlenecks in the crucial trajectory planning stage: 1. The path geometry model is overly simplified and fails to accurately reflect the anatomical curvature of the pedicle. Existing systems often use straight lines or single arcs connecting the entry and target points as the planned path. However, the pedicle runs along an anteromedial arc in the sagittal plane and has a figure-eight distribution in cross-section. Straight paths struggle to capture this three-dimensional curvature, especially in the thoracic segments, where it can easily lead to lateral wall penetration or intrusion into the spinal canal. A few studies have attempted quadratic curve fitting, but these still cannot accurately describe the complex spatial curvature of the pedicle axis.

[0004] 2. Separation of geometric path planning and robot helical motion control. Screw insertion is a typical helical motion process of "advancing and rotating simultaneously." Existing methods typically generate discrete path points in image space first, and then map them to joint space through inverse kinematics. This two-step method not only fails to consider the velocity and acceleration constraints of robot joints during the planning stage, easily leading to execution shocks and vibrations, but more importantly, it ignores the helical propulsion characteristics of the screw during the planning stage, causing a deviation between the planned geometric centerline and the actual screw insertion posture, thus failing to guarantee the executability of the path from the source.

[0005] 3. Optimization goals are singular, making it difficult to simultaneously consider safety, smoothness, and biomechanical performance. Clinically, an excellent screw placement path requires a comprehensive evaluation of three conflicting indicators: safety requires the path to be far from the cortex; biomechanical performance requires the path to pass through high bone density areas to enhance screw retention; and robotic feasibility requires a smooth change in path curvature. Existing optimization methods often focus solely on maximizing the safety distance, failing to incorporate bone density distribution into the path optimization system or constrain changes in path curvature. The resulting paths often compromise on certain aspects, resulting in limited overall clinical benefits.

[0006] 4. Anatomical structure extraction and planning algorithms are disconnected, and the safe execution of the path lacks closed-loop feedback. The extraction of key anatomical features such as the pedicle cortex boundary and cancellous bone passage relies heavily on manual annotation by doctors or segmentation by third-party software, failing to form an automated closed loop with the planning algorithm. At the same time, the feed rate mostly uses preset constant values ​​or simple trapezoidal curves, without adaptive adjustment based on real-time safety margins. When the path approaches the cortex, it cannot actively reduce the speed to reduce the risk of penetration. Summary of the Invention

[0007] To overcome the above-mentioned shortcomings, this invention is proposed to provide solutions or at least partially solve the problems in the trajectory planning of existing pedicle orthopedic robots, such as the inability of the path geometry model to conform to anatomical curvature, the separation of geometric planning and helical motion control, the single optimization objective, and the lack of closed-loop feedback for safe execution.

[0008] In a first aspect, the present invention provides a trajectory planning method for a pedicle screw fixation robot, comprising the following steps: The planned entry point and target point of the pedicle screw are obtained, and an initial three-dimensional path connecting the entry point and the target point is generated using a trigonometric Bézier curve; wherein, the control points of the trigonometric Bézier curve include at least a first control point coinciding with the entry point, a fourth control point coinciding with the target point, and several intermediate control points located between the entry point and the target point. Based on the triangular Bezier curve and its analytical derivative, the rotational propulsion process of the screw moving along the curve is uniformly modeled as the screw exponential product of helical motion, thus obtaining the mapping relationship from path parameters to robot end pose. Using the coordinates of the intermediate control points as optimization variables, a comprehensive cost function is constructed, and an adaptive differential evolution algorithm is used for iterative optimization to output the optimized intermediate control points in order to determine the optimal path. The comprehensive cost function at least integrates a smoothness cost term that characterizes the degree of curvature change of the path, a safety cost term that characterizes the distance from the path to the cortical bone boundary, and a biomechanical cost term that characterizes the bone density distribution along the path. The optimal path is discretized and velocity is planned, and based on the mapping relationship of the helical motion, motion commands that can be executed by the robot are generated.

[0009] Preferably, the optimal path is discretized and speed planned, specifically including: Discretize the path using equal-parameter intervals or equal-arc-length intervals; Using a safety distance as a constraint, an adaptive S-shaped planning is performed on the feed rate: when the safety distance corresponding to a path point is less than the first threshold, the maximum allowable feed rate is reduced; when the safety distance is greater than the second threshold, the maximum allowable feed rate is restored or increased. Based on the velocity planning results and helical motion mapping, the motion command sequence in the joint space is output.

[0010] Preferably, the safe distance corresponding to a waypoint is calculated as follows: The parameterized equation for the pedicle centerline is: , ,in s =0 corresponds to the in-point. s =1 corresponds to the point.

[0011] In parameters s At that point, the cross-section perpendicular to the center line is approximately circular, and its radius is... r(s) Defined as the distance from the centerline to the outer surface of the cortical bone. Cortical bone thickness is a fixed value. =2 mm, then the radius from the centerline to the inner wall of the cortical bone (the boundary of the cancellous bone) is: For any point p in space, first project it onto the center line to obtain the projection parameters: Therefore, the safe distance from any point p on the path to the inner wall of the pedicle is defined as: A positive value indicates that any point p is located inside the cancellous bone channel, while a negative value indicates that the bone has penetrated the inner wall and entered the cortical bone or the outside. Both the first and second thresholds are set according to clinical safety requirements, ensuring that any path point meets the criteria. ≥1.5 mm.

[0012] Preferably, generating an initial three-dimensional path connecting the entry point and the target point using a triangular Bézier curve includes: Using an nth-order trigonometric Bézier curve, its basis functions are: Where n ≥ 2; When n=3, the control points include a first control point P, a fourth control point P3, a second control point P1, and a third control point P2; wherein , For the variable to be optimized, As the entry point, For the exit point; The triangular Bézier curve is expressed as follows: In the initial state, each control point is evenly distributed on the line connecting P0 and P3 to generate an initial straight path.

[0013] Preferably, the rotational propulsion process of the screw moving along the curve is uniformly modeled as a spiral motion exponential product, including: The screw motion is decomposed into a composite of a translational helix along the tangent of the path and a rotational helix rotating about the tangent; wherein, the screw axis of the translational helix is ​​determined based on the first derivative of the path, and the screw axis of the rotational helix is ​​determined based on the second derivative of the path. Using the exponential product formula Real-time calculation of the pose of the end effector; where It is a translational spiral that moves along the centerline. It is a rotating spiral about its own axis; The joint angle is parameterized using triangular splines.

[0014] Preferably, a centerline is given. and its tangential direction ,structure: in, The translation component of the translation screw is equal to the velocity vector of the screw moving along the center line; Let be the translation component of the rotating helix. Since the axis of rotation passes through the current path point and there is no translation along the axis, therefore... It is a zero vector.

[0015] Preferably, the comprehensive cost function The expression is: Where X is a variable vector containing the coordinates of intermediate control points. , , These are the weighting coefficients for each cost item, used to balance the importance of smoothness, safety, and biomechanical performance. A larger weight value indicates that the objective has a higher priority. For the smoothness cost term: ; in, Let the curvature of the path be... Curvature with respect to parameters t The derivative of this term, which penalizes the curvature abrupt change, ensures that the generated path is smooth and avoids violent acceleration impacts on the robot joints.

[0016] For safety-related costs: ; in, M This represents the number of sampling points along the path. This is a preset safety margin (usually 1.5mm). For the first k The shortest distance from each sampling point to the inner wall of the pedicle (a positive value indicates that it is located inside the inner wall).

[0017] Biomechanical cost term: This represents the bone mineral density field mapped from CT values.

[0018] Preferably, the variable vector X is constructed as follows: in, These are the x, y, z coordinates of the second control point (the first control point in the middle) of the triangular Bézier curve. The x, y, z coordinates of the third control point (the second control point in the middle) of the triangular Bézier curve; To optimize the variable vector, a 6-dimensional real vector is used, meaning each mutated individual is represented by 6 independent variables, corresponding to the coordinates of two points in 3D space. By optimizing these 6 variables, the shape of the curve can be changed to minimize the overall cost function value while satisfying safety constraints.

[0019] Preferably, obtaining the planned entry point and target point for the pedicle screw includes: A parametric geometric model comprising the vertebral body and bilateral pedicles is constructed; wherein the vertebral body is generated in cylindrical coordinates according to the following parametric equations: in, ,factor Simulates the anatomical feature of a vertebral body that is slightly thicker in the middle; The pedicle is modeled as a conical cylinder, with its radius along the centerline. The pedicles of the left and right vertebrae are symmetrical relative to the sagittal plane.

[0020] In a second aspect, the present invention provides a trajectory planning system for a pedicle screw fixation robot, comprising: The acquisition module is used to acquire the planned entry point and target point of the pedicle screw, and to generate an initial three-dimensional path connecting the entry point and the target point using a trigonometric Bézier curve; wherein, the control points of the trigonometric Bézier curve include at least a first control point coinciding with the entry point, a fourth control point coinciding with the target point, and several intermediate control points located between the entry point and the target point. The first calculation module is used to model the rotational propulsion process of the screw moving along the curve as a spiral motion exponential product based on the triangular Bezier curve and its analytical derivative, and obtain the mapping relationship from the path parameters to the robot end pose. The second calculation module is used to construct a comprehensive cost function with the coordinates of the intermediate control point as the optimization variable, and to perform iterative optimization using an adaptive differential evolution algorithm to output the optimized intermediate control point in order to determine the optimal path. The comprehensive cost function at least integrates a smoothness cost term that characterizes the degree of curvature change of the path, a safety cost term that characterizes the distance from the path to the cortical bone boundary, and a biomechanical cost term that characterizes the bone density distribution along the path. The path generation module is used to discretize and speed plan the optimal path, and generate motion commands that the robot can execute based on the mapping relationship of the helical motion.

[0021] Compared with existing technologies, the beneficial effects of the pedicle screw orthopedic robot trajectory planning method provided by this invention are as follows: 1. This invention uses triangular Bezier curves to construct a three-dimensional initial path connecting the entry point and the target point. Relying on multiple control points to flexibly adjust the trajectory shape, it can accurately adapt to the complex and irregular skeletal anatomy of the pedicle, breaking through the limitations of traditional straight lines and simple curved trajectories. It realizes the flexible construction of a three-dimensional path for pedicle surgery, with the trajectory conforming to the physiological structure of the bone and having stronger adaptability.

[0022] 2. By using the analytical derivative of trigonometric Bezier curves, the combined motion of screw insertion and propulsion of pedicle screws is transformed into a spiral motion exponential product model. This establishes a precise mapping relationship between path parameters and robot end-effector pose, fully restoring the combined motion characteristics of the screw implantation process. This solves the problem that traditional single motion modeling cannot match the coordinated operation of screw rotation and propulsion, significantly improving the accuracy of robot end-effector pose solution and the completeness and scientific nature of motion modeling.

[0023] 3. Construct a comprehensive cost function integrating smoothness, safety distance, and biomechanics dimensions, and conduct trajectory optimization in conjunction with multiple constraints: Curvature smoothness cost can effectively reduce trajectory curvature fluctuations, reduce tremors, impacts, and speed abrupt changes during orthopedic robot movement, and ensure the stability of surgical movement; Cortical bone boundary safety cost can continuously constrain the safety distance between the trajectory and key bone boundaries, effectively avoiding surgical risks such as bone wall puncture, spinal canal injury, and nerve and blood vessel compression; Bone density biomechanical cost optimizes the path in combination with the actual mechanical distribution characteristics of the bone, reducing problems such as bone fracture, bone damage, and screw loosening caused by screw implantation, and improving postoperative implantation stability and bone biomechanical safety.

[0024] 4. Using intermediate control points as optimization variables, an adaptive differential evolution algorithm is used for iterative optimization. This algorithm has excellent global optimization capabilities and adaptive adjustment characteristics, which can effectively avoid local optima problems, efficiently complete trajectory parameter optimization, and quickly solve the global optimal surgical path. It balances optimization efficiency and trajectory adaptability, meeting the needs of precise planning in orthopedic surgery.

[0025] 5. Discretize the optimal trajectory and match it with refined velocity planning. Combine the spiral motion pose mapping relationship to generate standardized robot motion commands, realize the seamless connection between trajectory planning and robot motion control, ensure that the orthopedic robot motion process is stable, controllable and precise, reduce human operation error and surgeon experience dependence, and improve the positioning accuracy and surgical standardization of pedicle screw implantation. Attached Figure Description

[0026] The disclosure of this invention will become more readily understood with reference to the accompanying drawings. It will be readily understood by those skilled in the art that these drawings are for illustrative purposes only and are not intended to limit the scope of protection of this invention. Furthermore, similar numbers in the drawings are used to denote similar components, wherein: Figure 1 This is a schematic diagram of the main steps of a pedicle osteotomy robot trajectory planning method according to an embodiment of the present invention; Figure 2 This is a three-dimensional model of the spine according to an embodiment of the present invention; Figure 3 This is a cross-sectional anatomical diagram of the pedicle according to an embodiment of the present invention; Figure 4 It is a screw insertion channel according to an embodiment of the present invention; Figure 5 This is a safety assessment of screws of different diameters according to an embodiment of the present invention; Figure 6 This refers to the left-side trajectory and control points according to an embodiment of the present invention; Figure 7This refers to the right-side trajectory and control points according to an embodiment of the present invention; Figure 8 This is a comparison of curvature distribution according to an embodiment of the present invention; Figure 9 It is a helical spinor axis according to an embodiment of the present invention; Figure 10 This is a comparison of the left-side trajectory before and after optimization according to an embodiment of the present invention; Figure 11 This is a comparison of the right-side trajectory before and after optimization according to an embodiment of the present invention; Figure 12 This is a JADE optimization convergence curve according to an embodiment of the present invention; Figure 13 This is a comparison of various cost components according to an embodiment of the present invention; Figure 14 This is a Cartesian space S-shaped velocity planning curve according to an embodiment of the present invention; Figure 15 This is a bilateral synchronization error according to an embodiment of the present invention; Figure 16 It is a safety margin distribution along the trajectory according to an embodiment of the present invention; Figure 17 This is a bone density distribution along a trajectory according to an embodiment of the present invention. Detailed Implementation

[0027] Some embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0028] In the description of this invention, "module" and "processor" can include hardware, software, or a combination of both. A module can include hardware circuitry, various suitable sensors, communication ports, memory, and may also include software components, such as program code, or a combination of software and hardware. A processor can be a central processing unit, microprocessor, image processor, digital signal processor, or any other suitable processor. The processor has data and / or signal processing capabilities. The processor can be implemented in software, in hardware, or a combination of both. Non-transitory computer-readable storage media includes any suitable medium capable of storing program code, such as magnetic disks, hard disks, optical disks, flash memory, read-only memory, random access memory, etc. The term "A and / or B" means all possible combinations of A and B, such as only A, only B, or A and B. The terms "at least one A or B" or "at least one of A and B" have a similar meaning to "A and / or B" and can include only A, only B, or A and B. The singular terms "a" or "this" can also include plural forms.

[0029] Example 1 like Figure 1-17 As shown, the trajectory planning method for the pedicle osteotomy robot in this embodiment of the invention mainly includes the following steps S1-S4.

[0030] Step S1: Obtain the planned entry point and target point of the pedicle screw, and generate an initial three-dimensional path connecting the entry point and the target point using a trigonometric Bézier curve; wherein, the control points of the trigonometric Bézier curve include at least a first control point coinciding with the entry point, a fourth control point coinciding with the target point, and several intermediate control points located between the entry point and the target point.

[0031] In this embodiment, by extracting the anatomical structure of the pedicle from spinal medical images, the entry and target points for screw insertion can be automatically determined, avoiding the subjective bias and inefficiency caused by manual annotation by doctors in traditional methods. A trigonometric Bézier curve is used to generate the initial 3D path, which differs from the straight-line paths or ordinary polynomial Bézier curves commonly used in existing technologies. This approach leverages the analytical properties of trigonometric functions to provide a precise geometric property calculation basis for subsequent steps. Control points include the first and last control points coinciding with the entry and target points, as well as intermediate control points located between them. Initially, all control points are evenly distributed on the line connecting the entry and target points, forming an initial straight-line path, which serves as the starting point for subsequent optimization.

[0032] Step S2: Based on the triangular Bezier curve and its analytical derivative, the rotational propulsion process of the screw moving along the curve is uniformly modeled as the spiral exponential product form of the helical motion, thus obtaining the mapping relationship from the path parameters to the robot end pose.

[0033] In this embodiment, the screw insertion process is not a simple translational motion, but a compound helical motion of "advancing and rotating simultaneously." Existing methods typically perform kinematic mapping separately after geometric planning, resulting in a disconnect between the two stages. This can lead to joint velocities or accelerations exceeding limits during robot execution. This step parametrically models the helical motion during the planning stage, utilizing the analytically differentiable property of trigonometric Bézier curves to unify the geometric path and kinematic expression within the same mathematical framework. This allows for the direct calculation of the robot's end-effector pose from the path parameters, ensuring the kinematic executability of the planned path from the outset and eliminating the biases introduced by the traditional two-step method.

[0034] Step S3: Using the coordinates of the intermediate control point as optimization variables, construct a comprehensive cost function, use an adaptive differential evolution algorithm for iterative optimization, and output the optimized intermediate control point to determine the optimal path; the comprehensive cost function at least integrates a smoothness cost term representing the degree of curvature change of the path, a safety cost term representing the distance from the path to the cortical bone boundary, and a biomechanical cost term representing the bone density distribution along the path.

[0035] In this embodiment, the screw placement path needs to simultaneously satisfy three conflicting criteria: the path must be sufficiently smooth to ensure the stability of robot movement; the path must stay away from the cortical bone boundary throughout to ensure safety; and the path must pass through high bone density areas as much as possible to enhance the screw's pull-out resistance. The comprehensive cost function constructed in this step integrates smoothness, safety, and biomechanical performance into a single scalar function. Using the coordinates of intermediate control points as optimization variables, since the initial and final control points are fixed by the entry and target points, adjusting the intermediate control points can change the three-dimensional shape of the path. An adaptive differential evolution algorithm is used for global optimization, which can find the control point position with the minimum comprehensive cost in a complex six-dimensional search space, allowing the path to evolve from an initial straight line to an optimal curve that conforms to the anatomical curvature of the pedicle and balances multiple clinical requirements.

[0036] Step S4: Discretize and speed plan the optimal path, and generate motion commands that the robot can execute based on the mapping relationship of the spiral motion.

[0037] In this embodiment, the optimal continuous path obtained in step S3 is discretely sampled at fixed time periods to obtain a sequence of path points that the robot can execute sequentially. The design of the velocity planning stage takes into account both motion smoothness and safety: on the one hand, a smooth velocity curve is used to ensure the smoothness of the start and stop process; on the other hand, a safety distance is introduced as a feedback constraint to automatically reduce the feed speed when the path point approaches the cortical bone boundary to improve safety. The velocity planning results are combined with the helical motion mapping established in step S2 to output the target pose of the end effector at each sampling time, and then converted into motion commands for each joint of the robot through inverse kinematics, finally forming a command sequence that can be directly adapted to mainstream surgical robots.

[0038] Based on steps S1-S4 above, firstly, by using triangular Bézier curves to generate the initial path, the problem of straight or circular paths failing to conform to the anatomical curvature of the pedicle in existing technologies is solved. Secondly, the analytical derivative of the triangular Bézier curve is used to uniformly model the helical motion during the planning stage, eliminating the disconnect between geometric planning and motion control, and ensuring the robot's executability of the path from the planning source. Then, by constructing a comprehensive cost function that integrates smoothness, safety, and biomechanical performance and using an adaptive differential evolution algorithm for global optimization, a comprehensive balance of multiple clinical indicators is achieved, overcoming the limitations of single-objective optimization. Finally, by introducing velocity planning with safety distance constraints, a fully closed-loop process from anatomical modeling to safe execution is formed, significantly improving pin placement accuracy and surgical safety.

[0039] In one embodiment, such as Figure 2-4 As shown, step S1 involves obtaining the planned entry point and target point for the pedicle screw, including: A parametric geometric model comprising the vertebral body and bilateral pedicles is constructed. The vertebral body is generated in cylindrical coordinates according to the following parametric equations: in, ,factor Simulates the anatomical feature of a vertebral body that is slightly thicker in the middle; The pedicle is modeled as a conical cylinder, with the center line connected to the entry point. With the exit point mm, its radius along the centerline according to The pedicles of the left and right vertebrae are symmetrical relative to the sagittal plane.

[0040] Figure 5The safety assessment of screws with different diameters is shown in the figure. The horizontal axis represents the screw diameter (in mm), and the vertical axis represents the safety margin (in mm). The left side (blue bar) and the right side (red bar) represent the safety margin of the left and right pedicles under different screw diameters, respectively. The horizontal black dashed line represents the minimum safety margin threshold (1.5 mm), and the green dashed line represents the recommended safety margin (2.0 mm). As can be seen from the figure, the larger the screw diameter, the smaller the safety margin on both sides. Therefore, this embodiment selects a screw with a diameter of 5.0 mm to ensure the safety of the screw placement process.

[0041] In this embodiment, the vertebral body is generated using parametric equations in a cylindrical coordinate system. By introducing a sinusoidal modulation factor, the vertebral body exhibits a slightly thicker shape in the middle along the height direction, which conforms to the actual anatomical characteristics of the human vertebral body. The pedicles are modeled as conical cylinders, with their centerlines connecting the entry and exit points. The radius changes linearly from the proximal to the distal end along the centerline, and the left and right pedicles are mirror-symmetrical with respect to the midsagittal plane. This modeling method yields a complete three-dimensional geometric model including the cortical bone boundary and cancellous bone passage, providing a precise anatomical reference for subsequently defining the safety distance function and constraint conditions.

[0042] In one embodiment, generating an initial 3D path connecting the ingress point and the target point using a triangular Bézier curve includes: Using an nth-order trigonometric Bézier curve, its basis functions are: Where n≥2; When n=3, the control points include a first control point P, a fourth control point P3, a second control point P1, and a third control point P2; wherein , For the variable to be optimized, As the entry point, For the exit point; The triangular Bézier curve is expressed as follows: In the initial state, each control point is evenly distributed on the line connecting P0 and P3 to generate an initial straight path.

[0043] In this example Figure 6 and Figure 7 The diagram shows the initial paths (blue / red solid lines) of the triangular Bézier curves on the left and right sides, along with their control points (circles) and control polygons (dashed lines). The first and last control points are fixed at the inlet and outlet points, respectively, while the two middle control points are initially evenly distributed on the line connecting the inlet and outlet points, forming the initial straight path. Figure 8 The curvature of the initial paths on the left and right sides was compared along the normalized arc length parameter. tThe distribution of the curves is shown in the figure. As can be seen from the figure, the curvature of both the left and right trajectories remains small and smooth, indicating that the initial path generated by the triangular Bézier curve has good geometric smoothness, providing a good starting point for subsequent multi-objective optimization.

[0044] In this embodiment, the basis functions of the trigonometric Bézier curve are composed of power combinations of sine and cosine, which is fundamentally different from the Bernstein polynomials used in traditional Bézier curves. The analytic derivative property of trigonometric functions allows the tangent vector and curvature at any point on the curve to be calculated accurately directly using the derivatives of the basis functions, without the need for numerical difference approximation. The curve order n≥2; when n=3, it is a 4th-order trigonometric Bézier curve with four control points. The first and last control points P0 and P3 are fixed at the in-point and out-point positions, respectively, while the two middle control points P1 and P2 are variables to be optimized. Initially, all control points are evenly distributed on the line connecting the in-point and out-point, forming an initial straight path, which serves as the search starting point for subsequent multi-objective optimization.

[0045] In one embodiment, the rotational propulsion process of the screw moving along the curve is uniformly modeled as a spiral motion exponential product, including: The screw motion is decomposed into a composite of a translational helix along the tangent of the path and a rotational helix rotating about the tangent; wherein, the screw axis of the translational helix is ​​determined based on the first derivative of the path, and the screw axis of the rotational helix is ​​determined based on the second derivative of the path. Using the exponential product formula Real-time calculation of the pose of the end effector; where It is a translational spiral that moves along the centerline. It is a rotating spiral about its own axis; The joint angle is parameterized using triangular splines.

[0046] In this embodiment, screw insertion is essentially a composite motion of forward movement and rotation. This is decomposed into two orthogonal helical motions: the screw axis of the translational screw is determined based on the first derivative (i.e., the tangent vector) of the trigonometric Bézier curve, describing the feed motion along the path direction; the screw axis of the rotational screw is determined based on the second derivative of the curve, describing the rotational motion around the screw's own axis. The two helices are combined using an exponential product formula, and a proportional relationship is established using the joint angles and arc lengths parameterized by trigonometric splines. Therefore, the pose matrix of the end effector can be directly calculated given the path parameter t.

[0047] In one embodiment, given a centerline and its tangential direction ,structure: in, The translation component of the translation screw is equal to the velocity vector of the screw moving along the center line; Let be the translation component of the rotating helix. Since the axis of rotation passes through the current path point and there is no translation along the axis, therefore... It is a zero vector.

[0048] In this embodiment, the spinor axis direction of the translation helix is ​​taken as the path tangent vector. The velocity component is taken as the first derivative of the path. The direction of the spinor axis of the rotating helix is ​​also taken as... However, the velocity component is a zero vector, indicating rotation in place. Joint angle It is proportional to the cumulative arc length along the path, and the scaling factor is determined by the motion parameters; joint angle Also proportional to the arc length, the scaling factor is determined by the screw's thread lead, which ensures that the screw rotates exactly one revolution for every pitch advance, conforming to the physical motion law of clinical screw placement.

[0049] In this example Figure 9 This diagram illustrates the screw axis of helical motion at a specific moment along the path. The blue and red lines represent the composite axis of the two orthogonal helices during screw insertion on the left and right sides, respectively. This axis is tangential to the path and passes through the current path point. This screw axis representation allows for real-time calculation of the screw's end-effector pose, providing direct parameterized input for robot control.

[0050] In one embodiment, the comprehensive cost function The expression is: Where X is a variable vector containing the coordinates of intermediate control points. , , The weighting coefficients for each cost item are used to balance the importance of smoothness, safety, and biomechanical performance. The larger the weight value, the higher the priority of the objective.

[0051] For the smoothness cost term: ; For safety-related costs: ; Biomechanical cost term: This is the bone mineral density field mapped from the CT values, typically ranging from [0,1] or the corresponding HU value. Taking a negative value for this term maximizes the bone mineral density integral during optimization, ensuring the guide path passes through high-density bone regions and enhancing the mechanical stability of screw fixation.

[0052] In this embodiment, the smoothness cost term is the integral of the path curvature change rate along the entire path. The smaller this value, the smoother the path curvature change, and the more stable the joint movements during robot execution. The safety cost term adopts a quadratic penalty function form: a penalty is incurred when the distance between a path point and the cortical bone boundary is lower than a safety threshold, and the closer the distance, the greater the penalty; no cost is incurred for path points that meet the safety requirements. The biomechanical cost term is the negative integral of the bone density of the area traversed by the path. The higher the bone density, the smaller this term (the better), meaning that the optimization algorithm tends to choose paths through high-density bone areas to improve the pull-out resistance after screw insertion.

[0053] Figure 13 The comparison of various cost components after optimization based on the algorithm proposed in this example is presented. Among them, the safety cost of screw implantation is dominant, while smoothness and biomechanics are reasonably balanced, and the overall cost is significantly reduced.

[0054] In one embodiment, the variable vector X is constructed as follows: in, . These are the x, y, z coordinates of the second control point (the first control point in the middle) of the triangular Bézier curve. The x, y, z coordinates of the third control point (the second control point in the middle) of the triangular Bézier curve; To optimize the variable vector, a 6-dimensional real vector is used, meaning each mutated individual is represented by 6 independent variables, corresponding to the coordinates of two points in 3D space. By optimizing these 6 variables, the shape of the curve can be changed to minimize the overall cost function value while satisfying safety constraints.

[0055] In this embodiment, since the initial and final control points P0 and P3 are fixed by the entry and target points, only the spatial positions of the two intermediate control points P1 and P2 can be adjusted. Each intermediate control point has three coordinate components, so the optimization variable X is a six-dimensional vector. This six-dimensional vector is simultaneously optimized within the search space of the adaptive differential evolution algorithm. The algorithm searches for the point in the six-dimensional space that minimizes the comprehensive cost function J(X) through mutation, crossover, and selection operations. The coordinates of P1 and P2 corresponding to this point are the optimal intermediate control point positions.

[0056] In one embodiment, step S4, discretizing and speed planning the optimal path, specifically includes: Discretize the path using equal-parameter intervals or equal-arc-length intervals; Using a safety distance as a constraint, an adaptive S-shaped planning is performed on the feed rate: when the safety distance corresponding to a path point is less than the first threshold, the maximum allowable feed rate is reduced; when the safety distance is greater than the second threshold, the maximum allowable feed rate is restored or increased. Based on the velocity planning results and helical motion mapping, the motion command sequence in the joint space is output.

[0057] In this embodiment, firstly, the path parameters are sampled at equal intervals according to a fixed control cycle, discretizing the continuous curve into a finite number of path points. Then, an S-shaped velocity curve is used to plan the feed rate: the S-shaped curve ensures continuous acceleration and avoids the impact problem of a trapezoidal velocity curve. Based on this, a safety distance feedback mechanism is introduced: the safety distance of each path point from the cortical bone boundary is calculated in real time; when the safety distance is lower than a first threshold, the maximum allowable feed rate is automatically reduced; when the safety distance recovers to above a second threshold, the original speed is restored. This achieves a safe closed-loop control where "the closer to the danger zone, the slower the feed." Finally, combined with the helical motion mapping established in the preceding steps, the path parameters of each discrete point are converted into the end effector pose, and then the motion commands for each joint of the robot are obtained through inverse kinematics. Figure 14 A Cartesian S-shaped velocity curve is planned. The velocities on the left and right sides accelerate smoothly from zero and automatically decelerate when the safe distance is below a threshold (where the velocity peak decreases), achieving "slow advance near the bone".

[0058] In one embodiment, the safe distance corresponding to a waypoint is calculated as follows: The parameterized equation for the pedicle centerline is: , ,in s =0 corresponds to the in-point. s =1 corresponds to the point.

[0059] In parameters s At that point, the cross-section perpendicular to the center line is approximately circular, and its radius is... r(s) Defined as the distance from the centerline to the outer surface of the cortical bone. Cortical bone thickness is a fixed value. =2 mm, then the radius from the centerline to the inner wall of the cortical bone (the boundary of the cancellous bone) is: For any point p in space, first project it onto the center line to obtain the projection parameters: Therefore, the safe distance from any point p on the path to the inner wall of the pedicle is defined as: A positive value indicates that any point p is located inside the cancellous bone channel, while a negative value indicates that the bone has penetrated the inner wall and entered the cortical bone or the outside. Both the first and second thresholds are set according to clinical safety requirements, ensuring that any path point meets the criteria. ≥1.5 mm.

[0060] In this embodiment, the inner wall of the pedicle is the inner boundary of the cortical bone, obtained by subtracting the cortical bone thickness from the outer surface radius of the pedicle. For any point p on the path, it is first projected onto the centerline of the inner wall of the pedicle. The projection parameters are obtained from the above. s * Then calculate the inner wall radius at that point. Distance from p to the centerline The difference. A positive value indicates that the path point is within the safe area, and a negative value indicates that the inner wall has been penetrated. Clinically, this distance is required to be no less than 1.5 mm, which is used as the first threshold for triggering deceleration in speed planning and the threshold δ in the safety penalty term.

[0061] The final optimization results can be found in this example. Figure 10 and Figure 11 The two figures represent the comparison of the screw trajectories before and after optimization on the left and right sides, respectively. The dashed line represents the initial straight path, and the solid line represents the optimized path. As shown in the results, the optimized path curves inward, better conforming to the anatomical orientation of the pedicle.

[0062] The final optimization results in this example demonstrate a significant improvement in the safety of pedicle screw implantation surgery based on this trajectory optimization algorithm, as shown in Table 1. The minimum safety margin for the left screw is 6.53 mm, and for the right screw, it is 7.38 mm, both significantly exceeding the clinical safety threshold of 1.5 mm. The optimized path remains entirely within the pedicle cortex, greatly reducing the risk of cortical penetration. The adaptive deceleration strategy automatically reduces the feed rate when the safety distance falls below the threshold, effectively minimizing the impact force when the screw enters the cortical bone.

[0063] Table 1 In this example Figure 16 This represents the safety margin distribution along the trajectory. The margins for both the left and right screw trajectories are greater than 1.5 mm throughout (black dashed line), with minimum values ​​of 6.47 mm and 7.38 mm respectively, far exceeding the safety threshold, demonstrating that the optimized path is highly safe.

[0064] Furthermore, based on Figure 17The results show that the mean bone mineral density of the optimized path was significantly improved compared to the initial straight path. Specifically, the left side saw a 10.0% increase (from 341.94 HU to 376.13 HU), and the right side saw a 7.5% increase (from 341.94 HU to 367.69 HU). Screw pull-out force and fatigue life were correspondingly enhanced, improving the long-term stability of the internal fixation.

[0065] Example 2 A trajectory planning system for a pedicle screw orthopedic robot includes: an acquisition module for acquiring the planned entry point and target point of a pedicle screw, and generating an initial three-dimensional path connecting the entry point and the target point using a trigonometric Bézier curve; wherein the control points of the trigonometric Bézier curve include at least a first control point coinciding with the entry point, a fourth control point coinciding with the target point, and several intermediate control points located between the entry point and the target point; and a first calculation module for modeling the rotational propulsion process of the screw moving along the curve as a spiral exponential product based on the trigonometric Bézier curve and its analytical derivative, and obtaining a path parameter... The system includes: a mapping relationship from the coordinates of the intermediate control point to the robot's end-effector pose; a second calculation module, used to construct a comprehensive cost function with the intermediate control point coordinates as optimization variables, iteratively optimize using an adaptive differential evolution algorithm, and output the optimized intermediate control point to determine the optimal path; the comprehensive cost function at least integrates a smoothness cost term characterizing the degree of path curvature change, a safety cost term characterizing the distance from the path to the cortical bone boundary, and a biomechanical cost term characterizing the bone density distribution along the path; and a path generation module, used to discretize and velocity plan the optimal path, and generate robot-executable motion commands based on the mapping relationship of the helical motion. In one embodiment, a description of the specific functions can be found in steps S1-S4.

[0066] The aforementioned pedicle screw fixation robot trajectory planning device is used for execution Figure 1 The illustrated embodiments of the pedicle osteopathic robot trajectory planning method are similar in their technical principles, the technical problems they solve, and the technical effects they produce. Those skilled in the art can clearly understand that, for the sake of convenience and brevity, the specific working process and related descriptions of the pedicle osteopathic robot trajectory planning device can be found in the embodiments of the pedicle osteopathic robot trajectory planning method, which will not be repeated here.

[0067] Those skilled in the art will understand that the various modules in the device can be adaptively split or combined. Such splitting or combining of specific modules will not cause the technical solution to deviate from the principles of the present invention; therefore, the technical solutions after splitting or combining will fall within the protection scope of the present invention.

[0068] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the original technical features, and the technical solutions resulting from these changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A trajectory planning method for a pedicle screw fixation robot, characterized in that, Includes the following steps: The planned entry point and target point of the pedicle screw are obtained, and an initial three-dimensional path connecting the entry point and the target point is generated using a trigonometric Bézier curve; wherein, the control points of the trigonometric Bézier curve include at least a first control point coinciding with the entry point, a fourth control point coinciding with the target point, and several intermediate control points located between the entry point and the target point. Based on the triangular Bezier curve and its analytical derivative, the rotational propulsion process of the screw moving along the curve is uniformly modeled as the screw exponential product of helical motion, thus obtaining the mapping relationship from path parameters to robot end pose. Using the coordinates of the intermediate control points as optimization variables, a comprehensive cost function is constructed, and an adaptive differential evolution algorithm is used for iterative optimization to output the optimized intermediate control points in order to determine the optimal path. The comprehensive cost function at least integrates a smoothness cost term that characterizes the degree of curvature change of the path, a safety cost term that characterizes the distance from the path to the cortical bone boundary, and a biomechanical cost term that characterizes the bone density distribution along the path. The optimal path is discretized and velocity is planned, and based on the mapping relationship of the helical motion, motion commands that can be executed by the robot are generated.

2. The method according to claim 1, characterized in that, Discretization and speed planning of the optimal path specifically include: Discretize the path using equal-parameter intervals or equal-arc-length intervals; Using a safety distance as a constraint, an adaptive S-shaped planning is performed on the feed rate: when the safety distance corresponding to a path point is less than the first threshold, the maximum allowable feed rate is reduced; when the safety distance is greater than the second threshold, the maximum allowable feed rate is restored or increased. Based on the velocity planning results and helical motion mapping, the motion command sequence in the joint space is output.

3. The method according to claim 2, characterized in that, The safe distance corresponding to a waypoint is calculated as follows: The parameterized equation for the pedicle centerline is: , ,in s =0 corresponds to the in-point. s =1 corresponds to the output point; In parameters s At that point, the cross-section perpendicular to the center line is approximately circular, and its radius is... r(s) Defined as the distance from the centerline to the outer surface of the cortical bone; the radius from the centerline to the inner wall of the cortical bone is: in, This refers to the thickness of the cortical bone. For any point p in space, first project it onto the center line to obtain the projection parameters: Therefore, the safe distance from any point p on the path to the inner wall of the pedicle is defined as: like A positive value indicates that any point p is located inside the cancellous bone channel. A negative value indicates penetration through the inner wall into the cortical bone or the exterior, and both the first and second thresholds are set according to clinical safety requirements, ensuring that any path point meets the criteria. ≥1.5mm.

4. The method according to claim 1, characterized in that, An initial 3D path connecting the ingress point and the target point is generated using a triangular Bézier curve, including: Using an nth-order trigonometric Bézier curve, its basis functions are: Where n≥2; When n=3, the control points include a first control point P, a fourth control point P3, a second control point P1, and a third control point P2; wherein , For the variable to be optimized, As the entry point, For the exit point; The triangular Bézier curve is expressed as follows: In the initial state, each control point is evenly distributed on the line connecting P0 and P3 to generate an initial straight path.

5. The method according to claim 1, characterized in that, The rotational propulsion process of the screw moving along this curve is uniformly modeled as a spiral motion exponential product, including: The screw motion is decomposed into a composite of a translational helix along the tangent of the path and a rotational helix rotating about the tangent; wherein, the screw axis of the translational helix is ​​determined based on the first derivative of the path, and the screw axis of the rotational helix is ​​determined based on the second derivative of the path. Using the exponential product formula Real-time calculation of the pose of the end effector; where It is a translational spiral that moves along the centerline. It is a rotating spiral about its own axis; The joint angle is parameterized using triangular splines.

6. The method according to claim 5, characterized in that, Given centerline and its tangential direction ,structure: in, The translation component of the translation screw is equal to the velocity vector of the screw moving along the center line; Let be the translation component of the rotating helix. Since the axis of rotation passes through the current path point and there is no translation along the axis, therefore... It is a zero vector.

7. The method according to claim 4, characterized in that, The comprehensive cost function The expression is: Where X is a variable vector containing the coordinates of intermediate control points. , , These are the weighting coefficients for each cost item, used to balance the importance of smoothness, safety, and biomechanical performance. A larger weight value indicates that the objective has a higher priority. For the smoothness cost term: ； in, Let the curvature of the path be... Curvature with respect to parameters t The derivative; For safety-related costs: ； in, M This represents the number of sampling points along the path. This is a preset safety margin; For the first k The shortest distance from each sampling point to the inner wall of the pedicle; Biomechanical cost term: This represents the bone mineral density field mapped from CT values.

8. The method according to claim 7, characterized in that, The variable vector X is constructed as follows: in, These are the x, y, and z coordinates of the second control point of the triangular Bézier curve. These are the x, y, and z coordinates of the third control point of the triangular Bézier curve. To optimize the variable vector, a 6-dimensional real vector is used, meaning that each mutated individual is represented by 6 independent variables, corresponding to the coordinates of two 3D spatial points.

9. The method according to claim 1, characterized in that, Obtain the planned entry and target points for the pedicle screws, including: A parametric geometric model comprising the vertebral body and bilateral pedicles is constructed; wherein the vertebral body is generated in cylindrical coordinates according to the following parametric equations: in, ,factor Simulates the anatomical feature of a vertebral body that is slightly thicker in the middle; The pedicle is modeled as a conical cylinder, with its radius along the centerline. The pedicles of the left and right vertebrae are symmetrical relative to the sagittal plane.

10. A trajectory planning system for a pedicle screw fixation robot, characterized in that, include: The acquisition module is used to acquire the planned entry point and target point of the pedicle screw, and to generate an initial three-dimensional path connecting the entry point and the target point using a trigonometric Bézier curve; wherein, the control points of the trigonometric Bézier curve include at least a first control point coinciding with the entry point, a fourth control point coinciding with the target point, and several intermediate control points located between the entry point and the target point. The first calculation module is used to model the rotational propulsion process of the screw moving along the curve as a spiral motion exponential product based on the triangular Bezier curve and its analytical derivative, and obtain the mapping relationship from the path parameters to the robot end pose. The second calculation module is used to construct a comprehensive cost function with the coordinates of the intermediate control point as the optimization variable, and to perform iterative optimization using an adaptive differential evolution algorithm to output the optimized intermediate control point in order to determine the optimal path. The comprehensive cost function at least integrates a smoothness cost term that characterizes the degree of curvature change of the path, a safety cost term that characterizes the distance from the path to the cortical bone boundary, and a biomechanical cost term that characterizes the bone density distribution along the path. The path generation module is used to discretize and speed plan the optimal path, and generate motion commands that the robot can execute based on the mapping relationship of the helical motion.

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