Cutter grinding force constrained robot bone grinding multi-target trajectory optimization method

Abstract

The invention provides a tool grinding force constrained robot bone grinding multi-target trajectory optimization method, which comprises the following steps of: discretizing into point cloud data according to a CT image of a bone bridge, establishing a directed 3D grinding path planning method, and obtaining a grinding path of a tool at the tail end of a robot; according to a mechanical model of robot grinding, a robot bone grinding multi-target trajectory optimization method is established in combination with total time and smoothness of robot motion, and optimal motion parameters of robot bone grinding are obtained. According to the technical scheme provided by the invention, robot-assisted bone grinding can be realized.

Description

Technical Field

[0001] The present invention relates to a multi-objective trajectory optimization method for robotic bone grinding with tool grinding force constraint, belonging to the field of robotic bone grinding processing.

Background Art

[0002] Osteotomy is the standard method for treating epiphyseal premature closure. However, surgeons mainly rely on visual and tactile judgments of the boundaries of the bone bridge, but the accuracy of real-time grinding during the operation is limited, and this limitation significantly increases the risk of surgical failure. Robotic-assisted surgical systems, due to their advantages in precise lesion localization and surgical planning, significantly reduce tissue damage and shorten the postoperative recovery time. In the past few decades, the research on trajectory planning of this system has mainly focused on laparoscopic surgery, total hip or knee replacement, tunnel remodeling for knee ligament reconstruction, and trauma and spinal surgery. However, the research on robotic grinding planning for adolescents with epiphyseal closure is relatively scarce. Thus, it can be seen that the multi-objective trajectory optimization method for robotic bone grinding with tool grinding force constraint is of great significance for osteotomy.

[0003] Early path planning methods mainly relied on basic image processing and geometric modeling, but did not consider the impact of biomechanics on the safety of the operation. To address this limitation, fracture reduction surgery considered the impact of biomechanics on the path planning of robotic-assisted surgery. However, this is completely different from the application scenario of robotic-assisted osteotomy. To sum up, conducting research on a multi-objective trajectory optimization method for robotic bone grinding with tool grinding force constraint has important theoretical research value.

Summary of the Invention

[0004] In view of this, the present invention provides a multi-objective trajectory optimization method for robotic bone grinding with tool grinding force constraint, providing diverse and high-quality solutions for robotic-assisted bone grinding.

[0005] The present invention provides a multi-objective trajectory optimization method for robotic bone grinding with tool grinding force constraint, including:

[0006] According to the CT image of the bone bridge, it is discretized into point cloud data, and a directed 3D grinding path planning method is established to obtain the grinding path of the tool at the end of the robot.

[0007] According to the mechanical model of robotic grinding, combined with the total movement time and smoothness of the robot, a multi-objective trajectory optimization method for robotic bone grinding is established to obtain the optimal movement parameters for robotic bone grinding.

[0008] In the above method, the step of according to the CT image of the bone bridge, discretizing it into point cloud data, establishing a directed 3D grinding path planning method, and obtaining the grinding path of the tool at the end of the robot includes:

[0009] Based on the CT medical image data in.nii.gz format, all voxel positions are traversed in three-dimensional space, and all coordinate points are traversed in a loop. During each traversal, if the current voxel value is 1, that is, it belongs to the region of interest, its coordinates are added as a three-dimensional point to the point cloud set. Finally, all three-dimensional coordinates that meet the conditions constitute the bone bridge point cloud data. Set the grinding depth layer_thinckness, and segment the point cloud data;

[0010] Based on the segmented point cloud data, construct the boundary of the 2D point cloud data, and the boundary size is (x min , x max ) and (y min , y max );

[0011] Based on the boundary of the point cloud, construct a grid for dividing the 2D point cloud data to divide the planning area. The shape of the grid is square, and the side length size is Grid_size, satisfying the following conditions:

[0012] Grid_size > p

[0013] where p is the point cloud resolution;

[0014] Based on the point cloud data within the grid range, calculate its center point, and then construct a 3D directed path point, satisfying the following conditions:

[0015]

[0016] where n is the number of point clouds within the grid, (x i , y i ) is the point cloud data within the grid, and (x center , y center ) is the center point of the point cloud data within the grid;

[0017] Based on the grinding head diameter of the tool, design the feed rate Point_space and path spacing Line_space of grinding;

[0018] Based on the set depth layer_thinckness, splice the 2D directed path into a 3D directed path.

[0019] In the above method, based on the mechanical model of robot grinding, combined with the total robot movement time and smoothness, establish a multi-objective trajectory optimization method for robot bone grinding to obtain the optimal motion parameters of robot bone grinding, including:

[0020] Measure the grinding efficiency of the robot based on the total time and use it as the first optimization objective, satisfying the following conditions:

[0021]

[0022] Among them, t i is the grinding time between each path point;

[0023] Based on the joint impact to measure the smoothness of robot grinding, which is used as the second optimization objective and satisfies the following conditions:

[0024]

[0025] Among them, represents the impact of the i-th joint related to time.

[0026] Based on the fact that the magnitude of the robot grinding force affects the bone tissue activity, which is a necessary condition to ensure grinding safety. The mapping relationship between the grinding force in the feed direction and the bone density, feed speed and rotational speed. Therefore, the grinding force model is set as the third optimization objective and satisfies the following conditions:

[0027]

[0028] Among them, S3 is the grinding force in the feed direction, ρ is the bone density, n is the rotational speed of the spherical grinding head, k ρ 、k v 、k n are the influence factors of bone density, feed speed and rotational speed, and φ is a constant term.

[0029] Based on the Jacobian matrix of the robot, describe the relationship between the end effector velocity v ee and the joint velocity and satisfy the following conditions:

[0030]

[0031] Among them, v ee is the linear velocity of the end effector, then v ee = f.

[0032] Based on the grinding force model and the robot Jacobian matrix, the mapping relationship between the grinding force in the feed direction and the joint space parameters is constructed and satisfies the following conditions:

[0033]

[0034] It can be seen from the above technical solutions that the present invention has the following beneficial effects:

[0035] In the technical solution of the present invention, a multi-objective trajectory optimization method for robotic bone grinding with tool grinding force constraint is obtained. Based on the CT images of the bone bridge, it is discretized into point cloud data, and a directed 3D grinding path planning method is established to obtain the grinding path of the tool at the end of the robot. According to the mechanical model of robotic grinding, combined with the total movement time and smoothness of the robot, a multi-objective trajectory optimization method for robotic bone grinding is established to obtain the optimal movement parameters for robotic bone grinding. At the same time, it provides a theoretical basis for the research of the robotic bone grinding system.

Description of the Drawings

[0036] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative and laborious efforts, other drawings can be obtained based on these drawings.

[0037] Figure 1 It is a schematic diagram of the overall framework of the multi-objective trajectory optimization method for robotic bone grinding considering tool grinding force constraint provided by the embodiments of the present invention;

[0038] Figure 2 It is a schematic diagram of the overall framework of the multi-objective trajectory optimization method for robotic bone grinding considering tool grinding force constraint provided by the embodiments of the present invention;

[0039] Figure 3 Schematic diagram of the grinding path planner based on the point cloud features of the bone bridge provided by the embodiments of the present invention: (a) Bone bridge segmented from CT image; (b) 3D point cloud data of the bone bridge; (c) 2D point cloud data and boundaries; (d) 2D grinding path planning; (e) 2D directed grinding path; (f) Multi-layer 3D directed grinding path;

[0040] Figure 4 It is a schematic diagram of the point cloud segmentation algorithm provided by the embodiments of the present invention;

[0041] Figure 5 It is a schematic diagram of the 2D directed path planning algorithm provided by the embodiments of the present invention;

[0042] Figure 6 It is a schematic diagram of the 3D directed path planning algorithm provided by the embodiments of the present invention;

[0043] Figure 7 It is a schematic diagram of the improved NSGA-II algorithm provided by the embodiments of the present invention;

[0044] Figure 8 It is a schematic diagram of the working principle of the RGS provided by the embodiments of the present invention;

[0045] Figure 9 It is a schematic diagram of the SAW working principle provided in the embodiments of the present invention;

[0046] Figure 10 It is a schematic diagram of the Pareto front of the MOP series functions provided in the embodiments of the present invention: (a) Pareto front of the MOP2 function; (b) Pareto front of the MOP4 function;

[0047] Figure 11 It is a schematic diagram of the GD and SP indicators of MOP2 provided in the embodiments of the present invention;

[0048] Figure 12 It is a schematic diagram of the GD and SP indicators of MOP4 provided in the embodiments of the present invention;

[0049] Figure 13 It is a schematic diagram of the Pareto front provided in the embodiments of the present invention;

[0050] Figure 14 It is a schematic diagram of the motion state - position, speed, acceleration and jerk of the robot provided in the embodiments of the present invention;

[0051] Figure 15 It is the intention of the physical experiment provided in the embodiments of the present invention: (a) Model bone and biological bone before grinding; (b) Model bone and biological bone after grinding;

Specific Embodiment

[0052] For a better understanding of the technical solution of the present invention, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0053] It should be clear that the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0054] The embodiments of the present invention provide a multi - objective trajectory optimization method for robot bone grinding with tool grinding force constraint, as Figure 1 shown. Without being limited to the foregoing, the multi - objective trajectory optimization method for robot bone grinding with tool grinding force constraint is applicable to the field of orthopedic surgery and provides efficient, smooth and safe motion parameters for robot bone grinding during surgical procedures to ensure bone bridge resection. The method includes the following steps:

[0055] Step 101, discretize the CT image of the bone bridge into point cloud data, establish a directed 3D grinding path planning method, and obtain the grinding path of the tool at the end of the robot;

[0056] Specifically, as Figure 2As shown in the figure, first, the segmentation of point cloud data. Based on the osteophyte segmented from the CT image, the point cloud data is extracted. Secondly, 2D path planning. Based on the distance between point clouds, 2D point cloud data and boundaries are generated layer by layer, and then a 2D grinding path planning method is designed to generate a 2D directed path. Finally, 3D path planning. The directed paths of each layer are combined to form a multi-layer 3D directed grinding path.

[0057] Further, for the segmentation of point cloud data, load the medical image data in the.nii.gz format, such as Figure 3 (a) shown, traverse all voxel positions in the three-dimensional space, and loop through all coordinate points. During each traversal, if the current voxel value is 1, that is, it belongs to the region of interest, then its coordinates are added to the point cloud set as a three-dimensional point. Finally, all three-dimensional coordinates that meet the conditions constitute the osteophyte point cloud data, as Figure 3 (b) shown. Set the grinding depth layer_thickness and segment the point cloud data, specifically Algorithm 1, as Figure 4 shown.

[0058] Further, based on the segmented point cloud data, construct the boundary of the 2D point cloud data, and the boundary size is (x min , x max ) and (y min , y max ), as Figure 3 (c) shown;

[0059] Based on the boundary of the point cloud, construct a grid for dividing the 2D point cloud data to divide the planning area. The shape of the grid is square, and the side length is Grid_size, as Figure 3 (d) shown, satisfying the following conditions:

[0060] Grid_size > p

[0061] where p is the point cloud resolution;

[0062] Based on the point cloud data within the grid range, calculate its center point, and then construct a 3D directed path point, satisfying the following conditions:

[0063]

[0064] where n is the number of point clouds within the grid, (x i , y i ) is the point cloud data within the grid, and (x center , y center ) is the center point of the point cloud data within the grid;

[0065] Design the feed rate Point_space and path spacing Line_space for grinding according to the diameter of the grinding head of the tool, as shown in Figure 3 (d), to form a 2D directed path, as shown in Figure 3 (e), and the specific algorithm 2, as shown in Figure 5 ;

[0066] Furthermore, according to the set depth layer_thinckness, splice the 2D directed paths into 3D directed paths, as shown in Figure 3 (f), and the specific algorithm 3, as shown in Figure 6 .

[0067] Step 102: Based on the mechanical model of robot grinding, combined with the total robot movement time and smoothness, establish a multi-objective trajectory optimization method for robot bone grinding to obtain the optimal motion parameters for robot bone grinding;

[0068] Furthermore, measure the grinding efficiency of the robot according to the total time and use it as the first optimization objective, satisfying the following conditions:

[0069]

[0070] where t i is the grinding time between each path point;

[0071] Measure the smoothness of robot grinding according to joint impact and use it as the second optimization objective, satisfying the following conditions:

[0072]

[0073] where represents the impact of the i-th joint related to time.

[0074] Since the magnitude of the robot grinding force affects bone tissue activity, it is a necessary condition to ensure grinding safety. The mapping relationship between the grinding force in the feed direction and bone density, feed speed, and rotational speed. Therefore, set the grinding force model as the third optimization objective, satisfying the following conditions:

[0075]

[0076] where S3 is the grinding force in the feed direction, ρ is the bone density, n is the rotational speed of the spherical grinding head, k ρ , k v , k n are the influence factors of bone density, feed speed, and rotational speed, and φ is a constant term.

[0077] According to the Jacobian matrix of the robot, describe the end velocity v ee and the joint velocity The relationship between them satisfies the following conditions:

[0078]

[0079] where v ee is the linear velocity of the end effector, then v ee = f.

[0080] Based on the grinding force model and the robot Jacobian matrix, the mapping relationship between the grinding force in the feed direction and the joint space parameters is constructed, satisfying the following conditions:

[0081]

[0082] Furthermore, NSGA-II (Non-dominated Sorting Genetic Algorithm II) is based on the natural law of survival of the fittest, and gradually generates excellent individual solutions during the search process through genetic operators, and finally obtains the global optimal solution. NSGA-II is improved by integrating the RGS module, the DBX module and the SAW module, as Figure 7 shown.

[0083] The RGS process is as Figure 8 shown. First, a parent population P of size N is randomly initialized, N is set to be a multiple of 4, and the population is sorted according to non-dominated sorting. Then, the sorted population is divided into 4 elements in order. Using the principle of combinatorics, 2 are selected from these 4 elements for pairing, and there are 6 possible pairing situations, namely (X1, X2), (X1, X3), (X1, X4), (X2, X3), (X2, X4), (X3, X4). Based on RGS, a pair of individuals formed are I A = (X1, X1, X1, X2, X2, X3) and I B = (X2, X3, X4, X3, X4, X4). During the iteration process, I A is responsible for guiding the population to move towards the optimal region, and I B is responsible for increasing the diversity of the population. In addition, RGS directly calculates the objective function value, and has a lower time complexity and is easier to implement compared with the traditional comparison loop method.

[0084] The DBX process performs crossover operations based on the principle that "individuals with better objective function values are closer to the optimal region", solving the blindness of the binary crossover method in the traditional genetic algorithm. The specific crossover method is to take I A as the center and the direction vector d ij as the crossover direction, and generate new individuals along a random step size. The DBX process can be mathematically expressed as:

[0085]

[0086] Among them, \(i\) represents the \(i\)-th individual, \(j\) represents the variable dimension, and the parameter \(r\) ij is a uniformly distributed random number within the interval \([-1, 1]\). Different from the traditional fixed-step crossover, the step size of DBX is randomly generated by the parameter \(r\) ij which expands the search range.

[0087] The SAW process realizes the adaptive mutation function. As Figure 9 shown, it has six adaptive mutation operations. Which mutation method to choose is determined by SuccessRate. Each offspring solution Offspring is generated using six mutation methods. After obtaining all the offspring solutions, SuccessMark is reset to \([1, 1, 1, 1, 1, 1]\). Once an offspring solution survives in the competition with the parent, the corresponding position of the mutation method it uses will be incremented by 1, which means that the probability of this method being selected in the next iteration is greater.

[0088]

[0089] Among them, \(i = 1, 2, 3, 4, 5, 6\). In the first iteration, let SuccessMark be initialized to \([1, 1, 1, 1, 1, 1]\).

[0090] To further evaluate the effectiveness of the method, the GD and SP criteria are used to evaluate the convergence and diversity of the improved NSGA-II algorithm.

[0091] The specific GD index, which measures the average distance between the solution set and the true Pareto front, is shown in the formula:

[0092]

[0093] Among them, \(n\) is the number of solutions in the solution set, and \(d\) i is the Euclidean distance between the \(i\)-th solution and the true Pareto front.

[0094] The specific SP index, which measures the distribution uniformity among the solutions in the solution set, is shown in the formula:

[0095]

[0096] In the formula, \(n\) is the number of solutions in the solution set, and \(d\) i is the Euclidean distance between the \(i\)-th solution and the true Pareto front.

[0097] The original algorithm and the improved algorithm are verified using the classical test functions of the MOP series. The relevant parameter settings are: population size 50, number of iterations 100. The comparison of the fronts of the algorithms before and after improvement is asFigure 10 As shown, it can be seen that the Pareto fronts before and after improvement are basically the same, and the improved Pareto front is denser and more uniform.

[0098] As Figure 11 shown, the improved NSGA-II algorithm has a faster convergence speed in terms of the GD metric. As Figure 12 shown, the SP metric of the improved NSGA-II algorithm has a smaller value when the number of generations is relatively low, and the distribution of the solution set is more uniform. When the number of generations is relatively high, the values are similar, and the uniformity of the solution set distribution is similar.

[0099] Furthermore, the performance of the algorithm is quantitatively analyzed using the mean and standard deviation of GD and SP, as shown in Table 1. We found that compared with NSGA-II, the average value of GD of MOP2 in this algorithm decreased by 1.7e-2, and the average value of SP decreased by 0.13e-2. The average value of GD of MOP4 in this algorithm decreased by 1.03e-2, and the average value of SP decreased by 0.386e-1. Moreover, the algorithm in this paper obtained the lowest mean GD and the lowest mean SP for each MOP. Compared with the benchmark algorithm, this algorithm can find a set of non-dominated solutions with better convergence and wider distribution, and can obtain the optimal solutions for the three objectives of S1, S2, and S3.

[0100] Taking S1, S2, and S3 as the optimization objectives and time t as the decision variable, the Pareto front obtained by the improved NSGA-II multi-objective optimization algorithm is as Figure 13 shown. The closer to point A, the less the time consumption, the worse the smoothness of the joint, and the greater the grinding force. The closer to point B, the more the time consumption, the better the smoothness of the joint, and the smaller the grinding force. It is found that the smoothness of the joint and the grinding force are in the same direction, and in the opposite direction to the time consumption. The specific values of the three points in the Pareto front are shown in Table 2.

[0101] As Figure 13 shown, point C is the final solution of the multi-objective trajectory optimization, with a total time of 104.92143 s. The contact force during grinding is 0.18556 N, and the smoothness is 19.82931 rad 2 / s 3 . The motion parameters of each joint are as Figure 14 shown.

[0102] Figure 15 This is a physical experiment of the model bone and the biological bone, using an artificially made bone bridge. CT images were taken before and after grinding, and the same neural network model was used for segmentation respectively. The fitting degrees of the bone bridge before and after grinding were calculated, as shown in Table 3. It was found that the fitting degrees were generally higher than 90%.

[0103] Table 1 Comparison results of the indicators of 5 algorithms

[0104]

[0105] Table 2 Numerical Analysis of Trajectory Optimization

[0106]

[0107] Table 3 Bone Bridge Fitting Degree before and after Grinding

[0108]

Claims

1. A multi-objective trajectory optimization method for robot bone grinding with tool grinding force constraints, characterized in that: The method comprises: Based on the CT images of the bone bridge, the images were discretized into point cloud data, and a directed 3D grinding path planning method was established to obtain the grinding path of the robot end tool. According to the mechanical model of robotic grinding and combined with the total motion time and smoothness of the robot, a multi-objective trajectory optimization method for robotic bone grinding was established to obtain the optimal motion parameters of robotic bone grinding.

2. The method according to claim 1, characterized in that Based on the CT image of the bone bridge, the point cloud data is discretized and a directed 3D grinding path planning method is established to obtain the grinding path of the robot end tool, including: Based on the CT medical image data in .nii.gz format, all voxel positions are traversed in three-dimensional space, and all coordinate points are traversed in a loop. During each traversal, if the current voxel value is 1, that is, it belongs to the region of interest, its coordinates are added to the point cloud collection as a three-dimensional point. Finally, all three-dimensional coordinates that meet the conditions constitute the bone bridge point cloud data, and the grinding depth layer_thinckness is set to segment the point cloud data; Based on the segmented point cloud data, construct the boundary of the 2D point cloud data, the boundary size is (x min ,x max ) and (y min ,y max ); According to the boundary of the point cloud, a grid is constructed to divide the 2D point cloud data to divide the planning area. The shape of the grid is a square with a side length of Grid_size, and the following conditions are met: Grid_size>p Where p is the point cloud resolution; Based on the point cloud data within the grid range, calculate its center point and then construct a 3D directed path point, satisfying the following conditions: Where n is the number of point clouds in the grid, (x i ,y i ) is the point cloud data within the grid, (x center ,y center ) is the center point of the point cloud data within the grid; According to the grinding head diameter of the tool, design the grinding feed amount Point_space and path spacing Line_space; According to the set depth layer_thinckness, the 2D directed paths are spliced ​​into 3D directed paths.

3. The method according to claim 1, characterized in that Based on the mechanical model of robot grinding, combined with the total motion time and smoothness of the robot, a multi-objective trajectory optimization method for robot bone grinding is established to obtain the optimal motion parameters of robot bone grinding, including: The robot's grinding efficiency is measured based on the total time and is taken as the first optimization goal, satisfying the following conditions: Among them, t i is the grinding time between each waypoint; The smoothness of robot grinding is measured according to joint impact and is taken as the second optimization goal, satisfying the following conditions: in, Represents the time-dependent impact of the joint. The influence of the robot grinding force on bone tissue activity is a necessary condition to ensure grinding safety. The mapping relationship between the grinding force in the feed direction and bone density, feed speed and rotation speed. To this end, the grinding force model is set as the optimization target three, satisfying the following conditions: in, S3 is the grinding force in the feed direction, ρ is the bone density, n is the rotation speed of the spherical grinding head, k ρ , k v , k n is the influencing factor of bone density, feed speed and rotation speed, and φ is a constant term. According to the Jacobian matrix of the robot, describe the terminal velocity v ee and joint speed The relationship between them satisfies the following conditions: Among them, v ee is the linear velocity of the end effector, then v ee =f. According to the grinding force model and the robot Jacobian matrix, the mapping relationship between the grinding force in the feed direction and the joint space parameters is constructed, which meets the following conditions:

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