CN112603543A - Method for improving bone sawing precision and safety of robotic bone surgery - Google Patents

Method for improving bone sawing precision and safety of robotic bone surgery Download PDF

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CN112603543A
CN112603543A CN202011438434.1A CN202011438434A CN112603543A CN 112603543 A CN112603543 A CN 112603543A CN 202011438434 A CN202011438434 A CN 202011438434A CN 112603543 A CN112603543 A CN 112603543A
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robot
virtual boundary
rep
simulated
repulsive force
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芦颖僖
侯礼春
徐李雪
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Nanjing Linghua Microelectronics Technology Co ltd
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    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
    • A61B34/30—Surgical robots
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B17/00—Surgical instruments, devices or methods, e.g. tourniquets
    • A61B17/16—Bone cutting, breaking or removal means other than saws, e.g. Osteoclasts; Drills or chisels for bones; Trepans
    • A61B17/17—Guides or aligning means for drills, mills, pins or wires

Abstract

The invention discloses a method for improving bone sawing precision and safety in robotic bone surgery, belonging to the field of medical robot control; the invention provides a position compensation virtual boundary based on a simulation force field, which can take the cortical bone of the lower layer as a rejection surface so as to prohibit the tail end from exceeding the cortical bone of the lower layer.

Description

Method for improving bone sawing precision and safety of robotic bone surgery
Technical Field
The invention belongs to the field of medical robot control, and particularly relates to a method for improving bone sawing precision and safety in robotic bone surgery.
Background
The robot operation system is a comprehensive body integrating a plurality of modern high-tech means. Is mainly used for orthopedics, cardiac surgery and prostatectomy. The surgeon can operate the machine far away from the operating table, which is totally different from the traditional operation concept, and the operation using the robot is increasingly popular. When the robot is used for operation, the hands of the doctor do not touch the patient. Once the incision site is determined, the robotic arm, which carries the navigator and other surgical tools, performs the cutting, hemostasis and suturing actions, and the surgeon simply sits on the console, usually an operating room, and observes and guides the robotic arm through its work. In the case of bone sawing using an actual robot in an orthopedic surgery, the cutting tip is prohibited from protruding beyond the underlying cortical bone, so that it is necessary to design an appropriate method to reject the tip from passing through the underlying cortical bone from the viewpoint of safety.
Disclosure of Invention
The invention provides a method for improving the precision and safety of bone sawing in robotic bone surgery, which is based on the position compensation virtual boundary of a simulated force field, wherein the virtual boundary can take the cortical bone of the lower layer as a rejection surface, so that the tail end is forbidden to exceed the cortical bone of the lower layer.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a method for improving the precision and safety of bone sawing in robotic bone surgery comprises the following steps:
step S1, setting a manual simulated attraction potential field at the target point position of the sawed bone to generate attraction, so that the attraction generates attraction on the tail end of the robot, and the tail end of the robot is guided to move to the target point, wherein the movement track is a guide type virtual boundary based on the attraction field;
step S2, adopting the FIRAS function to establish an artificial simulated repulsion field, wherein the repulsion force born by the tail end of the robot when the tail end of the robot is close to the virtual boundary tends to be infinite, and determining a repulsion constant k for avoiding the tail end of the robot from being subjected to infinite simulated repulsion forcerepIs used for limiting the maximum value of the simulated repulsive force so as to ensure the stability of the control system;
step S3, compensating the position error caused by the control period in the process of approaching the virtual boundary;
and step S4, in the process of further osteotomy of the bone saw, in the action area of the simulated force field, the closer the robot is to the virtual boundary, the larger the simulated repulsive force is, so that the moving capability of the robot in the direction to the virtual boundary is smaller until the tail end of the robot moves to the virtual boundary.
The above steps, the simulated attraction potential field function U in step S1attDescribed by the following formula:
Figure BDA0002821479550000021
in the formula Katt-a gain factor;
x-position coordinates of the robot tip;
Xg-the position coordinates of the target point.
Gravitational force F generated by the gravitational fieldattNegative gradient for gravitational potential:
Figure BDA0002821479550000022
as can be seen from equation (2), the attractive force increases linearly with decreasing distance between the robot and the target point, showing a trend of- ∞ → 0;
simulating repulsive force field function U in step S2repAs shown in formula (3):
Figure BDA0002821479550000023
in the formula krep-a force constant;
r-the minimum distance of the robot end to the virtual boundary;
r0-simulating the working distance of the repulsive force field artificially;
at r0The outer region is not influenced by a repulsive force field, the repulsive force generated by the repulsive force field is a negative gradient of repulsive force potential energy, and a repulsive force function is shown as a formula (4):
Figure BDA0002821479550000024
repulsive force FrepIn the direction of UrepDirection of negative gradient of magnitude FrepCan be seen from equation (4) as the modulus at r0In the region, the larger r is, FrepThe smaller(ii) a The smaller r is, FrepThe larger; when r → 0, Frep→ infinity, i.e. the repulsive force experienced when the robot tip is infinitely close to the virtual boundary tends to be infinite, and in order to avoid the robot tip being subjected to infinite simulated repulsive force, k needs to be determinedrepFor limiting the maximum value of the analog force to ensure the stability of the control system, where F is setrepHas a threshold value of FmaxSetting the safety distance r ', when r is r', let Frep＝FmaxThe repulsive constant k can be reversely solved by the formula (4)rep；
The specific process of compensating the position error due to the control period in step S3 is: the current velocity at the end of the robot is of the formula VoutBy TdRepresenting the control period, the position error Δ R due to the control period can be represented as:
ΔR＝Vout·Td (5)
by DtRepresenting the projection factor in the direction of the minimum distance from the robot end to the virtual boundary, the position error Δ R in that direction*Comprises the following steps:
ΔR*＝Dt·ΔR (6)
so that the actual distance r from the robot end to the virtual boundary*Comprises the following steps:
r*＝r-ΔR* (7)
by r*Instead of r in equation (4), compensation for the position error is achieved.
Step S4 introduces the change admittance factor kτPreventing the robot from crossing the virtual boundary and realizing the function of a refused virtual boundary, wherein an admittance factor k is used in the virtual boundaryτIs represented as follows:
kτ＝kτ·cτ (8)
wherein c isτIntensity coefficient of admittance factor, cτIs a function of the simulated repulsive force in the simulated force field, and is expressed as follows:
Figure BDA0002821479550000031
in the formula cb-controlling the coefficient of the damping intensity;
ca-a minimum damping intensity coefficient;
Frep-simulated repulsion in equation (4);
therefore, in the region r where the repulsive force field acts0In the interior, the closer the robot is to the virtual boundary, the larger the simulated repulsive force is, so that the intensity coefficient c of the admittance factor isτThe smaller this makes the robot less capable of moving in the r direction until the end of the robot moves to the virtual boundary and the intensity coefficient reaches the minimum value ca。
Has the advantages that: the invention provides a method for improving the precision and safety of bone sawing in robotic bone surgery, and provides a position compensation virtual boundary based on a simulated force field, wherein the virtual boundary can use a cortical bone on the lower layer as a rejection surface so as to prohibit the tail end from exceeding the cortical bone on the lower layer.
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FIG. 1 is a diagram of a model for velocity-based position compensation in accordance with an embodiment of the present invention;
FIG. 2 is a comparison graph of speed variation curves with and without virtual boundaries in an embodiment of the present invention.
Detailed Description
The invention is described in detail below with reference to the following figures and specific examples:
a method for improving the precision and safety of bone sawing in robotic bone surgery comprises the following steps:
step S1, setting a manual simulated attraction potential field at the target point position of the sawed bone to generate attraction, so that the attraction generates attraction on the tail end of the robot, and the tail end of the robot is guided to move to the target point, wherein the movement track is a guide type virtual boundary based on the attraction field;
step S2, adopting the FIRAS function to establish an artificial simulated repulsion field, wherein the repulsion force born by the tail end of the robot when the tail end of the robot is close to the virtual boundary tends to be infinite, and determining a repulsion constant k for avoiding the tail end of the robot from being subjected to infinite simulated repulsion forcerepIs used for limiting the maximum value of the simulated repulsive force so as to ensure the stability of the control system;
step S3, compensating the position error caused by the control period in the process of approaching the virtual boundary;
and step S4, in the process of further osteotomy of the bone saw, in the action area of the simulated force field, the closer the robot is to the virtual boundary, the larger the simulated repulsive force is, so that the moving capability of the robot in the direction to the virtual boundary is smaller until the tail end of the robot moves to the virtual boundary.
The simulation force generation method needs to consider physical characteristics of a motion space, such as rigidity, deformation and the like, and can generate the simulation force only when collision occurs, and the simulation force field method successfully avoids the conditions, establishes the simulation force through the position characteristics of the tail end of the robot, and reduces the complexity of an algorithm.
The simulation force field adds the motion space of the robot to the virtual artificial stress field, so that the robot is acted by the simulation force. The algorithm establishes a simulated force field function based on the tail end position of the robot, and then calculates the simulated force, thereby controlling the motion direction of the robot. The simulation force field is composed of a simulation gravitational field and a simulation repulsive field, wherein the simulation force field is introduced into a virtual boundary, the target point generates a gravitational force to the robot, and the force monotonically increases along with the shortening of the distance; the obstacle generates repulsion to the robot, and monotonically decreases with increasing distance. And controlling the movement direction of the robot and the position of the robot according to the change of the attractive force and the repulsive force.
Simulated gravity in step S1
In controlling the movement of the robot, the robot needs to move according to a desired track, and the track is composed of a certain number of point coordinates, and the robot needs to move from one point to another point. In response to such movement, willAnd setting a manual simulated attraction potential field at the position of the target point to generate attraction, so that the robot end is attracted, and the end is guided to move to the target point, namely the guiding type virtual boundary based on the attraction field. Gravitational field function UattCan be described by the following formula:
Figure BDA0002821479550000041
in the formula Katt-a gain factor;
x-position coordinates of the robot tip;
Xg-the position coordinates of the target point.
Gravitational force F generated by the gravitational fieldattNegative gradient for gravitational potential:
Figure BDA0002821479550000051
as can be seen from equation (2), the attractive force linearly increases with decreasing distance between the robot and the target point, and tends to- ∞ → 0.
Simulated repulsive force in step S2
Establishing artificial simulated repulsion field and potential field function U by using FIRAS functionrepDescribed as shown in formula (3):
Figure BDA0002821479550000052
in the formula krep-a force constant;
r-the minimum distance of the robot end to the virtual boundary;
r0-simulating the working distance of the repulsive force field artificially;
at r0The outer region is not influenced by a repulsive force field, the repulsive force generated by the repulsive force field is a negative gradient of repulsive force potential energy, and a repulsive force function is shown as a formula (4):
Figure BDA0002821479550000053
repulsive force FrepIn the direction of UrepDirection of negative gradient of magnitude FrepThe die of (1). From equation (4), it can be seen that at r0In the region, the larger r is, FrepThe smaller; the smaller r is, FrepThe larger; when r → 0, Frep→ ∞, i.e. the repulsive force experienced when the robot tip approaches an obstacle infinitely tends to infinity. To avoid subjecting the robot tip to an infinite analog force, k needs to be determinedrepIs used to limit the maximum value of the analog force to ensure the stability of the control system. Here, F is setrepHas a threshold value of FmaxBy setting the safety distance r ', when r is r', r is r, let Frep＝FmaxThe repulsive constant k can be reversely solved by the formula (4)rep。
Velocity-based position compensation in step S3
In the actual engineering, because a control system of the robot has a certain operation period, when the end of the robot is detected to move to the virtual boundary, the end of the robot often exceeds the virtual boundary, that is, the radius of the end of the robot is larger than Δ R (as shown in fig. 1); it is therefore necessary to compensate for this position error due to the control cycle, the current velocity of the robot tip being of the formula VoutHere by TdRepresenting the control period, the position error Δ R due to the control period can be represented as:
ΔR＝Vout·Td (5)
here by DtRepresenting the projection factor in the direction of the minimum distance from the robot end to the virtual boundary, the position error Δ R in that direction*Comprises the following steps:
ΔR*＝Dt·ΔR (6)
so that the actual distance r from the robot end to the virtual boundary*Comprises the following steps:
r*＝r-ΔR* (7)
here by r*Instead of r in equation (4), compensation for the position error is achieved.
At the same time, the introduction of the change admittance factor kτThe robot can be prevented from penetrating the virtual boundary, thereby realizing the function of a rejection type virtual boundary. Therefore, the invention provides a damping type virtual boundary based on position compensation. In this virtual boundary, the admittance factor k is here givenτIs represented as follows:
kτ＝kτ·cτ (8)
wherein c isτIntensity coefficient of admittance factor, here cτIs a function of the simulated repulsive force in the simulated force field, and is expressed as follows:
Figure BDA0002821479550000061
in the formula cb-controlling the coefficient of the damping intensity;
ca-a minimum damping intensity coefficient;
Frep-simulated repulsion in equation (4).
Therefore, in the simulated force field action region r0The closer the robot is to the virtual boundary, the greater the simulated repulsive force, and thus the intensity coefficient c of the admittance factorτThe smaller this makes the robot less capable of moving in the r direction until the end of the robot moves to the virtual boundary and the intensity coefficient reaches the minimum value ca。
And performing an experiment for the close approach of the tail end of the robot to the target point, and realizing the quick and stable movement of the tail end of the robot to the vicinity of the target point under the assistance of a virtual boundary based on position compensation, and avoiding exceeding the position of the target point.
For safety reasons and for better simulation of the actual situation of cutting the bone, the maximum feed speed V of the robot is setmax1 mm/s. Defining the initial coordinate P of the robot end in a space coordinate system0The number of the channels for (200,100) the equation for the rejection surface is z 94 in mm. In the experiment, the tail end of the robot is controlled to move from an initial position to a virtual boundary with the z being 94 according to a certain speed under the assistance of a damping type virtual boundary based on position compensation and under the assistance of no virtual boundary. Here, the experiment is carried out by using a UR5 six-axis surgical robot, and the position of the robot in the experiment is tracked and monitored in real time by using a PST device.
In the experiment, set up Fmax50N; the safe distance r' is 0.1 mm; simulating the range r of the force field0Coefficient c of damping strength controlled to 3mmb1, minimum damping strength coefficient c a0. Since the virtual boundary is z 94, only the speed in the z-axis direction needs to be limited to a certain degree, and a desired method of the robot is set in a direction perpendicular to the z-axis.
Here, 20 experiments were performed for the damping type virtual boundary assist based on the position compensation and the assist without the virtual boundary, respectively. Based on experimental data, the docking time, the docking precision, the number of penetrations, and the penetration probability are analyzed, and the obtained comparison parameters are shown in table 1.
TABLE 1 comparison of the results
Type (B) Mean time(s) Parking accuracy (mm) Number of penetrations Penetration probability
With virtual boundaries 6.6 0.0819 0 0
Without virtual boundaries 6.36 0.0579 8 40％
As can be seen from table 1, the probability of the robot end penetrating the virtual boundary is 40% in the case of no virtual boundary, and 0 in the case of a virtual boundary, so that it is safer to have a virtual boundary only from the safety viewpoint. For the average time, it takes 6.6s with the virtual boundary and 6.36s without the virtual boundary, and the difference in the required time is only 0.24 s. For the stopping progress, the precision of the virtual boundary-free process is higher, the precision is 0.579mm, but the stopping precision of the virtual boundary-free process can also meet the actual engineering requirements. By combining the experimental results, the safety performance is better when the virtual boundary exists, the difference between the average consumed time and the time without the virtual boundary is almost equal, and the parking precision is within an acceptable range, so that the virtual boundary is considered to be better.
Here, the velocity in the z-axis direction in the experiment process is analyzed, and ideal velocity change curves without a virtual boundary and with a virtual boundary are obtained respectively (as shown in fig. 2). As can be seen from fig. 2, in the absence of a virtual boundary, the speed is always constant at the beginning, and is directly reduced to 0 when the detection reaches a safe distance, and in an ideal case, the deceleration reaches infinity, which affects the stability of the whole system, and in a serious case, the system may be damaged or crashed, so that the method should be avoided. When a virtual boundary exists, the speed is decelerated from constant to slow speed, then is decelerated quickly, and finally is decelerated slowly, the speed change is relatively gentle and many, the stability of the system can be ensured to a certain extent, and the motion characteristics of the robot are met. The area enclosed by the speed curve is known as the walking distance, and obviously, the area enclosed by the speed curve is larger without a virtual boundary, which also verifies that the parking progress of the speed curve is probably higher, and also shows that the penetration probability of the speed curve is larger.
Comparing the actual curve with the ideal curve with the virtual boundary, it can be seen that the actual speed curve and the ideal speed curve are substantially coincident before 4.7 s. The ideal speed is reduced earlier than the actual curve after 4.7s, because in the actual engineering, the actual current has a delay phenomenon, and some links of the control period also occupy a part of time, and the factors cause the actual movement speed to have a hysteresis phenomenon. There is a crossing between 6s-7.2s of the actual speed and the ideal speed, in which crossing the actual speed decrease speed is greater than the ideal speed, because the magnitude of the speed is inversely proportional to the distance of movement, while the actual curve moves a greater distance and therefore its speed will be smaller, after which the actual speed decreases to 0 faster than the ideal speed. Comparing the areas enclosed by the 2 curves, it can be found that the areas have little difference, which indicates that the speed change in the actual engineering can basically meet the ideal situation.
The foregoing is only a preferred embodiment of this invention and it should be noted that modifications can be made by those skilled in the art without departing from the principle of the invention and these modifications should also be considered as the protection scope of the invention.

Claims (6)

1. A method for improving the precision and safety of bone sawing in robotic bone surgery is characterized by comprising the following steps:
step S1, setting a manual simulated attraction potential field at the target point position of the sawed bone to generate attraction, so that the attraction generates attraction on the tail end of the robot, and the tail end of the robot is guided to move to the target point, wherein the movement track is a guide type virtual boundary based on the attraction field;
step S2, adopting the FILAS function to establish an artificial simulated repulsion fieldThe repulsion force born by the robot tail end approaching the virtual boundary tends to be infinite, and in order to avoid the robot tail end from being subjected to infinite simulation repulsion force, the repulsion constant k is determinedrepIs used for limiting the maximum value of the simulated repulsive force so as to ensure the stability of the control system;
step S3, compensating the position error caused by the control period in the process of approaching the virtual boundary;
and step S4, in the process of further osteotomy of the bone saw, in the action area of the simulated force field, the closer the robot is to the virtual boundary, the larger the simulated repulsive force is, so that the moving capability of the robot in the direction to the virtual boundary is smaller until the tail end of the robot moves to the virtual boundary.
2. The method for improving bone sawing precision and safety in robotic bone surgery as claimed in claim 1, wherein the simulated gravitational potential field function U in step S1attDescribed by the following formula:
Figure FDA0002821479540000011
in the formula Katt-a gain factor;
x-position coordinates of the robot tip;
Xg-the position coordinates of the target point.
Gravitational force F generated by the gravitational fieldattNegative gradient for gravitational potential:
Figure FDA0002821479540000012
3. the method for improving the precision and safety of bone sawing in robotic bone surgery as claimed in claim 1, wherein the simulation of the repulsive force field function U2 is performed in step S2repAs shown in formula (3):
Figure FDA0002821479540000013
in the formula krep-a force constant;
r-the minimum distance of the robot end to the virtual boundary;
r0-simulating the working distance of the repulsive force field artificially;
at r0The outer region is not influenced by a repulsive force field, the repulsive force generated by the repulsive force field is a negative gradient of repulsive force potential energy, and a repulsive force function is shown as a formula (4):
Figure FDA0002821479540000021
repulsive force FrepIn the direction of UrepDirection of negative gradient of magnitude FrepCan be seen from equation (4) as the modulus at r0In the region, the larger r is, FrepThe smaller; the smaller r is, FrepThe larger; when r → 0, Frep→ infinity, the repulsive force that is experienced when the robot tip approaches the virtual boundary infinitely tends to infinity.
4. A method for robotic bone surgery to improve bone sawing accuracy and safety as claimed in claim 3 wherein k is determined in order to avoid the robot end from being subjected to infinite simulated repulsion forcesrepTo limit the maximum value of the simulated force to ensure the stability of the control system, setting FrepHas a threshold value of FmaxSetting the safety distance r ', when r is r', let Frep＝FmaxThe repulsive constant k is inversely solved by the formula (4)rep。
5. The method for improving the accuracy and safety of bone sawing in robotic bone surgery as claimed in claim 1, wherein the concrete process of compensating the position error caused by the control cycle in step S3 is: the current velocity at the end of the robot is of the formula VoutBy TdIndicating a control periodThen the position error Δ R due to the control period can be expressed as:
ΔR＝Vout·Td (5)
by DtRepresenting the projection factor in the direction of the minimum distance from the robot end to the virtual boundary, the position error Δ R in that direction*Comprises the following steps:
ΔR*＝Dt·ΔR (6)
so that the actual distance r from the robot end to the virtual boundary*Comprises the following steps:
r*＝r-ΔR* (7)
by r*Instead of r in equation (4), compensation for the position error is achieved.
6. The method for improving the precision and safety of bone sawing in robotic bone surgery as claimed in claim 1, wherein step S4 is introduced to change the admittance factor kτPreventing the robot from crossing the virtual boundary and realizing the function of a refused virtual boundary, wherein an admittance factor k is used in the virtual boundaryτIs represented as follows:
kτ＝kτ·cτ (8)
wherein c isτIntensity coefficient of admittance factor, cτIs a function of the simulated repulsive force in the simulated force field, and is expressed as follows:
Figure FDA0002821479540000031
in the formula cb-controlling the coefficient of the damping intensity;
ca-a minimum damping intensity coefficient;
Frep-simulated repulsion in equation (4);
in the region r where the simulated repulsive force acts0In the inner, the closer the robot is to the virtual boundary, the larger the simulated repulsive force is, and thus the strength of the admittance factor isCoefficient cτThe smaller this makes the robot less capable of moving in the r direction until the end of the robot moves to the virtual boundary and the intensity coefficient reaches the minimum value ca。
CN202011438434.1A 2020-12-07 2020-12-07 Method for improving bone sawing precision and safety of robotic bone surgery Withdrawn CN112603543A (en)

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Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110111880A (en) * 2019-04-22 2019-08-09 北京航空航天大学 The Artificial Potential Field paths planning method and device based on obstacle classification of flexible needle

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110111880A (en) * 2019-04-22 2019-08-09 北京航空航天大学 The Artificial Potential Field paths planning method and device based on obstacle classification of flexible needle

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* Cited by examiner, † Cited by third party
Title
朱杰宝: "基于位置补偿的阻尼型虚拟夹具算法", 《脊柱手术机器人磨削过程状态感知与安全控制》 *

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Application publication date: 20210406