技术领域technical field
本发明属于控制算法领域，涉及一种控制系统建模方法，具体是一种基于区间2型模糊逻辑控制器的柔性针靶点追踪控制方法。The invention belongs to the field of control algorithms, and relates to a control system modeling method, in particular to a flexible needle target point tracking control method based on an interval-2 type fuzzy logic controller.
背景技术Background technique
近年来，医疗机器人技术发展迅速，机器人辅助微创手术成了重点研究对象。穿刺术作为微创外科手术中的典型技术，在药物放置、组织活检、局部麻醉和近距离放射等方面有着显著作用。In recent years, medical robot technology has developed rapidly, and robot-assisted minimally invasive surgery has become a key research object. As a typical technique in minimally invasive surgery, puncture plays a significant role in drug placement, tissue biopsy, local anesthesia, and brachytherapy.
在传统的穿刺手术中，由于手术过程中受到医生情绪和经验等方面的影响，穿刺手术的效果很难保证，并且会增加手术过程中病人的痛苦。而传统的刚性针的穿刺轨迹基本为一条直线，对于较复杂的情况，如遇到器官、血管或者神经在穿刺轨迹上，难以做出有效的反应。In the traditional puncture operation, due to the influence of the doctor's emotion and experience during the operation, the effect of the puncture operation is difficult to guarantee, and it will increase the pain of the patient during the operation. However, the puncture trajectory of traditional rigid needles is basically a straight line, and it is difficult to respond effectively to more complicated situations, such as encountering organs, blood vessels or nerves on the puncture trajectory.
相比，柔性针由镍钛合金制成，弹性较好，针尖采用非对称斜面，在穿刺时受到组织施加的非均匀的力，针尖会朝着受力方向发生偏转，通过旋转柔性针控制针尖朝向来控制柔性针的偏转方向，使柔性针按照预定轨迹进行穿刺。并且柔性针的针管更加细长，可以减小手术切口，降低手术的不适感，术后恢复更快，并且降低了手术的风险。In contrast, the flexible needle is made of nickel-titanium alloy, which has better elasticity. The needle tip adopts an asymmetric slope. When the needle is subjected to a non-uniform force exerted by the tissue during puncture, the needle tip will deflect in the direction of the force, and the needle tip can be controlled by rotating the flexible needle. The orientation is used to control the deflection direction of the flexible needle, so that the flexible needle can puncture according to the predetermined trajectory. And the needle tube of the flexible needle is more slender, which can reduce the surgical incision, reduce the discomfort of the operation, recover faster after the operation, and reduce the risk of the operation.
穿刺手术是否成功主要在于是否能达到所需的穿刺精度，当穿刺精度不能满足需求时，会造成组织损伤或者放射量不够等情况，增加患者的痛苦。而由于组织的各向异性和个体差异性，在柔性针进给时无法保证转角与目标转角相同，所以在实际手术中一定会存在靶向误差。因此仅仅依靠柔性针穿刺路径规划很难实现预定的穿刺轨迹运动并到达靶点，需要针对该问题提出新的控制策略和方法。The success of puncture surgery mainly depends on whether the required puncture accuracy can be achieved. When the puncture accuracy cannot meet the requirements, it will cause tissue damage or insufficient radiation dose, which will increase the pain of the patient. However, due to tissue anisotropy and individual differences, the rotation angle cannot be guaranteed to be the same as the target rotation angle when the flexible needle is fed, so there must be targeting errors in actual surgery. Therefore, it is difficult to achieve the predetermined puncture trajectory and reach the target only by flexible needle puncture path planning, and new control strategies and methods need to be proposed for this problem.
现阶段关于柔性针模型和路径规划的研究较多，但鲜有对穿刺控制的研究。At present, there are many studies on flexible needle models and path planning, but few studies on puncture control.
发明内容Contents of the invention
为了使柔性针能够尽可能快速、准确地到达预定靶点，最终误差控制在可接受范围内；本发明提出了一种基于区间2型模糊逻辑控制器的柔性针靶点追踪控制方法，并用仿真对控制结果进行检验。In order to enable the flexible needle to reach the predetermined target as quickly and accurately as possible, the final error is controlled within an acceptable range; the present invention proposes a flexible needle target tracking control method based on interval 2 type fuzzy logic controller, and uses simulation Check the control results.
具体步骤如下：Specific steps are as follows:
步骤一、在惯性坐标系XOY下建立柔性针动力学模型，得到模型的相关参数；Step 1. Establish a flexible needle dynamics model under the inertial coordinate system XOY, and obtain relevant parameters of the model;
柔性针动力学模型对柔性针针轴与针头斜面的交点进行运动学分析；The kinematic analysis of the intersection point of the flexible needle shaft and the needle slope is carried out by the dynamic model of the flexible needle;
相关参数包括：柔性针针尖的绝对速度v，柔性针偏转角度柔性针偏转的转动角速度转角偏差和位置偏差S；The relevant parameters include: the absolute velocity v of the tip of the flexible needle, the deflection angle of the flexible needle The rotational angular velocity of flexible needle deflection Corner deviation and position deviation S;
首先，柔性针动力学模型如下：First, the flexible needle dynamics model is as follows:
是惯性坐标系XOY下x轴方向的速度，是惯性坐标系XOY下y轴方向的速度； is the velocity in the x-axis direction in the inertial coordinate system XOY, is the velocity in the y-axis direction of the inertial coordinate system XOY;
根据柔性针偏转角度计算柔性针的针偏转动角速度According to the flexible needle deflection angle Calculate needle deflection angular velocity for flexible needles
其中r为柔性针的曲率半径。where r is the radius of curvature of the flexible needle.
柔性针的转角偏差为：Rotation angle deviation of flexible needle for:
柔性针的位置偏差S根据柔性针的预定轨迹和实际轨迹进行计算：The position deviation S of the flexible needle is calculated according to the predetermined trajectory and the actual trajectory of the flexible needle:
为柔性针的预定轨迹,为柔性针的实际轨迹。 is the predetermined trajectory of the flexible needle, is the actual trajectory of the flexible needle.
步骤二、利用运动学模型的位置偏差S、位置偏差变化率转角偏差和转角偏差变化率作为区间2型模糊逻辑控制器的输入，针尖的绝对速度v和柔性针偏转的转动角速度为输出。Step 2. Using the position deviation S and position deviation change rate of the kinematic model Corner deviation and the rate of change of the corner deviation As the input of interval 2 type fuzzy logic controller, the absolute velocity v of the needle tip and the rotational angular velocity of the deflection of the flexible needle for output.
精确输入量precise input
输出量Output
步骤三、精确输入量x经过模糊化器后，模糊成用语言变量描述的2型模糊集；Step 3: After passing through the fuzzifier, the precise input quantity x is fuzzy into a type 2 fuzzy set described by linguistic variables;
2型模糊集用不确定标准差高斯隶属函数表示；Type 2 fuzzy sets are represented by Gaussian membership functions with uncertain standard deviations;
步骤四、建立IF-THEN的规则库，将2型模糊集经过规则库的推理引擎得到区间2型的输出模糊集；Step 4, establish the rule base of IF-THEN, obtain the output fuzzy set of interval type 2 through the reasoning engine of the rule base through the type 2 fuzzy set;
规则库包括绝对速度v的规则和转动角速度的规则，两者的规则条数不定；具体形式为：The rule base includes rules for absolute velocity v and rotational angular velocity The number of rules for both is variable; the specific form is:
……...
即绝对速度v的第一条规则：如果位置偏差S为零，位置偏差变化率为正值且绝对值大，则绝对速度v为负值且绝对值大；绝对值的大小范围根据人为设定。That is, the first rule of the absolute velocity v: if the position deviation S is zero, the rate of change of the position deviation is a positive value and the absolute value is large, then the absolute speed v is negative and the absolute value is large; the size range of the absolute value is set manually.
……...
转动角速度的第一条规则：如果转角偏差为正值且绝对值大，转角偏差变化率为正值且绝对值大，则偏转角度为负值且绝对值大；rotational angular velocity The first rule of : if the corner deviation is positive and the absolute value is large, the rate of change of the corner deviation is a positive value and the absolute value is large, the deflection angle is negative and has a large absolute value;
步骤五、对推理出的输出模糊集进行降型和解模糊化，得到最终的绝对速度v和柔性针偏转的转动角速度输出。Step 5: Perform down-type and defuzzification on the inferred output fuzzy set to obtain the final absolute velocity v and the rotational angular velocity of the flexible needle deflection output.
输出u1与u2的解模糊化均用面积中心法，采用两个不同的规则库。The defuzzification of output u1 and u2 both uses the center of area method and uses two different rule bases.
步骤六、将最终的绝对速度v和柔性针偏转的转动角速度作为柔性针的输入，进行柔性针的靶向追踪。Step 6. Calculate the final absolute velocity v and the rotational angular velocity of the flexible needle deflection As the input of the flexible needle, the target tracking of the flexible needle is performed.
步骤七、根据柔性针的靶向追踪得到柔性针输出的实际轨迹并计算与预定轨迹的位置偏差和角度偏差，返回步骤二，将两个偏差反馈给区间2型模糊逻辑控制器后作为输入进行控制，直至位置偏差为0或达到目标位置。Step 7. Obtain the actual trajectory output by the flexible needle according to the targeted tracking of the flexible needle And calculate the position deviation and angle deviation from the predetermined trajectory, return to step 2, and feed back the two deviations to the interval type 2 fuzzy logic controller as input for control until the position deviation is 0 or reaches the target position.
本发明的优点在于：The advantages of the present invention are:
一种基于区间2型模糊逻辑控制器的柔性针靶点追踪控制方法，利用区间2型模糊逻辑控制器进行靶点追踪控制，使用这种控制器控制由于规则库数据库均为设定好的，只需读取储存好的数据即可，所以计算量减小，计算速度加快，柔性针响应更快，并且能够对于系统的不确定性进行降低。A flexible needle target tracking control method based on an interval 2 type fuzzy logic controller, using an interval 2 type fuzzy logic controller to perform target tracking control, using this controller to control because the rule base database is all set, It only needs to read the stored data, so the calculation amount is reduced, the calculation speed is accelerated, the flexible needle responds faster, and the uncertainty of the system can be reduced.
附图说明Description of drawings
图1为本发明在惯性坐标系XOY下建立的柔性针动力学模型；Fig. 1 is the flexible needle dynamics model that the present invention establishes under the inertial coordinate system XOY;
图2为本发明一种基于区间2型模糊逻辑控制器的柔性针靶点追踪控制方法的流程图；Fig. 2 is a flow chart of a flexible needle target point tracking control method based on interval 2 type fuzzy logic controller of the present invention;
图3为本发明建立的IF-THEN的规则库；Fig. 3 is the rule base of the IF-THEN that the present invention establishes;
图4为本发明通过区间2型模糊逻辑控制器控制柔性针的靶向追踪简图；Fig. 4 is a schematic diagram of the target tracking of the flexible needle controlled by the interval type 2 fuzzy logic controller of the present invention;
图5为本发明区间2型模糊逻辑控制器的原理图。Fig. 5 is a schematic diagram of an interval 2 type fuzzy logic controller of the present invention.
具体实施方案specific implementation plan
下面将结合附图和实例对本发明作进一步的详细说明。The present invention will be further described in detail below in conjunction with accompanying drawings and examples.
本发一种基于区间2型模糊逻辑控制器的柔性针靶点追踪控制方法，如图5所示，通过建立柔性针动力学模型，利用运动学模型的参数作为区间2型模糊逻辑控制器的输入，经过模糊化器后，得到2型模糊集；建立规则库将2型模糊集经过推理引擎得到输出模糊集；进行降型和解模糊化，得到最终的绝对速度v和柔性针偏转的转动角速度输出，作为柔性针的输入，进行柔性针的靶向追踪，同时将追踪的柔性针的实际位置与期望位置的偏差，通过区间2型模糊逻辑控制器对穿刺速度和转动角度进行控制。The present invention is a flexible needle target point tracking control method based on interval 2 type fuzzy logic controller. Input, after passing through the fuzzifier, get type 2 fuzzy set; establish a rule base to pass the type 2 fuzzy set through the inference engine to get the output fuzzy set; perform de-fuzzification and de-fuzzification to get the final absolute velocity v and the rotational angular velocity of the flexible needle deflection The output is used as the input of the flexible needle to track the target of the flexible needle, and at the same time, the deviation between the actual position of the tracked flexible needle and the expected position is controlled by the interval 2 fuzzy logic controller to control the puncture speed and rotation angle.
如图2所示，具体步骤如下：As shown in Figure 2, the specific steps are as follows:
步骤一、在惯性坐标系XOY下建立柔性针动力学模型，得到模型的相关参数；Step 1. Establish a flexible needle dynamics model under the inertial coordinate system XOY, and obtain relevant parameters of the model;
如图1所示，柔性针动力学模型对柔性针针轴与针头斜面的交点进行运动学分析；As shown in Figure 1, the flexible needle dynamics model performs kinematic analysis on the intersection of the flexible needle axis and the needle slope;
相关参数包括：柔性针针尖的绝对速度v，柔性针偏转角度柔性针偏转的转动角速度转角偏差和位置偏差S；The relevant parameters include: the absolute velocity v of the tip of the flexible needle, the deflection angle of the flexible needle The rotational angular velocity of flexible needle deflection Corner deviation and position deviation S;
首先，在惯性坐标系XOY下建立柔性针模型First, the flexible needle model is established in the inertial coordinate system XOY
是惯性坐标系XOY下x轴方向的速度，是惯性坐标系XOY下y轴方向的速度； is the velocity in the x-axis direction in the inertial coordinate system XOY, is the velocity in the y-axis direction of the inertial coordinate system XOY;
求得obtain
根据柔性针偏转角度计算柔性针的针偏转动角速度According to the flexible needle deflection angle Calculate needle deflection angular velocity for flexible needles
其中r为柔性针的曲率半径。where r is the radius of curvature of the flexible needle.
柔性针的转角偏差为：Rotation angle deviation of flexible needle for:
柔性针的位置偏差S根据柔性针的预定轨迹和实际轨迹进行计算：The position deviation S of the flexible needle is calculated according to the predetermined trajectory and the actual trajectory of the flexible needle:
为柔性针的预定轨迹,为柔性针的实际轨迹。 is the predetermined trajectory of the flexible needle, is the actual trajectory of the flexible needle.
步骤二、利用运动学模型的位置偏差S、位置偏差变化率转角偏差和转角偏差变化率作为区间2型模糊逻辑控制器的输入，针尖的绝对速度v和柔性针偏转的转动角速度为输出。Step 2. Using the position deviation S and position deviation change rate of the kinematic model Corner deviation and the rate of change of the corner deviation As the input of interval 2 type fuzzy logic controller, the absolute velocity v of the needle tip and the rotational angular velocity of the deflection of the flexible needle for output.
通过区间2型模糊逻辑控制器控制柔性针的靶向追踪简图如图4所示。The schematic diagram of the target tracking of the flexible needle controlled by the interval 2 fuzzy logic controller is shown in Fig. 4 .
模糊控制器设计的基本方法是：The basic method of fuzzy controller design is:
①确定模糊控制器的输入变量与输出变量① Determine the input variables and output variables of the fuzzy controller
②设计模糊逻辑控制器的模糊规则；② Design the fuzzy rules of the fuzzy logic controller;
③进行模糊化和解模糊化操作，得到柔性针的绝对速度v和偏转的转动角速度③ Perform fuzzification and defuzzification operations to obtain the absolute velocity v of the flexible needle and the rotational angular velocity of the deflection
区间2型模糊逻辑控制器包括模糊化、规则库的推理引擎和解模糊，由于推理引擎输出为2型模糊集，所以，解模糊部分包括降型器和解模糊化器两部分。Interval type 2 fuzzy logic controller includes fuzzification, inference engine of rule base and defuzzification. Since the output of inference engine is type 2 fuzzy set, the defuzzification part includes de-fuzzifier and defuzzifier.
精确输入量precise input
输出量Output
步骤三、精确输入量x经过模糊化器后，将精确的输入模糊成可用语言变量描述的2型模糊集；Step 3: After the precise input quantity x passes through the fuzzifier, the precise input is fuzzy into a type 2 fuzzy set that can be described by language variables;
2型模糊集用不确定标准差高斯隶属函数为表示，前件隶属函数为不确定均值隶属函数，即：Gaussian membership function with uncertain standard deviation for type 2 fuzzy sets Indicates that the antecedent membership function is an uncertain mean membership function, namely:
xk：精确输入量x，k＝1,2,3,4；xk : precise input quantity x, k=1,2,3,4;
固定的平均值； Fixed average;
不确定的标准差，取值范围为 Uncertain standard deviation, the value range is
不确定的平均值，取值范围为 An indeterminate mean value in the range of
固定的标准差； fixed standard deviation;
以位置偏差S、位置偏差变化率和针尖的绝对速度v为例，进行模糊化过程为：Take position deviation S, position deviation change rate Taking the absolute velocity v of the needle tip as an example, the fuzzing process is:
其中X是一个2维笛卡尔积空间，X＝X1×X2，其中Xk是输入xk的测量域(k＝1，2)。其中由如下隶属函数表示：Where X is a 2-dimensional Cartesian product space, X=X1 ×X2 , where Xk is the measurement field of input xk (k=1, 2). in It is represented by the following membership function:
此外，also,
将这两个式子带入到中，可得：Put these two expressions into , we can get:
对应任意M个规则下的N条规则在模糊逻辑系统的触发部分，其中N≤M。所以这个输出2型模糊逻辑集的隶属函数为：N rules corresponding to any M rules are in the triggering part of the fuzzy logic system, where N≤M. So the membership function of this output type 2 fuzzy logic set is:
即完成精确输入量的模糊化。That is, the fuzzification of the precise input quantity is completed.
步骤四、建立IF-THEN的规则库，将2型模糊集经过规则库的推理引擎得到区间2型的输出模糊集；Step 4, establish the rule base of IF-THEN, obtain the output fuzzy set of interval type 2 through the reasoning engine of the rule base through the type 2 fuzzy set;
如图3所示，设定NB、NS、Z、PS、PB五个语言变量，即负大、负小、零、正小、正大五个等级。由于位置偏差始终不小于零，所以有绝对速度v的相关规则3×5＝15个和转动角速度的相关规则5×5＝25个，规则库共40个规则；具体形式为：As shown in Figure 3, set five language variables NB, NS, Z, PS, and PB, that is, five levels of negative large, negative small, zero, positive small, and positive large. Since the position deviation is always not less than zero, there are related rules of absolute velocity v 3×5=15 and rotational angular velocity 5×5=25 relevant rules, the rule base has 40 rules in total; the specific form is:
……...
即绝对速度v的第一条规则：如果位置偏差S为零，位置偏差变化率为正值且绝对值大，则绝对速度v为负值且绝对值大；绝对值的大小范围根据人为设定。That is, the first rule of the absolute velocity v: if the position deviation S is zero, the rate of change of the position deviation is a positive value and the absolute value is large, then the absolute speed v is negative and the absolute value is large; the size range of the absolute value is set manually.
……...
转动角速度的第一条规则：如果转角偏差为正值且绝对值大，转角偏差变化率为正值且绝对值大，则偏转角度为负值且绝对值大；rotational angular velocity The first rule of : if the corner deviation is positive and the absolute value is large, the rate of change of the corner deviation is a positive value and the absolute value is large, the deflection angle is negative and has a large absolute value;
以此类推，按照规则库中所给值进行计算。By analogy, the calculation is performed according to the values given in the rule base.
步骤五、对推理出的输出模糊集进行降型和解模糊化，得到最终的绝对速度v和柔性针偏转的转动角速度输出。Step 5: Perform down-type and defuzzification on the inferred output fuzzy set to obtain the final absolute velocity v and the rotational angular velocity of the flexible needle deflection output.
去模糊化一般有三种方式：面积中心法、面积等分法和极值法。本发明中输出u1与u2的解模糊化均用面积中心法，采用两个不同的规则库。There are generally three methods of defuzzification: area center method, area equal division method and extreme value method. In the present invention, the defuzzificationof output u1 and u2both uses the area center method and two different rule bases.
在对于一个区间2型模糊逻辑系统，精确的输出量就是降型后集合的中心。对于一个区间2型模糊逻辑系统，输入和前件操作的触发强度是一个区间1型模糊集，并且只取决于它的最左点fl和最右点所以输出u1∈U被表示为：In an interval type 2 fuzzy logic system, the exact output quantity is the center of the reduced set. For an interval type 2 fuzzy logic system, the triggering strength of the input and antecedent operations is an interval type 1 fuzzy set and depends only on its leftmost pointfl and rightmost point So the output u1 ∈ U is represented as:
fi：最小区间1型模糊集Fi中的元素；fi : elements in the minimum interval type 1 fuzzy set Fi ;
输出的区间2型模糊集的形心； The centroid of the output interval type 2 fuzzy set;
针尖的绝对速度v的最小值用表示，即：The minimum value of the absolute velocity v of the needle tip is used means, that is:
相似的，针尖的绝对速度v的最大值用表示，即：Similarly, the maximum value of the absolute velocity v of the needle tip is given by means, that is:
用和的平均值来表示它的解模糊结果，即输出为use and to represent its defuzzification result, that is, the output is
同理，u2即转动角速度的计算方法与u1相同。Similarly, u2 is the rotational angular velocity The calculation method of is the same as that of u1 .
步骤六、将最终的绝对速度v和柔性针偏转的转动角速度作为柔性针的输入，进行柔性针的靶向追踪。Step 6. Calculate the final absolute velocity v and the rotational angular velocity of the flexible needle deflection As the input of the flexible needle, the target tracking of the flexible needle is performed.
步骤七、根据柔性针的靶向追踪得到柔性针输出的实际轨迹并计算与预定轨迹的位置偏差和角度偏差，返回步骤二，将两个偏差反馈给区间2型模糊逻辑控制器后作为输入进行柔性针的控制，直至位置偏差为0或达到目标位置。Step 7. Obtain the actual trajectory output by the flexible needle according to the targeted tracking of the flexible needle And calculate the position deviation and angle deviation from the predetermined trajectory, return to step 2, and feed back the two deviations to the interval type 2 fuzzy logic controller as input to control the flexible needle until the position deviation is 0 or reaches the target position.
| Application Number | Priority Date | Filing Date | Title |
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| CN201910455331.7ACN110244560A (en) | 2019-05-29 | 2019-05-29 | A Tracking Control Method of Flexible Needle Target Based on Interval 2 Type Fuzzy Logic Controller |
| CN202010461438.5ACN111650831A (en) | 2019-05-29 | 2020-05-27 | Design of interval 2 fuzzy logic controller for virtual flexible needle in medical robot controller |
| Application Number | Priority Date | Filing Date | Title |
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| CN201910455331.7ACN110244560A (en) | 2019-05-29 | 2019-05-29 | A Tracking Control Method of Flexible Needle Target Based on Interval 2 Type Fuzzy Logic Controller |
| Publication Number | Publication Date |
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| CN110244560Atrue CN110244560A (en) | 2019-09-17 |
| Application Number | Title | Priority Date | Filing Date |
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| CN201910455331.7APendingCN110244560A (en) | 2019-05-29 | 2019-05-29 | A Tracking Control Method of Flexible Needle Target Based on Interval 2 Type Fuzzy Logic Controller |
| CN202010461438.5APendingCN111650831A (en) | 2019-05-29 | 2020-05-27 | Design of interval 2 fuzzy logic controller for virtual flexible needle in medical robot controller |
| Application Number | Title | Priority Date | Filing Date |
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| CN202010461438.5APendingCN111650831A (en) | 2019-05-29 | 2020-05-27 | Design of interval 2 fuzzy logic controller for virtual flexible needle in medical robot controller |
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