Fuzzy active disturbance rejection controller and method for force feedback manipulator

Abstract

The application discloses a fuzzy active disturbance rejection controller and method of a force feedback manipulator, comprising a signal input module, a tracking differentiator, a fuzzy controller, a linear extended state observer and a force feedback system, the method comprising the following steps: step one, model establishment; step two, space expression establishment; step three, signal differentiation; step four, fuzzy extension; step five, disturbance addition; and step six, output control; compared with the existing fuzzy active disturbance rejection control technology of the force feedback manipulator, the application has strong adaptability and robustness, can process uncertainty and inaccurate information without depending on a specific system model, and can perform force feedback control; the fuzzy active disturbance rejection controller can estimate and compensate total disturbance received during work of the force feedback system in real time through the extended state observer, reduce disturbance factors on the disturbance of the dynamic model, and improve the overall anti-interference ability.

Description

Technical Field

[0001] This invention relates to the field of force feedback manipulator control technology, specifically to a fuzzy active disturbance rejection controller and method for a force feedback manipulator. Background Technology

[0002] Force feedback gloves are robotic hands that most closely resemble human hands; they integrate sensors and position controllers, allowing for accurate control by an external computer or connection to your existing machine platform. They have broad application prospects in numerous fields. However, existing fuzzy active disturbance rejection (ADR) control technology for force feedback robotic hands heavily relies on system models for force feedback control, resulting in poor adaptability and robustness. Furthermore, existing fuzzy ADR control technology for force feedback robotic hands cannot compensate for interference that occurs during operation, leading to poor anti-interference capabilities. Summary of the Invention

[0003] The purpose of this invention is to provide a fuzzy active disturbance rejection controller and method for force feedback manipulators to solve the problems mentioned in the background art.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a fuzzy active disturbance rejection controller for a force feedback manipulator, comprising a signal input module, a tracking differentiator, a fuzzy controller, a linearly extended state observer, and a force feedback system. One side of the signal input module is connected to the tracking differentiator, one side of the tracking differentiator is connected to the fuzzy controller, one side of the fuzzy controller is connected to the linearly extended state observer, and the linearly extended state observer is connected to one side of the tracking differentiator. One side of the linearly extended state observer is connected to the force feedback system.

[0005] The fuzzy active disturbance rejection control method for force feedback manipulator includes the following steps: Step 1, model establishment; Step 2, spatial expression establishment; Step 3, signal differentiation; Step 4, fuzzy expansion; Step 5, disturbance input; and Step 6, output control.

[0006] In step one above, the kinematic and dynamic models of the force feedback manipulator are constructed, and the formulas are as follows:

[0007] f(t) = kx

[0008]

[0009] By combining the two equations and differentiating them separately, we can obtain the speed control quantity for the DC motor:

[0010]

[0011] The controlled object based on the second-order force feedback system is:

[0012]

[0013] The above equation can be transformed to obtain:

[0014]

[0015] In step two above, the state-space expression of the force feedback manipulator is determined, and the state variable x1 = x is taken. So remember For the expanded state variables including displacement, velocity, and disturbance, the state-space expression of the force feedback system is:

[0016]

[0017] in, C = [1 0 0];

[0018] In step three above, the signal input module obtains the displacement signal v and inputs it into the tracking differentiator. The output v1 is the transitioned signal of the input displacement signal v, and the output signal v2 is the differential signal of the displacement signal v1. The discrete formulas for the system states v1 and v2 at the output port of the tracking differentiator are as follows:

[0019]

[0020] The formula for the tracking differentiator contains a core algorithmic component: the steepest control function. The tracking differentiator is designed to track changes in the input signal quickly and smoothly using the following tracking formula:

[0021]

[0022] The tracking differentiator includes the tracking speed factor r and the filter factor h0, both of which are preset parameters;

[0023] In step four above, after tracking the differentiator transition signal, the v1 and v2 signals are subtracted from the outputs z1 and z2 of the linearly extended state observer to obtain the inputs e1 and e2 of the fuzzy controller. The fuzzy controller is implemented based on the set fuzzy rules, and the calculated output is Δk. p and Δk d Then calculate k p 'and k d ', e1 and e2 with parameter k p 'and k d u0 is obtained by calculating the PD control rate;

[0024] In step five above, the original state variable is expanded in the linear extended state observer, and the total disturbance of the sum of external disturbance and internal disturbance is transformed into a new state variable. The input signals of the linear extended state observer are b0u and y, and the outputs are z1, z2 and z3.

[0025] In step six above, the compensated control quantity u is applied to the force feedback system to achieve precise control. The formula for the compensated control quantity is:

[0026]

[0027] Preferably, in step three, the tracking differentiator mainly tracks and smoothly transitions the input displacement signal, thereby preventing oscillations and interference caused by discontinuous or random disturbances in the input control signal of the force feedback system. It extracts continuous and differentiable displacement signals to prevent overshoot caused by large initial control output of the system, thereby improving the quality of the force feedback active disturbance rejection controller. The tracking differentiator includes the tracking speed factor r and the filtering factor h0, both of which are preset parameters.

[0028] Preferably, in step four, the fuzzy controller is implemented based on the set fuzzy rules, and the output obtained after calculation is Δk. p and Δk d Then calculate k p 'and k d ',Δk p and Δk d The fuzzy rule table is an adjustable parameter.

[0029] Preferably, in step four, the core idea of ​​the linear extended state observer algorithm is to expand the original state variable, transforming the total disturbance of the sum of external disturbances and internal disturbances into a new state variable. Then, the state variable after the extension state observer includes the original state variable and the state variable observed for the disturbance. The parameters included in the linear extended state observer are ω0 and β, which are adjustable parameters.

[0030] Preferably, in step four, the fuzzy controller needs to undergo fuzzification, followed by decision-making and defuzzification based on the rule base. First, the input universes of discourse for e1 and e2 are defined, and e1 and e2 are fuzzified. The range of e1 is divided into eight equal parts, represented by seven fuzzy subsets: NB, NM, NS, ZO, PS, PM, and PB. These fuzzy subsets represent the larger negative value, the median negative value, the smaller negative value, zero, the smaller positive value, the median positive value, and the larger positive value, respectively. The interval in which e1 is located is determined, and the membership degree of e1 is calculated. For NB and PB, Z-type and S-type membership functions are selected respectively to cover the large input caused by the initial estimation error. The other membership functions use the computationally simple triangular membership functions, as follows:

[0031]

[0032]

[0033]

[0034] The fuzzification process for e2 is similar to that for e1, requiring only a change in the universe of discourse. The membership functions of the input parameters e1 and e2 for the final fuzzy controller are respectively... Figure 4 , Figure 5 Set Δk p Output universe of discourse and Δk d The output universe of discourse, based on the membership degrees of e1 and e2 and Δk p and Δk d The increment of the fuzzy rule is calculated, which is the defuzzification. The defuzzification formula is as follows:

[0035]

[0036] in, It is the precise value after the defuzzification process, where x is the value within the fuzzy control variable's domain, μ(x) is the membership degree of x, and s represents the support of μ(x). The membership function of the input variable can be used to obtain the improved linear state error feedback law parameters based on the fuzzy control algorithm.

[0037]

[0038] The output of the fuzzy active disturbance rejection controller can then be obtained from the following:

[0039]

[0040] The adjustable parameter of the above fuzzy controller is Δk p and Δk d A fuzzy rule table.

[0041] Preferably, in step five, the design process for establishing a linear extended state observer for the force feedback system is as follows:

[0042] Based on the state-space expression, the expression for the linear extended state observer assisted by the second-order force feedback system model is as follows:

[0043]

[0044] Among them, u c =[uy] T It is a combination of control variables and state output variables, y c It is the output of the linearly extended state observer. C = [1 0 0], where L is the gain matrix of the observer to be designed. To simplify the design of the linearly extended state observer, the poles of the observer's characteristic equation can be placed at the same location -w0, which yields:

[0045] λ(s)=|sI-(A-LC)|=(s+w0) 3

[0046] The gain matrix of the linearly extended state observer can be obtained as follows:

[0047] L = [l1 l2 l3] T

[0048] Expanding the above equation and comparing the coefficients, we obtain the following parameters:

[0049]

[0050] Substituting into the above equation, we obtain the following form of the linear extended state observer assisted by the second-order force feedback system model:

[0051]

[0052] y c =z

[0053] As t→∞, the observed state variables z1→x, z2→x, z3→f in the linear extended state observer form are: The discrete linear extended state observer form corresponding to the continuous linear extended state observer form is:

[0054]

[0055] Among them, u d (k)=[u(k)y(k)] T For a force feedback system, y is a combination of discrete control variables and state variables. d (k) represents the output of the discrete linear extended state observer. The discretized system matrices of the force feedback system are φ, Γ, and H, respectively, while Lc This means we need to design the state feedback gain matrix of the discrete linear extended state observer separately. Similarly, we can choose the bandwidth β of the discrete linear extended state observer such that the discrete characteristic equation satisfies:

[0056] λ(z)=|zI-(φ-φL c H)|=(z-β) 3

[0057] The linearly extended state observer includes parameters w0 and β.

[0058] Compared with the prior art, the beneficial effects of the present invention are as follows: Compared with the existing fuzzy active disturbance rejection control technology of force feedback manipulators, the present invention has strong adaptability and robustness, and can handle uncertainties and inaccurate information and perform force feedback control without relying on a specific system model; the fuzzy active disturbance rejection controller of the present invention can estimate and compensate for the total disturbance received by the force feedback system in real time by extending the state observer, reduce the interference of disturbance factors on the dynamic model, and improve the overall anti-interference ability. Attached Figure Description

[0059] Figure 1 This is a schematic diagram of the overall structure of the present invention;

[0060] Figure 2 This is a flowchart of the method of the present invention;

[0061] Figure 3 This is a simulation connection diagram of the fuzzy active disturbance rejection controller of the present invention;

[0062] Figure 4 This is the framework of the fuzzy controller system of the present invention;

[0063] Figure 5 This is the membership function of the input variable e1 in this invention;

[0064] Figure 6 This is the membership function of the input variable e2 in this invention;

[0065] Figure 7 This is the dynamic model of the force feedback manipulator control system of the present invention;

[0066] In the diagram: 1. Signal input module; 2. Tracking differentiator; 3. Fuzzy controller; 4. Linear extended state observer; 5. Force feedback system. Detailed Implementation

[0067] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0068] Please see Figure 1 The present invention provides an embodiment of a fuzzy active disturbance rejection controller for a force feedback manipulator, comprising a signal input module 1, a tracking differentiator 2, a fuzzy controller 3, a linear extended state observer 4, and a force feedback system 5. One side of the signal input module 1 is connected to the tracking differentiator 2, one side of the tracking differentiator 2 is connected to the fuzzy controller 3, one side of the fuzzy controller 3 is connected to the linear extended state observer 4, and the linear extended state observer 4 is connected to one side of the tracking differentiator 2. One side of the linear extended state observer 4 is connected to the force feedback system 5.

[0069] Please see Figure 2-7 The present invention provides an embodiment of a fuzzy active disturbance rejection control method for a force feedback manipulator, comprising the following steps: Step 1, establishing a model; Step 2, establishing a spatial expression; Step 3, signal differentiation; Step 4, fuzzy expansion; Step 5, adding disturbance quantities; and Step 6, output control.

[0070] In step one above, a theoretical model of spring tension is established:

[0071] f(t) = kx

[0072] In the formula, k is the spring constant (N / mm), and x is the slider displacement (mm). A displacement model of the motor driven by the track is established:

[0073]

[0074] In the formula, v is the spring constant (mm / s). Differentiating both sides after combining the equations yields the DC motor speed control value:

[0075]

[0076] The controlled object based on the second-order force feedback system 5 is:

[0077]

[0078] In the formula, x is the state variable, u is the control quantity, i.e., the motor output torque, and w is the disturbance of the force feedback system 5. Since the parameters c, m, k, n, and R can all be measured in practice, the parameters of the state variable and control quantity of the second-order force feedback system 5 are known, while the disturbance w is unknown. Therefore, the formula can be transformed to obtain:

[0079]

[0080] in, The total disturbance is actually unknown, and It includes the total disturbance of both unknown total disturbance and total disturbance of known model information;

[0081] In step two above, the state variable x1 = x is taken. So remember For the expanded state variables including displacement, velocity, and disturbance, the above equation transforms into a continuous state-space expression:

[0082]

[0083] in, C = [1 0 0],

[0084] Set the parameters r and h0 in the tracking differentiator 2, and the adjustable parameter Δk of the model. p and Δk d The fuzzy rule table, ω0, and β;

[0085] In step three above, signal input module 1 obtains the displacement signal v and inputs it into tracking differentiator 2. The output v1 is the transitioned signal of the input displacement signal v, and the output v2 is the differential signal of displacement signal v1. The discrete formulas for the system states v1 and v2 at the output port of tracking differentiator 2 are as follows:

[0086]

[0087] The formula for tracking differentiator 2 includes a core algorithm component, namely the steepest control function fhan(v1,v2,r,h0), which enables the entire tracking differentiator 2 to quickly and smoothly track changes in the input signal. Its tracking formula is as follows:

[0088]

[0089] The tracking differentiator 2 includes the tracking speed factor r and the filter factor h0, both of which are preset parameters;

[0090] In step four above, after tracking the transition signal of differentiator 2, the v1 and v2 signals are subtracted from the outputs z1 and z2 of the linear extended state observer 4 to obtain the inputs e1 and e2 of the fuzzy controller 3. The input universes of discourse for e1 and e2 are defined, and e1 and e2 are fuzzified. The range of e1 is divided into eight equal parts, represented by seven fuzzy subsets: NB, NM, NS, ZO, PS, PM, and PB. These fuzzy subsets represent the larger negative value, the middle negative value, the smaller negative value, zero, the smaller positive value, the middle positive value, and the larger positive value, respectively. The interval in which e1 is located is determined, and the membership degree of e1 is calculated. If e1 belongs to two membership degrees, their corresponding weighted sum needs to be calculated. For NB and PB, Z-type and S-type membership functions are selected respectively to cover the large input caused by the initial estimation error. The other membership functions use the computationally simple triangular membership functions, as follows:

[0091]

[0092]

[0093]

[0094] The fuzzification process for e2 is similar to that for e1, requiring only a change in the universe of discourse. The membership functions of the input parameters e1 and e2 of the final adjusted fuzzy controller 3 are respectively... Figure 4 , Figure 5 Set Δk p Output universe of discourse and Δk d The output universe of discourse, based on the membership degrees of e1 and e2 and Δk p and Δk d The increment of the fuzzy rule is calculated, which is the defuzzification. The defuzzification formula is as follows:

[0095]

[0096] in, It is the precise value after the defuzzification process, where x is the value within the domain of the fuzzy control quantity, μ(x) is the membership degree of x, and s represents the support of μ(x). k is then calculated. p 'and k d ', e1 and e2 with parameter k p 'and k d 'U0 is obtained through PD control law calculation. The membership function of the input variable can be used to obtain the parameters of the improved linear state error feedback law based on the fuzzy control algorithm:'

[0097]

[0098] The output of the fuzzy active disturbance rejection controller can then be obtained from the following:

[0099]

[0100] The adjustable parameter of the aforementioned fuzzy controller 3 is Δk p and Δk d Fuzzy rule table

[0101] In step five above, the original state variable is expanded in the linear extended state observer 4, transforming the total disturbance of the sum of external and internal disturbances into a new state variable. The input signals of the linear extended state observer 4 are b0u and y, and the outputs are z1, z2, and z3. The design process of establishing the linear extended state observer 4 in the force feedback system 5 is as follows:

[0102] Based on the state-space expression, the expression for the linear extended state observer 4, assisted by the second-order force feedback system model 5, is as follows:

[0103]

[0104] Among them, u c =[uy] T It is a combination of control variables and state output variables, y c This is the output of the linearly extended state observer 4. C = [1 0 0], where L is the gain matrix of the observer to be designed. To simplify the design of the linearly extended state observer 4, the poles of the observer's characteristic equation can be placed at the same location -w0, which yields:

[0105] λ(s)=|sI-(A-LC)|=(s+w0) 3

[0106] The gain matrix of the linearly extended state observer 4 can be obtained as follows:

[0107] L = [l1 l2 l3] T

[0108] Expanding the above equation and comparing the coefficients, we obtain the following parameters:

[0109]

[0110] Substituting into the above equation, we obtain the following form for the linear extended state observer 4 assisted by the model of the second-order force feedback system 5:

[0111]

[0112] y c =z

[0113] As t→∞, the observed state variable z1→x in the linearly extended state observer 4, z3→f, the discrete linear extended state observer 4 form corresponding to the continuous linear extended state observer 4 form is:

[0114]

[0115] Among them, u d (k)=[u(k) y(k)] T For a force feedback system, y is a combination of discrete control variables and state variables. d (k) represents the output of the discrete linear extended state observer 4, and the discretized system matrices of the force feedback system 5 are φ, Γ, and H, respectively, while L c This means we need to design the state feedback gain matrix of the discrete linear extended state observer 4 separately. Similarly, we can choose the bandwidth β of the discrete linear extended state observer 4 such that the discrete characteristic equation satisfies:

[0116] λ(z)=|zI-(φ-φL c H)|=(z-β) 3

[0117] The linearly extended state observer 4 includes parameters w0 and β.

[0118] In step six above, the compensated control quantity u is applied to the force feedback system 5 to achieve precise control. The formula for the compensated control quantity is:

[0119]

[0120]

[0121] Table 1 Δk p Fuzzy rules

[0122]

[0123] Table 2 Δk d Fuzzy rules

[0124] Based on the above, the advantages of this invention are that, when used, it more effectively improves the robustness and anti-interference performance of force feedback control, and can be combined with the fuzzy controller 3 to realize the online adjustment of parameters in the linear state error feedback control law of linear active disturbance rejection control, i.e., fuzzy active disturbance rejection control, for precise control of force feedback manipulators.

[0125] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A fuzzy active disturbance rejection control method for a force feedback manipulator, comprising the following steps: Step 1, establishing a model; Step 2, establishing a spatial expression; Step 3, signal differentiation; Step 4, fuzzy expansion; Step 5, adding disturbance; and Step 6, output control; characterized in that: In step one above, the kinematic and dynamic models of the force feedback manipulator are constructed, and the formulas are as follows: ， ， By combining the two equations and differentiating them separately, we can obtain the speed control quantity for the DC motor: ， The controlled object based on the second-order force feedback system (5) is: ， The above equation can be transformed to obtain: ； In step two above, the state-space expression of the force feedback manipulator is determined, and the state variables are selected. , then remember For the expanded state variables including displacement, velocity, and disturbance, the state-space expression of the force feedback system (5) is: ， in, , , , ; In step three above, the signal input module (1) obtains the displacement signal. The input is fed into the tracking differentiator (2), and the output is... It is the input displacement signal The signal after transition, The signal is a displacement signal. The differential signal tracks the system state of the output port of the differentiator (2). and The discrete formula is as follows: ， The formula for the tracking differentiator (2) contains a core algorithmic component, namely the steepest control function. This allows the entire tracking differentiator (2) to quickly and smoothly track changes in the input signal. Its tracking formula is as follows: ， The tracking differentiator (2) includes the tracking velocity factor as a parameter. and filter factor All of these are preset parameters; In step three, the tracking differentiator (2) mainly tracks and smoothly transitions the input displacement signal, thereby preventing oscillations and interference caused by discontinuous or random disturbances in the input control signal of the force feedback system (5), and extracting continuous differentiable displacement signals to prevent overshoot caused by large initial control output of the system, thereby improving the quality of the force feedback active disturbance rejection controller. In step four above, after tracking the transition signal of the differentiator (2), Signals and The signals are compared with the output of the linear extended state observer (4). and The input of the fuzzy controller (3) is obtained by subtraction. and The fuzzy controller (3) is implemented based on the set fuzzy rules, and the output obtained after calculation is: and Then calculate to get and , and With parameters and Calculated through PD control rate ; In step five above, the original state variable is expanded in the linearly extended state observer (4), transforming the total disturbance of the sum of external and internal disturbances into a new state variable. The input signal of the linearly extended state observer (4) is... and The output is , and The linearly extended state observer (4) contains the following parameters: and , and These are adjustable parameters; In step six above, the compensated control quantity The force feedback system (5) is applied to achieve precise control. The formula for the compensated control quantity is: ； The fuzzy active disturbance rejection controller of the force feedback manipulator includes a signal input module (1), a tracking differentiator (2), a fuzzy controller (3), a linear expansion state observer (4), and a force feedback system (5). The signal input module (1) is connected to the tracking differentiator (2) on one side, the tracking differentiator (2) is connected to the fuzzy controller (3) on one side, the fuzzy controller (3) is connected to the linear expansion state observer (4) on one side, and the linear expansion state observer (4) is connected to one side of the tracking differentiator (2). The linear expansion state observer (4) is connected to the force feedback system (5) on one side.

2. The fuzzy active disturbance rejection control method for a force feedback manipulator according to claim 1, characterized in that: In step four and These are the adjustable parameters of the fuzzy controller.

3. The fuzzy active disturbance rejection control method for a force feedback manipulator according to claim 1, characterized in that: In step four, the fuzzy controller (3) needs to undergo fuzzification, followed by decision-making and defuzzification based on the rule base. First, set... and The input domain of discourse, for and To blur, The range is divided into eight equal parts, represented by seven fuzzy subsets: NB, NM, NS, ZO, PS, PM, and PB. These fuzzy subsets represent the larger negative value, the median negative value, the smaller negative value, zero, the smaller positive value, the median positive value, and the larger positive value, respectively. Calculate the interval where it is located. The membership degrees are calculated, with Z-type and S-type membership functions chosen for NB and PB respectively to cover the large input caused by the initial estimation error. The other membership functions are simple triangular membership functions, as follows: ， ， ， in, For input parameters, The left endpoint of the interval The middle value of the interval. The right endpoint of the interval; The fuzzing process and Similarly, only the domain range needs to be changed to obtain the input of the adjusted fuzzy controller (3). and ,set up Output universe and The output universe of discourse, according to and Membership degree and and The increment of the fuzzy rule is calculated, which is the defuzzification. The defuzzification formula is as follows: ， in, It is the precise value after the deblurring process. The value is within the domain of the fuzzy control quantity. yes The membership value, express The support of the input variables and the membership functions of the input variables can be used to obtain the parameters of the improved linear state error feedback law based on the fuzzy control algorithm: ， The output of the fuzzy active disturbance rejection controller can then be obtained from the following: ， The adjustable parameters of the above fuzzy controller (3) are as follows: and A fuzzy rule table.

4. The fuzzy active disturbance rejection control method for a force feedback manipulator according to claim 1, characterized in that: In step five, the design process of establishing the linear expansion state observer (4) for the force feedback system (5) is as follows: Based on the state-space expression, the expression for the linear extended state observer (4) assisted by the second-order force feedback system (5) model is: ， in, It is a combination of control variables and state output variables as input. It is the output of the linearly extended state observer (4). , , , To simplify the design of the linearly extended state observer (4), the poles of the observer's characteristic equation can be placed in the same position, which is the observer gain matrix that needs to be designed. Up, that is: ， The gain matrix of the linearly extended state observer (4) can be obtained as follows: ， Expanding the above equation and comparing the coefficients, we obtain the following parameters: ， Substituting into the above equation, we obtain the following form for the linear extended state observer (4) assisted by the model of the second-order force feedback system (5): ， ， when At that time, the observed state variables in the linearly extended state observer (4) , , The discrete linear extended state observer (4) corresponding to the continuous linear extended state observer (4) is as follows: ， in, For a force feedback system (5), the combination of discrete control quantities and state variables, As the output of the discrete linear extended state observer (4), the discretized system matrices of the force feedback system (5) are respectively , , ,and This refers to the state feedback gain matrix of the discrete linear extended state observer (4) that we need to design separately. Similarly, we can take the bandwidth of the discrete linear extended state observer (4). Make the discrete characteristic equation satisfy: ， The parameters included in the linearly extended state observer (4) are: and .

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