Fast Estimation Method for Unknown Terms of Flying Robot Model Based on Fuzzy Rule Interpolation

Abstract

The present invention relates to a method for quickly estimating unknown terms of a flying robot model based on fuzzy rule interpolation. The method includes: using the input error of the flying robot as the input of a fuzzy estimator; dividing the input and output domains of the fuzzy estimator to obtain input fuzzy sets and output fuzzy sets, and giving initial fuzzy rules; designing a fuzzy estimator without interpolation function by using a product inference engine, a singleton fuzzifier, and a center-average defuzzifier in combination with the initial fuzzy rules; judging whether fuzzy rule interpolation is needed according to a threshold; if the fuzzy interpolation function is called, first determining the representative values of the reference input membership function and the output, using the interpolation method to solve for the new input membership function and output representative values, calculating the rule strength of the newly generated fuzzy rules, and judging to obtain the output weight values; designing a fuzzy rule interpolation estimator by combining the initial fuzzy rules and the newly generated fuzzy rules by interpolation. The present invention is used to realize the estimation of unknown terms in the modeling of flying robots.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicles, and particularly relates to a method for quickly estimating unknown terms of a flight robot model based on fuzzy rule interpolation. Background Art

[0002] In recent years, flight robots have attracted wide attention due to their strong mobility and high flexibility. As an innovative robot system, flight robots have shown excellent capabilities in many complex scenarios and challenging applications, such as industrial inspection, agricultural detection, security observation, search and rescue, etc. Among them, quadrotor unmanned aerial vehicles are one of the most popular representatives of flight robots, with the characteristics of strong mobility and high flexibility, and are well-known for their hovering ability, portability, and controllability. However, in the actual process, various uncertainty factors need to be considered. Because the designed unmanned aerial vehicle controller is required to have the characteristics of fast response and time-varying characteristics, various disturbances from the environment and the uncertain terms of the unmanned aerial vehicle dynamics modeling model are usually difficult to be perfectly handled. At the same time, due to the underactuated, strongly coupled, and nonlinear characteristics of quadrotor unmanned aerial vehicles, it poses a great challenge to the design of control strategies for stable motion with modeling uncertain terms. Therefore, it is necessary to design an estimator for modeling uncertain terms with good estimation performance to improve the stability of the designed unmanned aerial vehicle controller.

[0003] Many scholars have made various attempts and proposed a variety of estimation methods to improve the estimation accuracy of modeling uncertainties. The fuzzy logic method has been extended from the field of mathematics to the field of unmanned aerial vehicles (UAVs). The estimation and control strategy implemented using fuzzy rules is a representative and popular method because of its interpretable and understandable nature, which helps to establish an interpretable mapping from the physical meaning to the technical level. Only by pre-giving fuzzy rules according to the designer's experience in advance, and then designing a fuzzy system according to the fuzzy rules to solve the nonlinear problem of UAV modeling uncertainties. Its advantage is that it does not require too much prior knowledge about the details of the modeling uncertainties. It is precisely because some specific details of the modeling uncertainties are difficult to obtain in advance that the fuzzy method has a certain applicability in solving nonlinear problems in the field of UAVs. However, when the fuzzy rule base becomes large, the computational burden may increase significantly. At the same time, in the practical process, whether obtained directly from domain experts, or from historical data, or a combination of both, it is a difficult task to obtain a complete fuzzy rule database. Therefore, in order to balance reducing the computational amount in the design of the fuzzy method and reducing the number of fuzzy rules given by the designer based on experience, different researchers have proposed some theoretical methods. However, for the model uncertainties of UAVs, the fuzzy rules given by the designer based on experience are usually incomplete. Then, without increasing a large amount of computation and under the premise of incomplete and sparse fuzzy rules, can the fuzzy method still be used to estimate the UAV modeling uncertainties and improve the stability of the designed UAV control system? This is a research direction worthy of study. Summary of the Invention

[0004] The purpose of the present invention is to provide a fast estimation method for unknown terms of a flying robot model based on fuzzy rule interpolation, which can improve the estimation accuracy of unknown terms in UAV modeling, thereby improving the stability of the UAV control system.

[0005] To achieve the above object, the technical solution of the present invention is: a fast estimation method for unknown terms of a flying robot model based on fuzzy rule interpolation, comprising the following steps:

[0006] Step S1: Design a fuzzy estimator for estimating unknown terms in flying robot modeling using the fuzzy interpolation method, and use the input error e of the flying robot and as the input of the fuzzy estimator;

[0007] Step S2: Divide the universes of discourse of the input and output of the fuzzy estimator to obtain two input fuzzy sets A1, A2 and an output fuzzy set B1, and give initial fuzzy rules;

[0008] Step S3: Using a product inference engine, a singleton fuzzifier, and a center-average defuzzifier, combined with the given initial fuzzy rules, design a fuzzy estimator without interpolation function;

[0009] Step S4: Determine whether to use fuzzy rule interpolation according to the pre-designed threshold. If the membership value is greater than the threshold, use the above fuzzy estimator without interpolation function; otherwise, call the fuzzy interpolation function to further design a fuzzy rule interpolation estimator;

[0010] Step S5: If the fuzzy rule interpolation function is called, first find its representative value Rep(x) according to the triangular membership function. Then calculate the input interpolation scale factor λ Rep (x) and the output interpolation scale factor λ Rep (B). Next, according to the transformation equation composed of the input and output interpolation scale factors, the reference input membership function, and the reference output representative value, calculate the newly generated input membership function after interpolation and the corresponding new output representative value after interpolation. Finally, bring the input value into the newly generated membership function to solve the rule strength of the newly generated fuzzy rule, and determine the domain where the new output is located according to the new output representative value to obtain its weight value;

[0011] Step S6: Combine the initial fuzzy rules and the newly generated fuzzy rules by interpolation to design a fuzzy estimator with interpolation function for estimating the unknown terms in the flight robot modeling.

[0012] In an embodiment of the present invention, the specific content of the step S1 is as follows:

[0013] Define the input error as: e = χ - χ d , where χ = [x, y, z, φ, θ, ψ] T is the trajectory input of the flight robot, and are the first and second derivatives of the input χ, p = [x, y, z] T is used as the position matrix of the UAV, Φ = [φ, θ, ψ] T is the attitude angle matrix, and φ, θ, and ψ are the roll angle, pitch angle, and yaw angle respectively. χ d = [x d , y d , z d , φ d , θ d , ψ d T is the desired trajectory of the flight robot, is the first derivative of the desired trajectory.

[0014] Select the input error e, as the input of the fuzzy estimator, and define it as:​ Fuzzy estimator Designed to estimate the modeling unknowns of a flying robot.

[0015] In an embodiment of the present invention, the step S2 is specifically as follows:

[0016] Step S21: First, the inputs of the fuzzy estimator, namely the position tracking error e and the velocity tracking error of the flying robot are respectively divided into 3 universes of discourse: negative (N), zero (ZO), and positive (P), obtaining two corresponding input fuzzy sets A1 = {N, ZO, P} and A2 = {N, ZO, P}, where each input universe of discourse has a corresponding triangular membership function given by the designer.

[0017] The numerical range of the modeling unknowns of the flying robot is used as the output universe of discourse. The output universe of discourse is divided into 8 sub-output universes: negative large (N4), negative medium (N3), negative small (N2), negative zero (N1), positive zero (P1), positive small (P2), positive medium (P3), and positive large (P4), obtaining the output fuzzy set B1 = {N4, N3, N2, N1, P1, P2, P3, P4}. Each output universe of discourse has a corresponding weight value. The output fuzzy set is numerically quantified, and [-4u0, 4u0] is selected as the range of the output fuzzy set, that is, the range of the unknowns, where u0 is an unknown constant. Therefore, the output fuzzy set can be expressed as: B1 = {-4u0, -3u0, -2u0, -u0, 0, u0, 2u0, 3u0, 4u0}. The output universe of discourse N4 represents the range [-4u0, -3u0], and so on, obtaining the corresponding range for each output universe of discourse.

[0018] Step S22: The fuzzy estimator is described by the following general form of IF-THEN fuzzy rules:

[0019]

[0020] In the general form of the fuzzy rules, and represent the universes of discourse in the fuzzy sets of the inputs e and of the fuzzy estimator, where l i = 1, 2, 3, and l j = 1, 2, 3 correspond to the three universes of discourse: negative (N), zero (ZO), and positive (P) in the input fuzzy sets. is the output fuzzy set, where k = 1, 2,..., 8 corresponds to the 8 output universes of discourse in the output fuzzy set. As shown in Table 1, 9 fuzzy rules are provided, constituting the initial fuzzy rule base.

[0021] Table 1 Initial Fuzzy Rules of the Fuzzy Estimator

[0022]

[0023] In one embodiment of the present invention, step S3 is specifically as follows:

[0024] According to the 9 initial fuzzy rules given in Table 1, a product inference engine, a singleton fuzzifier, and a center-average defuzzifier are used to design a fuzzy estimator without an interpolation function, that is:

[0025]

[0026] In, γ m is a constant representing the weight value of the output universe of discourse corresponding to each fuzzy rule. and are the membership values of the inputs e, . For the sake of simplicity, the fuzzy basis function is defined as:

[0027]

[0028] where the fuzzy basis function ξ0(z) is a 9-dimensional matrix, and γ0 ∈ R 9×1 is a matrix composed of γ m .

[0029] Considering the approximation error ζ0 of the proposed fuzzy estimator without an interpolation function, the fuzzy estimator without an interpolation function can be expressed as follows:

[0030]

[0031] In one embodiment of the present invention, step S4 is specifically as follows:

[0032] Although the initial fuzzy rule base shown in Table 1 seems to cover all the input ranges of the fuzzy estimator, due to the fundamental norm of the membership function, whether an input can be matched by any rule in the rule base depends on a certain threshold, which is the condition for judging whether interpolation is needed and can be adjusted according to the actual situation.

[0033] Considering that the initial fuzzy rules given according to expert experience are incomplete and not comprehensive, a fuzzy rule interpolation method is introduced on the basis of the initial fuzzy rules to improve the estimation accuracy of the fuzzy estimator. A new fuzzy rule in this interpolation method is artificially constructed from two existing fuzzy rules. For any input of the fuzzy estimator, the membership degree can be calculated through the current membership function. If the membership value μ max is greater than the threshold, the above-mentioned fuzzy estimator without an interpolation function is adopted; if the membership degree μ maxIf it is less than an adjustable threshold value determined according to the actual situation, it means that the input is not dominated by the membership function of the current fuzzy set. Then, the fuzzy rule interpolation method generates a new membership function, a newly generated fuzzy rule, and an interpolated output fuzzy universe for this undominated input.

[0034] In an embodiment of the present invention, the step S5 is specifically as follows:

[0035] Step S51: If the fuzzy rule interpolation function is called, first, the representative value of the membership function needs to be calculated. For the convenience of discussion and simplification, a trigonometric function is selected as the membership function to obtain the value of the fuzzy membership degree. The representative value of the triangular membership function is defined as the average value of the coordinates of its three key points (a0, a1, a2), where a0 and a2 respectively represent the left intersection point and the right intersection point of the triangular membership function with the input axis, and a1 represents the value on the input axis corresponding to the vertex of the trigonometric function.

[0036] Given two reference fuzzy sets without loss of generality: A r1 Denoted as (a r10 , a r11 , a r12 ), A r2 Denoted as (a r20 , a r21 , a r22 ), the representative value of this fuzzy set is defined as follows:

[0037]

[0038] According to the membership function corresponding to each universe of discourse in the fuzzy set, the corresponding representative value of the membership function is calculated. The value input to the fuzzy estimator is defined as the representative value of the input: Rep(e) and Rep(r1) and Rep(r2) are defined as the representative values of the membership functions corresponding to the two reference fuzzy rules mentioned in the interpolation.

[0039] Step S52: Calculate the input interpolation scale ratio to construct a new intermediate fuzzy rule between two adjacent reference fuzzy rules. The input interpolation scale ratio λ Rep (e), Is:

[0040]

[0041] Define λ Rep (x) as the representative value of the interpolation scale ratio, where when x = e, λ Rep (x) = λ Rep (e); When,

[0042] When the input of the fuzzy estimator is multiple, the output interpolation scale is obtained by averaging the input interpolation scales, as shown below:

[0043]

[0044] Step S53, the conversion equation of fuzzy rule interpolation is as follows:

[0045]

[0046]

[0047] The newly generated fuzzy membership function A'=(a'0, a'1, a'2) is calculated by the conversion equation. The newly generated fuzzy membership value can be calculated by bringing the input of the fuzzy estimator into the new membership function.

[0048]

[0049] Definition b rj0 and b rj2 is the value of the left and right endpoints of the output domain interval corresponding to the reference fuzzy rule, b rj1 is the value of the midpoint, where j = 1, 2. By combining equations (9) and (10), we can find the output representative value Rep(B') after interpolation. The output interval after interpolation is determined by Rep(B'), that is, the new output domain after interpolation is determined. Since each output domain has a corresponding weight value, the output weight value of the newly generated fuzzy rule can be determined for the design of the fuzzy estimator.

[0050] According to the above steps, a new fuzzy rule can be obtained, and the total number of fuzzy rules in the fuzzy rule base is equivalently increased by one. The rule strength of the newly generated fuzzy rule and the weight of the new output domain after interpolation can also be obtained by calculating the conversion equation, and introduced into the defuzzification process when constructing the fuzzy estimator.

[0051] In one embodiment of the present invention, step S6 is specifically as follows:

[0052] Step S61: for the input variable e of the fuzzy estimator, Divide it into two fuzzy sets, where l i and l j Both represent the domain of the input fuzzy set. The input fuzzy set is as follows:

[0053]

[0054] Given the input of the fuzzy estimator Define the number of newly generated fuzzy rules after fuzzy rule interpolation as k. Fuzzy estimator with interpolation function It is designed and constructed from the 9 initial fuzzy rules shown in Table 1 and the k newly generated fuzzy rules after interpolation.

[0055] Step S62: Use a product inference engine, a singleton fuzzifier, and a center-average defuzzifier to design a fuzzy estimator with interpolation function, that is:

[0056]

[0057] a n is the rule strength of the nth fuzzy rule added after fuzzy rule interpolation, as shown. γ m is a constant representing the weight value of the output universe of discourse corresponding to each fuzzy rule.

[0058]

[0059] For the sake of simplicity, the fuzzy basis function is defined as:

[0060]

[0061] where the fuzzy basis function ξ(z) is a matrix of dimension 9 + k, and γ ∈ R 9+k is composed of γ m matrix.

[0062] Considering the approximation error ζ, the fuzzy estimator with interpolation function can be expressed as follows:

[0063]

[0064] Step S63: Because new fuzzy rules are generated during the fuzzy rule interpolation process, the fuzzy estimator with interpolation uses more fuzzy rules when constructing the estimator than the fuzzy estimator without interpolation function. Therefore, the estimation accuracy can be improved, and the fuzzy rule base can be automatically enriched.

[0065] When interpolation is not required, no new fuzzy rules are generated, and the following equation is satisfied:

[0066]

[0067] Combined with (11) and (15), it is equivalent to the fuzzy estimator without interpolation function. Therefore, the fuzzy estimator without interpolation function and the fuzzy estimator with interpolation function can be unifiedly constructed, and are collectively referred to as the fuzzy estimator.

[0068] Compared with the prior art, the present invention has the following beneficial effects: The present invention studies the problem of rapid estimation of modeling unknown terms based on the fuzzy interpolation method. First, the input error of the flying robot is used as the input of the fuzzy estimator. Considering that the fuzzy rules given by the designer according to expert experience may be incomplete and do not fully cover the input, a fuzzy rule interpolation method is proposed. Based on the incomplete and sparse fuzzy rules, and combined with the newly generated fuzzy rules by the fuzzy rule interpolation method, a fuzzy estimator is constructed to estimate the modeling unknown terms. The following gain effects are achieved compared with the prior art:

[0069] (1) A rapid estimation method for unknown terms based on fuzzy interpolation is proposed, which helps to improve the ability of sparse initial fuzzy rules that cannot fully cover the problem space by using the given input and existing initial rules.

[0070] (2) The proposed estimation method can start from limited expert experience. Although the initial fuzzy rules are small in number and sparse, new fuzzy rules are generated by interpolation to gradually enrich the fuzzy rule base, and it is also possible to achieve rapid estimation of unknown terms and improve the estimation accuracy to a certain extent. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 is a schematic diagram of the process structure of an embodiment of the present invention.

[0072] Figure 2 is a schematic diagram of the control effect of the X, Y, and Z axis components in the position controller of the flying robot according to an embodiment of the present invention.

[0073] Figure 3 is a schematic diagram of the tracking error of the X, Y, and Z axis components in the position controller of the flying robot according to an embodiment of the present invention.

[0074] Figure 4 is the roll angle in the attitude controller of the flying robot according to an embodiment of the present invention is a schematic diagram of the control effect of the pitch angle θ and yaw angle ψ.

[0075] Figure 5 is the roll angle in the attitude controller of the flying robot according to an embodiment of the present invention is a schematic diagram of the tracking error of the pitch angle θ and yaw angle ψ. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0076] The technical solution of the present invention will be specifically described below with reference to the accompanying drawings.

[0077] Please refer to Figure 1 , the present invention provides a rapid estimation method for unknown terms of a flying robot model based on fuzzy rule interpolation, including the following steps:

[0078] Step S1. Define the input error as: e = χ - χ d , where χ = [x, y, z, φ, θ, ψ] T is the trajectory input of the flying robot, and are the first and second derivatives of the input χ, p = [x, y, z] T is the position matrix of the UAV, Φ = [φ, θ, ψ] T is the attitude angle matrix, and φ, θ, ψ are the roll angle, pitch angle, and yaw angle respectively. χ d = [x d , y d , z d , φ d , θ d , ψ d T is the desired trajectory of the flying robot, is the first derivative of the desired trajectory.

[0079] Select the input error e, as the input of the fuzzy estimator, and define it as: Fuzzy estimator is designed to estimate the unknown terms in the modeling of the flying robot.

[0080] Step S2. Divide the input and output of the fuzzy estimator into universes of discourse, obtain two input fuzzy sets A1, A2 and one output fuzzy set B1, and give the initial fuzzy rules; specifically as follows:

[0081] Step S21. First, divide the input of the fuzzy estimator, i.e., the position tracking error e and the velocity tracking error of the flying robot, into 3 universes of discourse of negative (N), zero (ZO), and positive (P) respectively, to obtain two corresponding input fuzzy sets A1 = {N, ZO, P} and A2 = {N, ZO, P}, where each input universe of discourse has a corresponding triangular membership function given by the designer.

[0082] ​Take the numerical range of the unknown terms in the flight robot model as the output universe of discourse. Divide the output universe of discourse into 8 sub-output universes: negative large (N4), negative medium (N3), negative small (N2), negative zero (N1), positive zero (P1), positive small (P2), positive medium (P3), and positive large (P4), to obtain the output fuzzy set B1 = {N4, N3, N2, N1, P1, P2, P3, P4}. Each output universe of discourse has a corresponding weight value. Numerically represent the output fuzzy set, and select [-4u0, 4u0] as the range of the output fuzzy set, that is, the range of the unknown terms, where u0 is an unknown constant. Therefore, the output fuzzy set can be expressed as: B1 = {-4u0, -3u0, -2u0, -u0, 0, u0, 2u0, 3u0, 4u0}. The output universe of discourse N4 represents the range [-4u0, -3u0], and so on, to obtain the corresponding ranges for each output universe of discourse.

[0083] Step S22: The fuzzy estimator is described by the following general form of IF-THEN fuzzy rules:

[0084]

[0085] In the general form of the fuzzy rules, and represent the universes of discourse in the fuzzy sets of the inputs e and to the fuzzy estimator, where l i = 1, 2, 3, and l j = 1, 2, 3 correspond to the three universes of discourse: negative (N), zero (ZO), and positive (P) in the input fuzzy sets. is the output fuzzy set, where k = 1, 2,..., 8 corresponds to the 8 output universes of discourse in the output fuzzy set. As shown in Table 1, 9 fuzzy rules are provided, which constitute the initial fuzzy rule base.

[0086] Table 1 Initial Fuzzy Rules of the Fuzzy Estimator

[0087]

[0088] Step S3: Adopt a product inference engine, a singleton fuzzifier, and a center-average defuzzifier, and combine the given initial fuzzy rules to design a fuzzy estimator without interpolation function; specifically as follows:

[0089] According to the 9 initial fuzzy rules given in Table 1, use a product inference engine, a singleton fuzzifier, and a center-average defuzzifier to design a fuzzy estimator without interpolation function That is:

[0090]

[0091] In, γ mis a constant representing the weight value of the output universe of discourse corresponding to each fuzzy rule. and are the membership degree values of the input e, . For the sake of simplicity, the fuzzy basis function is defined as:

[0092]

[0093] where the fuzzy basis function ξ0(z) is a 9-dimensional matrix;

[0094] Considering the approximation error ζ0 of the proposed fuzzy estimator without interpolation function, the fuzzy estimator without interpolation function can be expressed as follows:

[0095]

[0096] where γ0 ∈ R 9×1 is a matrix composed of γ m .

[0097] Step S4: Determine whether to use fuzzy rule interpolation according to the pre-designed threshold. If the membership degree value is greater than the threshold, use the above-mentioned fuzzy estimator without interpolation function; otherwise, call the fuzzy interpolation function to further design the fuzzy rule interpolation estimator; specifically as follows:

[0098] Although the initial fuzzy rule base shown in Table 1 seems to cover all input ranges of the fuzzy estimator, due to the fundamental specification of the membership function, whether an input can be matched by any rule in the rule base depends on a certain threshold, which is the condition for judging whether interpolation is needed and can be adjusted according to the actual situation.

[0099] Considering that the initial fuzzy rules given according to expert experience are incomplete and not comprehensive, on the basis of the initial fuzzy rules, a fuzzy rule interpolation method is introduced to improve the estimation accuracy of the fuzzy estimator. A new fuzzy rule in this interpolation method is artificially constructed from two existing fuzzy rules. For any input of the fuzzy estimator, the size of the membership degree can be calculated through the current membership function. If the membership degree value μ max is greater than the threshold, use the above-mentioned fuzzy estimator without interpolation function; if the size of the membership degree μ max is less than the adjustable threshold predetermined according to the actual situation, it means that this input is not dominated by the membership function of the current fuzzy set. Then the fuzzy rule interpolation method generates a new membership function, a newly generated fuzzy rule and the interpolated output universe of discourse for this undominated input.

[0100] Step S5: If the fuzzy rule interpolation function is called, first determine the representative values of the reference input membership function and the output, then use the interpolation method to solve for the new input membership function and the output representative values, and finally calculate the rule strength of the newly generated fuzzy rule and determine the output weight value; specifically as follows:

[0101] Step S51: If the fuzzy rule interpolation function is called, first calculate the representative value of the membership function. For the convenience of discussion and simplification, the trigonometric function is selected as the membership function to obtain the value of the fuzzy membership degree. The representative value of the triangular membership function is defined as the average of the coordinates of its three key points (a0, a1, a2), where a0 and a2 respectively represent the left and right intersections of the triangular membership function with the input axis, and a1 represents the value on the input axis corresponding to the vertex of the trigonometric function.

[0102] Given two reference fuzzy sets without loss of generality: A r1 Denoted as (a r10 , a r11 , a r12 ), A r2 Denoted as (a r20 , a r21 , a r22 ), the representative value of this fuzzy set is defined as follows:

[0103]

[0104] According to the membership function corresponding to each domain in the fuzzy set, the corresponding representative value of the membership function is calculated. The value input to the fuzzy estimator is defined as the representative value of the input: Rep(e) and Rep(r1) and Rep(r2) are defined as the representative values of the membership functions corresponding to the two reference fuzzy rules mentioned in the interpolation.

[0105] Step S52: Calculate the input interpolation scale ratio to construct a new intermediate fuzzy rule between two adjacent reference fuzzy rules. The input interpolation scale ratio λ Rep (e), is:

[0106]

[0107] Define λ Rep (x) as the representative value of the interpolation scale ratio, where when x = e, λ Rep (x) = λ Rep (e); When

[0108] When the input of the fuzzy estimator is multi-input, the output interpolation scale ratio is obtained by averaging the input interpolation scale ratios, as shown below:

[0109]

[0110] Step S53: The transformation equation for fuzzy rule interpolation is as follows:

[0111]

[0112]

[0113] The newly generated fuzzy membership function A'=(a'0,a'1,a'2) is calculated by the transformation equation. Substituting the input of the fuzzy estimator into the new membership function can calculate the newly generated fuzzy membership degree value.

[0114]

[0115] Define b rj0 and b rj2 as the left and right endpoint values of the output universe interval corresponding to the reference fuzzy rule, and b rj1 as the value of the midpoint, where j = 1, 2. By combining equations (9) and (10), the representative value Rep(B') of the interpolated output can be obtained. The interpolated output interval is judged by Rep(B'), that is, the new output universe after interpolation is judged. Since each output universe has a corresponding weight value, the weight value of the newly generated fuzzy rule output can be determined for designing the fuzzy estimator.

[0116] As described above, a new fuzzy rule can be obtained, and the total number of fuzzy rules in the fuzzy rule base is equivalently increased by one. The rule strength of the newly generated fuzzy rule and the weight of the new output domain after interpolation can also be calculated by the transformation equation and introduced into the defuzzification process when constructing the fuzzy estimator.

[0117] Step S6. Combine the initial fuzzy rules and the newly generated fuzzy rules by interpolation to design a fuzzy estimator with interpolation function for estimating the unknown terms in the flight robot modeling; specifically as follows:

[0118] Step S61. For the input variable e of the fuzzy estimator, divide it into two fuzzy sets, where l i and l j both represent the universe of the input fuzzy set. The input fuzzy sets are as follows:

[0119]

[0120] Given the input of the fuzzy estimator Define the number of newly generated fuzzy rules after fuzzy rule interpolation as k. The fuzzy estimator with interpolation function Constructed by designing and building with the 9 initial fuzzy rules shown in Table 1 and the k newly generated fuzzy rules after interpolation.

[0121] Step S62: Use a product inference engine, a singleton fuzzifier, and a center-average defuzzifier to design a fuzzy estimator with interpolation function, that is:

[0122]

[0123] a n is the rule strength of the nth fuzzy rule added after fuzzy rule interpolation, as shown. γ m is a constant representing the weight value of the output universe of discourse corresponding to each fuzzy rule.

[0124]

[0125] For the sake of simplicity, the fuzzy basis function is defined as:

[0126]

[0127] where the fuzzy basis function ξ(z) is a matrix of dimension 9 + k, and γ ∈ R 9+k is the matrix composed of γ m components.

[0128] Considering the approximation error ζ, the fuzzy estimator with interpolation function can be represented as follows:

[0129]

[0130] Step S63: Because new fuzzy rules are generated during the fuzzy rule interpolation process, the fuzzy estimator with interpolation uses more fuzzy rules when constructing the estimator compared to the fuzzy estimator without interpolation function. Therefore, the estimation accuracy can be improved, and the fuzzy rule base can be automatically enriched.

[0131] When interpolation is not required, no new fuzzy rules are generated, and the following equation is satisfied:

[0132]

[0133] Combining (11) and (15), it is equivalent to the fuzzy estimator without interpolation function. Therefore, the fuzzy estimator without interpolation function and the fuzzy estimator with interpolation function can be unifiedly constructed and are collectively referred to as the fuzzy estimator.

[0134] In this embodiment, referring to Figures 2 - 5, a specific application example is used to illustrate the operation of the present invention in detail. According to the fast estimation method based on fuzzy rule interpolation proposed by the present invention, it mainly studies the control tracking effect of a flying robot during flight by using a fuzzy estimator based on the fuzzy rule interpolation method considering the influence of unknown terms in the flying robot modeling. The specific settings are as follows:

[0135] 1) The flying robot controller adopts an adaptive sliding mode controller, considering the influence of the dynamic model modeling error and external disturbances on the flying robot.

[0136] 2) The system parameters of the flying robot are shown in Table 2:

[0137] Table 2 Flying robot system parameters

[0138]

[0139] 3) Trigonometric functions are selected as the membership functions for designing the fuzzy estimator. Among them, the representative values of the membership functions for position control are: A 1N =(-1.5, -1, -0.3), A 1ZO =(-0.55, -0.05, 0.65), A 1P =(0.5, 1, 1.7), A 2N =(-7.5, -5, -1.5), A 2ZO =(-2.75, -0.25, 3.25), A 2P =(2.5, 5, 8.5); the representative values of the membership functions for attitude control are: A 1N =(-0.75π, -0.5π, -0.1π), A 1ZO =(-0.3π, -0.05π, 0.35π), A 1P =(0.25π, 0.5π, 0.9π), A 2N =(-1.5π, -π, -0.2π), A 2ZO =(-0.6π, -0.1π, 0.7π), A 2P =(0.5π, π, 1.8π).

[0140] As Figures 2 - 5 shown, the fuzzy estimator further designed according to the estimation method of this embodiment is applied to the design of the flying robot controller, which can enable the flying robot to track the target trajectory under disturbances in terms of position and attitude, and then enable the flying robot to move with a small steady-state error. With small error fluctuations and short response time, the proposed estimation method is considered good and has a high estimation accuracy. Figures 2 - 5 It proves the effectiveness and superiority of the present invention.

[0141] The above are the preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention in terms of the functions and effects produced shall fall within the protection scope of the present invention.

Claims

1. A method for quickly estimating unknown terms of a flying robot model based on fuzzy rule interpolation, characterized in that It includes the following steps: Step S1. Take the input error e of the flying robot and as the input of the fuzzy estimator; Step S2: Divide the universe of discourse of the input and output of the fuzzy estimator to obtain an input fuzzy set A1, an output fuzzy set A2, and an output fuzzy set B1, and give initial fuzzy rules; Step S3: Adopt a product inference engine, a singleton fuzzifier, and a center-average defuzzifier, and combine with the given initial fuzzy rules to design a fuzzy estimator without interpolation function; Step S4: Determine whether fuzzy rule interpolation needs to be adopted according to the pre-designed threshold. If the membership value is greater than the threshold, adopt a fuzzy estimator without interpolation function; otherwise, call the fuzzy rule interpolation function; Step S5: If the fuzzy rule interpolation function is called, first determine the representative values of the reference input membership function and the output, then use the interpolation method to solve the new input membership function and the output representative values, and finally calculate the rule strength of the newly generated fuzzy rules and judge to obtain the output weight value; Step S6: Combine the initial fuzzy rules and the newly generated fuzzy rules to design a fuzzy rule interpolation estimator with fuzzy interpolation function to realize the estimation of the unknown items in the flight robot modeling; The specific content of step S4 is as follows: Based on the initial fuzzy rules, a fuzzy rule interpolation method is introduced; for any input of the fuzzy estimator, the membership degree is calculated through the current membership function; if the membership degree value μ max is greater than the threshold, a fuzzy estimator without interpolation function is adopted; if the membership degree μ max is less than the predetermined adjustable threshold, it means that this input is not dominated by the membership function of the current fuzzy set, and then a new membership function, a newly generated fuzzy rule and the interpolated output fuzzy universe are generated for this undominated input through the introduced fuzzy rule interpolation method. The specific content of step S5 is as follows: Step S51: If the fuzzy rule interpolation function is called, first select a trigonometric function as the membership function to obtain the value of the fuzzy membership degree; the representative value of the triangular membership function is defined as the average value of the coordinates of three key points (a0, a1, a2), where a0 and a2 respectively represent the left and right intersections of the triangular membership function with the input axis, and a1 represents the value on the input axis corresponding to the vertex of the trigonometric function; Given two reference fuzzy sets without loss of generality: A r1 Denoted as (a r10 , a r11 , a r12 ), A r2 Denoted as (a r20 , a r21 , a r22 ), the representative value of this fuzzy set is defined as follows: According to the membership function corresponding to each universe of discourse in the fuzzy set, the representative value of the corresponding membership function is calculated by (5); the values input to the fuzzy estimator are defined as the representative values of the inputs: Rep(e) and Rep(r1) and Rep(r2) are defined as the representative values of the membership functions corresponding to the two reference fuzzy rules mentioned in the interpolation; Step S52: Calculate the input interpolation scale ratio according to (6) to construct new intermediate fuzzy rules between two adjacent reference fuzzy rules, and the input interpolation scale ratio is λ Rep (e), is as follows: Define λ Rep (x) is the representative value of the interpolation scale, where when x = e, λ Rep (x) = λ Rep (e); When When the input of the fuzzy estimator is multi-input, the output interpolation scale is obtained by averaging the input interpolation scales, as follows: The conversion equation of fuzzy rule interpolation is as follows: The newly generated fuzzy membership function A'=(a'0, a1', a'2) is calculated by the conversion equation (8), and the input of the fuzzy estimator is brought into the new membership function to calculate the newly generated fuzzy membership degree value; Define b rj0 and b rj2 are the values of the left and right endpoints of the output universe interval corresponding to the reference fuzzy rule, and b rj1 is the value of the midpoint, where j = 1, 2; By combining equations (9) and (10), the representative value Rep(B') of the interpolated output is obtained; The interpolated output interval is judged by Rep(B'), that is, the new output universe after interpolation is judged; Since each output universe has a corresponding weight value, the size of the output weight value of the newly generated fuzzy rule is determined for the design of the fuzzy estimator; Through the above steps, a new fuzzy rule is obtained, and the total number of fuzzy rules in the fuzzy rule base is equivalently increased by one; it is also possible to calculate the rule strength of the newly generated fuzzy rules and the weight of the new output domain after interpolation through the conversion equation and introduce them into the defuzzification process when constructing the fuzzy estimator.

2. The rapid estimation method for unknown terms of a flying robot model based on fuzzy rule interpolation according to claim 1, characterized in that The specific content of step S1 is as follows: Define the input error as: the position tracking error \(e = \chi-\hat{\chi}\) d , the velocity tracking error where \(\chi = [x,y,z,\varphi,\theta,\psi]\) T is the trajectory input of the flying robot, and are the first and second derivatives of the input \(\chi\), \(p = [x,y,z]\) T serves as the position matrix of the UAV, \(\varPhi = [\varphi,\theta,\psi]\) T is the attitude angle matrix, \(\varphi\), \(\theta\), \(\psi\) are the roll angle, pitch angle and yaw angle respectively, \(\hat{\chi}\) d = [x d ,y d ,z d ,\varphi d ,\theta d ,\psi d T is the desired trajectory of the flying robot, is the first derivative of the desired trajectory;​ Select the input error as the input of the fuzzy estimator, which is defined as: Fuzzy estimator is designed to estimate the modeling unknown terms of the flying robot.

3. The method for quickly estimating unknown terms of a flying robot model based on fuzzy rule interpolation according to claim 2, characterized in that The specific content of step S2 is as follows: Step S21: First, the inputs of the fuzzy estimator, namely the position tracking error e and the velocity tracking error of the flying robot, are respectively divided into three universes of discourse: negative N, zero ZO, and positive P, to obtain two corresponding input fuzzy sets A1 = {N, ZO, P} and A2 = {N, ZO, P}, where each input universe of discourse has a corresponding triangular membership function. Take the numerical range of the modeling unknowns of the flying robot as the output universe of discourse. Divide the output universe of discourse into 8 sub-output universes, namely Negative Large N4, Negative Medium N3, Negative Small N2, Negative Zero N1, Positive Zero P1, Positive Small P2, Positive Medium P3, and Positive Large P4, to obtain the output fuzzy set B1 = {N4, N3, N2, N1, P1, P2, P3, P4}. Each output universe of discourse has a corresponding weight size. Numerically represent the output fuzzy set, and select [-4u0, 4u0] as the range of the output fuzzy set, that is, the range of the unknowns, where u0 is an unknown constant. The output fuzzy set is expressed as: B1 = {-4u0, -3u0, -2u0, -u0, 0, u0, 2u0, 3u0, 4u0}. The output universe of discourse N4 represents the range [-4u0, -3u0], and so on, to obtain the corresponding range of each output universe of discourse. Step S22: The fuzzy estimator is described by the following general form of IF-THEN fuzzy rules: In the general form of the fuzzy rule (1), and represent the universes of discourse in the fuzzy sets of the fuzzy estimator inputs e and , where l i = 1, 2, 3, and l j = 1, 2, 3 correspond to the three universes of discourse of negative N, zero ZO, and positive P in the input fuzzy sets; is the output fuzzy set, where k = 1, 2,..., 8 correspond to the 8 output universes of discourse in the output fuzzy set; and the following 9 fuzzy rules are provided: Rule 1: When the input is N and e is N, the output is P4; Rule 2: When the input is N and e is ZO, the output is P1; Rule 3: When the input is N and e is P, the output is N1; Rule 4: When the input is ZO and e is N, the output is P2; Rule 5: When the input is ZO and e is ZO, the output is N1; Rule 6: When the input is ZO and e is P, the output is N2; Rule 7: When the input is P and e is N, the output is P3; Rule 8: When the input is P and e is ZO, the output is N2; Rule 9: When the input is P and e is P, the output is N4; Based on the above 9 fuzzy rules, an initial fuzzy rule base is constructed.

4. The method for quickly estimating unknown terms of a flying robot model based on fuzzy rule interpolation according to claim 3, characterized in that The specific content of step S3 is as follows: According to the given nine initial fuzzy rules, a fuzzy estimator without interpolation function is designed by using a product inference engine, a singleton fuzzifier, and a center-average defuzzifier. That is: Among them, γ m is a constant representing the weight value of the output universe of discourse corresponding to each fuzzy rule; and are the membership degree values of the inputs e, ; the fuzzy basis function is defined as: Among them, the fuzzy basis function ξ0(z) is a 9-dimensional matrix. Consider the approximation error ζ0 of the fuzzy estimator without interpolation function. The fuzzy estimator without interpolation function is expressed as follows: where Υ0∈R 9×1 is a matrix composed of γ m ​ 5. The method for quickly estimating unknown terms of a flying robot model based on fuzzy rule interpolation according to claim 4, characterized in that, The specific content of step S6 is as follows: Step S61: For the input variables of the fuzzy estimator Divide them into two fuzzy sets, where l i and l j both represent the universe of discourse of the input fuzzy sets; the input fuzzy sets are as follows: Input of a given fuzzy estimator Define the number of newly generated fuzzy rules after fuzzy rule interpolation as k; a fuzzy estimator with interpolation function Designed and constructed from the initial fuzzy rules and the newly generated k fuzzy rules Step S62: Adopt a product inference engine, a singleton fuzzifier, and a center-average defuzzifier to design a fuzzy estimator with interpolation function, that is: a n is the rule strength of the nth fuzzy rule added after fuzzy rule interpolation, γ m is a constant representing the weight value of the output universe of discourse corresponding to each fuzzy rule; The fuzzy basis function is defined as: Among them, the fuzzy basis function ξ(z) is a (9 + k)-dimensional matrix. Consider the approximation error ζ. The fuzzy estimator with interpolation function is expressed as follows: where Υ ∈ R 9+k is a matrix composed of γ m ; Step S63: When interpolation is not required, no new fuzzy rules are generated, and the following equation is satisfied: Combining (11) and (15) is equivalent to the fuzzy estimator without interpolation function. Therefore, the fuzzy estimator without interpolation function and the fuzzy estimator with interpolation function are uniformly constructed by (11) and are collectively referred to as the fuzzy estimator.

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