An interval estimation method and system based on observer and reachability analysis

Abstract

The present invention relates to an interval estimation method and system based on an observer and reachability analysis. The present application models an omnidirectional Mecanum wheel automatic guided vehicle and constructs a discrete time nonlinear system to solve the problem that the modeling of the system in the prior art is not practical. On this basis, a novel interval estimation method is proposed, which is to design a T-N-L structure observer and adopt H ∞ The technology attenuates interference, and finally uses reachability analysis to determine the range of motion state of the omnidirectional Mecanum wheel automatic guided vehicle. The application not only improves the accuracy of displacement and speed range estimation of the omnidirectional Mecanum wheel automatic guided vehicle, but also reduces the conservatism of observer design.

Description

Technical Field

[0001] The present invention relates to the field of computer control technology, and in particular to an interval estimation method and system based on observer and reachability analysis. Background Art

[0002] An automatic guided vehicle (AGV) is an unmanned mobile platform with safety protection and various transfer functions. It is equipped with electromagnetic, visual or laser automatic guidance devices to achieve travel along a predetermined track. As an intelligent mobile platform, AGV is widely used in various industries due to its flexible and efficient operation mode and highly intelligent and flexible characteristics.

[0003] Most of the AGVs on the market today are based on non-omnidirectional mobile platforms. As the application industry continues to expand and the level of intelligence continues to improve, higher requirements are placed on the performance and application scope of AGVs, and omnidirectional mobile platform AGVs with integrity constraints have emerged. Compared with ordinary wheeled AGVs, AGVs based on Mecanum wheel mobile platforms are free from the limitations of turning radius, can rotate in place and move omnidirectionally within a certain space, and can adjust their posture in a timely and effective manner when facing obstacles. They have stronger mobility and adaptability in complex indoor environments, narrow passages or workshops. In recent years, researchers have introduced various state estimation methods for AGVs to improve their navigation and control performance, in order to better handle uncertainty, interference, noise, and attacks.

[0004] However, there are still some problems in the current related research. In terms of modeling methods, since the Mecanum wheel AGV may experience various situations such as slip, friction, load changes and external disturbances during movement, a suitable modeling method is needed to fit the reality. Moreover, linear or nonlinear continuous systems are not applicable to reality. The data of omnidirectional AGV in real life is discrete, and linear modeling ignores the influence of factors such as friction, load changes, external disturbances and measurement noise. Modeling also inevitably has model uncertainty, so it is necessary to improve the accuracy of modeling. However, most modeling in the existing technology only considers the influence of one aspect and ignores other aspects. Although some studies have considered multiple situations, they treat nonlinear terms as disturbances when observing and controlling them. In terms of research issues, most researchers focus on trajectory tracking and path planning of omnidirectional AGVs, and use the Romberg observer for state feedback. In fact, this is all based on a relatively accurate model. For nonlinear discrete AGV models with interference, more attention should be paid to how to estimate the unmeasurable state of the omnidirectional AGV and improve its estimation accuracy. Instead of considering the problem in a general model, various complex application scenarios, such as the measurement noise of the positioning system when the omnidirectional AGV is moving on roads with different friction coefficients, will cause its state to change, and there may be external interference factors. In addition, the Lumberg observer has nonlinear terms, external disturbances, uncertain terms and measurement noise. In reality, it is difficult for these Lumberg-like observers to ensure that they can maintain ideal estimation accuracy and robustness. Summary of the invention

[0005] To this end, the technical problem to be solved by the present invention is to overcome the problem that the modeling in the prior art is not in line with reality, there are model inaccuracies, and it is difficult for the observer to ensure that the ideal estimation accuracy and robustness can be maintained. In order to solve the above technical problems, the present invention provides an interval estimation method and system based on an observer and reachability analysis, and considers load changes, sliding friction, viscous friction, slip and external disturbance factors to model the omnidirectional Mecanum wheel automatic guided vehicle, overcome the shortcomings of the model not being in line with reality, and the proposed interval estimation method has unique advantages in processing systems with disturbances, uncertainties, and measurement noise, and is more robust than traditional estimation methods, which not only improves the accuracy of displacement and velocity interval estimation of the omnidirectional Mecanum wheel automatic guided vehicle, but also reduces the conservatism of the observer design.

[0006] In order to achieve the above object, the main technical solutions adopted by the present invention include:

[0007] In a first aspect, the present invention provides an interval estimation method based on an observer and reachability analysis, comprising: obtaining parameters of an omnidirectional Mecanum wheel automatic guided vehicle; constructing a discrete time nonlinear system of the omnidirectional Mecanum wheel automatic guided vehicle according to the parameters; and obtaining an H of a TNL structure by processing nonlinear terms according to the discrete time nonlinear system. ∞ observer; obtaining an error dynamic system according to the discrete-time nonlinear system and the observer, and determining a gain matrix of the observer; performing a reachability analysis on the error dynamic system according to the gain matrix of the observer to perform an interval estimation on the state of the omnidirectional Mecanum wheel automatic guided vehicle, and obtaining an interval of the state of the omnidirectional Mecanum wheel automatic guided vehicle.

[0008] In one embodiment of the present invention, the specific steps of constructing the discrete-time nonlinear system of the omnidirectional Mecanum wheel automatic guided vehicle according to the parameters include: establishing a kinematic model of the omnidirectional Mecanum wheel automatic guided vehicle and a dynamic model of the omnidirectional Mecanum wheel automatic guided vehicle according to the parameters; obtaining the dynamic system of the omnidirectional Mecanum wheel automatic guided vehicle according to the kinematic model and the dynamic model; and discretizing the state space equations of the dynamic system to obtain a discrete-time nonlinear system.

[0009] In one embodiment of the present invention, the kinematic model is expressed as:

[0010]

[0011] in, is the angular velocity of the bth wheel in the omnidirectional Mecanum wheel automatic guided vehicle, R is the wheel radius of the omnidirectional Mecanum wheel automatic guided vehicle, X r O r Y r is a relative coordinate system, ψ is a rotation angle relative to the relative coordinate system;

[0012] d1 is the width of the omnidirectional Mecanum wheel automatic guided vehicle d2 is the length of the omnidirectional Mecanum wheel automatic guided vehicle

[0013] The kinetic model is expressed as:

[0014]

[0015] in, τ=[τ1 τ2 τ3 τ4] T , τ b(b=1, 2, 3, 4) is the torque generated by the ath motor in the omnidirectional Mecanum wheel automatic guided vehicle; τ d is an unknown bounded disturbance, ΔM, ΔF is an uncertain term; represents the second-order derivative of the rotation angle with respect to time; (b=1, 2, 3, 4) is the static friction force of the bth wheel in the omnidirectional Mecanum wheel automatic guided vehicle;

[0016]

[0017] J ω is the moment of inertia of the Mecanum wheel of the omnidirectional Mecanum wheel automated guided vehicle around the central axis, is the viscous friction coefficient, J Z is the moment of inertia of the omnidirectional Mecanum wheel automated guided vehicle about its center of rotation, and m is the total mass of the omnidirectional Mecanum wheel automated guided vehicle.

[0018] In one embodiment of the present invention, the dynamic system is expressed as:

[0019]

[0020]

[0021] Where z1 = [x q y q ψ] T , X q O q Y q is the inertial coordinate system, for The pseudo-reversal,

[0022]

[0023]

[0024]

[0025] The discrete-time nonlinear system is expressed as:

[0026] z k+1 =Az k +Bτ k +f k +D w w k

[0027] y k =Czk +D v v k

[0028] Where, k represents the kh moment; h is the sampling period; τ k is the torque generated at time k, y k is the output, f k =-h[0f(z k ) T ] T is a nonlinear term, w k is the lumped disturbance, v k To measure noise, A, C, D w , D v are all constant matrices.

[0029] In one embodiment of the present invention, the observer is expressed as:

[0030]

[0031] Among them, δ k is the intermediate variable, For z k The estimate of I n (n=3, 6, 9) represents the n-dimensional identity matrix, T+NC=I6, is an arbitrary matrix, represents n'-dimensional Euclidean space, is the pseudo-inverse of Γ.

[0032] In one embodiment of the present invention, the specific steps of obtaining the error dynamic system according to the discrete-time nonlinear system and the observer include:

[0033] definition

[0034] An initial error dynamic equation is obtained according to the discrete-time nonlinear system and the observer; the initial error dynamic equation is expressed as:

[0035] e k+1 =(TA-LC)e k +TΔf k +F m β

[0036] Among them, e k is the state error, L is the observer gain, F m =[TD w -LD v -ND v],

[0037] According to the rewritten Lipschitz property, there exists a first function and two constants Make in, η6(i) represents the i-th column of the 6-dimensional identity matrix I6, η6(j) represents the j-th column of the 6-dimensional identity matrix I6;

[0038] definition Among them, θ k is contained in a convex set, which is represented by a set of vertices Polyhedron The vertex set It is expressed as:

[0039]

[0040] Where i = 1, 2, ..., 6, j = 1, 2, ..., 6, ν(i, j) represents the element in the i-th row and j-th column of the matrix ν, is a known matrix, and Determined by the upper and lower bounds of the nonlinear term;

[0041] According to the vertex set Δf k The initial error dynamic equation is rewritten as an error dynamic system; the error dynamic system is expressed as:

[0042] e k+1 =E m e k +F m β

[0043] Among them, E m =TA(θ k )-LC.

[0044] In one embodiment of the present invention, the specific steps of determining the gain matrix of the observer include:

[0045] If there are a preset constant ε, a disturbance attenuation constant γ, a matrix H, a matrix Y and a matrix P, so that the LMI condition is satisfied, and the LMI condition is solvable, then the gain matrix of the observer is obtained;

[0046] Among them, 0<ε<1, γ>0, and is a positive definite matrix;

[0047] The LMI condition is expressed as:

[0048]

[0049] Π3=(-YD v ) T , Π5=-P; * denotes a term derived from symmetry;

[0050] The gain matrix of the observer is expressed as:

[0051]

[0052]

[0053] L=P -1 Y

[0054] In one embodiment of the present invention, according to the gain matrix of the observer, by performing a reachability analysis on the error dynamic system, the state of the omnidirectional Mecanum wheel automatic guided vehicle is estimated, and the specific steps of obtaining the interval of the state of the omnidirectional Mecanum wheel automatic guided vehicle include: obtaining the analysis result by performing a reachability analysis on the error dynamic system According to the gain matrix of the observer and the analysis results The upper and lower bounds of the state of the omnidirectional Mecanum wheel automatic guided vehicle are obtained; the upper and lower bounds of the state of the omnidirectional Mecanum wheel automatic guided vehicle are expressed as:

[0055]

[0056] in, is the upper bound of the state of the omnidirectional Mecanum wheel automated guided vehicle, z k is the lower bound of the state of the omnidirectional Mecanum wheel automatic guided vehicle;

[0057] The interval of the state of the omnidirectional Mecanum wheel automatic guided vehicle is obtained according to the initial value corresponding to the observer when k=0 and the upper and lower bounds of the state of the omnidirectional Mecanum wheel automatic guided vehicle.

[0058] In one embodiment of the present invention, the error dynamic system is subjected to reachability analysis according to the following formula:

[0059]

[0060]

[0061]

[0062]

[0063] in, Box() is an interval box, and e 0 are the upper and lower bounds of the error at the initial moment, V, M0, W are diagonal matrices, F k-i is the polyhedron obtained by the recursive method.

[0064] In a second aspect, the present invention provides an interval estimation system based on an observer and reachability analysis, comprising: an acquisition module for acquiring parameters of an omnidirectional Mecanum wheel automatic guided vehicle; a discrete-time nonlinear system construction module for constructing a discrete-time nonlinear system of the omnidirectional Mecanum wheel automatic guided vehicle according to the parameters; an observer design module for obtaining an observer of a TNL structure by processing nonlinear terms according to the discrete-time nonlinear system; obtaining an error dynamic system according to the discrete-time nonlinear system and the observer, and determining a gain matrix of the observer; and an interval estimation module for performing an interval estimation of the state of the omnidirectional Mecanum wheel automatic guided vehicle by performing a reachability analysis on the error dynamic system according to the observer, and obtaining an interval of the state of the omnidirectional Mecanum wheel automatic guided vehicle.

[0065] The above technical solution of the present invention has the following advantages compared with the prior art:

[0066] The interval estimation method and system based on observer and reachability analysis described in the present invention considers various situations such as slip, friction, load change, sliding friction, viscous friction and external disturbance in the movement of an omnidirectional Mecanum wheel automatic guided vehicle, models the omnidirectional Mecanum wheel automatic guided vehicle, and constructs a discrete time nonlinear system in control theory, so that the model is more practical and the accuracy of modeling is improved; when designing an observer, the present application linearizes and simplifies the nonlinear model by using the rewritten Lipschitz condition, and at the same time utilizes H ∞ The technology is used to minimize the influence of lumped uncertainty, lumped disturbance and noise, and the interval of the state is determined by reachability analysis, which not only improves the accuracy of interval estimation, but also reduces the conservatism of observer design; the application can perform interval estimation on the unmeasurable state of the omnidirectional Mecanum wheel automatic guided vehicle during movement, and then provide available signals for trajectory tracking and path planning of the omnidirectional Mecanum wheel automatic guided vehicle, which has unique advantages in processing systems with disturbances, uncertainties and measurement noise, and is more robust than traditional estimation methods, which not only improves the accuracy of displacement and velocity interval estimation of the omnidirectional Mecanum wheel automatic guided vehicle, but also reduces the conservatism of observer design. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below according to specific embodiments of the present invention in conjunction with the accompanying drawings, wherein

[0068] Figure 1 is an overall flow chart of an interval estimation method based on observer and reachability analysis according to a preferred embodiment of the present invention;

[0069] Figure 2 yes Figure 1 The interval estimation method based on observer and reachability analysis obtains the flow chart of discrete-time nonlinear system;

[0070] Figure 3 A block diagram of an interval estimation system based on an observer and reachability analysis provided by an embodiment of the present invention;

[0071] Figure 4 yes Figure 1 A schematic diagram of an omnidirectional Mecanum wheel automated guided vehicle based on an observer and an interval estimation method for reachability analysis. DETAILED DESCRIPTION

[0072] In order to better explain the present invention and facilitate understanding, the present invention is described in detail below in conjunction with the accompanying drawings through specific embodiments. Although exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided in order to enable a clearer and more thorough understanding of the present invention and to be able to fully convey the scope of the present invention to those skilled in the art.

[0073] First, refer to Figure 1 , Figure 2 As shown, a preferred embodiment of the present invention provides an interval estimation method based on an observer and reachability analysis, comprising:

[0074] S1, obtaining the parameters of the omnidirectional Mecanum wheel automatic guided vehicle;

[0075] Specifically, the relevant parameters of the omnidirectional Mecanum wheel automatic guided vehicle are shown in Table 1, and the parameter values ​​of the omnidirectional Mecanum wheel automatic guided vehicle are shown in Table 2.

[0076] Table 1 Parameters of omnidirectional mecanum wheel automatic guided vehicle

[0077]

[0078] Table 2 Parameters of omnidirectional Mecanum wheel automatic guided vehicle

[0079]

[0080] Reference Figure 4 As shown, in this embodiment, the omnidirectional Mecanum wheel automatic guided vehicle has four Mecanum wheels, wherein the first-order derivative of the rotation angle with respect to time also represents the angular velocity, Figure 4 M1, M2, M3, and M4 are four independent motors, and f1, f2, f3, and f4 are the friction forces on the four wheels.

[0081] S2, construct the discrete-time nonlinear system of the omnidirectional Mecanum wheel automatic guided vehicle according to the parameters;

[0082] S2 specifically includes:

[0083] S21, establishing a kinematic model of the omnidirectional Mecanum wheel automatic guided vehicle and a dynamic model of the omnidirectional Mecanum wheel automatic guided vehicle according to the parameters;

[0084] Specifically, 1. The kinematic model of the omnidirectional Mecanum wheel automatic guided vehicle can be described as:

[0085]

[0086] in, So, we can get

[0087] is the pseudo-inverse of matrix J and

[0088] Through the relationship between the inertial coordinate system and the relative coordinate system, we can get:

[0089]

[0090] in,

[0091] According to Table 1 and Table 2, is the angular velocity of the bth wheel in the omnidirectional Mecanum wheel automatic guided vehicle, R is the wheel radius of the omnidirectional Mecanum wheel automatic guided vehicle, X r O r Y r is the relative coordinate system, ψ is the rotation angle relative to the relative coordinate system; d1 is the width of the omnidirectional Mecanum wheel automatic guided vehicle d2 is the length of the omnidirectional Mecanum wheel AGV

[0092] 2. The dynamic model of the omnidirectional Mecanum wheel automatic guided vehicle can be established according to the Euler-Lagrange equation:

[0093]

[0094] Among them, τ=[τ1 τ2 τ3 τ4] T ,

[0095]

[0096]

[0097]

[0098] And, J ω is the moment of inertia of the Mecanum wheel of the omnidirectional Mecanum wheel AGV around the central axis, is the viscous friction coefficient, J Z is the moment of inertia of the omnidirectional Mecanum wheel AGV around its center of rotation, and m is the total mass of the omnidirectional Mecanum wheel AGV.

[0099] According to Table 1 and Table 2, τ b (b=1, 2, 3, 4) is the torque generated by the bth motor in the omnidirectional Mecanum wheel automatic guided vehicle; F sb (b=1, 2, 3, 4) is the static friction force of the bth wheel in the omnidirectional Mecanum wheel automatic guided vehicle.

[0100] Taking into account wheel friction, load variation, model uncertainty, external disturbances, and measurement noise, it can be concluded that:

[0101]

[0102] So it can be rewritten as:

[0103]

[0104] in, τ d is an unknown bounded disturbance, ΔM, ΔF is an uncertain term; represents the first-order derivative of the rotation angle with respect to time, Represents the second derivative of the rotation angle with respect to time.

[0105] S22, obtaining the dynamic system of the omnidirectional Mecanum wheel automatic guided vehicle according to the kinematic model and the dynamic model;

[0106] Specifically, according to the combination of kinematic model and dynamic model, we define z1=[x q y q ψ] T , Then the dynamic system of the omnidirectional Mecanum wheel automatic guided vehicle can be described as:

[0107]

[0108] Where z1 = [x q y q ψ] T , X q O q Y q is the inertial coordinate system, for of pseudo-rebellion;

[0109]

[0110]

[0111]

[0112] S23, discretize the state space equations of the dynamic system to obtain a discrete-time nonlinear system.

[0113] Specifically, by discretizing the state space equation of the omnidirectional Mecanum wheel automatic guided vehicle, a discrete time nonlinear system can be finally obtained; the discrete time nonlinear system is expressed as:

[0114]

[0115] Where, k represents the kh moment; h is the sampling period; τ k is the torque generated at time k, f k =-h[0 f(z k ) T ] T is a nonlinear term, w k =w d (k) is the lumped disturbance, y k is the output, v k To measure noise, A, C, D w , D v are all constant matrices.

[0116] and in And they are all known vectors. represents n'-dimensional Euclidean space. According to the definition of polyhedron we can express it as:

[0117] z0∈<c0,M0> ,

[0118] Where V, M0, W are diagonal matrices, and are their diagonal elements.

[0119] S3, according to the discrete time nonlinear system, by processing the nonlinear terms, we get the H of the TNL structure ∞ Observer; obtain the error dynamic system according to the discrete-time nonlinear system and the observer, and determine the gain matrix of the observer;

[0120] Specifically, in order to perform interval estimation on the unmeasurable state of the omnidirectional Mecanum wheel automated guided vehicle during its motion, it is necessary to first design an observer to estimate the state.

[0121] The observer designed for discrete-time nonlinear systems takes the following form:

[0122]

[0123] Among them, δ k is the intermediate variable, For z k The estimate of I n (n=3, 6, 9) represents the n-dimensional identity matrix, T+NC=I6, is an arbitrary matrix, represents n'-dimensional Euclidean space, is the pseudo-inverse of Γ.

[0124] definition Then, through the discrete-time nonlinear system and the observer, the error dynamic system can be obtained as follows:

[0125] e k+1 =(TA-LC)e k +TΔf k +F m β (9);

[0126] Among them, e k is the state error, L is the observer gain, F m =[TD w -LD v -ND v ],

[0127] According to the rewritten Lipschitz property, there exists a function and two constants So that:

[0128]

[0129] definition Obviously, θ kis contained in a convex set, which can be represented by a polyhedron with vertices To represent, and the vertex set As shown below

[0130]

[0131] in, η6(i) represents the i-th column of the 6-dimensional identity matrix I6, η6(j) represents the j-th column of the 6-dimensional identity matrix I6; i = 1, 2, ..., 6, j = 1, 2, ..., 6, ν(i, j) represents the element of the i-th row and j-th column of the matrix ν, is a known matrix, and Determined by the upper and lower bounds of the nonlinear term;

[0132] Based on the above equations, the error dynamic system can be rewritten as

[0133] e k+1 =E m e k +F m β (12);

[0134] Among them, E m =TA(θ k )-LC.

[0135] Given a constant 0<ε<1, if there exists a scalar γ>0 and a matrix And is a positive definite matrix; so that the following LMI conditions hold:

[0136]

[0137] in, Π3=(-YD v ) T , Π5=-P; * denotes a term derived from symmetry.

[0138] If the LMI condition is solvable, the observer parameters and gains can be determined as follows:

[0139]

[0140] Specifically, the LMI of formula (13) can be rewritten as:

[0141]

[0142] in,

[0143] So it can be decomposed into:

[0144]

[0145] By using Schur complement, equation (16) can be restated as

[0146]

[0147] Define a Lyapunov function as:

[0148]

[0149] Next, we will complete it in two steps:

[0150] Step 1: When β = 0, we apply forward difference to equation (18) and get:

[0151]

[0152] Formula (17) means Then (19) can be transformed into an inequality:

[0153] ΔV k ≤(ε-1)V k (20);

[0154] Obviously we can get:

[0155] V k+1 ≤…≤ε k V1≤ε k+1 V0 (21);

[0156] Since V k ≥ λ (P)‖e k ‖ 2 and Then we can get:

[0157]

[0158] in, λ (P) and They represent the maximum and minimum values ​​of the real part of the eigenvalue of the matrix P, V0 is the Lyapunov function when k = 0, and V1 is the Lyapunov function when k = 1. By transposing the terms, we get:

[0159]

[0160] Where e0 is the initial error;

[0161] When 0<ε<1, according to formula (23)

[0162] Step 2: When β≠0, let:

[0163]

[0164] By using zero initial conditions, we obtain:

[0165]

[0166] So, we can get:

[0167]

[0168] set up Then according to formula (17), we can get:

[0169]

[0170] Therefore, it can be known that This also means Right now

[0171] The observer of the present application adopts a TNL structure, which reduces the conservatism of the observer design, and the observer designed by the present application combines H ∞ Technology is used to further attenuate the influence of external disturbances and measurement noise. In addition, in the design process of the observer, the design conditions are transformed into solving linear matrix inequalities.

[0172] S4, according to the gain matrix of the observer, by performing reachability analysis on the error dynamic system, the state of the omnidirectional Mecanum wheel automatic guided vehicle is estimated, and the state interval of the omnidirectional Mecanum wheel automatic guided vehicle is obtained.

[0173] Specifically, the upper and lower bounds of the state of the omnidirectional Mecanum wheel automatic guided vehicle can be expressed as:

[0174]

[0175] Given the initial value, the interval can be obtained through the above formula Then in the above formula Through reachability analysis, it can be obtained. Therefore, we can get:

[0176]

[0177] in, Box() is an interval box, and e 0 are the upper and lower bounds of the error at the initial moment, V, M0, W are diagonal matrices, F k-i is the polyhedron obtained by the recursive method.

[0178] Specifically, according to the error dynamic equation of the observer, we can know:

[0179]

[0180] Since z0∈<c0,M0> and That is, when k = 0, the initial value of the observer is:

[0181]

[0182] Where e0 is the estimated error when k=0, z0 is the initial value of the system, is the initial value of the observer, c0 is a constant, It means to define O as I.

[0183] therefore Then for the nonlinear initial value:

[0184]

[0185] This means Δf0∈<0,f0>.

[0186] in, in, k f is a known constant, is the upper bound of e0.

[0187] set up z0∈<c0,M0> ,

[0188] Moreover, ‖Δf0‖∈<0,f0>, e0∈<0,M0>.

[0189] The matrix V, M0, W is a diagonal matrix whose elements are the noise, initial error and upper and lower bounds of the disturbance, respectively. Then, by iterating and recursively solving the error equation, we can obtain

[0190] Then e k The reachable set of is:

[0191]

[0192] Among them, this application involves the following concepts and contents:

[0193] 1. An interval vector It can also be called a box, and its definition is as follows

[0194]

[0195] For simplicity, it is represented as

[0196] in μ=[μ1,...,μ n ] T , a vector whose components are equal to the interval [-1,1] Represented as a hypercube B h =[-1,1] h .

[0197] For two interval vectors and have

[0198]

[0199] 2. For a collection The smallest interval vector that contains it is called an interval box, as shown below:

[0200]

[0201] in, μ=[μ1,...,μ n ] T .

[0202] The minimum interval vector also means that for any vector u∈U, is the one that contains u i The minimum interval vector of .

[0203] Represents a series of combinations, namely:

[0204]

[0205] According to the above two concepts and contents and formula (21), we can get:

[0206]

[0207] So, we can get

[0208] Among them, k ≥ 0, because so

[0209] Finally, the upper and lower bounds of the state of the omnidirectional Mecanum wheel automated guided vehicle can be obtained through equation (27).

[0210] This application performs interval estimation on the state application reachability analysis. The interval estimation accuracy is further improved by using the wrapping effect of the interval box.

[0211] In the above process of this application, the following concepts and contents are also involved, including:

[0212] 1. An n-dimensional, m-order centrosymmetric polyhedron is defined as:

[0213]

[0214] in, represents the center vector, which is a polyhedron The center of is the shape matrix of the polyhedron Z; B m ∈[-1,1] m is an interval vector, and the entire centrosymmetric polyhedron is its affine transformation. There are two forms of operation:

[0215]

[0216] For any polyhedron It has the following operational properties:

[0217]

[0218] 2. If the observer is an H ∞ Observer, then it satisfies the following conditions:

[0219] If ω(k) = 0, when k approaches infinity, e(k) approaches 0

[0220] If ω(k)≠0, under zero initial conditions, the following inequality holds:

[0221]

[0222] Where e(k) is the system error, γ is the disturbance attenuation constant, ω(k) is the lumped disturbance / uncertainty, and γ>0. If the above conditions are met, then it is the H ∞ Observer.

[0223] Interval Box The weight of is determined by the following formula:

[0224]

[0225] in, is a polyhedron of order m.

[0226] 3. Existence Matrix H∈R m×n , and any matrix If rank(E) = z, then the general solution for DE = F is as follows:

[0227]

[0228] Among them, I y is the identity matrix of the y dimension.

[0229] 4. For There are two constants and And a function

[0230] Satisfy the following formula:

[0231]

[0232] where the function G(x) satisfies the Lipschitz condition and η n (i) represents the n-dimensional identity matrix I n The i-th column, η n (j) represents the n-dimensional identity matrix I n The jth column of .

[0233] g ij Has the following form:

[0234]

[0235] Among them, α β(j) =[β(1)…β(j)α(j+1)…α(n)] T , G i (x) represents the i-th subfunction of G(x). In particular, it satisfies: β(0) =α,α β(n) =β.

[0236] This application is about the interval estimation method of the unmeasurable state of the omnidirectional Mecanum wheel automatic guided vehicle. Aiming at the factors that may affect the omnidirectional Mecanum wheel automatic guided vehicle during movement, a more accurate and more practical discrete time nonlinear system model is established. Through the processing and utilization technology of nonlinear terms, the state of the omnidirectional Mecanum wheel automatic guided vehicle is estimated by the two-step method. This application first designs the observer of the structure, and then determines the interval of the state through accessibility analysis, namely the interval box method, which can effectively perform interval estimation on the state of the system.

[0237] This application uses the Euler-Lagrange equation to model the omnidirectional Mecanum wheel automatic guided vehicle, taking into account uncertainty, load changes, static sliding friction, external disturbances and measurement noise, in order to solve the shortcoming that the modeling of the system in the prior art is not practical. On this basis, a novel interval estimation method is designed for the state of the discrete-time nonlinear system after modeling. This application combines the TNL structure observer with the reachability analysis and uses the H ∞ First, the TNL structure observer used in this application can provide a more rigorous estimate than the Romberg observer method. By processing the nonlinear terms, it can determine the state interval based on reachability analysis. ∞ The technology minimizes the impact of lumped interference / uncertainty and noise on the omnidirectional Mecanum wheel automatic guided vehicle, thereby ensuring the estimation accuracy and greatly improving the tolerance to factors such as lumped interference / uncertainty and noise. The observer design can be completed by solving the LMI.

[0238] In this embodiment, the technicians can complete the interval estimation of the omnidirectional Mecanum wheel automatic guided vehicle by performing parameter correction on the software simulation and the actual system.

[0239] Second, as Figure 3 As shown, this embodiment provides an interval estimation system 600 based on an observer and reachability analysis, including: an acquisition module 601, a discrete-time nonlinear system construction module 602, an observer design module 603, and an interval estimation module 604. The acquisition module 601 is used to acquire the parameters of the omnidirectional Mecanum wheel automatic guided vehicle; the discrete-time nonlinear system construction module 602 is used to construct the discrete-time nonlinear system of the omnidirectional Mecanum wheel automatic guided vehicle according to the parameters; the observer design module 603 is used to obtain the observer of the TNL structure by processing the nonlinear terms according to the discrete-time nonlinear system; the error dynamic system is obtained according to the discrete-time nonlinear system and the observer, and the gain matrix of the observer is determined; the interval estimation module 604 is used to perform an interval estimation of the state of the omnidirectional Mecanum wheel automatic guided vehicle by performing reachability analysis on the error dynamic system according to the observer, and obtain the interval of the state of the omnidirectional Mecanum wheel automatic guided vehicle.

[0240] According to the interval estimation system based on observer and reachability analysis provided in this embodiment, since it is used to implement the steps of the interval estimation method based on observer and reachability analysis provided in the first aspect of the present invention, the interval estimation system based on observer and reachability analysis has all the technical effects of the interval estimation method based on observer and reachability analysis, which will not be repeated here.

[0241] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0242] Obviously, those skilled in the art can make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention should also include these modifications and variations.

[0243] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may alter, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. An interval estimation method based on observer and reachability analysis, characterized in that: include: Get the parameters of the omnidirectional Mecanum wheel automatic guided vehicle; Constructing a discrete-time nonlinear system of the omnidirectional Mecanum wheel automatic guided vehicle according to the parameters; According to the discrete-time nonlinear system, the H of the TNL structure is obtained by processing the nonlinear terms. ∞ observer; obtaining an error dynamic system according to the discrete-time nonlinear system and the observer, and determining a gain matrix of the observer; According to the gain matrix of the observer, by performing a reachability analysis on the error dynamic system, an interval estimation of the state of the omnidirectional Mecanum wheel automatic guided vehicle is performed, and an interval of the state of the omnidirectional Mecanum wheel automatic guided vehicle is obtained; The observer is expressed as: Among them, δ k is the intermediate variable, For z k The estimate of I n represents the n-dimensional identity matrix, n = 3, 6, 9; K∈ 6×9 is an arbitrary matrix, n' represents n'-dimensional Euclidean space, is the pseudo-inverse of Γ; A and C are both constant matrices; L is the observer gain; τ k is the torque generated at time k, y k is the output; h is the sampling period; for The pseudo-inverse of ; M is the shape matrix of the polyhedron; According to the gain matrix of the observer, by performing a reachability analysis on the error dynamic system, the state of the omnidirectional Mecanum wheel automatic guided vehicle is estimated, and the specific steps of obtaining the interval of the state of the omnidirectional Mecanum wheel automatic guided vehicle include: The analysis results are obtained by performing reachability analysis on the error dynamic system. According to the gain matrix of the observer and the analysis results The upper and lower bounds of the state of the omnidirectional Mecanum wheel automatic guided vehicle are obtained; the upper and lower bounds of the state of the omnidirectional Mecanum wheel automatic guided vehicle are expressed as: in, is the upper bound of the state of the omnidirectional Mecanum wheel automated guided vehicle, z k is the lower bound of the state of the omnidirectional Mecanum wheel automatic guided vehicle; The interval of the state of the omnidirectional Mecanum wheel automatic guided vehicle is obtained according to the initial value corresponding to the observer when k=0 and the upper and lower bounds of the state of the omnidirectional Mecanum wheel automatic guided vehicle. The reachability analysis of the error dynamic system is performed according to the following formula: in, Box() is an interval box, and e 0 are the upper and lower bounds of the error at the initial moment, V, M0, W are diagonal matrices, F k-i is the polyhedron obtained by the recursive method; D w , D v are all constant matrices.

2. The interval estimation method based on observer and reachability analysis according to claim 1, characterized in that: The specific steps of constructing the discrete-time nonlinear system of the omnidirectional Mecanum wheel automatic guided vehicle according to the parameters include: Establishing a kinematic model of the omnidirectional Mecanum wheel automatic guided vehicle and a dynamic model of the omnidirectional Mecanum wheel automatic guided vehicle according to the parameters; Obtaining a dynamic system of the omnidirectional Mecanum wheel automatic guided vehicle according to the kinematic model and the dynamic model; The state space equations of the dynamic system are discretized to obtain a discrete-time nonlinear system.

3. The interval estimation method based on observer and reachability analysis according to claim 2, characterized in that: The kinematic model is expressed as: in, is the angular velocity of the bth wheel in the omnidirectional Mecanum wheel automatic guided vehicle, b = 1, 2, 3, 4; R is the wheel radius of the omnidirectional Mecanum wheel automatic guided vehicle, X r O r Y r is a relative coordinate system, ψ is a rotation angle relative to the relative coordinate system; d1 is the width of the omnidirectional Mecanum wheel automatic guided vehicle d2 is the length of the omnidirectional Mecanum wheel automatic guided vehicle The kinetic model is expressed as: in, τ=[τ1 τ2 τ3 τ4] T , τ b is the torque generated by the b-th motor in the omnidirectional Mecanum wheel automatic guided vehicle, b = 1, 2, 3, 4; τ d is an unknown bounded disturbance, ΔM, ΔF is an uncertain term; represents the second derivative of the rotation angle with respect to time; F sb is the static friction force of the bth wheel in the omnidirectional Mecanum wheel automatic guided vehicle, b=1,2,3,4; J ω is the moment of inertia of the Mecanum wheel of the omnidirectional Mecanum wheel automated guided vehicle around the central axis, is the viscous friction coefficient, J Z is the moment of inertia of the omnidirectional Mecanum wheel automated guided vehicle about its center of rotation, and m is the total mass of the omnidirectional Mecanum wheel automated guided vehicle.

4. The interval estimation method based on observer and reachability analysis according to claim 3, characterized in that: The dynamic system is expressed as: Where z1 = [x q y q ψ] T , X q O q Y q is the inertial coordinate system, for The pseudo-reversal, The discrete-time nonlinear system is expressed as: z k+1 =Az k +Bτ k +f k +D w w k y k =Cz k +D v v k Where, k represents the kh moment; h is the sampling period; τ k is the torque generated at time k, y k is the output, f k =-h[0f(z k ) T ] T is a nonlinear term, w k is the lumped disturbance, v k To measure noise, A, C, D w , D v are all constant matrices.

5. The interval estimation method based on observer and reachability analysis according to claim 1, characterized in that: The specific steps of obtaining the error dynamic system according to the discrete-time nonlinear system and the observer include: definition The initial error dynamic equation is obtained according to the discrete-time nonlinear system and the observer; the initial error dynamic equation is expressed as: and k+1 =(TA-LC)e k +TΔf k +F m β Among them, e k is the state error, L is the observer gain, F m =[TD w -LD v -ND v ], According to the rewritten Lipschitz property, there exists a first function f ij,k : 6 × 6 → and two constants Make in, η6(i) represents the i-th column of the 6-dimensional identity matrix I6, η6(j) represents the j-th column of the 6-dimensional identity matrix I6; definition Among them, θ k is contained in a convex set, which is represented by a set of vertices Polyhedron The vertex set It is expressed as: Where i = 1, 2, ..., 6, j = 1, 2, ..., 6, ν(i, j) represents the element in the i-th row and j-th column of the matrix ν, is a known matrix, and ν∈ 6×6 Determined by the upper and lower bounds of the nonlinear term; According to the vertex set Δf k The initial error dynamic equation is rewritten as an error dynamic system; the error dynamic system is expressed as: And k+1 =And m And k +F m β Among them, E m =TA(θ k )-LC.

6. The interval estimation method based on observer and reachability analysis according to claim 5, characterized in that: The specific steps of determining the gain matrix of the observer include: If there are a preset constant ε, a disturbance attenuation constant γ, a matrix H, a matrix Y and a matrix P, so that the LMI condition is satisfied, and the LMI condition is solvable, then the gain matrix of the observer is obtained; Among them, 0<ε<1, γ>0, H∈ 6×9 , Y∈ 6×3 , P∈ 6×6 and is a positive definite matrix; The LMI condition is expressed as: in, , ,Π3=(-YD v ) T , Π5=-P; * denotes a term derived from symmetry; The gain matrix of the observer is expressed as:

7. An interval estimation system based on an observer and reachability analysis, used to execute the interval estimation method based on an observer and reachability analysis according to any one of claims 1 to 6, comprising: An acquisition module is used to obtain the parameters of the omnidirectional Mecanum wheel automatic guided vehicle; A discrete-time nonlinear system construction module, used for constructing a discrete-time nonlinear system of the omnidirectional Mecanum wheel automatic guided vehicle according to the parameters; The observer design module is used to obtain the H of the TNL structure by processing the nonlinear terms according to the discrete-time nonlinear system. ∞ observer; obtaining an error dynamic system according to the discrete-time nonlinear system and the observer, and determining a gain matrix of the observer; The interval estimation module is used to perform an interval estimation on the state of the omnidirectional Mecanum wheel automatic guided vehicle by performing a reachability analysis on the error dynamic system according to the observer, and obtain the interval of the state of the omnidirectional Mecanum wheel automatic guided vehicle.

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