A method and system for expanding the estimated vehicle stability domain of a quadratic sum programming algorithm

Abstract

The application discloses a method and system for expanding a vehicle stability domain estimated by a sum-of-squares programming algorithm, and belongs to the technical field of computers, and comprises the following steps: a rational polynomial-based whole vehicle polynomial model is constructed by combining a two-degree-of-freedom dynamics model of a vehicle and a rational polynomial nonlinear tire model; a vehicle stability region is estimated by a sum-of-squares programming algorithm based on the whole vehicle polynomial model, and a stability region boundary curve is obtained; the stability region boundary curve is subjected to discrete processing, and an initial point set is obtained; a convex hull of a stability domain expansion is obtained by trajectory inversion according to the stability region boundary curve and the initial point set; and the convex hull of the stability domain expansion is taken as an expanded stability region. The application can realize maximum estimation of a stability domain boundary, greatly improve the conservativeness of the stability domain, make the judgment of vehicle stability more accurate, and be favorable to improving the reliability of vehicle stability control.

Description

Technical Field

[0001] This application relates to the field of computer technology, and in particular to a method and system for estimating the vehicle stability domain using an extended square sum programming algorithm. Background Technology

[0002] The vehicle stability region can reflect and evaluate a vehicle's stability performance to a certain extent. Commonly used methods for determining the vehicle stability region include the phase plane method and the Lyapunov function method. The phase plane method for determining the vehicle stability region usually relies on a simplified dynamic model of a linear model, and its accuracy and reliability are limited when facing nonlinear characteristics and complex driving behaviors. For nonlinear systems, there is currently no universal method to estimate a suitable Lyapunov function.

[0003] Because rational functions are more effective than polynomials in capturing tire nonlinearity, sum-of-squares programming (SOSP) not only requires the application of a polynomial tire model but can also automatically search for the optimal polynomial Lyapunov function using semidefinite programming (SDP). Therefore, SOSP provides a more accurate estimate of the stable region during vehicle operation. However, the S-Procedure of SOS technology is a sufficient condition, which inevitably leads to a conservative approach in the stable region estimation. Expanding the vehicle stability domain is an inevitable trend in automotive technology development and innovation to improve vehicle safety, adaptability, and comfort. However, related technologies suffer from inadequacies in estimating the vehicle stability domain and the inability to accurately expand the stability domain. Summary of the Invention

[0004] The main objective of this application is to propose a method and system for expanding the vehicle stability domain estimated by the sum of squares programming algorithm, aiming to accurately expand the vehicle stability region estimated by the sum of squares programming algorithm.

[0005] To achieve the above objectives, one aspect of this application proposes a method for estimating the vehicle stability domain using an expanded sum-of-squares programming algorithm, the method comprising:

[0006] By combining the vehicle's two-degree-of-freedom dynamics model and the rational polynomial nonlinear tire model, a whole-vehicle polynomial model based on rational polynomials is constructed.

[0007] Based on the vehicle polynomial model, the vehicle stability region is estimated using a sum-of-squares programming algorithm, and the boundary curve of the stability region is obtained.

[0008] Discretize the boundary curve of the stable region to obtain an initial point set;

[0009] Based on the boundary curve of the stable region and the initial point set, the convex hull of the expanded stable region is obtained by reversing the trajectory;

[0010] The convex hull, which expands the stability region, is taken as the expanded stability region.

[0011] In some embodiments, constructing a whole-vehicle polynomial model based on rational polynomials by combining a two-degree-of-freedom vehicle dynamics model and a rational polynomial nonlinear tire model includes the following steps:

[0012] Force analysis was performed on the two-degree-of-freedom dynamic model of the vehicle to obtain the vehicle dynamic equations.

[0013] Based on the vertical load and the road adhesion coefficient, a fitted polynomial expression for the tire lateral force is obtained;

[0014] Based on the two-degree-of-freedom dynamic model of the vehicle, the expression for the tire slip angle is obtained;

[0015] Based on the tire slip angle expression, the vehicle dynamics equation and the polynomial tire lateral force expression are combined to obtain a rational polynomial vehicle polynomial model.

[0016] In some embodiments, estimating the vehicle stability region and obtaining the stability region boundary curve based on the vehicle polynomial model using a sum-of-squares programming algorithm includes the following steps:

[0017] Based on the aforementioned vehicle polynomial model and sum of squares formula, determine the polynomial constraints;

[0018] Obtain the second-order Lyapunov function of the vehicle linearization model at the equilibrium point to obtain the initial Lyapunov function;

[0019] The order of the continuously differentiable function is adjusted, and the initial Lyapunov function is iterated until the change in the shape factor of the polynomial constraint is less than a preset change threshold, thus obtaining the vehicle stability region.

[0020] A stable region boundary curve is generated based on the vehicle's stable region.

[0021] In some embodiments, discretizing the boundary curve of the stable region to obtain an initial point set includes:

[0022] Calculate the total length of the boundary curve of the stable region;

[0023] According to a preset number, points are uniformly selected from the boundary curve of the pre-stable region, and the points are located by accumulating length to generate an initial point set.

[0024] In some embodiments, obtaining the expanded convex hull of the stable region by trajectory reversal based on the stable region boundary curve and the initial point set includes the following steps:

[0025] The initial point set is used as the initial condition for solving the inverse differential equation at the first time point. The first corresponding point of each point in the initial point set is obtained by inverse integration, thus obtaining the first point set.

[0026] The convex hull including the first set of points is obtained using the Quick Hull algorithm;

[0027] The initial point set is used sequentially as the initial condition for solving the inverse differential equation within a preset time series, thereby obtaining the second corresponding point of each point in the initial point set, and thus obtaining the second point set;

[0028] Obtain any point from the convex hull to get the current point, and obtain the inward normal vector of the current point;

[0029] Construct a first preset condition based on the current point and the normal vector;

[0030] Obtain a first number of points that satisfy the first preset condition from the second set of corresponding points;

[0031] The second number of clusters generated by the second corresponding point is obtained using the DBSCAN algorithm;

[0032] Based on the first quantity and the second quantity, the convex hull of the stability region expansion is determined.

[0033] In some embodiments, determining the convex hull of the stability region expansion based on the first quantity and the second quantity includes the following steps:

[0034] When the first quantity and the second quantity do not meet the second preset condition, the preset time interval is reduced or the coefficient value of the preset time interval is increased, and the process of sequentially using the initial point set as the initial condition for solving the inverse differential equation within the preset time series, obtaining the second corresponding point of each point in the initial point set, and obtaining the second point set is repeated until the first quantity and the second quantity meet the second preset condition, and the convex hull of the stability region is obtained; wherein, the second preset condition is that the first quantity is equal to 0 and the second quantity is equal to 1.

[0035] In some embodiments, the first preset condition is:

[0036] (x i -p k )·n i >0;

[0037] Where, x i p represents the current point; k This represents the second corresponding point after the trajectory of each point in the initial point set is reversed; n i This represents the normal vector pointing inwards from the current point.

[0038] To achieve the above objective, another aspect of this application proposes a system for estimating the vehicle stability domain using an extended sum-of-squares programming algorithm, the system comprising:

[0039] The first module is used to combine the vehicle's two-degree-of-freedom dynamics model and the rational polynomial nonlinear tire model to construct a whole vehicle polynomial model based on rational polynomials.

[0040] The second module is used to estimate the vehicle's stable region based on the vehicle polynomial model and obtain the stable region boundary curve through a sum-of-squares programming algorithm.

[0041] The third module is used to discretize the boundary curve of the stable region to obtain an initial point set.

[0042] The fourth module is used to obtain the convex hull of the expanded stable region by reversing the trajectory based on the boundary curve of the stable region and the initial point set.

[0043] The fifth module is used to expand the convex hull of the stability region as the expanded stability region.

[0044] To achieve the above objectives, another aspect of this application provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the method described above.

[0045] To achieve the above objectives, another aspect of the embodiments of this application proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the methods described above.

[0046] The embodiments of this application include at least the following beneficial effects: This application provides a method and system for estimating the vehicle stability domain using an expanded square sum programming algorithm. This scheme constructs a whole vehicle polynomial model and estimates the boundary curve of the stability region. The boundary curve of the stability region is discretized to obtain an initial point set. Based on the initial point set, trajectory reversal is performed to obtain the convex hull of the expanded stability domain. This can achieve the maximum estimation of the stability domain boundary, greatly improve the conservative nature of the stability domain, make the judgment of vehicle stability more accurate, and help improve the reliability of vehicle stability control. Attached Figure Description

[0047] The accompanying drawings are used to provide a further understanding of the technical solutions of this application and constitute a part of the specification. They are used together with the embodiments of this application to explain the technical solutions of this application and do not constitute a limitation on the technical solutions of this application.

[0048] Figure 1This is a flowchart illustrating a method for estimating the vehicle stability domain using an expanded sum of squares programming algorithm, as provided in an embodiment of this application.

[0049] Figure 2 This is a schematic diagram of a nonlinear two-degree-of-freedom single-track model provided in an embodiment of this application;

[0050] Figure 3 This is a schematic diagram of the stable regions of different orders estimated by SOSP according to the embodiments of this application;

[0051] Figure 4 This is a schematic diagram of the stable region obtained by trajectory reversal based on SOSP, provided in an embodiment of this application.

[0052] Figure 5 This is a schematic diagram of a system module for estimating the vehicle stability domain using an expanded square sum programming algorithm provided in an embodiment of this application;

[0053] Figure 6 This is a schematic diagram of the hardware structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit it. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with those of this application; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this application as detailed in the appended claims.

[0055] Although functional modules are divided in the system diagram and a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the system or the order in the flowchart. The terms "first / S100," "second / S200," etc., in the specification, claims, and the aforementioned figures are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0056] It is understood that the terms “first,” “second,” etc., used in this application may be used herein to describe various concepts, but unless otherwise stated, these concepts are not limited by these terms. These terms are only used to distinguish one concept from another. For example, without departing from the scope of the embodiments of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the words “if,” “when,” or “in response to a determination” as used herein may be interpreted as “when…” or “when…” or “in response to a determination.”

[0057] As used in this application, the terms "at least one", "multiple", "each", "any", etc., "at least one" includes one, two or more, "multiple" includes two or more, "each" refers to each of the corresponding multiples, and "any" refers to any one of the multiples.

[0058] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0059] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0060] In related technologies, rational functions are more effective than polynomials in capturing tire nonlinearity. Sum-of-squares programming (SOSP) not only requires the application of a polynomial tire model but can also automatically search for the optimal polynomial Lyapunov function using semidefinite programming (SDP), thus providing a more accurate estimate of the stable region during vehicle operation. However, the S-Procedure in SOS technology is a sufficient condition, which inevitably leads to a conservative approach in the stable region estimation. To improve vehicle safety, adaptability, and comfort, expanding the vehicle stability domain is an inevitable trend in automotive technology development and innovation. However, related technologies suffer from inadequacies in estimating the vehicle stability domain and the inability to correctly expand the stability domain.

[0061] In view of this, this application provides a method and system for estimating the vehicle stability region using the expanded sum of squares programming algorithm. This scheme uniformly selects points on the stable region estimated by SOSP and uses them as the initial point set for the trajectory reversal method. By obtaining the discrete point set through reverse scoring, the convex hull of the discrete point set is found. After multiple iterations, the stable region estimated by SOSP is expanded, thereby improving the conservatism of the SOSP-estimated stable region and achieving correct expansion of the stable region.

[0062] This application provides a method for estimating the vehicle stability domain using an expanded square sum programming algorithm, relating to the field of computer technology. This method can be applied to a terminal, a server, or software running on either a terminal or a server. In some embodiments, the terminal can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, or in-vehicle terminal, but is not limited thereto. The server can be configured as an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The server can also be a node server in a blockchain network. The software can be an application implementing the method for estimating the vehicle stability domain using an expanded square sum programming algorithm, but is not limited to the above forms.

[0063] This application can be used in a wide variety of general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices. This application can be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform specific tasks or implement specific abstract data types. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0064] Figure 1 This is an optional flowchart of a method for estimating the vehicle stability domain using an expanded square sum programming algorithm provided in an embodiment of this application. Figure 1The method may include, but is not limited to, steps S100 to S500.

[0065] Step S100: Combine the vehicle's two-degree-of-freedom dynamics model and the rational polynomial nonlinear tire model to construct a whole-vehicle polynomial model based on rational polynomials.

[0066] Step S200: Based on the vehicle polynomial model, the stable region of the vehicle is estimated by the sum of squares programming algorithm to obtain the boundary curve of the stable region.

[0067] Step S300: Discretize the boundary curve of the stable region to obtain an initial point set.

[0068] Step S400: Based on the boundary curve of the stable region and the initial point set, obtain the convex hull of the expanded stable region by reversing the trajectory.

[0069] Step S500: The convex hull of the expanded stability region is taken as the expanded stability region.

[0070] Steps S100 to S500 as shown in the embodiments of this application involve constructing a polynomial model of the whole vehicle and estimating the boundary curve of the stable region. The boundary curve of the stable region is then discretized to obtain an initial point set. Based on the initial point set, trajectory reversal is performed to obtain the convex hull of the expanded stable region. This can achieve the maximum estimation of the boundary of the stable region, greatly improve the conservative nature of the stable region, make the judgment of vehicle stability more accurate, and help improve the reliability of vehicle stability control.

[0071] In some embodiments, step S100 may include, but is not limited to, steps S110 to S140:

[0072] Step S110: Perform force analysis on the two-degree-of-freedom dynamic model of the vehicle to obtain the vehicle dynamic equations.

[0073] Step S120: Based on the vertical load and the road adhesion coefficient, obtain the fitted polynomial expression for the tire lateral force.

[0074] Step S130: Based on the two-degree-of-freedom dynamic model of the vehicle, obtain the expression for the tire slip angle.

[0075] Step S140: Based on the tire slip angle expression, combine the vehicle dynamics equation and the polynomial tire lateral force expression to obtain a rational polynomial vehicle polynomial model.

[0076] In some embodiments, step S200 includes, but is not limited to, the following steps S210 to S240:

[0077] Step S210: Determine the polynomial constraints based on the vehicle polynomial model and the sum of squares formula;

[0078] Step S220: Obtain the second-order Lyapunov function of the vehicle linearization model at the equilibrium point to obtain the initial Lyapunov function;

[0079] Step S230: Adjust the order of the continuously differentiable function and iterate the initial Lyapunov function until the change in the shape factor of the polynomial constraint is less than a preset change threshold to obtain the vehicle stability region.

[0080] Step S240: Generate a stable region boundary curve based on the vehicle stable region.

[0081] In some embodiments, step S300 includes, but is not limited to, the following steps S310 to S320:

[0082] Step S310: Calculate the total length of the boundary curve of the stable region;

[0083] Step S320: Select points uniformly from the boundary curve of the pre-stable region according to a preset number, locate the points by accumulating length, and generate an initial point set.

[0084] In some embodiments, step S400 includes, but is not limited to, the following steps S410 to S480:

[0085] Step S410: Use the initial point set as the initial condition for solving the inverse differential equation at the first time point, and obtain the first corresponding point of each point in the initial point set by inverse integration, thus obtaining the first point set.

[0086] Step S420: Obtain the convex hull including the first point set using the Quick Hull algorithm;

[0087] Step S430: The initial point set is used as the initial condition for solving the inverse differential equation in the preset time series in sequence to obtain the second corresponding point of each point in the initial point set, and thus obtain the second point set;

[0088] Step S440: Obtain any point from the convex hull to get the current point, and obtain the inward normal vector of the current point;

[0089] Step S450: Construct a first preset condition based on the current point and the normal vector;

[0090] Step S460: Obtain the first number of points that satisfy the first preset condition from the second set of corresponding points;

[0091] Step S470: Obtain the second number of clusters generated by the second corresponding point using the DBSCAN algorithm;

[0092] Step S480: Determine the convex hull of the stability region expansion based on the first quantity and the second quantity.

[0093] In step S400 of some embodiments, the first preset condition is:

[0094] (x i -p k )·n i >0;

[0095] Where, x i p represents the current point; k n represents the second corresponding point of each point in the initial point set; i This represents the normal vector pointing inwards from the current point.

[0096] In some embodiments, step S480 includes, but is not limited to, the following step S481:

[0097] Step S481: When the first quantity and the second quantity do not meet the second preset condition, decrease the preset time interval or increase the coefficient value of the preset time interval, and return to execute the step of sequentially using the initial point set as the initial condition for solving the inverse differential equation in the preset time series, obtaining the second corresponding point of each point in the initial point set, and obtaining the second point set, until the first quantity and the second quantity meet the second preset condition, and obtain the convex hull of the stability region expansion; wherein, the second preset condition is that the first quantity is equal to 0 and the second quantity is equal to 1.

[0098] The solutions of this application embodiment will be described in detail and explained below with reference to specific application examples:

[0099] Before proceeding, some of the variables involved in the embodiments of this application are explained as follows:

[0100] The angular velocity of the center of mass deflection; v is the yaw acceleration; m is the total mass of the vehicle; x f is the longitudinal velocity; y The formula for fitting the tire curve; μ is the road adhesion coefficient; n i d is the numerator in the rational formula for tire lateral force; i n is the denominator in the rational formula for tire lateral force; f n is the molecule of the lateral force of the front wheel. r d is the denominator of the lateral force of the front wheel. r d is the denominator of the lateral force of the rear wheel. f denominator for the lateral force of the front wheel; x is the state variable of the entire vehicle system; I is the derivative of the state variables of the whole vehicle system; N is the numerator of the rational system of the whole vehicle; D is the denominator of the rational system of the whole vehicle; I z Let be the moment of inertia of the vehicle about the z-axis; Ω be the attraction domain of the system; t be time; x0 be the equilibrium point of the system; c be the boundary parameters of the attraction domain; λ be the shape factor of the polynomial constraint; R represent the set of real numbers; β be the sideslip angle of the center of mass of the model; w be the yaw rate of the model; F yf F is the lateral force of the front tire; yr δ is the lateral force of the front tires; I is the front wheel steering angle; z L represents the moment of inertia of the vehicle about the z-axis in the vehicle coordinate system. f L is the front wheelbase of the vehicle. r α is the rear wheelbase of the vehicle. i Let i represent the slip angle, i = f, r, where f represents the front wheel and r represents the rear wheel; p1, p2, q1, and q2 are all tire lateral force coefficients, where p1 and p2 are the coefficients of the numerator of the fitted tire formula, and q1 and q2 are the coefficients of the denominator of the fitted tire formula, which can be obtained by fitting the tire curve using the least squares method.

[0101] In this embodiment of the application, a method for estimating the vehicle stability region using an extended sum-of-squares programming algorithm is provided. This method can be applied to an extended stability region during vehicle operation determined by SOSP. Further, it can be implemented using the following steps 1-5:

[0102] Step 1: Combine the vehicle's two-degree-of-freedom dynamics model and the rational polynomial nonlinear tire model to construct a whole vehicle polynomial model based on rational polynomials.

[0103] Specifically, according to Figure 2 Force analysis was performed on the two-degree-of-freedom model shown, and the vehicle dynamics equations were established as follows:

[0104]

[0105] A rational polynomial function is constructed to fit the tire lateral force curve. The fitting formula is as follows:

[0106]

[0107] Introducing the vertical load and road adhesion coefficient into the fitting formula yields the polynomial tire lateral force, expressed as:

[0108]

[0109] The tire slip angle is obtained from the analysis of the vehicle's two-degree-of-freedom model. The expression for the tire slip angle is:

[0110]

[0111] By combining and simplifying the vehicle dynamics equations and the polynomial tire lateral force using the tire slip angle formula, a rational polynomial model of the whole vehicle is obtained. The expression for the whole vehicle polynomial model can be:

[0112]

[0113] The expression for the whole vehicle polynomial model can be written in standard state-space form as follows:

[0114]

[0115] Step 2: Based on the vehicle polynomial model constructed in Step 1, estimate the vehicle stability region using the sum of squares programming algorithm.

[0116] Specifically, first, the formula for the sum of squares is derived for the whole vehicle system. The region of attraction at the equilibrium point is:

[0117]

[0118] If there exists a continuously differentiable function V(x) such that:

[0119]

[0120] in, It represents the derivative of V(x); the vehicle system is a vehicle system whose input parameter is the front wheel steering angle.

[0121] Then the invariant set of D is a subset of the region of attraction, i.e., the stable region of the system. Define a region s containing variables s = {x ∈ R}. 2 |s(x)<θ}, such that λ is maximized and satisfies Therefore, solving the stability region problem can be transformed into an optimization problem:

[0122] max{λ}

[0123]

[0124] Based on the Generalized S-procedure, the above constraints are transformed into empty set constraints as follows:

[0125] max{λ}

[0126]

[0127] x≠0 is not a semi-algebraic form. We can make it equivalently constrained as l1(x)≠0 and l2(x)≠0, where l1(x) and l2(x) are both sum-of-squares forms and are positive definite, i.e.:

[0128] max{λ}

[0129]

[0130] Applying the point theorem, the empty set constraint is transformed into an equality constraint, expressed as:

[0131] max{λ}

[0132]

[0133] To minimize the number of iterations of the problem without changing its fundamental nature, let k1 = k2 = k3 = 0, q2 = l1, and l1 be a factor of q1. Then we have: That is, C(x)-l1(x)∈Σ. In the second constraint, let q3=q4=0, then q5=-(λ-s)q6-(Vc), that is, q6(x)(s(x)-λ)-(V(x)-c)∈Σ. In the third constraint, let q 10 =0, then Let l2 be a factor of q7 and q8, then l2 = q9. Right now

[0134] In the above formula: Σ represents the polynomial of the sum of squares of x; l1(x), l2(x), q1(x), ..., q 10 (x) are all polynomials sum of squares of x. Let V(x) be the gradient of the function V(x); k1, k2, and k3 are natural numbers.

[0135] Therefore, the specific expression for the sum-of-squares programming algorithm is:

[0136] max{λ}

[0137]

[0138] Substituting the standard state space obtained in step 1 into the above equation, we can transform each constraint into a polynomial constraint. The expression for the polynomial constraint is as follows:

[0139] max{λ}

[0140]

[0141] Furthermore, the Lyapunov function of the vehicle linearization model at the equilibrium point is obtained, and this is used as the initial Lyapunov function for subsequent iterations.

[0142] During the iteration process, the bilinear problem in the constraints is solved using the bisection method. The iteration process is as follows:

[0143] 1) By finding l2(x) If true, then the maximum value of c is determined.

[0144] 2) Let s(x) = x T Given x, fix V(x) and c, and find q1(x) such that q1(x)(s(x)-λ)-(V(x)-c)∈Σ, determine the maximum value of λ.

[0145] 3) Keeping c, λ, q1(x), and q2(x) fixed, find a function V(x) that makes all three constraints hold.

[0146] 4) Set the order of V(x) to 2, 4, 6, and 8 in sequence, and repeat the above iterative process to obtain the vehicle driving stability domain as: V(x)≤c;

[0147] Figure 3 The vehicle stability region is estimated using a sum-of-squares programming algorithm. The thin solid background line represents the phase trajectory, while the thicker lines show the stability regions obtained by V(x) at different orders, from smallest to largest: 2nd, 4th, 6th, and 8th orders. It can be seen that higher-order V(x) yields a larger stability region, but higher orders involve greater computation, and the resulting stability region remains conservative in the yaw rate direction.

[0148] Step 3: Based on the boundary curve of the stable region obtained in Step 2, obtain the convex hull by reversing the trajectory.

[0149] Specifically, the boundary curve of the stable region is discretized: the total length of the curve is calculated and a specified number of points are selected uniformly. The points on the curve are located by accumulating the length, and enough points are obtained to form an initial point set, denoted as S.

[0150] Using S as the solution to the inversion differential equation at the first time point t0 Given the initial conditions, the first corresponding point of each point is obtained through inverse integration, thus obtaining the first point set S. i ;

[0151] Obtain the contents of S using the Quick Hull algorithm. i The convex hull of S is denoted as Ω0. In some embodiments, S is first determined. i Connect the two points with the largest distance to form a line. Find the point farthest from the line and form a triangle with the two points before it. Determine the positional relationship between each point and the triangle using the cross product operation. Points inside or on the triangle will not be vertices of the convex hull and are not considered. Expand rapidly outwards in sequence until all points are inside the convex hull, and record S. i Connecting all vertices of the central convex hull in sequence yields a convex hull containing S. i The convex hull Ω0.

[0152] Step 4: Determine whether the convex hull obtained in Step 3 is the convex hull of the stable region expansion.

[0153] Specifically, S is used sequentially to solve the first time series t.i =t0+kΔt inverted differential equation Given the initial conditions, the second point set S of the corresponding points of each point is obtained by inverse integration. i+k In the above, t0 is the initial time, k is the coefficient value of the preset time interval (a positive integer), and Δt is the pre-designed time interval. i It is a time series. Trajectory reversal is to reverse the trajectory within the kΔt time interval.

[0154] Let each second corresponding point obtained from each reversal be p. k Take any point x on the convex hull Ω0. i Find point x. i The inward normal vector is n i Judge (x) in turn i -p k )·n i The sign of x, to obtain the satisfaction (x i -p k )·n i The first quantity m of the point >0; where the inward direction is determined by: assuming the convex hull is counterclockwise, the direction of the normal vector is determined to be within the region according to the right-hand rule.

[0155] The number n of clusters formed by the second corresponding point is obtained using the DBSCAN algorithm. Specifically, given the neighborhood radius ε and the minimum number of points MinPts within the neighborhood radius that become the core object, from any point x... i Start checking x i If there are at least MinPts objects in the ε-neighborhood of a point, mark it as a core point. Find all points on Ω0 that are density-reachable from a core sample point, forming a cluster. Randomly select the next unvisited point from the remaining objects, repeating the above iterative process until all points have been visited, obtaining the number n of clusters formed by the corresponding points. The neighborhood radius ε is generally obtained by plotting a k-distance graph; for two-dimensional data, the value of MinPts is generally 4.

[0156] In some embodiments, the condition for determining Ω0 as an expanded stability region is (the second preset condition): m = 0 and n = 1. If m = 0 and n = 1 are satisfied, then Ω0 is the expanded stability region. If not, steps 4 and 5 above are repeated by decreasing Δt or increasing the value of k. It should be noted that the value of k needs to be balanced between computational complexity and expanded stability region (the larger the value of k, the greater the computational complexity, but the stability region may not necessarily expand), until the condition is met and the expanded stability region is obtained.

[0157] Step 5: Use the convex hull of the expanded stability region as the expanded stability region.

[0158] The resulting expanded stable region is as follows Figure 4 As shown, Figure 4 In the diagram, the thin solid background line represents the phase trajectory, the thick black solid line represents the stability region estimated by SOSP, and the thick dashed line represents the stability region expanded by trajectory reversal. It can be seen that trajectory reversal significantly expands the vehicle's stability region, especially in the yaw rate direction.

[0159] The embodiments of this application have at least the following beneficial effects:

[0160] The stability region proposed in this application is closed; compared to the open vehicle stability region, it offers greater stability assurance. Constructing a rational polynomial function tire model better captures tire nonlinearity, resulting in a more accurate model. Furthermore, there is no need to solve for unstable equilibrium points during stability region estimation; SOSP estimation of the stability region does not require numerical integration and can be used for theoretical safety verification, thus yielding a more accurate estimated stability region. The trajectory reversal method is used to expand the SOSP-estimated stability region, maximizing the estimation of the stability region boundary and significantly improving its conservatism. This leads to more accurate vehicle stability assessments and more reliable vehicle stability control.

[0161] Please see Figure 5 This application also provides a system for estimating the vehicle stability domain using an extended square sum programming algorithm, which can implement the above-mentioned method for estimating the vehicle stability domain using an extended square sum programming algorithm. The system includes:

[0162] The first module 101 is used to combine the vehicle's two-degree-of-freedom dynamics model and the rational polynomial nonlinear tire model to construct a whole vehicle polynomial model based on rational polynomials.

[0163] The second module 102 is used to estimate the stable region of the vehicle based on the vehicle polynomial model and obtain the boundary curve of the stable region by using a sum-of-squares programming algorithm.

[0164] The third module 103 is used to discretize the boundary curve of the stable region to obtain an initial point set.

[0165] The fourth module 104 is used to obtain the convex hull of the expanded stable region by reversing the trajectory based on the boundary curve of the stable region and the initial point set.

[0166] The fifth module 105 is used to use the convex hull of the expanded stability region as the expanded stability region.

[0167] It is understood that the content of the above method embodiments is applicable to this system embodiment. The specific functions implemented in this system embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0168] This application also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the method for estimating the vehicle stability domain using the extended square sum programming algorithm described above. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0169] It is understood that the content of the above method embodiments is applicable to this device embodiment. The specific functions implemented by this device embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0170] Please see Figure 6 , Figure 6 The hardware structure of an electronic device according to another embodiment is illustrated. The electronic device includes:

[0171] The processor 201 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this application.

[0172] The memory 202 can be implemented as a read-only memory (ROM), static storage device, dynamic storage device, or random access memory (RAM). The memory 202 can store the operating system and other applications. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 202 and is called by the processor 201 to execute a method for estimating the vehicle stability domain using an expanded square sum programming algorithm according to an embodiment of this application.

[0173] Input / output interface 203 is used to implement information input and output;

[0174] The communication interface 204 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, network cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0175] Bus 205 transmits information between various components of the device (e.g., processor 201, memory 202, input / output interface 203, and communication interface 204);

[0176] The processor 201, memory 202, input / output interface 203 and communication interface 204 are connected to each other within the device via bus 205.

[0177] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method for estimating the vehicle stability domain using an expanded square sum programming algorithm.

[0178] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0179] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0180] The embodiments described in this application are for the purpose of more clearly illustrating the technical solutions of the embodiments of this application, and do not constitute a limitation on the technical solutions provided by the embodiments of this application. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of this application are also applicable to similar technical problems.

[0181] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of this application, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0182] The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0183] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0184] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0185] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0186] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the system embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection through some interfaces, apparatuses, or units, and may be electrical, mechanical, or other forms.

[0187] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0188] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0189] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0190] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A method for estimating the vehicle stability domain using an extended square sum programming algorithm, characterized in that, Includes the following steps: By combining the vehicle's two-degree-of-freedom dynamics model and the rational polynomial nonlinear tire model, a whole-vehicle polynomial model based on rational polynomials is constructed. Based on the vehicle polynomial model, the vehicle stability region is estimated using a sum-of-squares programming algorithm, and the boundary curve of the stability region is obtained. Discretize the boundary curve of the stable region to obtain an initial point set; Based on the boundary curve of the stable region and the initial point set, the convex hull of the expanded stable region is obtained by reversing the trajectory; The convex hull, which expands the stability region, is taken as the expanded stability region. The step of obtaining the convex hull of the expanded stable region by reversing the trajectory based on the boundary curve of the stable region and the initial point set includes the following steps: The initial point set is used as the initial condition for solving the inverse differential equation at the first time point. The first corresponding point of each point in the initial point set is obtained by inverse integration, thus obtaining the first point set. The convex hull including the first set of points is obtained using the Quick Hull algorithm; The initial point set is used sequentially as the initial condition for solving the inverse differential equation within a preset time series, thereby obtaining the second corresponding point of each point in the initial point set, and thus obtaining the second point set; Obtain any point from the convex hull to get the current point, and obtain the inward normal vector of the current point; Construct a first preset condition based on the current point and the normal vector; Obtain a first number of points that satisfy the first preset condition from the second set of corresponding points; The second number of clusters generated by the second corresponding point is obtained using the DBSCAN algorithm; Based on the first quantity and the second quantity, the convex hull of the stability region expansion is determined.

2. The method according to claim 1, characterized in that, The process of constructing a whole-vehicle polynomial model based on rational polynomials by combining a two-degree-of-freedom vehicle dynamics model and a rational polynomial nonlinear tire model includes the following steps: Force analysis was performed on the two-degree-of-freedom dynamic model of the vehicle to obtain the vehicle dynamic equations. Based on the vertical load and the road adhesion coefficient, a fitted polynomial expression for the tire lateral force is obtained; Based on the two-degree-of-freedom dynamic model of the vehicle, the expression for the tire slip angle is obtained; Based on the tire slip angle expression, the vehicle dynamics equation and the polynomial tire lateral force expression are combined to obtain a rational polynomial vehicle polynomial model.

3. The method according to claim 1, characterized in that, The process of estimating the vehicle's stable region and obtaining the stable region boundary curve based on the vehicle polynomial model and using a sum-of-squares programming algorithm includes the following steps: Based on the aforementioned vehicle polynomial model and sum of squares formula, determine the polynomial constraints; Obtain the second-order Lyapunov function of the vehicle linearization model at the equilibrium point to obtain the initial Lyapunov function; The order of the continuously differentiable function is adjusted, and the initial Lyapunov function is iterated until the change in the shape factor of the polynomial constraint is less than a preset change threshold, thus obtaining the vehicle stability region. A stable region boundary curve is generated based on the vehicle's stable region.

4. The method according to claim 1, characterized in that, The discretization of the boundary curve of the stable region to obtain an initial point set includes: Calculate the total length of the boundary curve of the stable region; According to a preset number, points are uniformly selected from the boundary curve of the stable region, and the points are located by accumulating length to generate an initial point set.

5. The method according to claim 1, characterized in that, Determining the convex hull of the stability region expansion based on the first quantity and the second quantity includes the following steps: When the first quantity and the second quantity do not meet the second preset condition, the preset time interval is reduced or the coefficient value of the preset time interval is increased, and the process of sequentially using the initial point set as the initial condition for solving the inverse differential equation within the preset time series, obtaining the second corresponding point of each point in the initial point set, and obtaining the second point set is repeated until the first quantity and the second quantity meet the second preset condition, and the convex hull of the stability region is obtained; wherein, the second preset condition is that the first quantity is equal to 0 and the second quantity is equal to 1.

6. The method according to claim 1, characterized in that, The first preset condition is: ； in, Indicates the current point; This represents the second corresponding point after the trajectory of each point in the initial point set is reversed; This represents the normal vector pointing inwards from the current point.

7. A system for estimating the vehicle stability domain using an extended square sum programming algorithm, characterized in that, include: The first module is used to combine the vehicle's two-degree-of-freedom dynamics model and the rational polynomial nonlinear tire model to construct a whole vehicle polynomial model based on rational polynomials. The second module is used to estimate the vehicle's stable region based on the vehicle polynomial model and obtain the stable region boundary curve through a sum-of-squares programming algorithm. The third module is used to discretize the boundary curve of the stable region to obtain an initial point set. The fourth module is used to obtain the convex hull of the expanded stable region by reversing the trajectory based on the boundary curve of the stable region and the initial point set. The fifth module is used to expand the convex hull of the stability region as the expanded stability region; Specifically, the fourth module is used for: The initial point set is used as the initial condition for solving the inverse differential equation at the first time point. The first corresponding point of each point in the initial point set is obtained by inverse integration, thus obtaining the first point set. The convex hull including the first set of points is obtained using the Quick Hull algorithm; The initial point set is used sequentially as the initial condition for solving the inverse differential equation within a preset time series, thereby obtaining the second corresponding point of each point in the initial point set, and thus obtaining the second point set; Obtain any point from the convex hull to get the current point, and obtain the inward normal vector of the current point; Construct a first preset condition based on the current point and the normal vector; Obtain a first number of points that satisfy the first preset condition from the second set of corresponding points; The second number of clusters generated by the second corresponding point is obtained using the DBSCAN algorithm; Based on the first quantity and the second quantity, the convex hull of the stability region expansion is determined.

8. An electronic device, characterized in that, Including the processor and memory; The memory is used to store programs; The processor executes the program to implement the method as described in any one of claims 1 to 6.

9. A computer storage medium storing a processor-executable program, characterized in that, The processor-executable program, when executed by the processor, is used to implement the method as described in any one of claims 1 to 6.

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