Method and system for expanding vehicle stability domain estimated by quadratic sum planning algorithm

Abstract

The invention discloses a method and a system for expanding a vehicle stability domain estimated by a quadratic sum planning algorithm, and belongs to the technical field of computers, and the method comprises the following steps: constructing a vehicle polynomial model based on a rational polynomial by combining a vehicle two-degree-of-freedom dynamic model and a rational polynomial nonlinear tire model; based on the vehicle polynomial model, estimating a vehicle stable region through a quadratic sum planning algorithm to obtain a stable region boundary curve; performing discrete processing on the stable region boundary curve to obtain an initial point set; according to the stable region boundary curve and the initial point set, obtaining a convex hull with an expanded stable region through track inversion; and taking the convex hull with the expanded stable region as an expanded stable region. The maximum estimation of the stability domain boundary can be realized, the conservative type of the stability domain is greatly improved, the judgment of the vehicle stability is more accurate, and the improvement of the reliability of the vehicle stability control is facilitated.

Description

Technical Field

[0001] The present application relates to the field of computer technology, and in particular to a method and system for expanding a vehicle stability domain estimated by a sum-of-squares programming algorithm. Background Art

[0002] The vehicle stability region can reflect and evaluate the stability performance of the vehicle to a certain extent. Common 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 the linear model, and its accuracy and reliability are limited when faced with nonlinear characteristics and complex driving behaviors. For nonlinear systems, there is currently no universal method to estimate a suitable Lyapunov function.

[0003] Since rational functions can capture the nonlinearity of tires more effectively than polynomials, the sum-of-squares programming (SOSP) not only needs to apply the polynomial tire model, but also can use the semi-positive definite programming (SDP) to automatically search for the optimal polynomial Lyapunov function, so the sum-of-squares programming can provide a more accurate estimation of the stable region during vehicle driving. However, the S-Procedure process of the SOS technology is a sufficient condition, which inevitably leads to the conservatism of the stable region estimation. In order to improve vehicle safety, adaptability and comfort, expanding the vehicle stability domain is an inevitable trend in the development and innovation of automotive technology. However, the relevant technologies have deficiencies in estimating the vehicle stability region and cannot correctly expand the stability region. Summary of the invention

[0004] The main purpose of the embodiments of the present application is to propose a method and system for expanding the vehicle stability region 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 purpose, an embodiment of the present application provides a method for expanding a vehicle stability region estimated by a sum-of-squares programming algorithm, the method comprising:

[0006] Combining the vehicle two-degree-of-freedom dynamics model and the rational polynomial nonlinear tire model, a vehicle polynomial model based on rational polynomials is constructed;

[0007] Based on the vehicle polynomial model, the vehicle stability region is estimated by a square sum programming algorithm to obtain a stable region boundary curve;

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

[0009] According to the stable region boundary curve and the initial point set, obtaining the convex hull of the expanded stable domain by trajectory inversion;

[0010] The convex hull obtained by enlarging the stable domain is used as the enlarged stable region.

[0011] In some embodiments, the step of combining the two-degree-of-freedom dynamics model of the vehicle and the rational polynomial nonlinear tire model to construct a rational polynomial-based vehicle polynomial model comprises the following steps:

[0012] Perform force analysis on the two-degree-of-freedom dynamics model of the vehicle to obtain the vehicle dynamics equation;

[0013] According to the vertical load and the road adhesion coefficient, the fitted polynomial tire lateral force expression is obtained;

[0014] According to the two-degree-of-freedom dynamic model of the vehicle, an 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 based on the vehicle polynomial model by a square sum programming algorithm to obtain a stable region boundary curve comprises the following steps:

[0017] Determining polynomial constraints according to the vehicle polynomial model and the sum-of-squares formula;

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

[0019] Adjusting the order of the continuously differentiable function, iterating the initial Lyapunov function until the change in the shape factor of the polynomial constraint is less than a preset change threshold, and obtaining a vehicle stability region;

[0020] A stability region boundary curve is generated according to the vehicle stability region.

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

[0022] Calculating 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 cumulative length to generate an initial point set.

[0024] In some embodiments, the step of obtaining the convex hull of the expanded stable domain by trajectory inversion according to the stable region boundary curve and the initial point set comprises the following steps:

[0025] Using the initial point set as the initial condition for solving the inverse differential equation at the first time point, obtaining the first corresponding point of each point in the initial point set by reverse integration, and obtaining a first point set;

[0026] Obtaining a convex hull including the first point set by using a Quick Hull algorithm;

[0027] Sequentially using the initial point set as initial conditions for solving the inverse differential equation in a preset time series, obtaining a second corresponding point of each point in the initial point set, and obtaining a second point set;

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

[0029] Constructing a first preset condition according to the current point and the normal vector;

[0030] Acquire a first number of points satisfying a first preset condition from the second corresponding point set;

[0031] Obtaining a second number of clusters generated by the second corresponding points by using a DBSCAN algorithm;

[0032] A convex hull of an expanded stable domain is determined according to the first number and the second number.

[0033] In some embodiments, determining the convex hull of the expanded stable domain according to the first number and the second number comprises the following steps:

[0034] When the first number and the second number do not meet the second preset condition, reduce the preset time interval or increase the coefficient value of the preset time interval, 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 number and the second number meet the second preset condition, and obtain the convex hull with the expansion of the stable domain; wherein the second preset condition is that the first number is equal to 0 and the second number is equal to 1.

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

[0036] (x i -p k )·n i >0;

[0037] Among them, x i Indicates the current point; p k Indicates the second corresponding point after the trajectory of each point in the initial point set is reversed; n i Represents the inward normal vector of the current point.

[0038] To achieve the above purpose, another aspect of the embodiment of the present application provides a system for expanding the vehicle stability region estimated by the sum-of-squares programming algorithm, the system comprising:

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

[0040] The second module is used to estimate the vehicle stability area through a square sum programming algorithm based on the vehicle polynomial model to obtain a stable area boundary curve;

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

[0042] A fourth module is used to obtain the convex hull of the expanded stable domain by trajectory inversion according to the stable region boundary curve and the initial point set;

[0043] The fifth module is used to use the convex hull of the expanded stable domain as the expanded stable region.

[0044] To achieve the above-mentioned purpose, another aspect of an embodiment of the present application provides an electronic device, the electronic device comprising a memory and a processor, the memory storing a computer program, and the processor implementing the above-mentioned method when executing the computer program.

[0045] To achieve the above objective, another aspect of an embodiment of the present application provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method described above is implemented.

[0046] The embodiments of the present application include at least the following beneficial effects: The present application provides a method and system for expanding the vehicle stability domain estimated by the sum-of-squares programming algorithm. The scheme constructs a polynomial model of the entire vehicle and estimates the boundary curve of the stable region, discretizes the boundary curve of the stable region to obtain an initial point set, and performs trajectory inversion based on the initial point set to obtain the convex hull of the expanded stable domain. This can achieve the maximum estimation of the boundary of the stable domain, greatly improve the conservatism of the stable domain, make the judgment of vehicle stability more accurate, and help improve the reliability of vehicle stability control. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The accompanying drawings are used to provide further understanding of the technical solution of the present application and constitute a part of the specification. Together with the embodiments of the present application, they are used to explain the technical solution of the present application and do not constitute a limitation on the technical solution of the present application.

[0048] Figure 1is a flow chart of a method for expanding a vehicle stability domain estimated by a sum-of-squares programming algorithm provided in an embodiment of the present application;

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

[0050] Figure 3 It is a schematic diagram of stable regions of different orders estimated by SOSP provided in an embodiment of the present application;

[0051] Figure 4 It is a schematic diagram of a stable region obtained by performing trajectory reversal based on SOSP provided in an embodiment of the present application;

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

[0053] Figure 6 It is a schematic diagram of the hardware structure of the electronic device provided in the embodiment of the present application. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application is further described in detail below in conjunction with the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application. When the following description refers to the 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 the embodiments of the present application. They are only examples of devices and methods consistent with some aspects of the embodiments of the present application as detailed in the attached claims.

[0055] Although the functional modules are divided in the system schematic diagram and the 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 above drawings 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 can be used to describe various concepts in this article, but unless otherwise specified, these concepts are not limited by these terms. These terms are only used to distinguish one concept from another concept. For example, without departing from the scope of the embodiment of the present application, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the words "if" and "if" as used herein can be interpreted as "at the time of" or "when" or "in response to determination".

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

[0058] Reference to "embodiments" herein means that a particular feature, structure, or characteristic described in conjunction with the embodiments may be included in at least one embodiment of the present application. The appearance of the phrase in various locations in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described herein may be combined with other embodiments.

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

[0060] In the related technology, rational functions can capture the nonlinearity of tires more effectively than polynomials. The sum of squares programming (SOSP) not only needs to apply the polynomial tire model, but also can use the semi-positive definite programming (SDP) to automatically search for the optimal polynomial Lyapunov function, so the sum of squares programming can provide a more accurate estimation of the stable area during vehicle driving. However, the S-Procedure process of the SOS technology is a sufficient condition, which inevitably leads to the conservatism of the stable area estimation. In order to improve vehicle safety, adaptability and comfort, expanding the vehicle stability domain is an inevitable trend in the development and innovation of automobile technology. However, the related technology has deficiencies in the estimation of the vehicle stability area and cannot correctly expand the stability area.

[0061] In view of this, a method and system for expanding the vehicle stability domain estimated by the sum-of-squares programming algorithm are provided in an embodiment of the present application. The scheme uniformly selects points on the stable region estimated by SOSP as the initial point set of the trajectory reversal method, obtains a discrete point set by reverse scoring, and then finds the convex hull of the discrete point set. After multiple iterative cycles, the stable region estimated by SOSP is expanded, thereby improving the conservatism of the stable region estimated by SOSP and achieving the correct expansion of the stable region.

[0062] A method for expanding the stability domain of a vehicle estimated by a sum-of-squares programming algorithm provided in an embodiment of the present application relates to the field of computer technology. A method for expanding the stability domain of a vehicle estimated by a sum-of-squares programming algorithm provided in an embodiment of the present application can be applied to a terminal, can be applied to a server, or can be software running in a terminal or a server. In some embodiments, the terminal can be a smart phone, a tablet computer, a laptop computer, a desktop computer, a smart speaker, a smart watch, and a vehicle-mounted terminal, etc., but is not limited to this; the server side can be configured as an independent physical server, or can be configured as a server cluster or distributed system composed of multiple physical servers, and can also be configured as a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, 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 that implements a method for expanding the stability domain of a vehicle estimated by a sum-of-squares programming algorithm, etc., but is not limited to the above forms.

[0063] The present application can be used in many general or special computer system environments or configurations. For example: 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, distributed computing environments including any of the above systems or devices, etc. The present 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. The present application can also be practiced in distributed computing environments, in which tasks are performed by remote processing devices connected through a communication network. In a distributed computing environment, program modules can be located in local and remote computer storage media including storage devices.

[0064] Figure 1 is an optional flowchart of a method for expanding the vehicle stability domain estimated by the sum-of-squares programming algorithm provided in an embodiment of the present application, Figure 1The method may include but is not limited to steps S100 to S500.

[0065] Step S100, combining the two-degree-of-freedom dynamics model of the vehicle and the rational polynomial nonlinear tire model, constructing a rational polynomial-based vehicle polynomial model.

[0066] Step S200, based on the vehicle polynomial model, the vehicle stability region is estimated by a square sum programming algorithm to obtain a stable region boundary curve.

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

[0068] Step S400: obtaining the convex hull of the expanded stable domain by trajectory inversion according to the stable region boundary curve and the initial point set.

[0069] Step S500: taking the convex hull of the expanded stable region as the expanded stable region.

[0070] In steps S100 to S500 shown in the embodiment of the present application, a polynomial model of the whole vehicle is constructed and a stable region boundary curve is estimated. The stable region boundary curve is discretized to obtain an initial point set. Trajectory inversion is performed based on the initial point set to obtain an expanded convex hull of the stable domain. This can achieve a maximum estimate of the stable domain boundary, greatly improve the conservatism of the stable domain, 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, performing force analysis on the two-degree-of-freedom dynamics model of the vehicle to obtain a vehicle dynamics equation.

[0073] Step S120, obtaining a fitted polynomial tire lateral force expression according to the vertical load and the road adhesion coefficient.

[0074] Step S130, obtaining an expression for the tire slip angle according to the two-degree-of-freedom dynamic model of the vehicle.

[0075] Step S140, 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.

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

[0077] Step S210, determining polynomial constraints according to the vehicle polynomial model and the sum-of-squares formula;

[0078] Step S220, obtaining a second-order Lyapunov function of the vehicle linearization model at the equilibrium point to obtain an initial Lyapunov function;

[0079] Step S230, adjusting the order of the continuously differentiable function, iterating the initial Lyapunov function until the change in the shape factor of the polynomial constraint is less than a preset change threshold, and obtaining a vehicle stability region;

[0080] Step S240: generating a stable region boundary curve according to 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, calculating the total length of the stable region boundary curve;

[0083] Step S320 , uniformly selecting points from the boundary curve of the pre-stable region according to a preset number, locating the points by cumulative length, and generating 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, using the initial point set as the initial condition for solving the inverse differential equation at the first time point, obtaining the first corresponding point of each point in the initial point set by reverse integration, and obtaining the first point set;

[0086] Step S420, obtaining a convex hull including the first point set by using a Quick Hull algorithm;

[0087] Step S430, sequentially using the initial point set as initial conditions for solving the inverse differential equation in a preset time series, obtaining a second corresponding point of each point in the initial point set, and obtaining a second point set;

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

[0089] Step S450, constructing a first preset condition according to the current point and the normal vector;

[0090] Step S460, acquiring a first number of points satisfying a first preset condition from the second corresponding point set;

[0091] Step S470, obtaining a second number of clusters generated by the second corresponding points by using a DBSCAN algorithm;

[0092] Step S480: determining the convex hull of the expanded stable domain according to the first number and the second number.

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

[0094] (x i -p k )·n i >0;

[0095] Among them, x i Indicates the current point; p k Represents the second corresponding point of each point in the initial point set; n i Represents the inward normal vector of the current point.

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

[0097] Step S481, when the first number and the second number do not meet the second preset condition, reduce the preset time interval or increase the coefficient value of the preset time interval, 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 number and the second number meet the second preset condition, and obtain the convex hull with the expansion of the stable domain; wherein the second preset condition is that the first number is equal to 0 and the second number is equal to 1.

[0098] The following is a detailed description of the embodiments of the present invention with reference to specific application examples:

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

[0100] is the sideslip angular velocity of the center of mass; is the yaw angular acceleration; m is the vehicle mass; v x is the longitudinal velocity; f y is the tire curve fitting formula; μ is the road adhesion coefficient; n i is the numerator in the rational tire lateral force formula; d i is the denominator in the rational tire lateral force formula; n f is the numerator of the front wheel lateral force; n r Denominator of the front wheel lateral force; d r is the denominator of the rear wheel lateral force; d f is the denominator of the front wheel lateral force; x is the state variable of the vehicle system; is the derivative of the state variable of the whole vehicle system; N is the numerator of the whole vehicle rational system; D is the denominator of the whole vehicle rational system; I z is the moment of inertia of the vehicle around the z-axis; Ω is the attraction domain of the system; t is time; x0 is the equilibrium point of the system; c is the boundary parameter of the attraction domain; λ is the shape factor of the polynomial constraint; R represents a real number set; β is the sideslip angle of the center of mass of the constructed model; w is the yaw angular velocity of the model; F yf is the cornering force of the front tire; F yr is the front wheel tire cornering force; δ is the vehicle front wheel turning angle; I z is the moment of inertia of the vehicle around the z-axis in the vehicle coordinate system; L f is the front wheelbase of the vehicle; L r is the rear wheelbase of the vehicle; α i represents the sideslip angle, i=f,r, f represents the front wheel, r represents the rear wheel; p1, p2, q1, q2 are all tire lateral force coefficients, among which p1 and p2 are the coefficients of the numerator of the tire fitting formula, q1 and q2 are the coefficients of the denominator of the tire fitting formula, which can be obtained by fitting the tire curve using the least squares method.

[0101] In an embodiment of the present application, a method for expanding the vehicle stability region estimated by the sum-of-squares programming algorithm is provided. The method can be applied to expand the stability region during vehicle driving determined by SOSP. Further, the method can be implemented as the following steps 1 to 5:

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

[0103] Specifically, according to Figure 2 The two-degree-of-freedom model shown in the figure is used for force analysis, and the vehicle dynamics equation is established as follows:

[0104]

[0105] Construct a rational polynomial function to fit the tire lateral force curve. The fitting formula is:

[0106]

[0107] Introducing the vertical load and road adhesion coefficient into the fitting formula, the polynomial tire lateral force can be obtained, which is expressed as:

[0108]

[0109] The tire slip angle is obtained based on the vehicle two-degree-of-freedom model analysis. The expression of the tire slip angle is:

[0110]

[0111] The vehicle dynamics equation and the polynomial tire lateral force are combined and simplified using the tire slip angle formula to obtain a rational polynomial vehicle polynomial model. The expression of the vehicle polynomial model can be:

[0112]

[0113] The expression of the vehicle polynomial model is written in the form of standard state space:

[0114]

[0115] Step 2: Based on the vehicle polynomial model constructed in step 1, estimate the vehicle stability area through the square sum programming algorithm.

[0116] Specifically, first derive the square sum formula, the vehicle system The attraction domain at the equilibrium point is:

[0117]

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

[0119]

[0120] in, 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 attraction domain, that is, the stable domain of the system. Define a region containing variables s = {x∈R 2 |s(x)<θ}, maximizes λ and satisfies Then the problem of solving the stability domain can be transformed into an optimization problem:

[0122] max{λ}

[0123]

[0124] According to the Generalized S-procedure, the above constraints are transformed into empty set constraints:

[0125] max{λ}

[0126]

[0127] x≠0 is not a semi-algebraic form, so we constrain it to be equivalent to l1(x)≠0 and l2(x)≠0, where l1(x) and l2(x) are both in the form of sum of squares and are positive definite, that is:

[0128] max{λ}

[0129]

[0130] Apply the positive point theorem to transform the empty set constraint into an equality constraint, the expression is:

[0131] max{λ}

[0132]

[0133] To minimize the number of problems while ensuring that the problem does not change, take k1=k2=k3=0, q2=l1, and l1 is a factor of q1, then 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, q8, l2 = q9, Right now

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

[0135] Therefore, the expression of the square sum planning algorithm is specifically:

[0136] max{λ}

[0137]

[0138] Substitute the standard state space obtained in step 1 into the above formula and transform each constraint into a polynomial constraint. The expression of 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 used as the initial Lyapunov function for subsequent iterations.

[0142] In the iterative process, the bilinear problem in the constraints is solved by bisection, and the iterative process is:

[0143] 1) By finding l2(x) so that Established, determine the maximum value of c;

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

[0145] 3) Keep c, λ, q1(x), q2(x) fixed and find the function V(x) that satisfies all three constraints above;

[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: V(x)≤c;

[0147] Figure 3 The vehicle stability region is estimated by the square sum planning algorithm. The thin solid line in the background is the phase trajectory. The different thick lines show the stability domains obtained by V(x) at different orders, from small to large, they are 2nd order, 4th order, 6th order, and 8th order. It can be seen that the higher order V(x) has a larger stability region, but the high-order calculation is large, and the obtained stability region is still conservative in the yaw rate direction.

[0148] Step 3: Based on step 2, obtain the boundary curve of the stable region and 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 uniformly selected, and the points on the curve are located by accumulating the length to obtain enough points to form an initial point set, which is recorded as S;

[0150] Take S as the solution to the inverse differential equation at the first time point t0 The initial conditions are obtained by reverse integration to obtain the first corresponding points of each point, and the first point set S is obtained. i ;

[0151] The Quick Hull algorithm is used to obtain the i The convex hull of is denoted as Ω0. In some embodiments, first determine S i Connect the two points with the largest distance between them to form a line. Find the farthest point off the line and form a triangle with the previous two points. Use the cross product operation to determine the positional relationship between each point and the triangle. Points inside and on the triangle will not be convex hull vertices and will not be considered. Expand outward quickly until all points are inside the convex hull and record S. i All the vertices of the convex hull in sequence can be connected to obtain the i The convex hull Ω0.

[0152] Step 4: Determine whether the convex hull obtained in step 3 is the convex hull of the expanded stable domain.

[0153] Specifically, S is used as the solution for the first time series ti =t0+kΔtInverse differential equation The initial conditions are used to obtain the second point set S of the corresponding points of each point through reverse integration. i+k ; In the above, t0 is the initial time, k is the coefficient value of the preset time interval, which is a positive integer; Δt is the pre-designed time interval; t i is a time series. Trajectory reversal is to reverse the trajectory within the kΔt time interval.

[0154] Each second corresponding point obtained by each inversion is set to p k , take any point x on the convex hull Ω0 i , find the point x i The normal vector pointing inward is n i , judge (x i -p k )·n i The positive and negative of (x i -p k )·n i >0 points, the first number m; wherein the inward direction is determined as follows: assuming that 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 of clusters formed by the second corresponding points n is obtained by the DBSCAN algorithm. Specifically, given the neighborhood radius ε and the minimum number of points MinPts within the neighborhood radius that become core objects, from any point x i Start checking x i Are there at least MinPts objects in the ε neighborhood? If so, mark them as core points. If so, mark them as core points. Find all points on Ω0 that are density-reachable from a core sample point to form a cluster. Randomly select the next unvisited point from the remaining objects and repeat the above iterative process until all points are visited, and get the number of clusters n formed by the corresponding points. The general neighborhood radius ε is obtained by drawing a k-distance graph; for two-dimensional data, the value of MinPts is generally 4.

[0156] In some embodiments, the condition for determining that Ω0 is an expanded stable domain is (second preset condition): m=0 and n=1. If m=0 and n=1 are satisfied, then Ω0 is an expanded stable region. If not satisfied, repeat the above steps 4 and 5 by reducing Δt or increasing the value of k. It should be noted that the value of k needs to balance the amount of calculation and the expansion of the stable domain (the larger the k value, the larger the amount of calculation, but the stable domain may not necessarily expand), until the conditions are met to obtain the expanded stable region.

[0157] Step 5: The convex hull of the expanded stable domain is used as the expanded stable region.

[0158] The obtained expanded stable region is as follows Figure 4 As shown, Figure 4 In the figure, the thin solid line in the background is the phase trajectory, the thick black solid line represents the stability domain estimated by SOSP, and the thick dotted line represents the stability domain expanded by trajectory inversion. It can be seen that the vehicle stability domain can be significantly expanded after trajectory inversion, especially in the yaw rate direction.

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

[0160] The stability domain proposed in the embodiment of the present application is closed; compared with the open vehicle stability area, the stability is more guaranteed. Building a rational polynomial function tire model can better capture the nonlinearity of the tire, and the higher the accuracy of the resulting model; and there is no need to solve the unstable equilibrium point in the process of estimating the stability domain. The use of SOSP to estimate the stability domain does not require numerical integration and can be used for theoretical safety verification, so the estimated stability domain is more accurate. The trajectory inversion method is used to expand the SOSP to estimate the stability domain, and the maximum estimation of the boundary of the stability domain is achieved, which greatly improves the conservatism of the stability domain. This makes the judgment of vehicle stability more accurate, thereby making the vehicle stability control more reliable.

[0161] See also Figure 5 The embodiment of the present application further provides a system for expanding the vehicle stability domain estimated by the sum-of-squares programming algorithm, which can implement the above-mentioned method for expanding the vehicle stability domain estimated by the sum-of-squares programming algorithm, and the system includes:

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

[0163] The second module 102 is used to estimate the vehicle stability region through a square sum programming algorithm based on the vehicle polynomial model to obtain a stable region boundary curve;

[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 domain by trajectory inversion according to the stable region boundary curve and the initial point set;

[0166] The fifth module 105 is configured to use the convex hull obtained by enlarging the stable domain as the enlarged stable region.

[0167] It can be understood that the contents of the above method embodiments are all applicable to the present system embodiments, the functions specifically implemented by the present system embodiments 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.

[0168] The embodiment of the present application also provides an electronic device, the electronic device includes a memory and a processor, the memory stores a computer program, and the processor implements the above-mentioned method of expanding the vehicle stability domain estimated by the square sum programming algorithm when executing the computer program. The electronic device can be any intelligent terminal including a tablet computer, a vehicle-mounted computer, etc.

[0169] It can be understood that the contents of the above method embodiments are all applicable to the present device embodiments, the functions specifically implemented by the present device embodiments 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] See also Figure 6 , Figure 6 The hardware structure of an electronic device of another embodiment is illustrated, and the electronic device includes:

[0171] The processor 201 may be implemented by a general-purpose CPU (Central Processing Unit), a microprocessor, an 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 the present application;

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

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

[0174] The communication interface 204 is used to realize the communication interaction between the device and other devices. The communication can be realized through a wired manner (such as USB, network cable, etc.) or a wireless manner (such as mobile network, WIFI, Bluetooth, etc.);

[0175] Bus 205 , which 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 , the memory 202 , the input / output interface 203 and the communication interface 204 are connected to each other in communication within the device via the bus 205 .

[0177] An embodiment of the present application also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the method for estimating the vehicle stability domain by the above-mentioned expanded square sum programming algorithm.

[0178] It can be understood that the contents of the above method embodiments are all applicable to the present storage medium embodiments, the functions specifically implemented by the present storage medium embodiments 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.

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

[0180] The embodiments described in the embodiments of the present application are intended to more clearly illustrate the technical solutions of the embodiments of the present application and do not constitute a limitation on the technical solutions provided in the embodiments of the present application. Those skilled in the art will appreciate that with the evolution of technology and the emergence of new application scenarios, the technical solutions provided in the embodiments of the present application are also applicable to similar technical problems.

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

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

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

[0184] The terms "first", "second", "third", "fourth", etc. (if any) in the specification of the present application and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any of their variations are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0185] It should be understood that in the present application, "at least one (item)" means one or more, and "plurality" means two or more. "And / or" is used to describe the association relationship of associated objects, indicating that three relationships may exist. For example, "A and / or B" can mean: only A exists, only B exists, and A and B exist at the same time, where A and B can be singular or plural. The character " / " generally indicates that the objects associated before and after are in an "or" relationship. "At least one of the following" or similar expressions refers to any combination of these items, including any combination of single or plural items. For example, at least one of a, b or c can mean: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, c can be single or multiple.

[0186] In the several embodiments provided in the present application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the system embodiments described above are only schematic. For example, the division of the above units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be an indirect coupling or communication connection through some interfaces, devices or units, which can be electrical, mechanical or other forms.

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

[0188] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0189] If the integrated unit is implemented in the form of 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 the present application, 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, and the computer software product is stored in a storage medium, including multiple instructions to enable a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of various embodiments of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (Read-Only Memory, referred to as ROM), random access memory (Random Access Memory, referred to as RAM), disk or optical disk and other media that can store programs.

[0190] The preferred embodiments of the present invention are described above with reference to the accompanying drawings, but the scope of the rights of the present invention is not limited thereto. Any modification, equivalent substitution and improvement made by a person skilled in the art without departing from the scope and essence of the present invention should be within the scope of the rights of the present invention.

Claims

1. A method for expanding the vehicle stability region estimated by the sum-of-squares programming algorithm, characterized in that: The following steps are involved: Combining the vehicle two-degree-of-freedom dynamics model and the rational polynomial nonlinear tire model, a vehicle polynomial model based on rational polynomials is constructed; Based on the vehicle polynomial model, the vehicle stability region is estimated by a square sum programming algorithm to obtain a stable region boundary curve; Discretizing the boundary curve of the stable region to obtain an initial point set; According to the stable region boundary curve and the initial point set, obtaining the convex hull of the expanded stable domain by trajectory inversion; The convex hull obtained by enlarging the stable domain is used as the enlarged stable region.

2. The method according to claim 1, characterized in that The method of combining the two-degree-of-freedom dynamics model of the vehicle and the rational polynomial nonlinear tire model to construct a rational polynomial-based vehicle polynomial model includes the following steps: Perform force analysis on the two-degree-of-freedom dynamics model of the vehicle to obtain the vehicle dynamics equation; According to the vertical load and the road adhesion coefficient, the fitted polynomial tire lateral force expression is obtained; According to the two-degree-of-freedom dynamic model of the vehicle, an 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 method of estimating the vehicle stability region based on the vehicle polynomial model by a square sum programming algorithm to obtain a stable region boundary curve comprises the following steps: Determining polynomial constraints according to the vehicle polynomial model and the sum-of-squares formula; Obtain the second-order Lyapunov function of the vehicle linearization model at the equilibrium point to obtain the initial Lyapunov function; Adjusting the order of the continuously differentiable function, iterating the initial Lyapunov function until the change in the shape factor of the polynomial constraint is less than a preset change threshold, and obtaining a vehicle stability region; A stability region boundary curve is generated according to the vehicle stability region.

4. The method according to claim 1, characterized in that: The step of performing discretization on the stable region boundary curve to obtain an initial point set includes: Calculating 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 pre-stable region, and the points are located by cumulative length to generate an initial point set.

5. The method according to claim 1, characterized in that The method of obtaining the convex hull of the expanded stable domain by trajectory inversion according to the stable region boundary curve and the initial point set comprises the following steps: Using the initial point set as the initial condition for solving the inverse differential equation at the first time point, obtaining the first corresponding point of each point in the initial point set by reverse integration, and obtaining a first point set; Obtaining a convex hull including the first point set by using a Quick Hull algorithm; Sequentially using the initial point set as initial conditions for solving the inverse differential equation in a preset time series, obtaining a second corresponding point of each point in the initial point set, and obtaining a second point set; Get any point from the convex hull to get the current point, and get the normal vector inward of the current point; Constructing a first preset condition according to the current point and the normal vector; Acquire a first number of points satisfying a first preset condition from the second corresponding point set; Obtaining a second number of clusters generated by the second corresponding points by using a DBSCAN algorithm; A convex hull of an expanded stable domain is determined according to the first number and the second number.

6. The method according to claim 5, characterized in that Determining the convex hull of the expanded stable domain according to the first quantity and the second quantity comprises the following steps: When the first number and the second number do not meet the second preset condition, reduce the preset time interval or increase the coefficient value of the preset time interval, 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 number and the second number meet the second preset condition, and obtain the convex hull with the expansion of the stable domain; wherein the second preset condition is that the first number is equal to 0 and the second number is equal to 1.

7. The method according to claim 5, characterized in that The first preset condition is: (x i -p k )·n i >0; Among them, x i Indicates the current point; p k Indicates the second corresponding point after the trajectory of each point in the initial point set is reversed; n i Represents the inward normal vector of the current point.

8. A system for expanding the stability region of a vehicle estimated by a sum-of-squares programming algorithm, characterized in that: include: The first module is used to combine the vehicle two-degree-of-freedom dynamics model and the rational polynomial nonlinear tire model to construct a vehicle polynomial model based on rational polynomials; The second module is used to estimate the vehicle stability area through a square sum programming algorithm based on the vehicle polynomial model to obtain a stable area boundary curve; The third module is used to discretize the boundary curve of the stable region to obtain an initial point set; A fourth module is used to obtain the convex hull of the expanded stable domain by trajectory inversion according to the stable region boundary curve and the initial point set; The fifth module is used to use the convex hull of the expanded stable domain as the expanded stable region.

9. An electronic device, characterized in that: including a processor and a memory; The memory is used to store programs; The processor executes the program to implement the method according to any one of claims 1 to 7.

10. A computer storage medium storing a program executable by a processor, characterized in that: The program executable by the processor is used to implement the method according to any one of claims 1 to 7 when executed by the processor.

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