Anti-rollover safety control law design method for heavy-duty vehicles based on control barrier function

Abstract

The application discloses a heavy vehicle anti-rollover safety control law design method based on a control barrier function, utilizes Newton's second law of motion and the law of conservation of angular momentum to analyze a vehicle lateral-yaw subsystem and a roll subsystem respectively, and constructs a three-degree-of-freedom state space model; the traditional lateral load transfer rate LTR for measuring vehicle rollover is re-stated by using state variables in the three-degree-of-freedom state space model, and a vehicle anti-rollover safety certificate and a barrier function are constructed; a control Lyapunov function and a control barrier function are constructed for the three-degree-of-freedom state space model, and a quadratic optimization framework is used to solve the anti-rollover control law which meets the requirements of heavy vehicle driving control tasks and the non-rollover safety constraint condition. The application does not depend on a large number of sensors and complex calculation algorithms, strives to achieve a more efficient control effect with fewer resources, and reduces the dependence on expensive hardware, so that a balance between cost and performance is found.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of vehicle control in traffic control systems, and particularly relates to a heavy vehicle anti-rollover safety control law design method based on a control barrier function. BACKGROUND

[0002] Heavy vehicles are widely used in freight logistics, construction engineering, mining, agricultural production and other fields due to their excellent transportation and carrying capacity. However, the unique structural characteristics of such vehicles, such as high center of mass, large mass and volume, and relatively narrow wheelbase, make them more prone to rollover accidents during driving. Especially in sharp turns, uphill driving or in the event of sudden situations, the risk of rollover increases significantly. In order to cope with these challenges, the research and development of anti-rollover control technology has become the focus of attention.

[0003] In recent years, existing vehicle anti-rollover technology has made considerable progress, and related research has further promoted innovation in this field. These studies mainly focus on using sensor networks, data fusion algorithms and artificial intelligence technology to enhance the stability of vehicles. For example, through multi-sensor fusion technology, real-time monitoring of vehicle speed, inclination angle, load distribution and other dynamic parameters is achieved, improving the system's ability to perceive and judge the state of the vehicle; by focusing on developing prediction models based on machine learning and artificial intelligence, historical data and real-time driving information are analyzed to predict potential rollover risks in advance and take proactive intervention measures; related research also involves vehicle chassis active control technology, which dynamically adjusts the vehicle's center of gravity position by adjusting the suspension or braking system to reduce the risk of rollover.

[0004] In contrast to the significant development of the above theoretical research, existing anti-rollover control technology faces the following challenges in practical application:

[0005] Cost and complexity: The dependence of existing anti-rollover technology on a large number of sensors and complex computing systems not only increases the cost of the system, but also makes maintenance and operation more complex, thereby limiting the popularization and application of existing anti-rollover technology;

[0006] Real-time problem: Although existing technology achieves real-time monitoring through sensors and data processing, in high-speed driving or dynamic changing environments, the system may not be able to respond to all sudden situations in time, so the lack of real-time performance may result in the system being unable to effectively prevent rollover accidents at critical moments;

[0007] Adaptability and robustness: Existing anti-rollover control technology often shows certain limitations in dealing with different terrains, weather conditions and various complex road conditions and variable working conditions, affecting its effectiveness in anti-rollover control. SUMMARY

[0008] The technical problem solved by the present application is to provide a heavy vehicle anti-rollover safety control law design method based on a control barrier function, which does not rely on a large number of sensors and complex calculation algorithms, but starts from the optimization of overall control logic and strategy, strives to achieve higher control effect with less resources, and reduces the dependence on expensive hardware, thereby balancing cost and performance.

[0009] To solve the above technical problems, the present application provides a heavy vehicle anti-rollover safety control law design method based on a control barrier function, comprising the following steps:

[0010] Step 1) Three-degree-of-freedom mathematical modeling of heavy vehicle: first, two-degree-of-freedom mathematical modeling of the lateral yaw subsystem of the heavy vehicle and single-degree-of-freedom mathematical modeling of the roll subsystem are performed, and then three-degree-of-freedom mathematical modeling of the heavy vehicle is performed according to the two-degree-of-freedom mathematical model and the single-degree-of-freedom mathematical model, to obtain a three-degree-of-freedom state space model of the heavy vehicle system;

[0011] Step 2) Construction of safety certificate based on traditional lateral load transfer rate LTR: first, the traditional lateral load transfer rate LTR is transformed, the state space variables of the three-degree-of-freedom state space model are used to describe the traditional lateral load transfer rate LTR as a new lateral load transfer rate LTR, and then the roll safety certificate and the barrier function are constructed; a safety set D is constructed for the new lateral load transfer rate LTR, the safety set D is used as a safety certificate for the new roll index LTR, a barrier function of the heavy vehicle is constructed based on the safety set D, and the characteristics of the barrier function on the safety set D and its boundary are used as a standard for judging the roll state of the heavy vehicle and designing the anti-rollover control;

[0012] Step 3) Anti-rollover safety control law design based on QP optimization solution: a control Lyapunov function is constructed to achieve the stabilization of the heavy vehicle, and a feasible set of global exponential stabilization control law of the system is obtained; then a safe control barrier function of the heavy vehicle is constructed, based on the roll safety certificate and the barrier function, the new lateral load transfer rate LTR is constrained on the set D defined by the safety certificate by using an extended K-class function and imposing constraint conditions, so that the set D is a safe invariant set, and then a feasible set of the anti-rollover safety control law of the heavy vehicle system is obtained; finally, the anti-rollover safety control law of the heavy vehicle is obtained based on the quadratic optimization QP solution.

[0013] Further, in step 1), the two-degree-of-freedom mathematical modeling of the lateral yaw subsystem is as follows:

[0014] Based on Newton's second law, the balance relationship between the lateral forces acting on the vehicle is analyzed to construct the dynamic equation of the side slip angle β at the center of gravity of the vehicle Where σ = C v +C h , ρ = Ch l h -C v l v ,C v ,C h for the rigidity coefficients of front and rear tires, l v and l h represent the distance between the vehicle center of gravity and the front axle and the distance between the vehicle center of gravity and the rear axle, v x is the forward speed of the vehicle, and δ is the front wheel steering angle.

[0015] Based on the angular momentum conservation theorem, the steering motion equation of the vehicle body under the action of lateral force on the tire is obtained:

[0016] where J zz is the moment of inertia of the vehicle body yaw rotation, is the steering angular velocity at the center of gravity of the vehicle body.

[0017] The lateral yaw subsystem of the heavy vehicle is constructed to obtain the side slip angle β and the steering angular velocity at the center of gravity as state variables, and the state space model is:

[0018] The two-degree-of-freedom mathematical modeling is completed.

[0019] Further, in step 1), the single-degree-of-freedom mathematical modeling of the roll subsystem is as follows:

[0020] Based on the parallel axis momentum conservation law, the heavy vehicle roll dynamics equation is constructed:

[0021]

[0022] where J xeq = J xx + mh 2 is the moment of inertia of the vehicle body roll rotation, h is the rotation radius of the vehicle load roll motion, φ is the roll angle of the center of gravity of the vehicle load, a y is the acceleration of the vehicle lateral motion; and the single-degree-of-freedom mathematical modeling is completed.

[0023] Further, in step 1), the three-degree-of-freedom state space model of the heavy vehicle is obtained by combining the yaw subsystem, the lateral subsystem, and the roll subsystem:

[0024]

[0025] Further, in step 2), the new lateral load transfer rate LTR is:

[0026]

[0027] Further, in step 2, the security set D is:

[0028] D={LTR∈R|-c roll <LTR<c roll ,c roll ∈[0,1]};

[0029] The barrier function is:

[0030] h1(φ)=c roll -LTR;h2(φ)=LTR+c roll ;

[0031] The characteristics of the barrier function h i (φ),i=1,2 on the security set D and its boundary are:

[0032]

[0033] Further, in step 3), based on the three-degree-of-freedom state space model, a control Lyapunov function L Ax V(x)+L B V(x)δ≤-c3||x|| 2 is constructed, and the feasible set {δ∈R|L Ax V(x)+L B V(x)δ≤-c3||x|| 2} of the global exponential stabilization control law of the closed-loop system is given.

[0034] Further, in step 3), the control barrier function satisfies the following conditions:

[0035] And the feasible set of the system rollover safety control is ensured

[0036] The beneficial effects of the present application are:

[0037] The present application researches anti-rollover control from the perspective of control design, and provides a different, more systematic and flexible solution. Starting from advanced control theory, a more concise and direct control strategy is designed for the characteristics of heavy-duty vehicles, which can reduce the complexity of the system while ensuring the real-time and effectiveness of the system. This method does not rely on a large number of sensors and complex calculation algorithms, but starts from the optimization of overall control logic and strategy, striving to achieve more efficient control effect with less resources, and reducing the dependence on expensive hardware, balancing between cost and performance.

[0038] Compared with the existing heavy vehicle rollover control technology, the present application fully depicts the influence of the roll dynamics on the dynamic characteristics of the heavy vehicle by utilizing the lateral subsystem, the yaw subsystem and the roll subsystem to form a three-degree-of-freedom state space model, and then the rollover control problem of the heavy vehicle is converted into the control design problem of the heavy vehicle under the state constraint by means of the barrier function; meanwhile, the automatic solution of the rollover control law is realized by utilizing the quadratic optimization framework, the complexity and difficulty brought by the traditional analytic control law design are avoided, the obtained rollover control law can not only ensure the no-rollover safety of the heavy vehicle during the running process, but also can effectively reduce the hardware cost of the existing vehicle control system updating and upgrading, and bring convenience for the actual engineering implementation and practical application. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 is the flow chart of the present application;

[0040] Figure 2 is the motion schematic diagram of the lateral yaw subsystem of the heavy vehicle of the present application;

[0041] Figure 3 is the motion schematic diagram of the roll subsystem of the heavy vehicle of the present application;

[0042] Figure 4 is the state change schematic diagram of the vehicle without adopting the rollover control scheme;

[0043] Figure 5 is the lateral load transfer rate change schematic diagram of the vehicle without adopting the rollover control scheme;

[0044] Figure 6 is the state change schematic diagram of the vehicle adopting the rollover control scheme of the present application;

[0045] Figure 7 is the lateral load transfer rate change schematic diagram of the vehicle adopting the rollover control scheme of the present application. DETAILED DESCRIPTION

[0046] The present application will be further described below in combination with the drawings and specific embodiments, so that those skilled in the art can better understand the present application and implement it, but the embodiments are not as the limitation of the present application.

[0047] Figure 1 is the flow chart of the implementation steps of the present application, and the implementation of the rollover safety control law design method of the heavy vehicle of the present application based on the control barrier function is as follows:

[0048] Step 1: three-degree-of-freedom mathematical modeling of the heavy vehicle:

[0049] First, the two-degree-of-freedom mathematical modeling of the lateral subsystem and the yaw subsystem of the heavy vehicle is carried out;

[0050] As shown in Figure 2 , the two front wheels and the two rear wheels of the vehicle are virtually located at the center of the vehicle, denoted as C v ,C h are the rigid coefficients of the front and rear tires, and α v ,α h are the side slip angles of the front and rear wheels, respectively. The lateral forces on the front and rear wheels of the heavy vehicle are denoted as S v =C v α v and S h =C h α h , respectively. Based on the side slip angle β at the center of mass of the vehicle body and the steering angular velocity The front and rear wheel side slip angles are further described as:

[0051]

[0052] where δ is the front wheel steering angle, l v and l h represent the distances between the center of mass of the vehicle and the front and rear axles, and v x is the forward speed of the vehicle.

[0053] Based on Newton's second law, the balance relationship between the lateral forces on the heavy vehicle can be obtained as follows:

[0054]

[0055] m is the sprung mass. By substituting α h in the formula, we get Further rearrangement of the formula using α v yields

[0056]

[0057] where σ = C v +C h , and ρ = C h l h -C v l v .

[0058] Using the angular momentum conservation theorem, the steering motion equation of the vehicle body under the action of the lateral forces on the tires is obtained as:

[0059]

[0060] By substituting α v ,α h in the formula, we get

[0061]

[0062] Among them, J zz The moment of inertia of the vehicle body during yaw rotation.

[0063] By combining the above equations of lateral motion and steering motion, we can obtain the sideslip angle β and steering angular velocity at the center of gravity for the lateral subsystem and yaw subsystem of the heavy-duty vehicle. State-space model describing state variables:

[0064]

[0065] Then, a single-degree-of-freedom mathematical model of the roll subsystem was performed:

[0066] like Figure 3 As shown, a linear force T is applied to the suspension system. spring =kφ and Under the conditions (where constant k is the deformation constant of the spring in the suspension system and constant c is the number of damping systems in the suspension system), the torque balance equation can be obtained based on the law of conservation of parallel axis momentum:

[0067]

[0068] Among them, J xeq =J xx +mh 2 J is the moment of inertia of the vehicle body during roll rotation. xx Let g be the moment of inertia of the sprung mass of the heavy-duty vehicle about the roll axis passing through its center of gravity, h be the radius of rotation of the vehicle's load roll motion, φ be the roll angle of the vehicle's load center of gravity, and a be the moment of inertia of the sprung mass of the heavy-duty vehicle about its roll axis passing through its center of gravity. y Let φ be the acceleration of the vehicle's lateral motion. When φ is small, by simplifying using cosφ≈1 and sinφ≈0, we can obtain the following equation of motion for the roll subsystem:

[0069]

[0070] Then, a three-degree-of-freedom mathematical model of the heavy-duty vehicle was developed:

[0071] Considering the influence of the roll subsystem on the lateral motion of heavy-duty vehicles, the lateral motion equation is rewritten as:

[0072]

[0073] Or it can be written as:

[0074]

[0075] Furthermore, the equation of motion for the vehicle body sideslip angle β considering roll dynamics is obtained:

[0076]

[0077] Utilizing Further refining the lateral dynamics subsystem, we can obtain:

[0078]

[0079] With the above yaw subsystem, lateral subsystem and roll subsystem, we can obtain the following three degrees of freedom state space model of heavy vehicle:

[0080]

[0081] Step 2: LTR-based safety certificate construction;

[0082] First, the lateral load transfer rate LTR is converted. The traditional lateral load transfer rate index

[0083] In traditional methods, the support forces F L and F R not only need to be equipped with additional sensors, but also directly affect the accuracy and timeliness of subsequent rollover control law.

[0084] As shown in Figure 3 , the roll motion around the roll center of rotation, the moment balance analysis can be obtained:

[0085] (where T is the wheelbase between the left and right wheels of the vehicle).

[0086] Thus, the traditional roll index LTR can be further described by the state space variables of the three degrees of freedom state space model to obtain a new lateral load transfer rate LTR:

[0087]

[0088] Roll safety certificate and barrier function construction;

[0089] For the above new lateral load transfer rate LTR, the following safety set D is constructed:

[0090] D = {LTR ∈ R | -c roll <LTR<c roll ,c roll ∈ [0, 1]} as the new lateral load transfer rate LTR safety certificate, where the constant c roll is the safety constraint boundary imposed on the new lateral load transfer rate LTR, R is the usual set of real numbers, and further based on the safety set D, the barrier function h of the heavy vehicle system is constructedi (φ), i = 1, 2:

[0091] h1(φ)=c roll -LTR; h2(φ)=LTR+c roll

[0092] Using the above obstacle function h i The following properties of (φ), i=1,2 on the safe set D and its boundary:

[0093] As a standard for judging the vehicle's roll state and for designing rollover prevention controls.

[0094] Step 3: Design of anti-rollover safety control law based on QP optimization solution, specifically, first constructing the control Lyapunov function to achieve vehicle stabilization.

[0095] Based on the fact that a fully controllable three-degree-of-freedom system must have a globally exponentially stabilizing control law, and using the inverse existence theorem of Lyapunov functions, it is certain that a positive definite Lyapunov function V(x) exists that satisfies...

[0096] c1||x|| 2 ≤V(x)≤c2||x|| 2

[0097] L Ax V(x)+L B V(x)δ≤-c3||x|| 2

[0098]

[0099] Where c1, c2, c3, and c4 are positive constants, and L denotes the derivative of the Lie derivative. Furthermore, based on the Lyapunov function V(x) mentioned above, the feasible set of global exponentially stabilizing control laws for the system is obtained:

[0100] {δ∈R|L Ax V(x)+L B V(x)δ≤-c3||x|| 2}

[0101] Subsequently, a control obstacle function to achieve vehicle safety is constructed. Based on the roll safety certificate and obstacle function given above, α is selected. i (i = 1, 2) are extended K-class functions with the following constraints:

[0102]

[0103] The new lateral load transfer ratio LTR can be constrained on the set defined by the safety certificate, i.e. the safety set D is a safety invariant set. Given that the condition can be re-described as:

[0104]

[0105] So h i (φ) (i = 1, 2) are also called control barrier functions of the heavy vehicle system.

[0106] Based on the constructed control barrier function h i (φ), the feasible set of the heavy vehicle system's rollover prevention safety control law can be obtained as follows:

[0107]

[0108] Finally, the rollover prevention safety control law of the heavy vehicle based on the quadratic optimization (QP) solution is constructed;

[0109] In order to obtain the control law that meets the system's stabilization control and rollover prevention safety at the same time, the following quadratic optimization (QP) framework is used:

[0110]

[0111] L Ax V(x) + L B V(x) δ ≤ -c3||x|| 2 + ε,

[0112] L Ax h1(φ) + L B h1(φ) δ ≥ -α1(h1(φ)),

[0113] L Ax h2(φ) + L B h2(φ) δ ≥ -α2(h1(φ)),

[0114] Under the premise of minimum modification of the existing vehicle control law δ nominal (x), the rollover prevention safety control law δ(·) that meets the heavy vehicle system's stabilization and rollover prevention constraints at the same time is obtained.

[0115] Heavy vehicle rollover prevention safety control case comparison, in order to further understand the present application, the application of the present application and the application of the present application are compared and verified, but it should be understood that these verifications are only for further illustration of the features and advantages of the present application, and are not a limitation of the claims of the present application.

[0116] Based on the selected heavy vehicle parameters as follows:

[0117] Parameter Value Unit Parameter Value Unit v x ]]> 50 m / s J xx ]]> 362.6 Kg.m 2 / s]] m 1224 Kg J zz ]]> 1280 Kg.m 2 / s]] h 0.375 m [C v ]]> 90240 N / rad l v ]]> 1.102 m C h ]]> 180000 N / rad l h ]]> 1.25 m T 1.51 m c 4000 Kg.m 2 / s]] k 36075 Kg.m 2 / s]]

[0118] Figures 4-7 Fig. 2 and Fig. 3 are control effect comparison diagrams of not using the embodiment of the present application and using the embodiment of the present application respectively. Although Figure 4 and Figure 6 all state variables in the system converge to a steady state, but Figure 5 the results show that the lateral load transfer ratio LTR of the vehicle in the state convergence process has broken through the safety constraint boundary. In contrast, Figure 7 shows that the lateral load transfer ratio LTR of the vehicle is always within the safety constraint range after using the embodiment of the present application, thereby realizing the design of rollover prevention control during the driving process of heavy vehicles.

[0119] The symbols appearing in the above equations with dots on top are first derivative or second derivative expressions, which are existing expressions and will not be described in detail.

[0120] The above-described embodiments are only preferred embodiments of the present application, and the protection scope of the present application is not limited thereto. Any equivalent replacement or transformation made by those skilled in the art based on the present application is within the protection scope of the present application.

Claims

1. A method for designing a rollover prevention safety control law for heavy-duty vehicles based on a control obstacle function, characterized in that, Includes the following steps: Step 1) Three-degree-of-freedom mathematical modeling of heavy-duty vehicles: First, perform two-degree-of-freedom mathematical modeling of the lateral yaw subsystem and single-degree-of-freedom mathematical modeling of the roll subsystem of the heavy-duty vehicle. Then, perform three-degree-of-freedom mathematical modeling of the heavy-duty vehicle based on the two-degree-of-freedom mathematical model and the single-degree-of-freedom mathematical model to obtain the three-degree-of-freedom state-space model of the heavy-duty vehicle system. Step 2) Safety certificate construction based on traditional lateral load transfer ratio (LTR): First, the traditional lateral load transfer ratio (LTR) is transformed. The state space variables of a three-degree-of-freedom state-space model are used to redefine the traditional lateral load transfer ratio (LTR) as a new lateral load transfer ratio (LTR). Then, roll safety certificate and obstacle function are constructed. For the new lateral load transfer ratio (LTR), a safety set D is constructed. The safety set D serves as the safety certificate for verifying the new roll index (LTR). An obstacle function for heavy-duty vehicles is constructed based on the safety set D. The characteristics of the obstacle function on the safety set D and its boundaries are used as the standard for judging the roll state of heavy-duty vehicles and designing rollover prevention control. Step 3) Design of anti-rollover safety control law based on QP optimization: Construct a control Lyapunov function to achieve stabilization of heavy-duty vehicles, and obtain the feasible set of global exponential stabilization control laws for the system; select the obstacle function from Step 2) as the control obstacle function for heavy-duty vehicle safety, and based on the rollover safety certificate and the obstacle function, adopt an extended... The new lateral load transfer rate (LTR) is constrained to the set D defined by the safety certificate by applying a class function and applying constraints, making set D a safety-invariant set, thereby obtaining the feasible set of the rollover-free safety control law for the heavy-duty vehicle system; finally, the rollover-prevention safety control law for the heavy-duty vehicle is obtained by solving the quadratic optimization QP. In step 2), the new lateral load transfer rate (LTR) is: , m For the sprung mass, Let be the deformation constant of the spring in the suspension system. This refers to the damping coefficient of the damper in the suspension system. The roll angle is the center of gravity of the vehicle's load. The track width between the left and right wheels of the vehicle; In step 2), the safety set D is: ; It is a constant, representing the safety constraint boundary imposed on the new transverse load transfer rate LTR; The barrier function is: ； Using the above barrier function The properties of the safe set D and its boundary are: 。 2. The method for designing anti-rollover safety control laws for heavy-duty vehicles based on control obstacle functions as described in claim 1, characterized in that, In step 1), the two-degree-of-freedom mathematical modeling steps of the lateral yaw subsystem are as follows: Based on Newton's second law, the balance relationship between the lateral forces acting on the vehicle is analyzed to construct the sideslip angle at the vehicle's center of gravity. dynamic equations ;in , These are the stiffness coefficients of the front and rear tires. and This indicates the distance between the vehicle's center of gravity and the front axle, and between the vehicle's center of gravity and the rear axle. The forward speed of the vehicle. This refers to the front wheel steering angle; Based on the law of conservation of angular momentum, the equation of motion for the vehicle body steering under the action of the lateral force on the tire is obtained: ;in, The moment of inertia of the vehicle body during yaw rotation. , The steering angular velocity at the vehicle's center of gravity; Construct a lateral yaw subsystem for heavy-duty vehicles with sideslip angle at the center of gravity. With steering angular velocity State-space model for state variables: Complete the mathematical modeling of two degrees of freedom.

3. The method for designing anti-rollover safety control laws for heavy-duty vehicles based on control obstacle functions as described in claim 2, characterized in that, In step 1), the steps for mathematical modeling the single degree of freedom of the roll subsystem are as follows: Constructing the roll dynamics equations for heavy-duty vehicles based on the law of conservation of momentum along parallel axes: ； in, The moment of inertia of the vehicle's roll rotation. The radius of rotation for the vehicle's roll motion under load. The roll angle is the center of gravity of the vehicle's load. Given the acceleration of the vehicle's lateral motion; complete the mathematical modeling for a single degree of freedom. J xx Let $\frac{ ... Let be the deformation constant of the spring in the suspension system. This refers to the damping coefficient of the damper in the suspension system. m This refers to the sprung mass.

4. The method for designing anti-rollover safety control laws for heavy-duty vehicles based on control obstacle functions as described in claim 3, characterized in that, In step 1), by combining the yaw subsystem, lateral subsystem, and roll subsystem, the following three-degree-of-freedom state-space model of the heavy-duty vehicle is obtained: 。 5. The method for designing anti-rollover safety control laws for heavy-duty vehicles based on control obstacle functions as described in claim 1, characterized in that, In step 3), based on the three-degree-of-freedom state-space model, a system is constructed that satisfies... By controlling the Lyapunov function, a feasible set of global exponentially stabilized control laws for the closed-loop system is obtained. , For Lyapunov functions, It is a positive number.

6. The method for designing anti-rollover safety control laws for heavy-duty vehicles based on control obstacle functions as described in claim 5, characterized in that, In step 3), the control barrier function satisfies the following condition: And obtain a feasible set of control measures to ensure the system has no rollover safety. .

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