A lane keeping control method for a commercial vehicle considering roll stability

Abstract

The present application relates to the field of automobile technology, and more particularly to a commercial vehicle lane keeping control method considering roll stability, which first establishes a vehicle dynamics model required for lateral control and stability control research, studies the control mechanism of vehicle lateral control and roll stability control, and creates conditions for the construction of related controllers; secondly, based on the related vehicle dynamics model and vehicle state and combined with the improved MPC, a commercial vehicle lane keeping controller is designed, and the optimal control amount is calculated to realize lane keeping control; finally, based on the differential braking principle, a commercial vehicle roll stability controller is designed, wherein the upper controller is used to calculate the additional yaw moment required by the vehicle to maintain stability, and the lower controller selects the target braking wheel based on the differential braking theory and calculates the target braking torque. The present application solves the technical problems of poor lane keeping and roll stability control effect of commercial vehicles in the prior art, and the vehicle is prone to instability.

Description

Technical Field

[0001] This invention relates to the field of automotive technology, and more specifically to a lane keeping control method for commercial vehicles that takes into account roll stability. Background Technology

[0002] While significant progress has been made in lane keeping and roll stability control research both domestically and internationally, several challenges remain. For instance, lane keeping control for passenger vehicles is relatively mature, but research on commercial vehicles is less so. Certain vehicle state variables required for algorithm design are not easily obtained, hindering the algorithm's effectiveness in real-world testing. Some lane keeping algorithms exhibit poor robustness, failing to adapt to complex and changing driving environments and variations in commercial vehicle parameters, potentially posing risks in real-world applications. Regarding roll stability control, some strategies involving the addition of external equipment increase operating costs for commercial vehicles, making large-scale application difficult. Other control strategies rely heavily on model accuracy, lacking the necessary robustness and adaptability to changes in vehicle parameters and complex operating conditions. Summary of the Invention

[0003] The purpose of this invention is to provide a lane keeping control method for commercial vehicles that takes into account roll stability, aiming to solve the technical problems of poor lane keeping and roll stability control in existing commercial vehicles, which makes the vehicles prone to instability.

[0004] To achieve the above objectives, the present invention provides a lane keeping control method for commercial vehicles that considers roll stability, comprising the following steps:

[0005] Construct vehicle lateral and roll dynamics models;

[0006] Establish a lane keeping controller for commercial vehicles based on vehicle-road reference relationships;

[0007] Establish a roll stability controller for commercial vehicles;

[0008] Perform the corresponding lane keeping and roll stability control operations.

[0009] Optionally, the vehicle lateral and roll dynamics model is constructed based on the vehicle's lateral, yaw, and roll dynamics characteristics, and the state equations describing the vehicle's lateral dynamics characteristics are as follows:

[0010]

[0011] Where m is the total vehicle mass, ω is the yaw rate of the vehicle body; v y v is the lateral velocity of the vehicle. x For longitudinal velocity; l f and l r These are the distances from the front and rear axles to the vehicle's center of gravity, respectively; IZ C is the equivalent moment of inertia of the vehicle about the z-axis; f and C r δ represents the lateral stiffness of the front and rear wheels, respectively, and δ is the front wheel steering angle.

[0012] Optionally, the vehicle roll motion dynamics equations in the vehicle lateral and roll dynamics model are expressed as follows:

[0013]

[0014] Among them, I x h is the moment of inertia of the vehicle about the x-axis. r The distance from the vehicle's center of gravity to the roll center, in meters. r For the sprung mass of the vehicle, This is the equivalent roll stiffness of the suspension. is the equivalent damping coefficient of the suspension. The roll angle is... The angular velocity is the roll rate. Let a be the roll acceleration. y Let g be the lateral acceleration of the vehicle body, and g be the acceleration due to gravity.

[0015] Optionally, the commercial vehicle lane-keeping controller is established based on model predictive control theory and combined with relevant formulas from the vehicle lateral dynamics model and the vehicle-road reference model, selecting e. sL , e aL , The front wheel steering angle δ is the state variable, and e is the control variable. s e represents the lateral deviation between the vehicle's center of gravity and the road centerline. sL Let L be the lateral deviation between the aiming point and the road centerline. Then, the heading deviation at the aiming point and its rate of change can be expressed as:

[0016] e aL =ψ-ψ desL

[0017]

[0018] Among them, ψ and These are the vehicle heading angle and its first derivative, ψ. desL and The expected heading angle and its first derivative at the pre-aiming point;

[0019] The lateral deviation at the aiming point and its rate of change can be expressed as:

[0020] e sL =e s -Le aL

[0021]

[0022] Optionally, the commercial vehicle roll stability controller uses differential braking as a stability control strategy and LTR as a roll evaluation index. The upper controller calculates the additional yaw moment based on MPC, while the lower controller decides which wheels to brake based on the vehicle state and calculates the braking torque of each target braking wheel based on the additional yaw moment.

[0023] This invention provides a lane-keeping control method for commercial vehicles that considers roll stability. First, a vehicle dynamics model is established to support lateral control and stability control research, and the control mechanisms of lateral control and roll stability control are studied, creating conditions for the development of relevant controllers. Second, based on the relevant vehicle dynamics model and vehicle state, and combined with an improved MPC (Multi-Purpose Control System), a lane-keeping controller for the commercial vehicle is designed, and the optimal control quantity is calculated to achieve lane-keeping control. Finally, a roll stability controller for the commercial vehicle is designed based on the differential braking principle. The upper-level controller calculates the additional yaw moment required for the vehicle to maintain stability, while the lower-level controller selects the target braking wheel and calculates the target braking torque based on differential braking theory. This invention can, to a certain extent, reduce the driver's workload and improve vehicle driving safety and the safety of the driver's life and property. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a schematic flowchart of a lane keeping control method for commercial vehicles that takes into account roll stability according to the present invention.

[0026] Figure 2 This is a schematic diagram of the vehicle lateral dynamics model of the present invention.

[0027] Figure 3 This is a schematic diagram of the vehicle roll dynamics model of the present invention.

[0028] Figure 4 This is a schematic diagram of the vehicle-road reference model provided by the present invention.

[0029] Figure 5 This is a comparison diagram of lateral deviation under the dual lane change lane keeping test condition of a specific embodiment of the present invention.

[0030] Figure 6This is a comparison chart of heading deviations under the dual lane change lane keeping test conditions of a specific embodiment of the present invention.

[0031] Figure 7 This is a comparison diagram of the front wheel steering angle under the dual lane change lane keeping test condition of a specific embodiment of the present invention.

[0032] Figure 8 This is a comparison diagram of yaw rate under the dual lane change lane keeping test condition of a specific embodiment of the present invention.

[0033] Figure 9 This is a comparison chart of LTR under the dual-line stability test conditions of a specific embodiment of the present invention.

[0034] Figure 10 This is a comparison diagram of the centroid side slip angle under the dual-track stability test condition of a specific embodiment of the present invention.

[0035] Figure 11 This is a comparison diagram of the roll angle under the dual-track stability test conditions of a specific embodiment of the present invention.

[0036] Figure 12 This is a comparison diagram of the roll angular velocity under the dual-track stability test conditions of a specific embodiment of the present invention. Detailed Implementation

[0037] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0038] The following explains the English abbreviations and terms used in the text. The following descriptions will also use abbreviations:

[0039] Lateral load transfer rate: LTR;

[0040] Model predictive control (MPC)

[0041] Please see Figure 1 This invention provides a lane keeping control method for commercial vehicles that considers roll stability, comprising the following steps:

[0042] S1: Construct vehicle lateral and roll dynamics models;

[0043] S2: Establish a lane keeping controller for commercial vehicles based on vehicle-road reference relationships;

[0044] S3: Establish a roll stability controller for commercial vehicles;

[0045] S4: Perform the corresponding lane keeping and roll stability control operations.

[0046] The following provides further explanation of the specific process steps:

[0047] S1. Construct the vehicle's lateral and roll dynamics models;

[0048] The vehicle lateral and roll dynamics model described herein investigated the control mechanisms of vehicle lateral control and roll stability control, laying the foundation for research on lane keeping control and roll stability control of commercial vehicles.

[0049] For details, please refer to Figure 2 The provided vehicle lateral dynamics model and Figure 3 The provided vehicle roll dynamics model includes the vehicle's lateral, yaw, and roll dynamic characteristics, specifically:

[0050] By analyzing the lateral motion of the vehicle, the following equations for lateral motion and torque balance can be derived:

[0051]

[0052]

[0053] In the formula: m is the vehicle mass, ψ is the vehicle yaw angle; v y v is the lateral velocity of the vehicle. x For longitudinal velocity; F yf and F yr These are the resultant lateral forces acting on the front and rear wheels of the vehicle, respectively; f and l r These are the distances from the front and rear axles to the vehicle's center of gravity, respectively; I Z Let be the vehicle's equivalent moment of inertia about the z-axis.

[0054] When the sideslip angle is small, the relationship between the lateral force on the wheel and its sideslip angle is as follows:

[0055] F yf =C af α1

[0056] F yr =C ar α2

[0057] In the formula, C αf and C αr α1 and α2 are the lateral stiffness of the front and rear wheels, respectively; α1 and α2 are the lateral slip angles of the front and rear wheels, respectively.

[0058] The expressions for calculating the front and rear wheel slip angles are as follows:

[0059]

[0060] From the above equations, the state equations describing the lateral dynamics of the vehicle can be obtained as follows:

[0061]

[0062] To conduct research on vehicle rollover prevention control, it is necessary to establish a whole-vehicle roll dynamics model. The vehicle roll motion dynamics equations are expressed as follows:

[0063]

[0064] Among them, I x Let be the vehicle's moment of inertia about the x-axis; h be the distance from the vehicle's center of mass CG to the roll center, in meters. s For the sprung mass of the vehicle, This is the equivalent roll stiffness of the suspension. is the equivalent damping coefficient of the suspension. The roll angle is... The angular velocity is the roll rate. Let T be the roll angle acceleration, and T be the wheel track.

[0065] S2. Establish a lane keeping controller for commercial vehicles based on vehicle-road reference relationships;

[0066] The commercial vehicle lane keeping controller includes studying the vehicle-road relative position relationship and designing a commercial vehicle lane keeping controller based on MPC. Considering that commercial vehicles have large variations in vehicle parameters and inaccurate vehicle models, the traditional MPC control has been improved by incorporating the prediction error of the model into the prediction output expression of the system, thereby improving the robustness of lane keeping control.

[0067] Specifically, the design of lane keeping controllers needs to consider the vehicle-road reference position relationship, therefore a vehicle-road reference relationship model needs to be established, such as... Figure 3 The relative position of the vehicle's current position and the reference center lane line can be represented as follows, where the lane line can be obtained by image recognition and processing through a camera installed on the vehicle, which can then obtain the trajectory equation of the lane center line in the vehicle coordinate system.

[0068] Where, e s e represents the lateral deviation between the vehicle's center of gravity and the road centerline. sL This refers to the lateral deviation between the aiming point and the road centerline.

[0069] Where the aiming distance is L, the heading deviation and its rate of change at the aiming point can be expressed as:

[0070] e aL =ψ-ψdesL

[0071]

[0072] Among them, ψ and These are the vehicle heading angle and its first derivative, ψ. desL and The desired heading angle and its first derivative at the target point are given respectively.

[0073] Similarly, the lateral deviation at the aiming point and its rate of change can be expressed as:

[0074] e sL =e s -Le aL

[0075]

[0076] To achieve lane keeping control of the vehicle, based on model predictive control theory and combined with relevant formulas from the vehicle's lateral dynamics model and the vehicle-road reference model, e is selected. sL , e aL , Let be the state variable, and the front wheel steering angle δ be the control variable. The following state-space equations for continuous vehicle lane-keeping control are obtained:

[0077]

[0078] In the formula: Let u = δ be the state variable, w = ρ be the control variable, and let a = C be the disturbance variable. f +C r b = C f l f -C r l r , but

[0079]

[0080] Take e s and e a The output quantity is given by the system's output equation: Y = Cx L

[0081] In the formula,

[0082] Take sampling period T s =0.02s, discretizing the equation yields:

[0083] x(k+1)=A e x(k)+B e u(k)+De w(k)

[0084] y(k)=C e x(k)

[0085] In the formula A e =AT s +I, B e =BT s C e =CD e =DT s .

[0086] To effectively constrain the system's control increment, thereby improving control stability and reducing the system's static error, the system's control quantity u(k) is transformed into a control increment Δu(k), and this is achieved by converting the current state value... and model predicted state values The error is introduced into the prediction output expression, which in turn corrects the predicted state of the system. Therefore, the system prediction output expression for the discrete state is obtained as follows:

[0087]

[0088] In the formula: Nc is the control step size, and Np is the prediction step size;

[0089] Considering the limitations of the steering system's control range during vehicle operation, and to ensure smooth control tracking, the following constraints are imposed on the control quantity and control increment:

[0090] δ min ≤δ(k)≤δ max

[0091] Δδ min ≤Δδ(k)≤Δδ max

[0092] In the formula, δ min and δ max These represent the minimum and maximum steering angles of the front wheels, respectively. Referring to relevant literature and combining the analysis and comparison of simulation test results, we take [-25, 25] here, Δδ min and Δδ max These are the minimum and maximum values ​​of the control increment, respectively, and here we take [-0.5, 0.5].

[0093] The expected output is defined as follows:

[0094]

[0095] Take the desired output y des=0, the optimization objective function for model prediction output and control quantity is as follows:

[0096]

[0097] Where N p It is the prediction time domain; T e, R e These are the weight matrices for output error and control increment, respectively; u k It is the desired front wheel steering angle δ, u generated by the controller. p The control quantity calculated by the controller at the previous moment. The objective function consists of two terms: the first term ensures that the current output quantity continuously approaches the reference output quantity; the second term guarantees the smooth change of the control quantity, avoiding large oscillations that could affect the normal operation of the vehicle.

[0098] The above objective optimization problem is transformed into a quadratic programming problem. The quadratic programming problem calculates the predicted expected front wheel steering angle. The calculated first control variable is applied to the system, and the process is repeated continuously to achieve lane keeping lateral control.

[0099] S3. Establish a roll stability controller for commercial vehicles;

[0100] A roll stability controller for commercial vehicles was established, including research on roll stability control strategies and evaluation indicators. A comparative analysis of common control methods and evaluation indicators was conducted, and differential braking was determined as the stability control strategy, with LTR (Low Tolerance Rate) used as the roll evaluation indicator. The controller also includes the design of a roll stability controller for commercial vehicles based on MPC (Multi-Level Control) and differential braking. The upper-level controller calculates the additional yaw moment based on MPC, while the lower-level controller determines the braking wheels based on the vehicle's state and calculates the braking torque of each target braking wheel based on the additional yaw moment, thereby achieving roll stability control for the commercial vehicle.

[0101] To reduce the risk of rollover in commercial vehicles under extreme conditions, and thus ensure the stability of lane keeping control and the overall safety of the vehicle, the following design of a roll stability controller for commercial vehicles is presented. First, based on the vehicle's lateral dynamics model and roll dynamics model, the following continuous state-space equation for the roll stability controller for commercial vehicles is obtained:

[0102]

[0103] Where the state variables are The control quantity is the additional yaw moment u L =M z The input interference is w L =δ, let: a = C f +C r b = C f l f-C r l r , but:

[0104]

[0105] To establish the predictive output equation, considering that the design purpose of this controller is to ensure the stability of the vehicle under rollover hazards, after referring to relevant literature, it was found that the approximate lateral load transfer coefficient LTR' has the advantages of simple calculation, strong adaptability, and timely and accurate feedback on the rollover situation of the vehicle. Therefore, LTR' is used as the output quantity here, and its expression is as follows:

[0106]

[0107] In the formula, the absolute value of LTR ranges from 0 to 1, and when this coefficient reaches 1, it represents that the vehicle has rolled over. The system's output equation can then be obtained as follows:

[0108]

[0109] In the formula

[0110] Similarly, with sampling period T s Discretize the state equations with a period of 0.02s. The discrete state equation expression is as follows:

[0111] x L (k+1)=A L x L (k)+B L u L (k)+D L w L (k)

[0112] y L (k)=C L x(k)

[0113] In the formula A L =AT s +I, B L =BT s C L =C,D L =DT s .

[0114] Combining the above formulas, we obtain [k,k+N] p The predicted output expression for the scattered state at time 1:

[0115]

[0116] In the formula:

[0117]

[0118]

[0119] To achieve roll stability of the vehicle under high-speed sharp turning conditions, the approximate vertical load factor LTR' of the vehicle was constrained, and the specific constraint equations are as follows:

[0120]

[0121] In the formula LTR' max This is the set vertical load threshold, which is set to 0.8.

[0122] Define the expected output

[0123] To achieve better and more stable control, the optimization objective function in the MPC controller is designed as follows:

[0124]

[0125] Where N p It predicts the time domain; The expected additional transverse torque ΔM generated by the controller z , It is the additional yaw moment calculated by the controller at the previous moment; It is the weight of the output of the rollover stability controller. These are the weights of the control increments in the rollover stability controller. The objective function consists of two terms: the first term ensures that the vehicle's output continuously approaches the desired value; the second term ensures smooth changes in the control quantity, avoiding large oscillations that could affect the vehicle's normal operation.

[0126] Similar to the design of lane keeping controllers, the above objective optimization problem is transformed into a quadratic programming problem. The first control variable calculated by the quadratic programming problem is applied to the system, and this process is repeated continuously to calculate the desired additional yaw moment, thus providing conditions for the realization of rollover stability control.

[0127] The commercial vehicle roll stability controller also includes the distribution of braking torque. For cargo vehicles, using single-wheel braking can avoid wheel lock-up due to excessive braking force. Therefore, by referring to relevant literature and studying the vehicle rollover mechanism, and considering the vehicle's steady-state steering characteristics, the differential braking control objects under different conditions are determined as shown in Table 1. Braking force is distributed between the outer front axle wheels and the outer rear axle wheels with a front-to-rear braking ratio of 1:0.6. The formulas for calculating the braking torque of the front and rear wheels based on the additional yaw moment output by the roll stability controller are as follows:

[0128]

[0129] Where R is the effective radius of the tire, L f L is the front axle track. r This refers to the rear axle track.

[0130] Table 1 Selection of Differential Braking Control Objects for Vehicles Under Different Stability States

[0131] Over-steering right wheel left wheel Insufficient turn left wheel right wheel

[0132] S4. Use the above controller to perform the corresponding lane keeping and roll stability control operations.

[0133] For further details, please refer to Figures 5 to 8 The present invention also provides a specific embodiment to verify the performance of the lane keeping controller, and builds a co-simulation system. The superiority of the built control strategy is explained by analyzing the simulation results.

[0134] The simulated vehicle's initial speed was 60 km / h, and a double lane change test condition was set, with the road adhesion coefficient set to 0.8. Specific simulation results are as follows: Figures 5 to 8 :

[0135] Figure 5 and Figure 6 The figures shown are comparison charts of lateral deviation and heading deviation under different controllers. Figure 5 It can be observed that the maximum lateral deviation of driver-preview control is 0.35m, while the maximum lateral deviation of traditional MPC control is around 0.3m, indicating that traditional MPC control has higher control precision than driver-preview control. The improved MPC maintains a maximum lateral deviation within 0.26m, demonstrating that the improved MPC control algorithm enhances the lane-keeping control performance of traditional MPC, reducing lateral deviation during control and improving driving safety. Through comparison... Figure 6 A comparison chart of heading deviations. Figure 7 Front wheel steering angle comparison diagram and Figure 8The comparison chart of yaw rates shows that the improved MPC algorithm has higher heading deviation, front wheel angle, and yaw rate than the other two algorithms to some extent. Specifically, the maximum values ​​for heading error, front wheel angle, and yaw rate of the improved MPC are -5°, 15°, and 26.2° / s, respectively, while the maximum values ​​for the relevant state variables of the traditional MPC control are -4°, -14.3°, and 25° / s. This is because the improved MPC algorithm responds faster to lateral deviations, resulting in slightly larger heading deviations, yaw rates, and steering wheel angles compared to the traditional MPC control. However, the relevant state variables remain within safe ranges, having a smaller impact on the overall lane-keeping control performance. In summary, the improved MPC algorithm stably achieves lane-keeping along the reference lane centerline, while ensuring vehicle control accuracy and driving safety.

[0136] Further, please refer to Figures 9 to 12 The present invention also provides specific embodiments to verify the performance of the roll stability controller, and builds a co-simulation system. The superiority of the stability control strategy is explained by analyzing the simulation results.

[0137] To further verify the overall effectiveness of the designed anti-rollover stability controller, a double lane change test simulation was set at 70km / h, while other vehicle-road conditions remained unchanged.

[0138] Figure 9 and Figure 10 The simulation compares the LTR (Landing Turn Rate) and sideslip angle of the vehicle under three control conditions: MPC control, PID control, and no control. It can be observed that under no control condition, after a relatively extreme steering control maneuver, the LTR reaches its maximum value of 1 at approximately 3 seconds, at which point the vehicle has completely rolled over, causing the simulation to stop. Both PID and MPC control effectively keep the vehicle's LTR within the roll threshold of 0.8, with a maximum value of approximately 0.64. However, comparing the overall curves reveals that PID control exhibits greater data fluctuation and poorer control stability, which to some extent affects overall safety. Figure 9 The comparison diagram of the centroid sideslip angle shown below. Figure 11 The comparison chart of roll angles shown and Figure 12The comparison chart of roll angular velocities shows that MPC control provides smoother and more stable data compared to PID control. Under PID control, the maximum sideslip angle, roll angle, and roll angular velocity are -2deg, -3.9deg, and 25deg / s, respectively, while under MPC control, these figures are -1.3deg, -3.8deg, and 10deg / s. This data comparison demonstrates that the designed MPC-based roll stability controller for commercial vehicles achieves the expected anti-rollover control effect and exhibits certain advantages over PID control.

[0139] The above description discloses only one preferred embodiment of the present invention, and should not be construed as limiting the scope of the present invention. Those skilled in the art will understand that all or part of the processes of the above embodiments can be implemented, and equivalent changes made in accordance with the claims of the present invention are still within the scope of the invention.

Claims

1. A lane keeping control method for commercial vehicles considering roll stability, characterized in that, Includes the following steps: Construct vehicle lateral and roll dynamics models; Establish a lane keeping controller for commercial vehicles based on vehicle-road reference relationships; The commercial vehicle lane keeping controller is established based on model predictive control theory and combined with relevant formulas from the vehicle lateral dynamics model and the vehicle-road reference relationship model. The front wheel steering angle is a state variable. To control the quantity, This refers to the lateral deviation between the vehicle's center of gravity and the road centerline. The lateral deviation between the aiming point and the road centerline is the aiming distance. Then the heading deviation and its rate of change at the aiming point can be expressed as: in, and These are the vehicle heading angle and its first derivative, respectively. and The expected heading angle and its first derivative at the pre-aiming point; The lateral deviation at the aiming point and its rate of change can be expressed as: ； Establish a roll stability controller for commercial vehicles; The commercial vehicle roll stability controller uses differential braking as a stability control strategy and LTR as a roll evaluation index. The upper controller calculates the additional yaw moment based on MPC, while the lower controller decides the braking wheels based on the vehicle state and calculates the braking torque of each target braking wheel based on the additional yaw moment. Perform the corresponding lane keeping and roll stability control operations.

2. The commercial vehicle lane keeping control method considering roll stability as described in claim 1, characterized in that, The vehicle lateral and roll dynamics model is constructed based on the vehicle's lateral, yaw, and roll dynamics characteristics. The state equations describing the vehicle's lateral dynamics characteristics are as follows: in, For the overall vehicle quality, The yaw rate of the vehicle body; Let be the lateral speed of the vehicle. Longitudinal velocity; and These are the distances from the front and rear axles to the vehicle's center of gravity, respectively. Let be the vehicle's equivalent moment of inertia about the z-axis; These are the lateral stiffness of the front and rear wheels, respectively. This refers to the steering angle of the front wheels.

3. The commercial vehicle lane keeping control method considering roll stability as described in claim 2, characterized in that, The vehicle roll motion dynamics equations in the vehicle lateral and roll dynamics model are expressed as follows: in, Let x be the moment of inertia of the vehicle about the x-axis; The distance from the vehicle's center of gravity to the roll center. For the sprung mass of the vehicle, This is the equivalent roll stiffness of the suspension. is the equivalent damping coefficient of the suspension. The roll angle is... The angular velocity is the roll rate. This is the roll acceleration. The lateral acceleration of the vehicle body. This is the acceleration due to gravity.

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