Controlling a curvature of the trajectory of a motor vehicle

Abstract

The invention relates to a method for controlling a curvature of the trajectory of a motor vehicle by specifying a steering angle which is based on the inversion of a conventional first-order differential equation for the curvature of the trajectory as a function of the steering angle according to the steering angle, wherein a plurality of estimated values of driving-dynamics-dependent and / or vehicle-dependent parameters are used, and the first derivative of the curvature of the trajectory is substituted by a weighted sum of (1) the inverses of an autonomous first-order differential equation for the deviation between the curvature of the trajectory and a target value for the curvature of the trajectory after the first derivative of the curvature of the trajectory and (2) a regression model.

Description

[0001] ZF Friedrichshafen AG File 211468-DE-NP Friedrichshafen 12.11.2024

[0002] Rules governing the curvature of a motor vehicle's trajectory

[0003] AREA OF INVENTION

[0004] The present invention relates to a method for controlling the curvature of the trajectory of a motor vehicle.

[0005] SUMMARY OF THE INVENTION

[0006] Accordingly, the following is planned:

[0007] - a method for controlling the curvature of a motor vehicle's trajectory by specifying a steering angle, which is based on the inversion of a first-order ordinary differential equation for the curvature of the trajectory as a function of the steering angle with respect to the steering angle, wherein several estimates of vehicle dynamics-dependent and / or vehicle-dependent parameters are used and the first derivative of the curvature of the trajectory is substituted by a weighted sum of (1) the inverse of an autonomous first-order differential equation for the deviation between the curvature of the trajectory and a target value for the curvature of the trajectory after the first derivative of the curvature of the trajectory and (2) a regression model.

[0008] Computer program products typically comprise a sequence of instructions that, when the program is loaded, cause hardware, such as actuators of a control unit, to perform a specific procedure that leads to a specific result, in this case, the setting of a steering angle.

[0009] A differential equation (often abbreviated as ODE, DG, or DGl.) is a mathematical equation for an unknown function of one or more variables, in which derivatives of this function also appear. An ordinary differential equation (often abbreviated as GDGL or ODE, English ordinary ZF Friedrichshafen AG File 211468-DE-NP Friedrichshafen 12.11.2024)

[0010] A differential equation is a differential equation in which, for a function of unknown origin, only derivatives with respect to exactly one variable occur.

[0011] Vehicle dynamics encompasses the analysis of distance, time, speed, acceleration, energy consumption, engine heat generation, drive forces, power output, resistances, towing capacities, and vehicle efficiency. Vehicle dynamics utilizes technical, physical, mathematical, and statistical principles. As spatial motion of bodies, vehicle dynamics considers the three translational movements along the principal axes: longitudinal motion, lateral motion, and vertical motion, often combined with longitudinal motion when driving uphill or downhill. Pure vertical motion is exemplified by lifting platforms and elevators. Furthermore, vehicle dynamics also considers the three rotational movements around the three principal axes: yaw around the vertical axis, pitch around the lateral axis, and roll around the longitudinal axis.Furthermore, vehicle dynamics also considers two types of vibrations, namely translational and rotational vibrations.

[0012] Accordingly, parameters dependent on driving dynamics include, for example, speed or acceleration.

[0013] Vehicle-dependent parameters include, for example, the nominal mass (unladen mass) of a vehicle.

[0014] Regression searches the space of conceivable mathematical functions for candidates that optimally describe given data. Regression is therefore a statistical process for modeling multiple variables by estimating the relationship between a dependent variable and one or more independent variables.

[0015] A standstill time can refer to a period during which the engine is switched off or during which a vehicle is not moving. ZF Friedrichshafen AG File 211468-DE-NP Friedrichshafen 12.11.2024

[0016] The basic idea of ​​the invention is to calculate the steering angle required to achieve the desired curvature of the vehicle trajectory based on a first-order differential equation for the curvature of the vehicle trajectory as a function of the steering angle. Estimates for vehicle dynamics-dependent and / or vehicle-dependent parameters are used in this calculation.

[0017] Furthermore, the first derivative of the curvature of the vehicle trajectory is replaced by a weighted sum of the following terms:

[0018] 1. The inverse of an autonomous first-order differential equation for the deviation between the curvature of the vehicle's trajectory and the target value of this curvature.

[0019] 2. A regression model.

[0020] Modeling using an ordinary differential equation is advantageous because numerous solution methods of sufficient accuracy and acceptable computational effort exist for this class of problems.

[0021] Advantageous designs and further developments result from the additional sub-claims and from the description.

[0022] For example, the following differential equation can be considered for model building:

[0023]

[0024] «a + Oo(^) «a = 6o 5f, (la) with

[0025] czo)^) = ( / f + 4) 2 <1 c r — rri (Q lf — c T / r ) (1b) «i (v x ) = 0 (cf + c r ) v x . (lc)

[0026]

[0027] b0= (lf + 4) Q c> (ld) where denotes

[0028] K a the actual curvature of a vehicle's trajectory,

[0029] v xthe longitudinal speed,

[0030] l f or l r the current distance between the center of gravity and the front or ZF Friedrichshafen AG File 211468-DE-NP Friedrichshafen 12.11.2024

[0031] Rear axle (unknown),

[0032] c f or c r the current stiffness of the front or rear axle (unknown),

[0033] m the current total vehicle mass (unknown),

[0034] 0 the current moment of inertia about a transverse axis passing through the center of mass (unknown)

[0035] The steering angle of the front axle.

[0036] Accordingly, the steering angle can be approximated, for example, by the following equation:

[0037] äi(v r ) (Ä r — ftp Ä — A'I y?(w, K a

[0038] Of = - - — - : -

[0039]

[0040] . (2a) b0

[0041] where

[0042] K r the target curvature of a vehicle's trajectory,

[0043] « = « a - «id er Curvature error,

[0044] k P Factor of the proportional component of the controller,

[0045] factor of the regression model,

[0046] <p(o), f) das Regressionsmodell,

[0047] <= ( / C r K r K a v x a x ) '

[0048]

[0049] ) the parameters of the regression model and

[0050] a Q or are each an estimate based on the nominal values ​​of unknown parameters.

[0051] It is also advisable to continuously adjust the regression model using a fitting model. For example, the following rule could be used for the fitting model:

[0052] V w9?(w,<) _ W = - ti (2b)

[0053]

[0054] ||| £) 112 where the gradient vector of <p bezüglich der ) bezeichnet. Wählt man für <p ein in den Parametern ro lineares Regressionsmodell, also <p(ro,f) = a> T (f) with <>(^) a vector of functions, for example a vector of radial basis functions, then one obtains ZF Friedrichshafen AG File 211468-DE-NP Friedrichshafen 12.11.2024

[0055]

[0056] According to a preferred embodiment of the invention, the vehicle dynamics-dependent and vehicle-dependent parameters include at least one of the following parameters: total mass of the vehicle including a payload of the vehicle, moment of inertia of the vehicle about a transverse axis, distance of the front axle to a center of gravity of the vehicle, distance of the rear axle to the center of gravity of the vehicle, cornering stiffness of a front axle, cornering stiffness of a rear axle.

[0057] It is understood that the aforementioned coefficients are variable and can be estimated, for example, using the nominal values ​​of the coefficients that a vehicle possesses upon delivery. It is also conceivable to modify these nominal values ​​using plausible correction values.

[0058] According to a preferred embodiment of the invention, the driving dynamics-dependent and / or vehicle-dependent parameters are adjusted for a journey, and the parameter adjustment begins anew, particularly after a predetermined idle time. It is also conceivable to use estimated values ​​from a previous journey to estimate a subsequent journey.

[0059] This allows us to illustrate that certain parameters primarily change between journeys and not during the journey itself. For example, it is conceivable that a vehicle occupant gets in or out between two journeys, and consequently the vehicle mass changes.

[0060] According to a preferred embodiment of the invention, the regression model depends on at least one of the following target and / or actual parameters:

[0061] Longitudinal speed, lateral speed, curvature of a vehicle trajectory, steering angle, where the aforementioned parameters may be derivatives with respect to time, actual parameters, and / or extrapolated parameters. ZF Friedrichshafen AG File 211468-DE-NP Friedrichshafen November 12, 2024

[0062] According to a preferred embodiment of the invention, the regression model is based on a lookup table, a Gaussian process, an artificial neural network, in particular a radial basis function network, a polynomial representation, in particular a Bezier curve or a Bezier surface.

[0063] Thus, the described procedure can be implemented with acceptable computational effort.

[0064] According to a preferred embodiment of the invention, parameters of the regression model are adjusted during a journey, assuming that the parameters change during a journey and / or remain constant during a journey.

[0065] For example, the static friction between a tire and a road surface depends on the road surface and its condition, and therefore changes during driving. Other parameters, such as the stiffness of various components, can be assumed to be constant during a journey.

[0066] A computer program product according to a method of an embodiment of the invention performs the steps of a method according to the preceding description when the computer program product runs on a computer, in particular an in-vehicle computer. When the program in question is used on a computer, the computer program product produces an effect, namely the setting or...

[0067] Changing the steering angle of the front axle of a vehicle.

[0068] It is understood that a control unit for a motor vehicle, onto which a computer program product as described above is loaded, is advantageous.

Claims

ZF Friedrichshafen AG File 211468-DE-NP Friedrichshafen 12.11.2024 Patent claims 1. Method for controlling the curvature of a motor vehicle's trajectory by specifying a steering angle, which is based on the inversion of a first-order ordinary differential equation for the curvature of the trajectory as a function of the steering angle with respect to the steering angle, where several estimates of vehicle dynamics-dependent and / or vehicle-dependent parameters are used and the first derivative of the curvature of the trajectory is substituted by a weighted sum of (1) the inverse of an autonomous first-order differential equation for the deviation between the curvature of the trajectory and a target value for the curvature of the trajectory after the first derivative of the curvature of the trajectory and (2) a regression model.

2. Method according to claim 1, where the regression model is continuously adjusted using a fitting model.

3. Method according to any of the foregoing claims, wherein the driving dynamics-dependent and / or vehicle-dependent parameters include at least one of the following parameters: Total mass of the vehicle including any payload of the vehicle, moment of inertia of the vehicle about a transverse axis, distance of the front axle to the center of gravity, distance of the rear axle to the center of gravity, cornering stiffness of a front axle, cornering stiffness of a rear axle.

4. Method according to any of the foregoing claims, where the driving dynamics-dependent and / or vehicle-dependent parameters are adjusted for a journey and the adjustment of the parameters starts again after a predetermined standstill period. ZF Friedrichshafen AG File 211468-DE-NP Friedrichshafen 12.11.2024 5. Method according to any of the foregoing claims, where the regression model depends on at least one of the following target and / or actual parameters: Longitudinal speed, lateral speed, curvature of a vehicle trajectory, steering angle; where the parameters mentioned may be derivatives with respect to time, actual parameters and / or extrapolated parameters.

6. Method according to any of the foregoing claims, wherein the regression model is based on a conversion table, on a Gaussian process, on an artificial neural network, in particular on a radial basis function network, on a polynomial representation, in particular a Bezier curve or a Bezier surface.

7. Method according to any of the foregoing claims, where parameters of the regression model are adjusted during a journey, assuming that the parameters change during a journey and / or remain constant during a journey.

8. Computer program product comprising program code means for carrying out the method according to any one of the preceding claims.

9. Control unit for a motor vehicle onto which a computer program product according to claim 8 is loaded.

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