DE102024202197A1 - Controlling a vehicle with estimation of a control-based time delay by a feedforward controller - Google Patents

Abstract

A method (600) with a feedforward controller (165) for controlling, in particular steering, a vehicle (110), in particular for autonomous driving, wherein the method (600) comprises the following steps: input (605) of a set of path curvatures (220), each describing a path to be traveled by the vehicle (110), into the feedforward controller (165); estimation (610) of a control-based time delay by the feedforward controller (165); selection (615) of a preview path curvature (235) from the set of path curvatures (220) based on the estimated control-based time delay and a driving parameter of the vehicle (110); Derivation (620) of a control variable of the feedforward controller (165) from the preview path curvature (235) and output (625) of the control variable of the feedforward controller (165), wherein the control variable of the feedforward controller (165) is used to control the vehicle (110).

Description

The present invention relates to a method for controlling, in particular steering, a vehicle, in particular for autonomous driving, using a controller, in particular a feedforward controller. The present invention further relates to a computer-implemented method, a data processing system, a computer program, and/or a computer-readable medium.

Modern vehicles, such as cars, trucks, buses, and similar vehicles, often feature a control system that supports and/or even replaces manual driving. This system can be considered an autonomous driving system, where "autonomous" can be understood as either partially autonomous, i.e., only supporting the driver, or fully autonomous, i.e., replacing the driver.

The output of the control system can be used to steer the vehicle. It is in the nature of control systems that the control system requires a certain amount of time to adjust the manipulated variable. Furthermore, depending on the control strategy, oscillations in the manipulated variable can occur during control. Today's state-of-the-art systems must be designed to be fast, i.e., to closely track the manipulated variable, and/or to enable a comfortable ride for passengers.

It is therefore an object of the present invention to provide a method for controlling a vehicle that is fast, in particular fast-tracking, and/or comfortable for the passengers. It is also an object of the present invention to provide a computer-implemented method, a data processing system, a computer program, and/or a computer-readable medium that is fast, in particular fast-tracking, and/or comfortable for the passengers.

The invention solves this problem by means of the subject matter of the independent claims. Subclaims specify preferred embodiments.

A method for controlling, in particular steering, a vehicle, in particular for autonomous driving, with a feedforward controller; comprises inputting a set of path curvatures, each describing a path to be traveled by the vehicle, to the feedforward controller; furthermore, estimating a control-based time delay by the feedforward controller; furthermore, selecting a preview path curvature from the set of path curvatures based on the estimated control-based time delay and a driving parameter of the vehicle; furthermore, deriving a manipulated variable of the feedforward controller from the preview path curvature and outputting the manipulated variable of the feedforward controller, wherein the manipulated variable of the feedforward controller is used to control the vehicle.

The control-based time delay is, for example, the time delay that occurs in a controller, for example in the feedforward controller and/or in other controllers. By estimating the control-based time delay and reusing the estimate, in particular for selecting the preview trajectory curvature, the precise trajectory curvature, namely the preview trajectory curvature, that enables fast and/or comfortable control can be selected in the pre-controller. A set of trajectory curvatures comprises, for example, several trajectory curvatures, in particular a sequence of trajectory curvatures. A driving parameter can be, for example, a driving speed, an acceleration, a deceleration, and/or a yaw rate of the vehicle. The preview trajectory curvature is preferably selected based on the estimated control-based time delay and the driving speed of the vehicle. After selecting the preview trajectory curvature, the manipulated variable is preferably output, which, for example, causes the vehicle to quickly and/or comfortably follow a desired driving trajectory, in particular a curve curvature.

Preferably, the control-based time delay is estimated using a machine learning algorithm, in particular a neural network. Driving parameters are expediently used as an input variable for the machine learning algorithm, in particular the neural network. Preferably, the machine learning algorithm, in particular the neural network, comprises a radial basis function. Advantageously, the machine learning algorithm, in particular the neural network, comprises an update law. In particular, by using a machine learning algorithm, the control-based time delay can be particularly precise and/or fast and/or convenient. Advantageously, a radial basis function is used in the feedforward controller, in particular to estimate the control-based time delay. Preferably, based on the estimated control-based time delay The preview curvature, in particular the preview path curvature, of the route ahead of the vehicle is generated and/or selected.

A feedback controller (feedforward controller) is preferably provided. Advantageously, an actual yaw rate of the vehicle is measured, in particular using a yaw rate sensor. Advantageously, a yaw rate error is determined from the difference between the actual yaw rate and a desired yaw rate. The yaw rate error is expediently processed in the feedback controller. Advantageously, the feedback controller outputs a manipulated variable of the feedback controller. Advantageously, the manipulated variable of the feedback controller, in particular together with the manipulated variable of the feedforward controller, is used to control, in particular to steer, the vehicle. Preferably, the feedforward controller estimates the control time of the feedback controller at least partially, in particular completely, when estimating the control-based time delay. Preferably, the feedforward controller takes the control time of the feedback controller into account at least partially, in particular completely, when estimating the control-based time delay. This allows, for example, the entire control-based time delay, especially that of the forward controller and/or reverse controller, to be estimated, thereby predicting the control-based time delay with particular precision. This allows for the establishment of a very good, particularly fast and/or convenient control system.

Preferably, the manipulated variable of the feedback controller is generated using a machine learning algorithm. Advantageously, the machine learning algorithm includes an online learning algorithm. The machine learning algorithm expediently includes a variable learning rate. Using the machine learning algorithm allows the feedback controller to control particularly well. The control-based time delay, which may also occur due to the machine learning algorithm, is estimated and/or taken into account, particularly in the feedforward controller. This enables fast and/or convenient overall control.

Advantageously, the feedback controller comprises a first feedback controller and a second feedback controller.

The first feedback controller advantageously comprises a neural network. In particular, the first feedback controller comprises an integral reinforcement learning algorithm. Advantageously, the yaw rate error and/or the desired yaw rate is an input variable for the integral reinforcement learning algorithm. In particular, the first feedback controller is an integral reinforcement learning (IRL) agent. The critical neural network is preferably adjusted online as part of an integral gain element, for example with a variable learning rate, in particular by gradient descent. Advantageously, the learning rate is a parabolic mapping. In particular, the parabolic mapping links the learning rate to the instantaneous yaw rate error. Advantageously, the IRL agent initiates a strategy iteration process, in particular without an initially permissible strategy. Advantageously, the IRL agent generates an approximately optimal control with one, in particular with exactly one, for example, critical, neural network.

The update law 190 for the critic NN 185: $$\widehat{\dot{W}}=\underset{\left\{ersterTerm\right\}}{\underbrace{\eta \left(z\right)\overline{\vartheta }\widehat{e}}}+\frac{\eta \left(z\right)\Xi \left(z,u\right)\left(\frac{\nabla {\vartheta }^T}{2}G{R}^{-1}\left(I_m-B\right)G^T\nabla \vartheta \widehat{\dot{W}}z\right)}{\left\{zweiterTerm\right\}}+\eta \left(z\right)\widehat{e}$$

Where $\widehat{e}={\displaystyle {\int }_{\left\{t-T\right\}}^{\left\{t\right\}}{e}^{-\gamma \left(\tau -t+T\right)}}\left[Q\left(z\right)+U\left(u\right)\right]d\tau +{\widehat{\dot{W}}}^T\Delta \vartheta$ the applicable HJB approximation error is Δϑ ≡ e ^-γT ϑ(z(t)) - ϑ(z(t - T)).

• ϑ(z(t)): Rⁿ → R^N: Regressor Vektor des kritischen neuronalen Netzwerks (mit N als der Anzahl verdeckter Neuronen), der zum augmentierten (verbesserten) Zustand z(t) berechnet wurde.
• Ŵ: Rⁿ → R^N: kritische NN Gewichte
• η(z): die variable Lernrate rate.
• ϑ̅: der normalisierte Regressionsvektor
• Ξ (z, u): die geglättete Schaltfunktion
• I_m: die Identitätsmatrix mit Dimension ‚m‘.
• $B=diag\left\{tan{h}^2\left({\tau }_{2i}\left(z\right)\right)\right\}\in R^{m\times m}:\text{wobei }{\tau }_2=\frac{1}{2u_m}{R}^{-1}{G}^T\nabla {\vartheta }^T\widehat{\dot{W}}\in R^m$
• R ∈ R^m×m: Penalty auf Steuerungen
• G ∈ R^m×m: Steuerungs Kopplungsmatrix des augmentierten Systems
• K₁ und K₂: Konstanten passender Dimensionen
• R: die Menge der realen Zahlen
• ∇: Gradient
• V:Rⁿ → R: die Bewertungsfunktion (Skalare Ausgabe des kritischen NN)
• z = (x - x_des; x_des) ∈ R²ⁿ: der augmentierte Zustand ist, der den augmentierten Zustand aus Zustandsfehler und Zielzustand umfasst
• y: Nachlassfaktor
• Q = z^TQ₁z: Rⁿ → R: Aufwand (auch: Kosten, Penalty) pro Schritt des augmentierten Zustands
• u_m ∈ R: maximaler Steuerungsaufwand (Sättigungsgrenze des Aktuators) $$U\left(u\right)=2u_m{\displaystyle {\int }_0^{-u_m\text{ tanh }A\left(z\right)}{\text{tanh}}^{-1}{\left(v/u_m\right)}^T}Rdv$$

Furthermore:

• ϑ(z(t)): R ⁿ → R ^N : Regressor vector of the critical neural network (with N as the number of hidden neurons) computed to the augmented (improved) state z(t).
• Ŵ: R ⁿ → R ^N : critical NN weights
• η(z): the variable learning rate.
• ϑ̅: the normalized regression vector
• Ξ (z, u): the smoothed switching function
• I _m : the identity matrix with dimension ‘m’.
• $B=diag\left\{tan{h}^2\left({\tau }_{2i}\left(z\right)\right)\right\}\in R^{m\times m}:\text{wobei }{\tau }_2=\frac{1}{2u_m}{R}^{-1}{G}^T\nabla {\vartheta }^T\widehat{\dot{W}}\in R^m$
• R ∈ R ^m×m : Penalty on controls
• G ∈ R ^m×m : Control coupling matrix of the augmented system
• K ₁ and K ₂ : constants of appropriate dimensions
• R: the set of real numbers
• ∇: Gradient
• V:R ⁿ → R: the evaluation function (scalar output of the critical NN)
• z = (x - x _des ; x _des ) ∈ R ²ⁿ : is the augmented state, which includes the augmented state from state error and target state
• y: discount factor
• Q = z ^T Q ₁ z: R ⁿ → R: Effort (also: cost, penalty) per step of the augmented state
• u _m ∈ R: maximum control effort (saturation limit of the actuator) $$U\left(u\right)=2u_m{\displaystyle {\int }_0^{-u_m\text{ tanh }A\left(z\right)}{\text{tanh}}^{-1}{\left(v/u_m\right)}^T}Rdv$$

Where U(z): R ^m → R is the cost (effort) per step of the control (if the boundary conditions of the actuator are considered) and the following applies: $A\left(z\right)=\frac{1}{2u_m}{R}^{-1}{G}^T\nabla V$ $$

In the update law given above, the first term minimizes the instantaneous approximation error, the second term comes into play when the Lyapunov value $\frac{1}{2}{Z}^{T}Z$ no longer decreases along the trajectories of the augmented system, and the third term determines the size of the residual set over which the state error converges.

The IRL Agent 200 is determined as follows: $$\delta =-u_{m}tanh\left(\frac{1}{2u_m}{R}^{-1}{G}^T\nabla {\vartheta }^T\widehat{\dot{W}}\right)$$

Advantageously, the second feedback controller comprises a directly adaptive neural network. Advantageously, the second feedback controller comprises an adaptive, neural network-based (NN-based) sliding mode control. Such a control can also be called ANNSMC (from ANN: "artificial neural network" and SMC: "sliding mode control"), NN-based sliding regime control, or NN-based sliding mode control. The adaptive, neural network-based sliding mode control is preferably used in conjunction with the IRL agent, in particular to distribute the learning load and/or to generate narrower cross-track errors. Advantageously, the learning rate is determined by a parabolic mapping of the yaw rate error. A variable control range for the error dynamics is expediently provided, in particular by the second feedback controller.

The ANNSMC 205 is updated according to the following formula: $${\dot{\widehat{W}}}_{annsmc}=-\gamma \left(e_{\dot{\psi }}\right)\varphi \left(s\right)$$

• w̅_annsmc NN Gewichte der radialen Basisfunktion (radial basis function RBF) eψ̇ = ψ̇ - ψ̇_des der Gierratenfehler
• s: (eψ̇, ψ̇_des, v_x, v_y) Eingaben ins RBFNN
• ϕ: s → Rⁿ die Ausgabe der verdeckten Schicht des RBFNN (eine Eingangsschicht - eine verdeckte Schicht und eine Ausgangsschicht), wobei n die Anzahl der Neuronen in der verdeckten Schicht ist.

Whereby:

• w̅ _annsmc NN weights of the radial basis function (RBF) eψ̇ = ψ̇ - ψ̇ _{des of} the yaw rate error
• s: (eψ̇, ψ̇ _des , v _x , v _y ) Inputs to RBFNN
• ϕ: s → R ⁿ is the output of the hidden layer of the RBFNN (one input layer - one hidden layer and one output layer), where n is the number of neurons in the hidden layer.

The control angle 210 of the ANNSMC is given as: $${\delta }_{annsmc}={\widehat{w}}_{annsmc}\varphi -k{e}_{\dot{\psi }}-\eta tanh\left(e_{\dot{\psi }}\right)$$ where $$k>0\wedge \eta >0$$

In particular, a feedforward control scheme based on time delay compensation is used in conjunction with a dual neural network feedback control, which includes, for example, the lane-keeping IRL agent and the adaptive neural network-based sliding mode control for autonomous steering control.

Advantageously, a control architecture, in particular an overall controller, comprises the kinematic feedforward control, in particular the feedforward controller, and a part with learning-based feedback, in particular the feedforward controller. Advantageously, the feedforward controller provides supervisory control, while the learning-based feedforward controller minimizes the yaw rate error. Advantageously, the effects of the time delay in the feedforward controller-assisted dual neural network feedback control architecture have been compensated, for example, by using a radial basis function to estimate the time delay at a specific time. Advantageously, the estimated time delay is used in the kinematic feedforward controller to actively select a variable time window for the path curvature ahead of the autonomous vehicle. Advantageously, the kinematic feedforward control, in particular the feedforward controller, calculates the steering angle based on this preview curvature, in particular instead of the actual curvature.

The kinematic forward control 180 is determined as follows: $${\delta }_{ff}=ta{n}^{-1}\left({\kappa }_{preview}*L\right)$$ where κ _preview is the (selected) preview curvature generated based on the estimated time delay and L: is the wheelbase of the vehicle.

Advantageously, an IRL agent is combined with an adaptive NN-based sliding mode control (ANNSMC) on the feedback path to minimize the yaw rate error for autonomous vehicles. The online learning load is advantageously shared between the two learning methods. Preferably, the IRL agent attempts to generate approximately optimal control strategies to minimize the Hamilton-Jacobi-Bellman (HJB) approximation error, in particular to reduce the yaw rate error, while the ANNSMC directly minimizes the yaw rate error. Advantageously, the combined approach is robust to various disturbances and perturbations, for example, due to the inherent robustness of the ANNSMC. In particular, when the error is large, for example, at the beginning of a turn, the agent will attempt to aggressively search for strategies in the parameter space, while the agent's aggressiveness decreases as the error decreases, for example, once the vehicle is aligned with the reference trajectory. This strategy, together with the “dead zone modification,” advantageously mitigates the problem of control oscillations due to the high adaptive gain in the feedback path.

The dead zone modification technique is a method for freezing the learning process of the online adaptation mechanism within a specific region of the state space. This means that when the vehicle enters this region of the state space, the NN weights are not updated and remain constant. For example, when the vehicle has approached the desired reference trajectory, this avoids unnecessary updating of the NN weights near the reference trajectory, thus preventing oscillations.

Advantageously, the method is at least partially, in particular completely, a computer-implemented method.

A data processing system, in particular a control architecture for controlling, in particular for steering, a vehicle, in particular for autonomous driving of a vehicle, with means for carrying out the method described herein.

A computer program, in particular a computer program product, comprising instructions which, when executed by a computer, cause the computer to carry out the method described therein.

A computer-readable medium containing instructions that, when executed by a computer, cause the computer to perform the method described herein.

A processing device can be configured to carry out a method described herein in whole or in part. For this purpose, the processing device can be implemented electronically and comprise a programmable microcomputer or microcontroller, and the method can be in the form of a computer program product with program code means. The computer program product can also be stored on a computer-readable data carrier. Features or advantages of the method can be transferred to the device, or vice versa.

• 1 eine beispielhafte schematische Darstellung einer Steuerungsarchitektur,
• 2 beispielhafte Ergebnisse einer Steuerung eines Fahrzeugs unter Verwendung der Erfindung und des Standes der Technik,
• 3 weitere beispielhafte Ergebnisse einer Steuerung eines Fahrzeugs unter Verwendung der Erfindung und des Standes der Technik,
• 4 weitere beispielhafte Ergebnisse einer Steuerung eines Fahrzeugs unter Verwendung der Erfindung und des Standes der Technik, und
• 5 ein Flussdiagramm eines Verfahrens mit einem Vorwärtsregler zur Steuerung eines Fahrzeugs darstellt.

The invention will now be described in more detail with reference to the accompanying figures, in which:

• 1 an exemplary schematic representation of a control architecture,
• 2 exemplary results of controlling a vehicle using the invention and the prior art,
• 3 further exemplary results of controlling a vehicle using the invention and the prior art,
• 4 further exemplary results of controlling a vehicle using the invention and the prior art, and
• 5 a flowchart of a method using a feedforward controller for controlling a vehicle.

1 shows an exemplary schematic representation of a control architecture 100. In the exemplary embodiment, the control architecture 100 is provided to provide a data processing system 105, in particular a control system, with which manual driving of a vehicle 110, such as a car, truck, bus, or similar vehicle 110, can be supported and/or replaced. The data processing system 105 can be considered an autonomous driving system, where autonomous can be understood as partially autonomous, ie, only supporting the driver, or fully autonomous, ie, replacing the driver.

The output of the data processing system 105 can be used to steer the vehicle 110, which is explained below in the exemplary embodiment. The control architecture 100 comprises a sensor, in particular a yaw rate sensor, for measuring an actual yaw rate 115 of the vehicle 110. The control architecture 100 comprises a controller 120, in particular an overall controller. The actual yaw rate 115 and a target yaw rate 125, in particular a desired yaw rate, are fed into the controller 120. The target yaw rate 125 is preferably derived from a target trajectory curvature 130, in particular a desired trajectory curvature. "Target" and/or "desired" are to be understood, for example, as meaning that this yaw rate and/or trajectory curvature is desired to be set for the vehicle 110.

It may be expedient for the target yaw rate 125 and/or the target path curvature 130 to be calculated in the controller 120, for example, using input variables such as a driving speed 135 of the vehicle 110 and/or a desired path curvature 130 to be traveled. The controller 120 calculates a yaw rate error 140 by determining the difference between the actual yaw rate 115 and the target yaw rate 125. The controller 120 outputs a total manipulated variable 145, which is used to control, in particular to steer, the vehicle 110. In the exemplary embodiment, the total manipulated variable 145 is composed of three variables, namely a first manipulated variable 150, in particular the manipulated variable of a feedforward controller 165, a second manipulated variable 155, and a third manipulated variable 160, in particular additively. The second manipulated variable 155 and the third manipulated variable 160, in particular additive, correspond in particular to the manipulated variable of a feedback controller 166. Additive can be understood as an addition and/or subtraction. It is conceivable that the total manipulated variable 145 can also be mathematically calculated, for example via weightings, functions, and/or the equal, is formed from the three manipulated variables 150, 155, 160. In a further embodiment, the total manipulated variable 145 can be composed of exactly three, or more than three variables.

The controller 120 includes the feedforward controller 165 and the feedback controller 166. The feedback controller 166 includes a first feedforward controller 170, also called the first sub-controller 170, and a second feedforward controller, also called the second sub-controller 175. The feedforward controller 165 outputs the first manipulated variable 150. The first feedforward controller 170 outputs the second manipulated variable 155. The second feedforward controller 175 outputs the third manipulated variable 160.

In the exemplary embodiment, the feedforward controller 165 is designed as a feedforward control 180, in particular a kinematic one. The feedforward controller 165 is provided to calculate the first manipulated variable 150 such that a desired path curvature can be achieved. In the exemplary embodiment, the desired path curvature corresponds to the path curvature 130 to be traveled, in particular the target path curvature 130. The second and third manipulated variables 155, 160 are used in the exemplary embodiment to correct the first manipulated variable 150 such that an overall manipulated variable 145 is generated, which causes the vehicle 110 to follow the desired travel trajectory, in particular the path curvature, precisely, quickly, and comfortably.

Input variables for the feedforward controller 165 include, for example, a set of path curvatures 220, the desired and/or current yaw rate 225, and the vehicle speed 230, in particular the lateral vehicle speed. The input variables for the feedforward controller 165 and the feedback controller 166 can be the same, in particular vehicle speed 135, 230, and/or yaw rate 225, 115.

A set of trajectory curvatures 220, for example, means that the set contains several trajectory curvatures. Depending on the boundary conditions such as driving speed 230, yaw rate 225, or the like, all trajectory curvatures in the set are suitable for traversing the desired driving trajectory. Depending on the driving speed 230, yaw rate 225, or the like, only one trajectory curvature can be selected from the set of trajectory curvatures, in particular a preview trajectory curvature 235 for precise, fast, and comfortable driving. It should be emphasized here that the preview trajectory curvature 235 can also be selected only in sections, and, for example, several preview trajectory curvatures arranged one after the other ultimately enable the trajectory to be traversed. Such a sequence can occur, for example, when the driving speed 230 and/or the yaw rate 225 of the vehicle 110 is changed when driving through the curve.

The selection of the preview path curvature 235 from the set of path curvatures 220 is also carried out, in particular, based on a control-based time delay. The control-based time delay is, for example, the time required by the controller 120 as a whole, and/or the feedforward controller 165, and/or the feedback controller 166, and/or the first reverse controller 170, and/or the second reverse controller 175 to calculate and/or output the respective manipulated variable 145, 150, 155, 160. A control-based time delay may occur, particularly when using machine learning in one and/or more of the controllers 120, 165, 166, 170, 175.

The feedforward controller 165 comprises a machine learning algorithm, in particular a neural network. For this purpose, the feedforward controller 165 comprises an update law 240, which is fed in particular with the vehicle speed 230 and/or the desired and current yaw rate 225. The feedforward controller comprises a radial basis function 245, or RBF for short. The radial basis function 245 is fed by the update law 240. The radial basis function 245 estimates the control-related time delay. Using this control-related time delay information, the preview path curvature is selected from the set of path curvatures 220. The preview path curvature is read into the feedforward control 180 to serve as the input variable for calculating the manipulated variable 150.

In the exemplary embodiment, the first feedback controller 170 generates the second manipulated variable 155 using a machine learning algorithm. The machine learning algorithm comprises an online algorithm. This can be understood, for example, to mean that the online algorithm does not need to be trained in advance, or does not need to be trained completely beforehand. Changing influencing variables, such as vehicle weight, friction between wheels and road surface, and the like, can be incorporated simultaneously, in particular without prior training. The machine learning algorithm is preferably stable; in particular, it comprises a stable update law. Stable can be understood, for example, to mean that the yaw rate error and/or a control and/or open-loop variable is limited.

In the exemplary embodiment, the first feedback controller 170 comprises a, in particular critical, neural network 185, an, in particular online, update law 190, optionally a gradient operator 195, and an IRL agent 200. "IRL" refers to "integral reinforcement learning," i.e., integral and/or amplifying and/or strengthening reinforcement learning. The neural network 185 comprises, in particular, a radial basis function, also called an RBF. In the exemplary embodiment, the update law 190 feeds the neural network 185. The output from the neural network 190, in particular the control variable to be further processed, is optionally revised and/or corrected using a gradient operator 195, for example, using the time derivative of the vehicle speed. The output from the gradient operator 195 flows into the IRL agent 200, which ultimately calculates and outputs the second control variable 155. The IRL agent 200 uses a variable learning rate, which is particularly efficient and fast. In the exemplary embodiment, the variable learning rate can be a function of vehicle speed 135 and/or yaw rate error 140. However, learning can also be based on yaw rate error 140 and/or its first time derivative, target yaw rate 125 and/or its first time derivative, and/or vehicle speed 135.

Input variables for the first reverse controller 170 are in particular the driving speed 135, the yaw rate error and/or the actual yaw rate 115.

In the exemplary embodiment, the second feedback controller 175 generates the third manipulated variable 160 using a machine learning algorithm. The machine learning algorithm comprises an online algorithm 205. This can be understood, for example, to mean that the online algorithm 205 does not need to be trained in advance, or does not need to be trained completely beforehand. Changing influencing variables, such as vehicle weight, friction between the wheels and the road surface, and the like, can be incorporated simultaneously, in particular without prior training. The machine learning algorithm is preferably stable, in particular comprising a stable update law. Stable can be understood, for example, to mean that the yaw rate error and/or a control and/or open-loop variable is limited.

In the exemplary embodiment, the second feedback controller 175 comprises a neural network 210, in particular a directly adaptive neural network 210. In the exemplary embodiment, the online algorithm 205 feeds the neural network 210. It may be expedient for the online algorithm 205 to feed a radial basis function network 215, which outputs a control variable to the neural network 210. It may also be expedient for the online learning algorithm to feed the neural network 210 directly. The output from the neural network 210 is the third control variable 160. The neural network 210 uses a variable learning rate, which is particularly efficient and fast, wherein in the exemplary embodiment, the variable learning rate can, for example, be a function of the driving speed 135 and the yaw rate error 140. However, learning can also be carried out based on yaw rate error 140 and/or its first time derivative, target yaw rate 125 and/or its first time derivative, and/or driving speed 135.

Input variables for the second reverse controller 175 are in particular the vehicle speed 135, the yaw rate error 140 and/or the actual yaw rate 115.

1 shows the data processing system 100, in particular a control architecture 105 for controlling, in particular for steering, a vehicle 110, in particular for autonomous driving of a vehicle 110, with means for carrying out the method described herein. The exemplary embodiment comprises a computer program (not shown in the figures), in particular a computer program product (not shown in the figures), with instructions which, when the program is executed by a computer (not shown in the figures), cause the computer to carry out the method described herein. The exemplary embodiment comprises a computer-readable medium (not shown in the figures) with instructions which, when executed by the computer, cause the computer to carry out the method described herein.

2 shows the result of the control using a method described herein in a first exemplary cornering. 2 top left shows a transverse deviation in a length dimension plotted over the travel time, 2 top right shows a course error angle in degrees plotted against the travel time, 2 bottom left shows a driven position in a length dimension, plotted in X and Y directions, 2 bottom right showed a current wheel angle in degrees plotted over the driving time. In 2 the method 300 described herein as well as two prior art methods 305, 310 are shown. 2 It can be clearly seen that the method 300 described herein enables faster and more precise control with greater comfort compared to the two methods 305, 310 according to the prior art.

3 shows the result of the control using a method described herein in a second exemplary cornering. 3 top left shows a transverse deviation in a length dimension plotted over the travel time, 3 top right shows a course error angle in degrees plotted against the travel time, 3 bottom left shows a driven position in a length dimension, plotted in X and Y directions, 3 bottom right showed a current wheel angle in degrees plotted over the driving time. In 3 the method 400 described herein as well as two prior art methods 405, 410 are shown. 3 It can be clearly seen that the method 400 described herein enables faster and more precise control with greater comfort compared to the two methods 405, 410 according to the prior art.

4 shows the result of the control using a method described herein in a third exemplary cornering. 4 top left shows a transverse deviation in a length dimension plotted over the travel time, 4 top right shows a course error angle in degrees plotted against the travel time, 4 bottom left shows a driven position in a length dimension, plotted in X and Y directions, 4 bottom right showed a current wheel angle in degrees plotted over the driving time. In 4 the method 500 described herein as well as two prior art methods 505, 510 are shown. 4 It can be clearly seen that the method 500 described herein enables faster and more precise control with greater comfort compared to the two prior art methods 505, 510.

5 shows, by way of example, the method 600 with a feedforward controller 165 for controlling, in particular steering, a vehicle 110, in particular for autonomous driving, wherein the method 600 comprises the following steps: input 605 of a set of path curvatures 220, each describing a path to be traveled by the vehicle 110, into the feedforward controller 165; estimation 610 of a control-based time delay by the feedforward controller 165; selection 615 of a preview path curvature 235 from the set of path curvatures 220 based on the estimated control-based time delay and a driving parameter, for example, driving speed 230 and/or yaw rate 225 of the vehicle 110; Derivation 620 of a control variable of the feedforward controller 165 from the preview path curvature 235 and output 625 of the control variable of the feedforward controller 165, wherein the control variable of the feedforward controller 165 is used to control the vehicle 110.

Reference symbol

100

Control architecture

105

data processing system

110

vehicle

115

Actual yaw rate

120

Controller

125

Target yaw rate

130

Target path curvature

135

Driving speed

140

Yaw rate error

145

Total control variable

150

first manipulated variable

155

second manipulated variable

160

third manipulated variable

165

Feedforward controller

166

Feedback controller

170

first reverse regulator

175

second reverse regulator

180

Feedforward control

185

Neural network

190

Update Law

195

Gradient operator

200

IRL Agent

205

Online algorithm

210

Neural network

215

Radial basis function network

220

Set of orbit curvatures

225

Yaw rate

230

Driving speed

235

Preview path curvature

240

Update Act

245

radial basis function

300

The method described herein

305

State-of-the-art procedures

310

State-of-the-art procedures

400

The method described herein

405

State-of-the-art procedures

410

State-of-the-art procedures

500

The method described herein

505

State-of-the-art procedures

510

State-of-the-art procedures

600

Proceedings

605

input

610

Estimation

615

Selection

620

Derivation

625

output

Claims (15)

Method (600) with a feedforward controller (165) for controlling, in particular steering, a vehicle (110), in particular for autonomous driving, wherein the method (600) comprises the following steps: input (605) of a set of path curvatures (220), each describing a path to be traveled by the vehicle (110), into the feedforward controller (165); estimation (610) of a control-based time delay by the feedforward controller (165); selection (615) of a preview path curvature (235) from the set of path curvatures (220) based on the estimated control-based time delay and a driving parameter of the vehicle (110); Derivation (620) of a control variable of the feedforward controller (165) from the preview path curvature (235) and output (625) of the control variable of the feedforward controller (165), wherein the control variable of the feedforward controller (165) is used to control the vehicle (110). Procedure (600) according to Claim 1 , wherein the control-based time delay is estimated using a machine learning algorithm (240, 245), in particular a neural network, and in particular wherein the driving parameter (230, 225) is used as an input variable for the machine learning algorithm (240, 245), in particular the neural network. Procedure (600) according to Claim 2 , wherein the machine learning algorithm (240, 245), in particular the neural network, comprises a radial basis function (245). Procedure (600) according to Claim 2 or 3 , wherein the machine learning algorithm (240, 245), in particular the neural network, comprises an update law (240). Method (600) according to one of the preceding claims, comprising a feedback controller (166), wherein an actual yaw rate (115) of the vehicle (110) is measured, in particular with a yaw rate sensor; wherein a yaw rate error (140) is determined from the difference between the actual yaw rate (115) and a desired yaw rate (125), wherein the yaw rate error (145) is processed in the feedback controller (166); wherein the feedback controller (166) outputs a manipulated variable of the feedback controller (166), which, in particular together with the manipulated variable of the feedforward controller (165), is used for controlling, in particular for steering, the vehicle (110); and wherein the feedforward controller (165) at least partially, in particular completely, takes into account and/or estimates the control time of the feedback controller (166) when estimating the control-based time delay. Procedure (600) according to Claim 5 , wherein the manipulated variable of the feedback controller (166) is generated using a machine learning algorithm. Procedure (600) according to Claim 6 , where the machine learning algorithm includes an online learning algorithm. Procedure (600) according to Claim 6 or 7 , where the machine learning algorithm includes a variable learning rate. Method (600) according to one of the Claims 5 until 8 , wherein the feedback controller comprises a first feedback controller (170) and a second feedback controller (175). Procedure (600) according to Claim 9 , wherein the first feedback controller (170) comprises a neural network (185), in particular wherein the first feedback controller (170) comprises an integral gain learning algorithm (200), in particular wherein the yaw rate error (140) is an input variable for the integral gain learning algorithm (200). Procedure (600) according to Claim 9 or 10 , wherein the second feedback controller (170) comprises a directly adaptive neural network (210). Method (600) according to one of the Claims 1 until 11 , wherein the method (600) is at least partially, in particular completely, a computer-implemented method. Data processing system, in particular a control architecture (100) for controlling, in particular for steering, a vehicle (110), in particular for autonomous driving of a vehicle (110), with means for carrying out the method (600) according to one of the Claims 1 until 12 . Computer program, in particular computer program product, with instructions which, when the program is executed by a computer, cause the computer to carry out the method (600) according to one of the Claims 1 until 12 to execute. A computer-readable medium having instructions which, when executed by a computer, cause the computer to perform the method (600) according to any one of Claims 1 until 12 to execute.