DE102020215214A1 - Functionally robust optimization of a vehicle control - Google Patents

Abstract

A method (300) for determining control parameters for a controller of a vehicle (305) comprises the steps of providing a model (100) of a system comprising the controller (110) and the vehicle (305); the model comprising a vector u of input values applied to the vehicle (305) by the controller (110); a vector y of output values observed at the vehicle (305); a vector p of driving parameters acting on the vehicle (305) from the outside; and a vector q of control parameters predetermined for the controller (110); determining a predetermined system condition related to the vector y; determining the p and q largest portion (225) of a space (200) spanned by the vectors, the system condition being satisfied at each point in the portion (225); and providing the control parameters associated with the section (225).

Description

The present invention relates to an optimization of control parameters of a controller for a vehicle. In particular, the invention relates to a functionally robust optimization.

A vehicle can be controlled by a controller. For example, a trajectory and a distance from a vehicle driving ahead can be influenced with respect to predetermined values. The controller provides control values acting on the vehicle based on influences acting on the vehicle and a driving condition of the vehicle, and a driving condition of the vehicle depends on past control values. The controller operates satisfactorily when a predetermined system condition is met. An example system condition may include a maximum deviation of the vehicle's position from a predetermined trajectory. The system condition is usually only met in certain combinations of control parameters.

The vehicle is typically exposed to driving parameters that are not directly or accurately known to the controller. For example, a coefficient of friction between a wheel of the vehicle and a surface can only be known imprecisely, with even a small change in the coefficient of friction being able to bring about a large change in the behavior of the vehicle in response to a predetermined control intervention. The controller can be parameterizable to change a relationship between input parameters and output parameters. For example, the controller may include a PID controller, and three example control parameters include a proportionality constant, an integration constant, and a derivative constant.

The controller is preferably parameterized in such a way that the system condition can still be maintained if the deviation between a specific and an applicable driving parameter is as large as possible. The parameterization can depend on many variables of the system, so that a very large state space would have to be analyzed exhaustively in order to determine optimal control parameters. In addition, determining compliance with the system condition is usually laborious. A function to determine compliance is not generally differentiable, so a point-by-point approach is required.

An object underlying the present invention is to provide an improved technique for determining control parameters for a control of a vehicle. The invention solves this problem by means of the subject matter of the independent claims. Subclaims reflect preferred embodiments.

A method for determining control parameters for a controller of a vehicle includes the steps of providing a model of a system including the controller and the vehicle; and determining a predetermined system condition with respect to a vector y. The model comprises a vector u of input values acting on the vehicle from the controller; a vector y of output values observed at the vehicle; a vector p of driving parameters acting on the vehicle from the outside; and a vector q of control parameters specified for the control. The method further provides for determining the largest p and q portion of a space spanned by the vectors, the system condition being satisfied at each point in the portion, and providing the control parameters associated with the portion.

Through the model-based approach, an efficient search for a suitable operating range of the controller can be realized in the space that can represent a state space of the system. In this way, a maximum control range can be determined with a maximum uncertainty range with regard to applicable driving parameters. In particular, it is proposed to determine the section based on machine learning methods. Such a method can be used in particular to determine a model or an approximation that shows a connection in the system that cannot be determined, or can only be determined poorly, using conventional methods.

The system condition may include that the output values, as may be summarized in vector y, differ by no more than a predetermined amount from output values determined by the controller. In other words, only a predetermined deviation of the vehicle state from a control target may be allowed. The controller preferably carries out movement control of the vehicle, it being possible for transverse control and/or longitudinal control to take place. For example, the controller can influence a trajectory of the vehicle, with a deviation of the actual trajectory from a predetermined trajectory only being allowed to have a specific extent, which in an exemplary embodiment can be approximately 0.5 m. In a similar way, the controller can maintain a minimum distance from a vehicle driving ahead, it still being tolerable to fall short of the minimum distance by, for example, about 1 m.

In a further preferred embodiment, first sections of the space are determined, with sizes of the first sections with regard to control parameters and/or driving parameters being at a maximum. Nevertheless, it is possible that in the first sections the section is determined, the size of which is maximum with regard to the driving parameters. Nested optimization can thus take place, with outer optimization taking place with regard to one or more control parameters and inner optimization taking place with regard to one or more driving parameters. The inner optimization can determine the worst case for each control parameter vector specified by the outer optimization. For each outer optimization candidate, an optimal inner optimization candidate can be found. The candidate finally selected can be optimal in terms of driving parameters and in terms of control parameters.

In a variant, sections of the driving parameters can contain the current value of the driving parameters.

The external optimization with respect to the control parameter q can be done in any way; it only needs the information about the size of the driving parameter range of p in which the desired system behavior is fulfilled. For example, if the information relates to a coefficient of friction, the information can indicate how large the range of the coefficient of friction is over which the system behavior is acceptable when the current value for q is used. This information is also referred to as an oracle for providing a promising candidate.

A first approximation model, which can also be referred to as a first approximation, can be created to determine the admissibility of a hyperrectangle depending on its position and size with respect to p and/or q. Based on the first approximation, a second portion of the space can be determined. It can then be determined whether the system condition is met throughout the second section. The first approximation, or the first approximation model, can be improved on the basis of the admissibility determined.

For the first approximation, a first Bayesian optimization method should be used in particular. In contrast to other optimization methods, a probabilistic model for a target function is created here and then updated and improved in an iterative process by adding further data points. The target function can include, for example, a maximum deviation of a trajectory of the controlled vehicle from a predetermined trajectory as a function of driving parameters. The basic idea of Bayesian optimization is that the entire information of all calculated data points can be used. Another crucial aspect of Bayesian optimization is the use of an acquisition function to determine the next data point to use. This acquisition function, which can be defined in many different ways, describes one form of the utility of the data points for the model. By determining the maximum of this function, the next data point to be used is selected, as a result of which a small number of required data points can be achieved with a good result at the same time.

A Gaussian process is preferably used to model a priori probabilities in order to approximate a relationship between parameters and system behavior and at the same time to provide information about the quality of the approximation model. For example, the so-called expected improvement (EI) can be used as an acquisition function. With just a few specific data points, Bayesian optimization can provide a model or an approximation that allows the worst case to be found, which is characterized, for example, by the maximum deviation of a position of the vehicle from a target position. By considering statistical relationships, data points that can contribute a high level of information can be used to further develop the model. In particular, a maximum deviation of the system behavior from a target behavior as a function of a section (interval) of a driving parameter and a control parameter can be modeled in this way.

In one embodiment, the system condition includes a comparison of a controller error to a predetermined threshold. The control error can include any variable, for example a distance or a percentage deviation of an actual value from a target value. Parameters of the second section that can be used in the model preferably include lower and upper limits of one or more driving parameters. It is preferred that a maximum control error, eg at a point, is determined for a given vector q in the second section; wherein the first approximation is improved with respect to the determined maximum control error. As a result, important information can be taken into account, especially if the maximum control error in the second section exceeds the threshold value, which is important for determining the further relationship between the position or size of the second section in space and compliance with the system condition in its range applies. Other second sections, which can be checked iteratively, can thus be better evaluated.

It is further preferred that a second approximation model for assessing the system behavior is determined as a function of the driving parameters and/or control parameters. On the basis of the second approximation model, which can also be referred to as the second approximation, the fulfillment of the system condition for the second section can be checked. In addition, with respect to the second approximation, it can be determined whether the system condition is allowable at all points in the second section.

For the second approximation, a second optimization method according to Bayes is to be used in particular. Here, too, a Gaussian process is preferably used for modeling a priori probabilities. The expected improvement (EI), for example, can also be used as an acquisition function.

The system condition may include a comparison of a controller error to a predetermined threshold. It may be determined whether all points in the second section are acceptable by determining a point in the second section where maximum control error occurs based on the second approximation and comparing the control error at the specific point to the predetermined threshold. A point is accepted if the control error at the particular point does not exceed the predetermined threshold. A section is admissible if all points within the section are admissible. The admissibility is advantageously determined for all points of a selected second section with regard to the second approximation, so that an exhaustive determination can be made with reasonable effort.

Using the second approximation, a probability can be determined with respect to a predetermined confidence, with which a point can be found in the second section at which an associated control error is greater than for an existing point. In this way, the point with the maximum control error (worst case) can be found in the second section in just a few steps.

For the present technique, a shape of the portion used can be chosen practically arbitrarily as long as the shape is continuous. It is preferred that a section is defined as a hyperrectangle in space such that ranges of parameters defining the section are independent of each other. Other possible shapes include, for example, a hyperellipse or hypersphere.

According to a second aspect of the present invention, an apparatus for determining control parameters for a controller of a vehicle comprises a model of a system comprising the controller and the vehicle; the model comprising a vector u of input values applied to the vehicle by the controller; a vector y of outputs observed on the vehicle or its model; a vector p of driving parameters acting on the vehicle from the outside; and a vector q of control parameters predetermined for the controller; an output device for providing the control parameters associated with the section; and a processing device. The processing device is set up to determine the section of a space spanned by the vectors that is largest with respect to p and q, a predetermined system condition with respect to y being fulfilled at each point in the section.

The processing device can be set up to carry out a method described herein in whole or in part. For this purpose, the processing device can include 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.

According to a third aspect of the present invention, a control device for controlling a vehicle is provided, wherein the control device is configured to determine values for acting on the vehicle on the basis of output values observed on the vehicle or on the model and predetermined control parameters. The control parameters are determined using a method described herein.

• 1 ein System;
• 2 einen beispielhaften Raum und beispielhafte Abschnitte des Raums; und
• 3 ein Ablaufdiagramm eines Verfahrens

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

• 1 a system;
• 2 an exemplary space and exemplary portions of the space; and
• 3 a flowchart of a method

represents.

1 10 shows a model 100 for a system that includes a vehicle 105 and a controller 110 . The controller 110 is set up to control the vehicle 105, in particular movement of the vehicle 105 can be controlled. The movement can take place in the longitudinal direction, in particular by controlling a drive motor or a braking system, and/or in the transverse direction, in particular by controlling a steering system.

Basically, the controller 110 processes one or more outputs observed at the vehicle 105, which outputs may be summarized in a vector y, and provides one or more inputs acting on the vehicle 105 and summarized in a vector u can become. A relationship between the input values and the output values can be influenced by choosing values for one or more control parameters, which can be combined in a vector q. A control response of the vehicle 105 to input values can be influenced by one or more driving parameters, which can be summarized in a vector p.

During the control of the vehicle 105, the controller 110 does not usually have direct access to values for driving parameters; instead, approximations, estimates, model values or substitute values that may otherwise contain errors are used, which can be combined in a vector p′. An exemplary driving parameter includes a coefficient of friction between a wheel of the vehicle 105 and a ground. Other possible driving parameters may relate to a speed or a pose of the vehicle 105 .

The controller 110 is intended to pursue a predetermined control target, for example with regard to an absolute or relative position or pose of the vehicle 105. It is intended to ensure that the control target can be achieved at least within a predetermined tolerance. For this purpose, a system condition can be formulated, which should always be fulfilled. The system condition may include a comparison of a quantitative value to a threshold. The qualitative value can preferably be determined by the controller 110 . For example, it may be required that a control error is less than a predetermined threshold. For example, if the controller 110 is configured to follow a predetermined trajectory, the control error may relate to a deviation of the trajectory from the predetermined trajectory, and the system condition may indicate that a magnitude of the control error is less than, for example, about 0.5 m.

It is proposed to use the model 100 to determine control parameters for the controller 110 in such a way that the control task can be fulfilled even if there is a deviation between a driving parameter and the associated substitute parameter, so that the system condition is fulfilled. In particular, a tolerance of the controller 110 with respect to such a deviation should be maximized as far as possible.

2 12 shows an exemplary space 200 and exemplary portions of the space 200. The vectors y, u, p' and q span a space or vector space, typically of many dimensions. The one in an upper section of 2 The space 200 shown shows a simplification to two dimensions, along with one more dimension for a value S used to determine whether a system condition is met.

Exemplary parameters from p are P1 and P2; the value S is plotted in a vertical direction. For example, in a transmission control, the parameters P1 and P2 could relate to hydraulic capacities and the value S could indicate a time required for a gear change engaged in the transmission. The system condition could be that the time must not be longer than 300 ms.

A surface 205 shows a relationship between P1, P2 and S. In practice, there are usually many more than two parameters involved in this relationship. The value S can be determined for any combination of values for the parameters, but a converse determination of parameters leading to a predetermined value is hardly possible. The value can be compared to a threshold to determine if the system condition is met. In the present example, for a threshold value of 300 ms, the surface 205 can be graphically intersected with a plane that runs parallel to the axes of the remaining driving parameters at a height of 300 ms. Locations where S exceeds the threshold are not allowed by the controller 110, while those where S is below the threshold are allowed.

In a lower section of 2 Invalid portions 210 and 215 are graphically represented as a projection of the interface into the P1-P1 plane. It is proposed to determine sections 220, 225 that are entirely within the allowable range. Then the largest section 225 is to be determined.

Overall, a section 225 is to be determined which is as large as possible with respect to p and with respect to q. A section 220, 225 with the shape of a hyperrectangle is preferably assumed, so that rectangular sections 220, 225 result in the two-dimensional space shown. The size of a section 220, 225 can then be determined as the product of differences between the upper and lower bounds of each parameter in the parameter vector p. In order to maximize the size of the section 220, 225 with respect to q, limits of parameters from q should be determined between which nominal values from q lie; and in order to maximize with respect to p, limits for parameters from p should be varied, between which nominal values from p lie. This results in a nested optimization problem in which an outer optimization with respect to q and an inner optimization with respect to the limits of p are performed. An inner optimization must be carried out for each outer optimization or for each candidate that is determined using the outer optimization.

In the present case, it is assumed that the external optimization of the section with respect to q is carried out using any method in such a way that one or more candidates for values from q are found in this way. In the following, the inner optimization of a section with regard to the limits of p is primarily described, which is based on a found candidate with regard to q. The optimization with respect to q can also be done using Bayesian optimization.

3 shows a flowchart of a method 300 that includes a first approximation 305 and a second approximation 345 . Both approximations are preferably carried out using Bayes methods based on Gauss processes.

For the first approximation 305, in a step 310 a first range for a parameter can be selected from p. A range is defined by a lower limit and an upper limit. If p includes more than one parameter, a range can be selected for each of the parameters included. Correspondingly, a first range for a parameter is selected from q.

In a step 315, the validity of the present range can be determined. For this purpose, it can be determined on the basis of the second approximation 345 whether the system condition is fulfilled at every point that lies within the formed boundaries. For this purpose, it is advantageously determined, for example, which value the system function assumes at a point within the limits in the worst case (worst case). This determination is preferably made on the basis of the second approximation 345. If the determined value is below the predetermined threshold value, then the tested candidate can be regarded as admissible. If enough candidates are examined, the largest can be selected from those found to be admissible. A first approximation described herein can be used to determine whether a sufficient number of candidates have already been checked.

Irrespective of the determined admissibility, limits of the candidate may be stored in a step 320, preferably together with the determined value of the worst case system function. Furthermore, on the basis of all such points determined so far, a first model or a first approximation for a relationship between a size and position of the hyperrectangle and its admissibility can be improved. In other words, the model for the first approximation can be extended by the newly determined point.

Then, in a step 325, the consideration of the current area combination can be ended and the first approximation can continue with step 310, in which a further combination of area boundaries can be determined on the basis of the model of the first approximation.

The second approximation 345 works in a similar way, for which in a step 350 a point can be selected in the current area combination—in the current hyperrectangle—that lies in the selected area. In a step 355, the vehicle and control model are used to determine whether the system condition is met at the selected point, or what value is determined at this point, which is compared to a threshold value to determine the system condition.

In a step 355, the second model can be extended by the specific point. In a step 360 it can be determined whether the system condition is fulfilled for all points of the current region combination. This determination is made with respect to the second model. In a step 365, the treatment of the current point within the current region combination can be terminated. The second approximation 345 can then continue with step 350, in which a further point is selected on the basis of the second model.

The point in step 350 is preferably selected in such a way that as much information as possible about the fulfillment of the system function is obtained. At the same time, with reference to a predetermined confidence, it can be determined with what probability there is another point within the area combination at which the system function is violated. The second approximation 345 can be iteratively continued in the manner described until the probability determined in step 350 is below a predetermined threshold value and a statement about the admissibility of the area currently under consideration is given can be hit. In other words, if the probability of finding a violation is less than a predetermined threshold, then the section or hyperrectangle is allowed. If the probability of finding a violation is greater than the threshold value, iteration can continue. Iterating can continue until either a violation is found or the probability of a violation is less than a predetermined threshold.

Reference List

100

model

105

vehicle

110

steering

y

Vector of output values observed at the vehicle

and

Vector of input values that affect the vehicle from the controller

p

Vector of driving parameters that affect the vehicle from the outside

p'

Vector of substitute values for the driving parameters

q

Vector of control parameters that are specified for the control

200

Space

205

Surface

210

first invalid section

215

second invalid section

220

first allowed section

225

second allowed section

300

procedure

305

first approximation

310

choose area

315

determine admissibility

320

extend first approximation by certain point

325

choose next area

345

second approximation

350

choose point

355

extend second model by certain point

360

check whether the system condition is fulfilled in the entire range

365

choose another point

Claims (11)

Method (300) for determining control parameters for a control of a vehicle (305); the method (300) comprising the steps of: providing a model (100) of a system comprising the controller (110) and the vehicle (305); the model comprising a vector u of input values applied to the vehicle (305) by the controller (110); a vector y of output values observed at the vehicle (305); a vector p of driving parameters acting on the vehicle (305) from the outside; and a vector q of control parameters predetermined for the controller (110); determining a predetermined system condition related to the vector y; determining the p and q largest portion (225) of a space (200) spanned by the vectors, the system condition being satisfied at each point in the portion (225); and providing the control parameters associated with the portion (225). Method (300) according to claim 1 , wherein the system condition comprises that the output values differ by no more than a predetermined amount from output values predetermined by the controller (110). Method (300) according to claim 1 or 2 , wherein first sections are determined, the sizes of which are maximum with respect to the control parameters and/or driving parameters. Method (300) according to one of the preceding claims, wherein the sections of the driving parameters contain the current value of the driving parameters. Method (300) according to one of the preceding claims, wherein a second section is determined on the basis of a first approximation for determining the admissibility of a first section depending on its position and size with regard to driving parameters; determining whether the system condition is satisfied throughout the second portion; and the first approximation is improved based on the determined allowability. Method (300) according to claim 5 , wherein the system condition comprises a comparison of a control error with a predetermined threshold; wherein a maximum control error is determined at a point in the second section; and wherein the first approximation is improved with respect to the determined maximum control error. Method (300) according to claim 5 or 6 , a point in the second section being determined on the basis of a second approximation for assessing the system behavior as a function of driving parameters; determining that the system condition is met at the specified point; the second approximation is improved based on the determined acceptability; and with respect to the second approximation, determining whether the system condition is valid at all points in the second section. Method (300) according to claim 7 , wherein the system condition comprises a comparison of a control error with a predetermined threshold; wherein determining whether all points in the second section are acceptable by determining a point in the second section at which a maximum control error occurs based on the second approximation and comparing the control error at the determined point to the predetermined threshold. A method (300) according to any one of the preceding claims, wherein a section is determined as a hyperrectangle in space (200). Device for determining control parameters for a controller (110) of a vehicle (305); the apparatus comprising: a model of a system comprising the controller (110) and the vehicle (305); the model comprising a vector u of input values applied to the vehicle (305) by the controller (110); a vector y of output values observed at the vehicle (305); a vector p of driving parameters acting on the vehicle (305) from the outside; and a vector q of control parameters predetermined for the controller (110); processing means arranged to determine the p and q largest portion of a space spanned by the vectors (200), a predetermined system condition with respect to y being satisfied at each point in the portion; and an output device for providing the control parameters associated with the section. Control device (110) for controlling a vehicle (305), the control device being set up to determine values to act on the vehicle (305) on the basis of output values observed at the vehicle (305) and predetermined control parameters; wherein the control parameters are adjusted by a method (300) according to any one of Claims 1 until 8th are determined.

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