DE102022201853A1 - Detection of critical traffic situations with Petri nets - Google Patents

Abstract

Method (100) for checking the extent to which a traffic situation (1) detected with at least one sensor is critical, with the steps: • the traffic situation (1) is converted into a graph (2) (110), with ◯ the nodes of the graph ( 2) correspond to possible positions of road users and ◯ the edges of the graph (2) are assigned weights, which give the nodes connected by an edge a value for the evaluation of the traffic situation (1) by the control system (10 ) assign relevant variable;• the graph (2) is transferred (120) to a Petri net (3) which links local state changes to conditions with which quantities of tokens are assigned to predetermined locations in the Petri net (3). , where◯ the nodes of the graph (2) correspond to locations in the Petri net,◯ the edges of the graph (2) correspond to local state changes and◯ the weights at the edges of the graph (2) define conditions for state changes;• es at least one transfer function (3a) of the Petri net (3) for the transition between global states of the Petri net (3) is determined (130);• this transfer function (3a) is used to evaluate (140) the extent to which the traffic situation (1st ) is critical (1a).

Description

The present invention relates to identifying which traffic situations are critical and may not be able to be controlled by a control system fed by sensor data.

State of the art

Driving assistance systems, control systems for robots and systems for at least partially automated driving of vehicles record traffic situations with the help of sensors and develop a proposal for the future behavior of the vehicle or robot. For the acceptance and approval of such systems, it is important that they provide a suggestion in every situation and do not fail to provide an answer in certain situations.

US 10,942,797 B2 discloses a method for fault tree analysis for technical systems, which continuously estimates the probability of an undesired event in the system. If the probability meets a predetermined criterion, countermeasures can be taken.

Disclosure of Invention

The invention provides a method for checking the extent to which a traffic situation detected with at least one sensor is critical in the sense that a control system for a vehicle or a robot is not able to determine an unambiguous suggestion for the future behavior of the vehicle or the robot. might be able to.

As part of the method, the traffic situation is analyzed in the form in which it is perceived by the at least one sensor. It is therefore examined to what extent the amount of information provided by the at least one sensor is sufficient for the control system to be able to come to a clear decision. It is therefore possible that a representation of the traffic situation recorded with a first sensor configuration turns out to be critical, while a further representation of the traffic situation recorded with a second sensor configuration does not turn out to be critical.

• • ein Verkehrsfluss zwischen den durch die Kante verbundenen Knoten; und/oder
• • Verkehrsregeln für die Fahrt zwischen den durch die Kante verbundenen Knoten; und/oder
• • eine Bevorrechtigung oder Wartepflicht für die Fahrt zwischen den durch die Kante verbundenen Knoten.

As part of the process, the traffic situation is converted into a graph. The nodes of this graph correspond to possible positions of road users. The edges of the graph are weighted. These weights each assign a value of a variable relevant to the evaluation of the traffic situation by the control system to the nodes that are connected by an edge. Examples of such sizes are

• • a traffic flow between the nodes connected by the edge; and or
• • traffic rules for driving between the nodes connected by the edge; and or
• • a priority or waiting obligation for the journey between the nodes connected by the edge.

The graph is fully described by its nodes and edges. It is transferred to a Petri net. Such a Petri net is a model of a discrete system based on locations that can be occupied by one or more tokens. The Petri net contains local state changes (transitions), the triggering of which is linked to conditions with which quantities of tokens are assigned to predetermined locations in the Petri net. To this extent, the tokens are comparable to coins or tokens. In a simple example, a Petri net in a vending machine can add up the values of inserted coins and, in response to the total value being at least equal to the price of a desired commodity, cause the machine to dispense that commodity.

For application to control systems, the nodes of the graph correspond to locations on the Petri net. The edges of the graph correspond to local state changes, because road users move over these edges when they change from one possible position to another. The weights at the edges of the graph set conditions for local state changes. For example, you determine how many tokens must be present at certain locations in order for the respective local state change to be triggered.

At least one transfer function of the Petri net is determined for the transition between global states of the Petri net. In particular, this global state can include, for example, the allocation of all locations of the Petri net with tokens. This transfer function is used to evaluate the extent to which the traffic situation is critical.

It was recognized that it is particularly easy to see from this transfer function to what extent the traffic situation is critical and the control system may not be able to find an appropriate answer. For example, experiments have shown that the eigenvalues of the transfer function, and here in particular the first eigenvalue, change drastically when the traffic situation unusual physical changes are made.

In such an experiment, a traffic situation in which a normal vehicle moves through the detection range of a radar sensor was first converted into a Petri net and the transfer function was evaluated. The traffic situation was then changed in such a way that the vehicle pulled a metallic beer can behind it on a string. The traffic situation changed in this way was converted into a Petri net in the same way, and the transfer function of this Petri net was evaluated. Compared to the original traffic situation, the first eigenvalue of the transfer function increased significantly.

In a particularly advantageous embodiment, it is thus evaluated according to a predetermined criterion from at least one eigenvalue of the transfer function and/or from a change in this eigenvalue to what extent the traffic situation is critical.

The knowledge of whether traffic situations prove to be critical and which traffic situations these are in detail can, in principle, be used for online monitoring of a control system with upstream sensors if sufficient computing power is available for evaluation in real time. Countermeasures can then be taken, for example, to prevent a possible situation in which the control system is no longer clearly capable of making decisions. For example, a driver of the vehicle may be prompted to take control of the vehicle, or the vehicle's speed may be reduced to allow the vehicle to go without suggestions from the control system for a period of time. If progressively more and more traffic situations turn out to be critical, this can also be taken as an indication, for example, that sensors are dirty, misaligned or degraded in some other way.

However, the main application of the method lies in the offline analysis of traffic situations for the purpose of proving that a control system with upstream sensors is suitable for use in traffic. in particular, individual traffic situations or types of traffic situations that are more critical than others can be identified. Experimental effort for tests on sensors and control systems can then preferably be focused on those traffic situations that turn out to be particularly critical in the offline analysis. For example, experimental investigations on radar sensors can cost several thousand euros per hour. This is somewhat analogous to the fact that most of the effort involved in customs and border controls is also targeted at people who fall into certain risk profiles. The goal is to only open those suitcases that actually contain prohibited goods or goods that are subject to duty.

In a particularly advantageous embodiment, those further nodes of the graph which are connected to a first node by edges correspond to those positions which, starting from a position corresponding to the first node, are in the detection range of the at least one sensor. In this way, the graph corresponds even better to the perception of the traffic situation by the at least one sensor. From the analysis of the traffic situation, it can then follow, for example, that this is no longer critical if the detection range of the sensor can be enlarged or another sensor can be added.

The at least one sensor can include, for example, a camera, a radar sensor, a lidar sensor and/or an ultrasonic sensor. The traffic situation can also be recorded multimodally, for example, with several sensor modalities at the same time.

In a further particularly advantageous embodiment, one and the same traffic situation is recorded redundantly and/or multimodally with at least two sensors. A separate graph, a separate Petri net and a separate transfer function of the respective Petri net are determined for the form of the traffic situation recorded by each of the sensors. The transfer functions are aggregated into an overall transfer function. This overall transfer function is used to evaluate the extent to which the traffic situation is critical. In this case, transfer functions can be aggregated, for example, by addition. This is much easier than creating a single Petri net for a redundant and/or multivariate recording of a traffic situation.

• • die exakte Dichte an Elementen (wie etwa Fahrzeugen, Fußgängern oder Verkehrszeichen) in der Verkehrssituation nur anhand mehrerer Messungen approximiert werden kann;
• • die Elemente der Verkehrssituation in unbekannter Weise und zu einem unbekannten Grade miteinander zusammenwirken (korrelieren), so dass die Verkehrssituation nicht als Markov-Prozess oder als Dempster-Shaefer-Prozess beschrieben werden kann; und
• • mehrere Sensoren verwendet werden.

For the dynamics of the traffic situation, redundancy can mean, for example, that

• • the exact density of elements (such as vehicles, pedestrians or traffic signs) in the traffic situation can only be approximated using multiple measurements;
• • the elements of the traffic situation interact (correlate) with each other in an unknown way and to an unknown degree, so that the traffic situation cannot be described as a Markov process or as a Dempster-Shaefer process; and
• • several sensors are used.

In a further particularly advantageous embodiment, the traffic situation is recorded at least partially as a time series of measurements. The graph is then transformed into a Petri net of time-dependent events, in which local state changes are also linked to temporal conditions. In this way, dynamic traffic situations, such as the approach of another vehicle, can be detected. One application in which the criticality of traffic situations is currently being actively examined is the "Front Cross Traffic Assistant", which uses radar to monitor an intersection in front of the vehicle and warns of approaching crossing traffic.

• • einer ersten Fortentwicklung A des globalen Zustandes des Petri-Netzes, die sich einstellt, wenn eine Belegung n aller Orte mit jeweiligen Anzahlen von Token unverändert bleibt,
• • einer zweiten Fortentwicklung B des globalen Zustandes des Petri-Netzes, die sich einstellt, wenn die Belegung n aller Orte mit jeweiligen Anzahlen von Token in eine Belegung m aller Orte mit jeweiligen Anzahlen von Token übergeht, und
• • einer dritten Fortentwicklung C des globalen Zustandes des Petri-Netzes, die sich einstellt, wenn eine Belegung p aller Orte mit jeweiligen Anzahlen von Token in die Belegung n aller Orte mit jeweiligen Anzahlen von Token übergeht,

ermittelt. Aus diesen drei Fortentwicklungen lassen sich Fixpunktgleichungen formulieren, und aus den Lösungen der Fixpunktgleichungen lässt sich wiederum die Übertragungsfunktion ermitteln.In a further particularly advantageous embodiment, the transfer function

• • a first development A of the global state of the Petri net, which occurs when an assignment n of all locations with the respective number of tokens remains unchanged,
• • a second development B of the global state of the Petri net, which occurs when the occupancy n of all locations with respective numbers of tokens changes into an occupancy m of all locations with respective numbers of tokens, and
• • a third development C of the global state of the Petri net, which occurs when an occupancy p of all locations with respective numbers of tokens changes to the occupancy n of all locations with respective numbers of tokens,

determined. Fixed point equations can be formulated from these three further developments, and the transfer function can in turn be determined from the solutions of the fixed point equations.

• • die Addition ⊕ zweier Elemente durch Maximumbildung über diese zwei Elemente und
• • die Multiplikation ⊗ zweier Elemente durch Addition dieser zwei Elemente ausgeführt wird. Auf einem solchen Semiring können die Fixpunktgleichungen als lineare Gleichungen aufgestellt werden.

The transfer function of the Petri net is particularly advantageously determined on a semiring on which

• • the addition ⊕ of two elements by taking the maximum over these two elements and
• • the multiplication ⊗ of two elements is performed by adding these two elements. The fixed point equations can be set up as linear equations on such a semiring.

$$\forall \text{a}.\text{b},\text{c}\in \text{D}\to (\text{c}\otimes \left(\text{a}\oplus \text{b}\right)=\left(\text{c}\otimes \text{a}\right)\oplus \left(\text{c}\otimes \text{b}\right)$$

$$\forall \text{a}\in \text{D }\to \left(\text{a}\otimes \epsilon \right)=\left(\mathrm{\epsilon }\otimes \text{a}\right)=\mathrm{\epsilon }$$

$$\forall \text{a}\in \text{D }\to \left(\text{a}\otimes \text{a}\right)=\text{a}.$$

The semiring is defined here by a set D of elements and operations for the addition ⊕ of two elements and the multiplication ⊗ of two elements. Here the addition ⊕ is associative and commutative and has a neutral element ε. The multiplication ⊗ is associative and has a neutral element e. On such a semiring, the following applies: $$\forall \text{a}.\text{b},\text{c}\in \text{D}\to \left(\text{a}\oplus \text{b}\right)\otimes \text{c}=\left(\text{a}\otimes \text{c}\right)\oplus \left(\text{b}\otimes \text{c}\right)$$

$$\forall \text{a}.\text{b},\text{c}\in \text{D}\to (\text{c}\otimes \left(\text{a}\oplus \text{b}\right)=\left(\text{c}\otimes \text{a}\right)\oplus \left(\text{c}\otimes \text{b}\right)$$

$$\forall \text{a}\in \text{D}\to \left(\text{a}\otimes e\right)=\left(\mathrm{e}\otimes \text{a}\right)=\mathrm{e}$$

$$\forall \text{a}\in \text{D}\to \left(\text{a}\otimes \text{a}\right)=\text{a}.$$

D in connection with the operations ⊕ and ⊗ forms an idempotent semifield. If the product ⊗ is commutative, then this semifield also becomes commutative. The set ℝ ∪ ⊕ {-∞} provided by maximum formation ⊕ and addition ⊗ is an idempotent semifield, also known as semiring algebra or max plus algebra. The numerical value of the neutral element ε of the addition ⊕ is -∞.

mit geeignet dimensionierten Matrizen $$A\left(k,r\right),B\left(k,r\right),r=k,k-\mathrm{1,}\dots ,k-M.$$

In a Petri net of time-dependent events, for each local state change j, times x _j (k), k = 1, T, at which the local state change j is triggered the kth time, can be specified as state variables, where T is the total duration the measurement is. These times x _j (k) can be combined into a state vector x(k). A vector u(k) of external variables can be introduced in an analogous manner. On the semiring algebra, x(k) then expands recursively according to $$\begin{array}{l}x\left(k\right)=A\left(k,k\right)\otimes x\left(k\right)\oplus A\left(k,k-1\right)x\left(k-1\right)\oplus ...\\ \oplus A\left(k,k-1\right)x\left(k-1\right)\otimes x\left(k-M\right)\\ \oplus B\left(k,k\right)\otimes \mathrm{and}\left(k\right)\oplus ...\oplus B\left(k,k-M\right)\otimes \mathrm{and}\left(k-m\right)\end{array}$$

with suitably dimensioned matrices $$A\left(k,\mathrm{right}\right),B\left(k,\mathrm{right}\right),\mathrm{right}=k,k-\mathrm{1,}...,k-M.$$

These matrices follow from the temporal evolution of the states of locations in a Petri net of time-dependent events. M is the maximum number of tokens at locations in the Petri net.

$$y=Cx$$

ausgewertet werden, worin x ein n-dimensionaler Evolutionsvektor, u ein p-dimensionaler Evolutionsvektor und y ein m-dimensionaler Evolutionsvektor ist.The transfer function of the Petri net can then advantageously be obtained from at least one solution of the fixed point equations $$x=Ax\otimes B\mathrm{and},$$

$$y=Cx$$

are evaluated, where x is an n-dimensional evolution vector, u is a p-dimensional evolution vector, and y is an m-dimensional evolution vector.

• • einem ersten Verschiebeoperator γ, dessen Potenzen zu Anzahlen von Token an Orten im Petri-Netz korrespondieren,
• • einem zweiten Verschiebeoperator δ, dessen Potenzen zu Anzahlen von lokalen Zustandsänderungen im Petri-Netz korrespondieren,
• • einem neutralen Element ε der Addition ⊕ und
• • einem neutralen Element e der Multiplikation ⊗

parametrisiert. Hiermit lassen sich die Fixpunktgleichungen als $$x=ax\otimes b,$$

$$y=ca*bu$$

ausdrücken, worin * die komplexe Konjugation bezeichnet und die Matrizen a, b, c in γ, δ, ε und e parametrisiert sind. In dieser Form lassen sich die Fixpunktgleichungen besonders einfach lösen, beispielsweise mit den Matrizen $$\text{a}=\left(\begin{array}{ccc}\mathrm{\epsilon }& \mathrm{\gamma }& \mathrm{\epsilon }\\ \mathrm{\delta }& \mathrm{\epsilon }& \mathrm{\epsilon }\\ \text{e}& \mathrm{\delta }& \mathrm{\gamma }{\mathrm{\delta }}^2\end{array}\right),\text{ b}=\left(\begin{array}{cc}{\mathrm{<figure-callout\; id="3"\; label="\delta "\; filenames="DE102022201853A1\_0025.png"\; state="\{\{state\}\}">\delta </figure-callout>}}^3& \mathrm{\epsilon }\\ \mathrm{\epsilon }& \mathrm{\gamma \delta }\\ \mathrm{\epsilon }& \mathrm{\epsilon }\end{array}\right),\text{ c}=\left(\begin{array}{ccc}\mathrm{\epsilon }& \mathrm{\gamma }& {\mathrm{\delta }}^3\end{array}\right).$$

In a further particularly advantageous embodiment, the transfer function of the Petri net

• • a first shift operator γ, whose powers correspond to numbers of tokens at locations in the Petri net,
• • a second shift operator δ, whose powers correspond to numbers of local state changes in the Petri net,
• • a neutral element ε of the addition ⊕ and
• • a neutral element e of multiplication ⊗

parameterized. With this, the fixed point equations can be written as $$x=ax\otimes b,$$

$$y=ca*b\mathrm{and}$$

express, where * denotes the complex conjugation and the matrices a, b, c are parameterized in γ, δ, ε and e. In this form, the fixed point equations can be solved particularly easily, for example with the matrices $$\text{a}=\left(\begin{array}{ccc}\mathrm{e}& \mathrm{g}& \mathrm{e}\\ \mathrm{\delta }& \mathrm{e}& \mathrm{e}\\ \text{e}& \mathrm{\delta }& \mathrm{g}{\mathrm{\delta }}^2\end{array}\right),\text{b}=\left(\begin{array}{cc}{\mathrm{\delta }}^3& \mathrm{e}\\ \mathrm{e}& \mathrm{\gamma \delta }\\ \mathrm{e}& \mathrm{e}\end{array}\right),\text{c}=\left(\begin{array}{ccc}\mathrm{e}& \mathrm{g}& {\mathrm{\delta }}^3\end{array}\right).$$

Then x = a*b is the smallest solution for the fixed point equation x = ax⊗b. The transfer function h of the Petri net thus becomes a matrix $$H=ca*b.$$

The eigenvalues of this matrix h, and here in particular the first eigenvalue, is a measure of how critical the traffic situation transferred to the Petri net is.

Which values of the investigated eigenvalues are to be regarded as critical depends on the respective traffic situation. For example, machine learning can be used to distinguish normal traffic situations from critical traffic situations. For example, vectors with one or more examined eigenvalues can be clustered unsupervised with the aim of forming a single cluster. The vectors associated with most traffic situations should then be found in this single cluster. This cluster will represent the non-critical traffic situations, as this is the norm, while a critical traffic situation is the exception.

Otherwise, for example, as mentioned above, a strong change in the examined eigenvalues can be evaluated as an indication that the traffic situation has developed critically.

As previously mentioned, checking whether a traffic situation is critical can be used in particular, for example, to check whether a control system as a whole is suitable for participating in traffic.

Therefore, the invention also provides a method for validating a control system for a vehicle or a robot.

As part of this method, traffic situations are provided, specifically in a form in which they are provided by at least one sensor during operation of the control system. The method described above is then used to evaluate the extent to which these traffic situations are critical.

A selection is made from the traffic situations in which more critical traffic situations are preferred over less critical traffic situations. For this selection, the criticality determined can be compared with a predetermined threshold value, for example. However, the traffic situations can also be arranged, for example, in an order of criticality, and a top N selection can then be made.

The control system and/or a simulation model of this control system is loaded with the traffic situations contained in the selection. In each case, it is checked whether the control system maps the traffic situation to a clear suggestion for the future behavior of the vehicle or the robot. In response to the fact that each traffic situation is mapped to a clear suggestion, it is determined that the control system is suitable for operating the vehicle or the robot.

The selection of the critical traffic situations can thus be used as a pre-filter in order to specifically load the control system or the simulation model with those traffic situations for which a failure of the control system or the simulation model is to be feared. The control system or the simulation model works correctly if it gives a clear suggestion for the future behavior of the vehicle or the robot for every traffic situation. A failure could be expressed, for example, in the fact that either no suggestion at all or several suggestions are determined for certain traffic situations. In the latter case, the transfer function of the control system or the simulation model at which a bifurcation at the point corresponding to this traffic situation. By now preferably examining traffic situations in which there is a concrete indication of such an undesirable behavior, a predefined safety level of the control system for participation in traffic can be examined with significantly less effort.

This is somewhat analogous to the fact that normal flight situations only make up a small part of the test to determine whether a pilot is fit for his or her job. Instead, the expensive simulator hours are preferably focused on overcoming error situations that are not part of everyday life in aviation.

In particular, the methods can be fully or partially computer-implemented. The invention therefore also relates to a computer program with machine-readable instructions which, when executed on one or more computers, cause the computer or computers to carry out one of the methods described. In this sense, control devices for vehicles and embedded systems for technical devices that are also able to execute machine-readable instructions are also to be regarded as computers.

The invention also relates to a machine-readable data carrier and/or a download product with the computer program. A downloadable product is a digital product that can be transmitted over a data network, i.e. can be downloaded by a user of the data network and that can be offered for sale in an online shop for immediate download, for example.

Furthermore, a computer can be equipped with the computer program, with the machine-readable data carrier or with the downloadable product.

Further measures improving the invention are presented in more detail below together with the description of the preferred exemplary embodiments of the invention with the aid of figures.

exemplary embodiments

• 1 Ausführungsbeispiel des Verfahrens 100 zur Prüfung, inwieweit eine Verkehrssituation 1 kritisch ist;
• 2 Ausführungsbeispiel des Verfahrens 200 zur Validierung eines Steuerungssystems 10;
• 3 Beispielhafte Überführung einer Verkehrssituation 1 über einen Graphen 2 in ein Petri-Netz 3.

It shows:

• 1 Exemplary embodiment of the method 100 for checking the extent to which a traffic situation 1 is critical;
• 2 Embodiment of the method 200 for validating a control system 10;
• 3 Exemplary transfer of a traffic situation 1 via a graph 2 to a Petri net 3.

1 FIG. 1 is a schematic flowchart of an exemplary embodiment of method 100 for checking the extent to which a traffic situation 1 is critical.

In step 110 the traffic situation 1 is converted into a graph 2 .

In step 120 the graph 2 is converted into a Petri net 3 . This Petri net 3 links local status changes to conditions with regard to the amounts of tokens that are assigned to predetermined locations in the Petri net 3 .

In step 130 at least one transfer function 3a of the Petri net 3 for the transition between global states of the Petri net 3 is determined.

In step 140, this transfer function 3a is used to evaluate the extent to which the traffic situation 1 is critical. The degree of criticality is denoted by the reference number 1a.

• • gemäß Block 111 ein eigener Graph 2,
• • gemäß Block 121 aus diesem eigenen Graphen 2 ein eigenes Petri-Netz 3 sowie
• • gemäß Block 131 eine eigene Übertragungsfunktion 3a für dieses eigene Petri-Netz 3

gebildet werden. Die so erhaltenen Übertragungsfunktionen 3a können dann gemäß Block 132 zu einer Gesamt-Übertragungsfunktion 3a* aggregiert werden. Es kann dann gemäß Block 141 aus dieser Gesamt-Übertragungsfunktion 3a* der Grad 1a an Kritikalität für die Verkehrssituation 1 ermittelt werden.According to block 105, one and the same traffic situation 1 can be detected redundantly with at least two sensors. It can then be used for the type of traffic situation detected by each of the sensors

• • according to block 111 a separate graph 2,
• • according to block 121 from this own graph 2 a separate Petri net 3 as well
• • According to block 131, a separate transfer function 3a for this separate Petri net 3

are formed. The transfer functions 3a obtained in this way can then be aggregated according to block 132 to form an overall transfer function 3a*. According to block 141, the degree 1a of criticality for the traffic situation 1 can then be determined from this overall transfer function 3a*.

According to block 106, the traffic situation 1 can be recorded at least partially as a time series of measurements. According to block 122, the graph 2 can then be converted into a Petri net 3 of time-dependent events, in which local state changes are additionally linked to temporal conditions.

According to block 133, the transfer function 3a can be determined from various developments A, B, C of the global state of the Petri net 3. The advancements A, B, C differ in their source and target states, which are each specified in assignments of the locations in the Petri net 3 with tokens.

$$y=Cx$$

ausgewertet werden.According to block 134, the transfer function 3a of the Petri net 3 can be determined on a semiring. According to block 135, the transfer function 3a of the Petri net 3 can consist of at least one solution of fixed-point equations $$x=Ax\otimes B\mathrm{and},$$

$$y=Cx$$

be evaluated.

• • einem ersten Verschiebeoperator γ, dessen Potenzen zu Anzahlen von Token an Orten im Petri-Netz 3 korrespondieren,
• • einem zweiten Verschiebeoperator δ, dessen Potenzen zu Anzahlen von lokalen Zustandsänderungen im Petri-Netz 3 korrespondieren,
• • einem neutralen Element ε der Addition ⊕ und
• • einem neutralen Element e der Multiplikation ⊗

parametrisiert werden.According to block 136, the transfer function 3a can

• • a first shift operator γ, whose powers correspond to numbers of tokens at locations in the Petri net 3,
• • a second shift operator δ, whose powers correspond to numbers of local state changes in the Petri net 3,
• • a neutral element ε of the addition ⊕ and
• • a neutral element e of multiplication ⊗

be parameterized.

$$y=ca*bu$$

ausgedrückt werden, worin * die komplexe Konjugation bezeichnet und die Matrizen a, b, c in γ, δ, ε und e parametrisiert sind. Gemäß Block 137a kann dann eine Transfermatrix $$h=ca*b$$

als Übertragungsfunktion 3a des Petri-Netzes 3 gewertet werden. Diese Transfermatrix h hat Eigenwerte 3b.According to block 137, the fixed point equations can then be used as $$x=ax\otimes b,$$

$$y=ca*b\mathrm{and}$$

can be expressed, where * denotes the complex conjugation and the matrices a, b, c are parameterized in γ, δ, ε and e. According to block 137a, a transfer matrix $$H=ca*b$$

be evaluated as a transfer function 3a of the Petri net 3. This transfer matrix h has eigenvalues 3b.

According to block 142, it is possible to evaluate to what extent the traffic situation 1 is critical according to a predefined criterion from at least one eigenvalue 3b of the transfer function 3a and/or from a change in this eigenvalue 3b. The result is the sought-after level 1a of criticality.

2 is a schematic flow chart of an embodiment of the method 200 for validating a control system 10 for a vehicle 50 or a robot 60.

In step 210, traffic situations 1 are provided in a form in which they are supplied by at least one sensor during operation of the control system 10 .

In step 220, the previously described method 100 is used to evaluate the extent to which these traffic situations 1 are critical. The result is the respective level 1a of criticality.

In step 230, a selection 1* is created from the traffic situations 1, in which more critical traffic situations 1 are preferred over less critical traffic situations 1.

In step 240, the control system 10 and/or a simulation model of this control system 10 is loaded with the traffic situations 1 contained in the selection 1*.

In step 250 it is checked in each case whether the control system 10 maps the traffic situation 1 to a clear proposal for the future behavior of the vehicle 50 or of the robot 60 . if this is the case (truth value 1), it is determined in step 260 that the control system 10 is suitable for operating the vehicle 50 or the robot 60 .

3 illustrates schematically how a traffic situation 1 can be converted into a graph 2 and from there into a Petri net 3 . Traffic situation 1 includes traffic flows between five locations H1 to H5. The traffic situation 1 is transferred to the directed graph 2, whose edges are assigned weights 1 to 6. These weights correspond to the strengths of the respective traffic flows.

The graph 2 is then converted into a Petri net 3 drawn as an example. This Petri net 3 consists of locations that are drawn as ovals and can be assigned tokens of two different types. in the in 3 shown example, the locations are marked with vertical lines on the one hand and dots on the other hand as tokens. Furthermore, there are local state transitions drawn in as horizontal lines, each of which is connected to one or more locations. Whether and when each local state transition is triggered depends on the one hand on the allocation of tokens to those locations that feed into the local state transition in the direction of the arrow. On the other hand, the state variables x ₁ , x ₂ , x ₃ set temporal boundary conditions for triggering local state transitions. The interaction of the local state transitions ultimately decides the extent to which input external variables u ₁ , u ₂ are processed into an output y of the Petri net 3 .

QUOTES INCLUDED IN DESCRIPTION

This list of documents cited by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Patent Literature Cited

• US 10942797 B2 [0003]

Claims (16)

Method (100) for checking the extent to which a traffic situation (1) detected with at least one sensor is critical in the sense that a control system (10) for a vehicle (50) or a robot (60) is not able to determine a clear proposal for the future behavior of the vehicle (50), or the robot (60), might be able to, with the steps: • The traffic situation (1) is converted (110) into a graph (2), where ◯ the nodes of the graph (2) correspond to possible positions of road users and ◯ the edges of the graph (2) are assigned weights which assign a value of a variable relevant to the evaluation of the traffic situation (1) by the control system (10) to the nodes connected by an edge; • the graph (2) is converted into a Petri net (3) (120) which links local state changes to conditions with which quantities of tokens are assigned to predetermined locations in the Petri net (3), where ◯ the nodes of the graph (2) correspond to locations in the Petri net, ◯ the edges of the graph (2) correspond to local state changes and ◯ the weights on the edges of the graph (2) set conditions for state changes; • at least one transfer function (3a) of the Petri net (3) for the transition between global states of the Petri net (3) is determined (130); • This transfer function (3a) is used to evaluate (140) the extent to which the traffic situation (1) is critical (1a). Method (100) according to claim 1 , wherein those further nodes of the graph (2) which are connected to a first node by edges correspond to those positions which, starting from a position corresponding to the first node, are in the detection range of the at least one sensor. Method (100) according to any one of Claims 1 until 2 , wherein the at least one sensor comprises a camera, a radar sensor, a lidar sensor, and/or an ultrasonic sensor. Method (100) according to any one of Claims 1 until 3 , wherein • one and the same traffic situation (1) is detected redundantly with at least two sensors (105); • a separate graph (2), a separate Petri net (3) and a separate transfer function (3a) of the respective Petri net (3) are determined for the form of the traffic situation (1) recorded by each of the sensors (111, 121 , 131); • the transfer functions (3a) are aggregated (132) to form an overall transfer function (3a*); and • the extent to which the traffic situation (1) is critical (1a) is evaluated (141) from this overall transfer function (3a*). Method (100) according to any one of Claims 1 until 4 , the traffic situation (1) being recorded at least partially as a time series of measurements (106) and the graph (2) being converted into a Petri net (3) of time-dependent events (122), in which local changes in status are additionally linked to temporal conditions are. Method (100) according to any one of Claims 1 until 5 , where the transfer function (3a) consists of • a first development A of the global state of the Petri net (3), which occurs when an occupancy n of all locations with respective numbers of tokens remains unchanged, • a second development B of the global state of the Petri net (3), which occurs when the allocation n of all locations with a respective number of tokens changes into an allocation m of all locations with a respective number of tokens, and • a third development C of the global state of the Petri net ( 3), which occurs when an occupancy p of all locations with respective numbers of tokens changes to the occupancy n of all locations with respective numbers of tokens (133). Method (100) according to any one of Claims 1 until 6 , whereby the transfer function (3a) of the Petri net (3) is determined on a semiring (134) on which • the addition ⊕ of two elements is carried out by forming a maximum over these two elements and • the multiplication ⊗ of two elements is carried out by adding these two elements becomes. Method (100) according to claim 6 and 7 , where the transfer function (3a) of the Petri net (3) consists of at least one solution of the fixed point equations $$x=Ax\otimes B\mathrm{and},$$

$$y=Cx$$

is evaluated (135), where x is an n-dimensional evolution vector, u is a p-dimensional evolution vector, and y is an m-dimensional evolution vector. Method (100) according to claim 6 and 7 as well as optionally additionally claim 8 , where the transfer function (3a) of the Petri net (3) with • a first shift operator γ, whose power zen correspond to numbers of tokens at locations in the Petri net (3), • a second shift operator δ, whose powers correspond to numbers of local state changes in the Petri net (3), • a neutral element ε of the addition ⊕ and • a neutral one Element e of the multiplication ⊗ is parameterized (136). procedure after claim 8 and 9 , where the fixed point equations as $$x=ax\otimes b,$$

$$y=ca*b\mathrm{and}$$

can be expressed (137), where * denotes complex conjugation and the matrices a, b, c are parameterized in γ, δ, ε and e. Method (100) according to claim 10 , where is a transfer matrix $$H=ca*b$$

is evaluated as a transfer function (3a) of the Petri net (3) (137a). Method (100) according to any one of Claims 1 until 11 , wherein according to a predetermined criterion from at least one eigenvalue (3b) of the transfer function (3a) and/or from a change in this eigenvalue (3b), the extent to which the traffic situation (1) is critical (1a) is evaluated (142). Method (200) for validating a control system (10) for a vehicle (50) or a robot (60) with the steps: • there are traffic situations (1) in a form as in the operation of the control system (10) of at least one sensor are provided, provided (210); • with the method (100) according to one of Claims 1 until 12 it is evaluated (220) to what extent these traffic situations (1) are critical (1a); • A selection (1*) is created (230) from the traffic situations (1), in which more critical traffic situations (1) are preferred over less critical traffic situations (1); • the control system (10) and/or a simulation model of this control system (10) is loaded (240) with the traffic situations (1) contained in the selection (1*); • It is checked (250) whether the control system (10) maps the traffic situation (1) to a clear proposal for the future behavior of the vehicle (50) or the robot (60); and • in response to each traffic situation (1) being mapped to a unique proposal, it is determined (260) that the control system (10) is suitable for operating the vehicle (50) or the robot (60). . Computer program containing machine-readable instructions which, when executed on one or more computers, cause the computer or computers to carry out a method (100, 200) according to one of Claims 1 until 13 to execute. Machine-readable data carrier and/or download product with the computer program Claim 14 . One or more computers with the computer program after Claim 14 , and/or with the machine-readable data medium and/or download product claim 15 .

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