Method for estimating a probability distribution of the maximum coefficient of friction at a current and/or future waypoint of a vehicle

Abstract

A method for estimating a probability distribution of the maximum coefficient of friction (μ) at a current and/or future waypoint (s, s*) of a vehicle. According to the method, a first probability distribution (WV1) for the maximum coefficient of friction (μ) at the waypoint (s) of the vehicle is determined by a Bayesian network from a first data set, which is, or was determined, for one, in particular current, waypoint (s) of the vehicle and which characterizes the maximum coefficient of friction (μ) at the waypoint (s) of the vehicle.

Claims

1. A method for estimating a probability distribution of a maximum coefficient of friction of at least one of a current and a future waypoint of a vehicle, the method comprising: determining topology of a roadway of the current waypoint along which the vehicle is currently traveling as well as the future waypoint of the vehicle via map data provided by a navigation system of the vehicle; determining at least one characteristic of at least one tire of the vehicle via at least one tire sensor of the vehicle; determining a first data set for the current waypoint of the vehicle which characterizes the maximum coefficient of friction at the current waypoint of the vehicle; and determining, from the first data set, a first probability distribution for the maximum coefficient of friction at the waypoint of the vehicle by a Bayesian network.

2. The method of claim 1, further comprising estimating a second probability distribution for the maximum coefficient of friction at the future waypoint of the vehicle from a second data set of the future waypoint by the Bayesian network; and determining a resulting probability distribution using a combination of the first and the second probability distributions.

3. The method of claim 2, wherein the Bayesian network forms a multi-level causal chain, and at least one of: subdividing the input nodes into one or more hierarchical levels, and subdividing the output nodes into one or more hierarchical levels.

4. The method according to claim 2, further comprising determining the second probability distribution by processing, as the second data set, data about the future waypoint which comprises at least one of: data related to a preceding vehicle, data related to a driver of a preceding vehicle, road topology, type of road surface, road conditions, road surface, type of intermediate medium, weather data comprising outside temperature, rain intensity, humidity, barometric pressure, precise map data (PRD), or data from intelligent infrastructure components.

5. The method according to claim 2, further comprising performing a convex combination for combining the first and the second probability distributions (WV1, WV2).

6. The method according to claim 5, further comprising, during the combination, processing a projection parameter (α) which represents a measure of a preview by weighting the first and the second probability distributions (WV1, WV2).

7. The method according to claim 6, further comprising processing at least one further projection parameter (α) in the combination.

8. The method according to claim 6, further comprising selecting the projection parameter (α) as a function of at least one of: a determined entropy of a relevant probability distribution; and data of a sensor of the vehicle available for determination of the maximum coefficient of friction (μ).

9. The method according to claim 2, further comprising processing, in addition to the second probability distribution for the maximum coefficient of friction (μ) at the future waypoint (s*), one or more further probability distributions for the maximum coefficient of friction (μ) at one or more further future waypoints (s*) to determine the resulting probability distribution for the maximum coefficient of friction (μ).

10. The method according to claim 1, further comprising forming a three-stage causal chain from nodes and edges of the Bayesian network, wherein input nodes of the Bayesian network each represent a factor influencing the maximum coefficient of friction, output nodes, which depend on the maximum coefficient of friction, represent either an impact or an effect of the maximum coefficient of friction, and any conditional interdependence, between the input node and either the maximum coefficient of friction or the maximum coefficient of friction and the output node, is represented by the edges.

11. The method according to claim 1, further comprising assigning a conditional probability to every node of the Bayesian network.

12. The method according to claim 1, further comprising defining at least one of the first data set and a second data set as: at least one of a longitudinal and a lateral acceleration of the vehicle, yaw rate, wheel speed(s), of estimation of a friction coefficient due to longitudinal dynamics of the vehicle; vehicle speed; slip; estimation of a friction coefficient based on lateral dynamics of the vehicle; estimation of a friction coefficient based on a combination of the longitudinal and the lateral dynamics of the vehicle; type of driver or driving style; outside temperature, intensity of rain, humidity, or barometric pressure moisture on road surface, type and condition of roadway or type of intermediate medium.

13. The method according to claim 1, wherein at least one of the first data set and a second data set being either provided or determined from one or more data sources, the data sources being: electronic stability control/brake, radar, camera, lidar, ultrasound, infrared system, driving state observer, steering system, weather data service, precise map data, and intelligent infrastructure components.

14. The method according to claim 1, further comprising determining a prior probability distribution for the maximum coefficient of friction for determining the first probability distribution from the first data set; for each output node, determining from the first data set a likelihood-probability distribution from an observation of a concrete output value at the current waypoint; for at least some output nodes, determining, in a correction step, a relevant posterior probability distribution for the maximum coefficient of friction using a Bayes formula from the prior probability distribution and the likelihood-probability distribution.

15. The method of claim 14, further comprising evaluating a relevant posterior probability distribution for the maximum coefficient of friction.

16. The method of claim 14, further comprising performing an additional consideration of vehicle acceleration in at least one of the determination and evaluation of the likelihood-probability distribution.

17. The method according to claim 16, further comprising performing evaluation of the relevant posterior probability distribution and selection of one of the posterior probability distributions by an entropy.

18. The method according to claim 1, further comprising selecting the future waypoint to be adaptive.

19. A method for estimating a probability distribution of a maximum coefficient of friction of at least one of a current and a future waypoint of a vehicle, the method comprising: determining a first data set for the current waypoint of the vehicle which characterizes the maximum coefficient of friction at the current waypoint of the vehicle; and determining, from the first data set, a first probability distribution for the maximum coefficient of friction at the waypoint of the vehicle by a Bayesian network; determining a prior probability distribution for the maximum coefficient of friction for determining the first probability distribution from the first data set; for each output node, determining from the first data set a likelihood-probability distribution from an observation of a concrete output value at the current waypoint; for at least some output nodes, determining, in a correction step, a relevant posterior probability distribution for the maximum coefficient of friction using a Bayes formula from the prior probability distribution and the likelihood-probability distribution; performing an additional consideration of vehicle acceleration in at least one of the determination and evaluation of the likelihood-probability distribution; performing evaluation of the relevant posterior probability distribution and selection of one of the posterior probability distributions by an entropy; and for a large entropy, carrying out at least one of a targeted steering intervention and either a wheel-specific, braking or acceleration intervention.

20. A device for estimating a probability distribution of a maximum coefficient of friction of at least one of a current and a future waypoint of a vehicle, the device comprising: means for determining a topology of a roadway of the current waypoint along which the vehicle is currently traveling as well as the future waypoint of the vehicle, via map data provided by a navigation system of the vehicle; means for determining at least one characteristic of at least one tire of the vehicle via at least one tire sensor of the vehicle; a first means to generate a first probability distribution for the maximum coefficient of friction at the current waypoint of the vehicle by a Bayesian network from a first data set, which either is or was determined for the current waypoint of the vehicle and which characterizes the maximum coefficient of friction at the current waypoint of the vehicle.

21. The device according to claim 20, further comprising: a second means for estimating a second probability distribution for the maximum coefficient of friction at the future waypoint of the vehicle from a second data set of the future waypoint, using the Bayesian network; and a third means for determining a resulting probability distribution by a combination of the first and the second probability distribution.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Below, the invention is described in more detail with reference to an exemplary embodiment in the drawings. In the Figures:

(2) FIG. 1 shows a schematic representation of a causal chain of a meta-model of a possible Bayesian network used in the method according to the invention;

(3) FIG. 2 shows a schematic representation of the data used by way of example in a Bayesian network;

(4) FIG. 3 shows a schematic representation of how likelihood and posterior distributions are generated from a prior distribution using a Bayesian network;

(5) FIG. 4 shows a schematic illustration of the determination of a resulting, combined probability distribution; and

(6) FIGS. 5a to 5b show exemplary embodiments of different resulting probability distributions.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(7) The method is based on a simplified Bayesian network, which consists of the nodes 1, 2, 3 and the edges 4, 5 and represents a three-stage causal chain, as shown in FIG. 1. The causal chain consists of influencing factors or causes u of the maximum coefficient of friction μ, the maximum coefficient of friction p itself and effects or effects y, which represent outputs of the Bayesian network according to FIG. 1. Interdependencies between the nodes 1 representing the influencing factors and the node 2 representing the maximum coefficient of friction are modeled as directed edges 4. Likewise, interdependencies between the node 2 representing the maximum coefficient of friction p and the node 2 representing the max. impact are modeled as directed edges 5. It will be appreciated that the Bayesian network may also include fewer (e.g., determination of a prior probability distribution at a future waypoint described below) or more than three causal stages. The latter is particularly the case if some nodes arranged on the input side are bundled in a further plane between the nodes 1 and 2 in FIG. 1 (for example for the classification of a road surface, a tire type or an intermediate medium). The advantage of such a Bayesian network is that both data from prior knowledge and from data for determining the conditional probabilities at the nodes and thus for determining the probability distribution of the max. friction coefficient μ can be used. In particular, there is the possibility of efficiently combining different, known or novel individual concepts based on direct and indirect methods for the estimation of the friction coefficient. In addition, the modular structure allows individual nodes 1 or 3 of the network to be added or omitted, which, while influencing the quality of the estimation of the friction coefficient, does not require any conceptual changes.

(8) Influencing factors u (i.e., node 1) on the maximum coefficient of friction μ (i.e., to node 2) are e.g. roadway (road) in terms of topology and condition, tire (tread, tire pressure, rubber compound, temperature, etc.), an intermediate medium present between the road surface and the tire (moisture, moisture, snow, ice, loose chippings, etc.) as well as the vehicle itself. Effects y (i.e. node 3) of the maximum coefficient of friction μ (i.e., of node 2) are e.g. slip, a yaw rate, a (maximum possible) acceleration and the like. In addition, there are further influencing factors u and effects y, which are not listed here.

(9) With reference to FIGS. 2 and 3, the steps to be carried out according to the invention for determining a first probability distribution, which determines the probability distribution of the maximum coefficient of friction μ below the vehicle (i.e., at a current waypoint of the vehicle), are described below. In a first step S1 of the method, prior probabilities P.sub.uF,pr(μ(S)|u(s)) for the maximum coefficient μ of friction under the vehicle existing at a current waypoint s are computed based on the given inputs u. The prior distribution WV.sub.pr thus generated can be determined discretely or as a continuous distribution, FIG. 2 showing a discrete distribution and FIG. 3 a continuous distribution. FIG. 2 shows possible inputs u(s), which can be used to determine WV.sub.pr.

(10) It goes without saying that the input data u(s) shown in FIG. 2 are chosen merely by way of example. The data may be provided by sensors of the vehicle itself or by service providers outside the motor vehicle.

(11) Data sources available in a vehicle are generally, for example, an ESC for providing accelerations, yaw rate, wheel speeds and possibly a coefficient of friction estimation, a radar system providing the vehicle speed, a driving state observer for providing an estimation of the slip and/or the coefficient of friction, a steering system for providing an estimation of the friction coefficient, a driving style rating/classification. The term estimation of the friction coefficient shall be understood as the provision of both a scalar and an interval for the maximum coefficient of friction. The evaluation or classification of a driving style can be determined for example on the basis of transmission data, pedal changing times, pedal gradients and/or transverse accelerations. It goes without saying that the relevant data are determined and provided by relevant control devices of the data sources.

(12) The data provided by a weather data service basically include all conceivable weather data, including outside temperature, rain intensity, humidity and barometric pressure.

(13) Topology-related data could be provided by a map provider. The topology includes inclines, curve curvatures, curve radii, roadway inclination angles, unevenness of the road, ripples in the road, potholes and the like. Such data may also include data about a road surface, road condition and type of road surface. The data about a road wetness can be provided by the combination of weather data and map data. In this context, historical as well as current and projected data are important. To determine properties of the road surface and/or an intermediate medium, additional or exclusively in-vehicle sensors such as, for example, camera, radar, lidar, infrared, ultrasound systems and/or components of an intelligent infrastructure can be used.

(14) The determination of the prior distribution WV.sub.pr can be performed, for instance, with the aid of a regression model which is adapted to a sufficiently large set of training data. For instance, a linear regression can be applied. Generally, however, a non-linear simple or multiple regression model can also be used. The setting of some coefficients of the regression model represents an option for incorporating semantic expert knowledge, which does not necessarily have to be mapped in the training data.

(15) Furthermore, in a second step S2, likelihood probabilities P.sub.uF,li(y(s)|μ(s)) under a given coefficient of friction μ and other parameters, such as, e.g. accelerations, are determined using another regression model based on a sufficiently large set of training data. Here, too, any regression model can be used (linear/nonlinear, simple/multinomial, parametric/nonparametric, etc.). The selection of a suitable method depends on the structure of the output data y(s). If there are continuous data, e.g. of a driving condition observer, a linear or non-linear regression is appropriate. For instance, if the source data include a driving style classification, categorical data is present. In that case, a (multinomial) logistic regression is appropriate. As described, the vehicle acceleration can be processed as a further parameter because, as a matter of principle, the quality of the estimation of the friction coefficient increases with increasing utilization of the coefficient of friction, i.e. the transmitted force on the tire. As a result, the determination of probability distributions WV.sub.li,i (where i=1 . . . K) for the observation of a concrete output value y(s) at the current waypoint s works for each of the k nodes 3 on the output side of the Bayesian network (see FIG. 3).

(16) In the exemplary embodiment considered in FIGS. 2 and 3, an estimation of the friction coefficient by the ESC, a vehicle acceleration, a yaw rate, a slip, an estimation of the friction coefficient by the DSO, an estimation of the friction coefficient by the steering system and a driving style classification are regarded as outputs y(s). It goes without saying that the output data y(s) shown in FIGS. 2 and 3 are chosen merely by way of example.

(17) The determination of the likelihood-probability distributions WV.sub.li,i represents an observation of the effects of the maximum coefficient of friction when the vehicle is traveling over the current waypoint. Based on these observed likelihood-probability distributions, a correction of the prior probability distribution WV.sub.pr determined in step S1 is conducted.

(18) Using the Bayes Formula

(19) $\begin{array}{cc}{P}_{\mathrm{uF},\mathrm{po},i}\left(\mu \in {\mu }_j.Math.u,y_i\right)=\frac{P\left(y_i.Math.\mu \in {\mu }_j\right).Math.P\left(\mu \in {\mu }_j.Math.u\right)}{\underset{j}{.Math.}P\left(y_i.Math.\mu \in {\mu }_j\right).Math.P\left(\mu \in {\mu }_j.Math.u\right)}& \left(1\right)\end{array}$
in a correction step (step S3) the a posteriori distributions P.sub.uF,po(μ(s)|u(s), y(s)) for the maximum coefficient of friction p under the vehicle are computed from the a priori distribution WV.sub.pr and the relevant likelihood distributions WV.sub.li,i for different outputs y(s), which are designated WV.sub.po,i in FIG. 3 (i=1 . . . k).

(20) In the next step, the present a posteriori distributions WV.sub.po,i are evaluated and one of them is selected. The a posteriori distributions WV.sub.po,i can be evaluated, for instance, by means of their entropy H using
H.sub.po,i=−Σ.sub.j P.sub.uF,po,i(μ∈μ.sub.j|u,y.sub.k).Math.ln P.sub.uF,po,i(μ∈μ.sub.j|u,y.sub.k)  (2).
This is a first probability distribution WV1 for the max. coefficient of friction μ under the vehicle at the current waypoint s.

(21) FIG. 3 figuratively illustrates the procedure described. There the successive sub-steps of the determination of the posterior probability distributions WV.sub.po,i for the maximum coefficient of friction μ under the vehicle available at the current waypoint s are shown for the given inputs and given outputs y(s). Likewise, the sub-steps of the determination of the likelihood distributions WV.sub.li,i and the evaluation and selection on the basis of the entropy H can be recognized. As can be seen schematically in FIG. 3, the probability distribution having minimal entropy H is selected. In FIG. 3, this is the posterior probability distribution WV.sub.po,i having the entropy H.sub.po,i≈3.6 as shown in the uppermost row.

(22) In a next step (see FIG. 4), the estimation of a second probability distribution WV2 for the maximum coefficient of friction in front of the vehicle is performed at a future waypoint s*. The future waypoint is also referred to as the projection point s*. Data on the future waypoint s* can be used to specify a prior probability distribution P.sub.vF,pr(μ(s*)|u(s*)) for the maximum coefficient of friction μ. These data may be, for instance, the road surface, the road condition, a possible intermediate medium (snow, moisture, rain), weather conditions (outside temperature, humidity, barometric pressure), data of a preceding vehicle, etc. The data may come from on-board sensors, other road users or an infrastructure component. The distribution WV2 obtained in this step represents a second probability distribution, which may be in discrete or continuous form, with FIG. 4 showing both. The determination of the second probability distribution WV2, like the determination of the prior distribution WV.sub.pr from step S1, can be conducted, for instance, with the aid of a regression model, which is adapted to a sufficiently large set of training data. For instance, a linear regression can be applied. Generally, however, a non-linear regression model can also be used. Setting some coefficients of the regression model represents an option for incorporating semantic expertise, which does not necessarily have to be mapped in the training data. In a final step, a computation of a resulting combined probability distribution WV.sub.res for the maximum coefficient of friction from the previously determined first probability distribution WV1 (cf. the procedure described in connection with FIGS. 2 and 3) and the second probability distribution WV2 for the maximum coefficient of friction at the future waypoint s*. The combination can be performed using a convex combination and a projection parameter α, where 0<α<1. The convex combination is conducted based on the equation
WV.sub.res=(1−α).Math.WV1+α.Math.WV2  (3)

(23) The projection parameter α characterizes how far ahead the estimation looks, by weighting the first and second probability distributions WV1 and WV2. A fixed projection parameter α can be selected. It can also be determined as a function of available data, such as the entropy of WV1 and/or WV2 or the type or scope of the data at the future point s*. In that case, the projection parameter α is re-selected every time when at least one of the two probability distributions WV1 and WV2 undergoes an update.

(24) The combination of the first probability distribution WV1 (posterior distribution based on data under the vehicle, P.sub.uF) and the second probability distribution WV2 (prior distribution from data at the projection point, P.sub.vF) and the computation of the resulting combined probability distribution WV.sub.res is illustrated in FIG. 4. By way of example, a projection parameter of α=0.3 was assumed.

(25) In computing a resulting probability distribution from more than two probability distributions, multiple projection parameters can be used to form a convex combination. This procedure is particularly useful if data about the maximum coefficient of friction at more than one projection point are available. The equation below applies:
WV.sub.res=Σ.sub.iα.sub.i,WVi where Σ.sub.iα.sub.i=1  (4)

(26) If the resulting probability distribution for the maximum coefficient of friction is not very informative (cf. the course of the probability distribution Pges (μ|u, y) in FIG. 5b), i. e. if the latter has a flat course, which can be recognized, for instance, by means of entropy, a direct, active method for determining the maximum coefficient of friction can be used, e.g. by a targeted (wheel-specific) steering and/or braking/acceleration intervention, in particular with a simultaneously briefly increased engine torque. In this way, the force transmitted to the tire is increased, which makes for an improved prediction quality at the outputs y(s). This results in a “more focused” course of a number of likelihood-probability distributions, which in turn is reflected in a “more focused” course of the resulting probability distribution as shown schematically in FIG. 5. Instead of considering the resulting probability distribution (as shown in FIG. 5), the course of the likelihood and/or posterior probability distributions for the maximum coefficient of friction under the vehicle can be used to derive a need for action in the sense of initiating a direct, active method for a more accurate estimation of the maximum coefficient of friction.

(27) In the event that the assumption of a maximum coefficient of friction μ slowly changing along the route of travel of the motor vehicle does not apply and the probability distributions WV1 and WV2 for the maximum coefficient of friction under or in front of the vehicle, for instance, measured using an expected value, strongly differ from each other, the projection parameter α can be adjusted to determine the point of change of the coefficient of friction more precisely. Alternatively, the vehicle may be prepared for new boundary conditions at the future waypoint. This can e.g. be done based on delay, prevention of further speed increase, and the like.

REFERENCE NUMERALS

(28) 1 node 2 node 3 node 4 edge 5 edge μ coefficient of friction WV1 first probability distribution WV2 second probability distribution WV.sub.res resulting probability distribution WV.sub.pr prior probability distribution WV.sub.li,i likelihood-probability distribution where i=1 . . . k WV.sub.po,i posterior-probability distribution where i=1 . . . k α projection parameter