FR3092914A1 - Method for determining the trajectory of a vehicle comprising four steered wheels - Google Patents

Abstract

Method for determining the trajectory of a vehicle comprising four steered wheels Method for determining the trajectory of a vehicle (1) comprising two front steered wheels (2f) and two rear steered wheels (2r), characterized in that it comprises: a first step (E31) of calculating a speed (v) of the vehicle, a second step (E32) of calculating a steering angle formed by the front wheels (δf), a third step (E33) of calculation of a steering angle formed by the rear wheels (δr), a fourth step (E34) of calculating a sliding angle (β) of the vehicle (1) as a function of: the steering angle formed by the front wheels (δf), the steering angle formed by the rear wheels (δr), and the speed (v) of the vehicle, a fifth step (E35) of calculating the trajectory of the vehicle as a function of the angle slip (β) of the vehicle (1). Figure for the abstract: figure 6

Description

Method for determining the trajectory of a vehicle comprising four steered wheels

The invention relates to a method for determining the trajectory of a vehicle comprising two steerable front wheels and two steered rear wheels. The invention also relates to a method for determining the distance separating an object from a vehicle comprising two steered front wheels and two steered rear wheels. The invention finally relates to a method for regulating the speed of a vehicle comprising two steered front wheels and two steered rear wheels.

State of the prior art

Motor vehicles may be equipped with an adaptive cruise control system. Such a system comprises means for detecting the environment of the vehicle such as a radar and can therefore detect other vehicles or objects on the roadway, in particular it can detect a vehicle which precedes it on the roadway. Then, the speed of the vehicle equipped with such an adaptive speed regulation system can be adjusted to maintain a substantially constant safety distance with the vehicle in front. Thus, such a system interacts with an engine control system and/or with a braking system in order to accelerate or decelerate the vehicle.

Since the adaptive cruise control system can autonomously control the vehicle speed, a particularly precise and reliable detection of the vehicle environment is required. Indeed, if the system does not detect an obstacle present in the path of the vehicle, the vehicle could accelerate or at least maintain its speed, and thus strike the obstacle in front of the vehicle. On the other hand, if the system incorrectly detects an obstacle in the path of the vehicle, it could order inappropriate braking of the vehicle. In this case, a collision with a vehicle driving behind the vehicle in question could occur.

When the vehicle is traveling in a straight line, the obstacles in the path of the vehicle are positioned in front of the vehicle and their detection is easy. When the vehicle is in a bend, the obstacles in the trajectory of the vehicle are not positioned in front of the vehicle and their detection requires a prior determination of the trajectory of the vehicle. Methods are known for adaptive control of the speed of a vehicle comprising an estimation of the trajectory of the vehicle. However, these methods rely on simplified kinematic models. In particular, these methods do not make it possible to predict in a sufficiently precise and reliable manner the trajectory of a vehicle equipped with four steered wheels.

Presentation of the invention

The object of the invention is to provide a method for determining the trajectory of a vehicle comprising two steerable front wheels and two steerable rear wheels remedying the above drawbacks and improving the methods for determining the trajectory of a known vehicle of the prior art.

More specifically, a first object of the invention is a method for determining the trajectory of a vehicle comprising two steered front wheels and two steered rear wheels which is precise and reliable.

A second object of the invention is a method that can be implemented by a computer of a motor vehicle without modifying the other methods of regulating the vehicle.

• une première étape de calcul d'une vitesse du véhicule,
• une deuxième étape de calcul d'un angle de braquage formé par les roues avant,
• une troisième étape de calcul d'un angle de braquage formé par les roues arrière,
• une quatrième étape de calcul d'un angle de glissement du véhicule en fonction :
  • de l'angle de braquage formé par les roues avant,
  • de l'angle de braquage formé par les roues arrière, et
  • de la vitesse du véhicule,
• une cinquième étape de calcul de la trajectoire du véhicule en fonction de l'angle de glissement du véhicule.

The invention relates to a method for determining the trajectory of a vehicle comprising two steered front wheels and two steered rear wheels, the method comprising:

• a first step of calculating a speed of the vehicle,
• a second step of calculating a steering angle formed by the front wheels,
• a third step of calculating a steering angle formed by the rear wheels,
• a fourth step of calculating a slip angle of the vehicle as a function of:
  • the steering angle formed by the front wheels,
  • the steering angle formed by the rear wheels, and
  • vehicle speed,
• a fifth step of calculating the trajectory of the vehicle as a function of the slip angle of the vehicle.

• la mesure d'un premier angle de braquage formé par les roues arrière au moyen d'un capteur d'angle de braquage des roues arrière, et
• le calcul d'un deuxième angle de braquage formé par les roues arrière en fonction d'une mesure d'un angle au volant du véhicule.

The third step may include:

• measuring a first steering angle formed by the rear wheels by means of a rear wheel steering angle sensor, and
• the calculation of a second steering angle formed by the rear wheels as a function of a measurement of an angle at the steering wheel of the vehicle.

The second steering angle can be calculated according to the formula:

in which :
δ_r ,_SWA denotes the second steering angle,
sign designates a function whose result is equal to 1 when its argument is strictly greater than 0, whose result is equal to -1 when its argument is strictly less than 0, and whose result is equal to 0 when its argument is equal to 0,
T_gs denotes a yaw gain of the vehicle,
δ_f designates the steering angle formed by the front wheels calculated by means of an angle sensor on the steering wheel,
sat designates a saturation angle of the rear wheels.

• une sous-étape de calcul d'une différence entre le premier angle de braquage et le deuxième angle de braquage, puis
• si ladite différence est strictement inférieure à un seuil, une sous-étape de calcul d'une moyenne pondérée du premier angle de braquage et du deuxième angle de braquage,
• si ladite différence est supérieure ou égale au seuil,
  • une sous-étape de test de cohérence du premier angle de braquage avec une ou plusieurs valeurs de l'angle de braquage formé par les roues arrières calculées lors d'une précédente itération du procédé de détermination, puis si le test de cohérence est négatif, une sous-étape de remplacement de la valeur du premier angle de braquage par une valeur de l'angle de braquage formé par les roues arrières calculée lors d'une précédente itération du procédé de détermination,
  • une sous-étape de test de cohérence du deuxième angle de braquage avec une ou plusieurs valeurs de l'angle de braquage formé par les roues arrières calculées lors d'une précédente itération du procédé de détermination, puis si le test de cohérence est négatif, une sous-étape de remplacement de la valeur du deuxième angle de braquage par une valeur de l'angle de braquage formé par les roues arrières calculée lors d'une précédente itération du procédé de détermination, puis
  • une sous-étape de calcul d'une moyenne pondérée du premier angle de braquage et du deuxième angle de braquage.

The third stage may include:

• a sub-step of calculating a difference between the first steering angle and the second steering angle, then
• if said difference is strictly less than a threshold, a sub-step of calculating a weighted average of the first steering angle and of the second steering angle,
• if said difference is greater than or equal to the threshold,
  • a sub-step of consistency test of the first steering angle with one or more values of the steering angle formed by the rear wheels calculated during a previous iteration of the determination method, then if the consistency test is negative, a sub-step of replacing the value of the first steering angle by a value of the steering angle formed by the rear wheels calculated during a previous iteration of the determination method,
  • a second steering angle consistency test sub-step with one or more values of the steering angle formed by the rear wheels calculated during a previous iteration of the determination method, then if the consistency test is negative, a sub-step of replacing the value of the second steering angle by a value of the steering angle formed by the rear wheels calculated during a previous iteration of the determination method, then
  • a sub-step of calculating a weighted average of the first steering angle and of the second steering angle.

The fourth step may comprise the calculation of a slip angle of the vehicle as a function, in addition, of a slip angle of the vehicle calculated during a previous iteration of the fourth step and as a function of an amplitude of a vehicle yaw.

The slip angle of the vehicle can be calculated according to the formula:

in which :
β^(k+1) denotes a slip angle of the vehicle at time k+1,
c_f designates a transverse stiffness index of an axle of the front wheels of the vehicle,
c_r designates a transverse stiffness index of an axle of the rear wheels of the vehicle,
m is the total mass of the vehicle,
v denotes the speed of the vehicle,
T designates a period of time between instants k and k+1,
β^k denotes a slip angle of the vehicle at time k,
l_f designates the distance separating the axis of the front wheels from a center of gravity of the vehicle,
l_r designates the distance separating the axis of the rear wheels from the center of gravity of the vehicle,
ω^k denotes an amplitude of a yaw movement of the vehicle at time k,
δ^k_f designates the steering angle of the front wheels calculated during the second step, at time k,
δ^k_r denotes the steering angle of the rear wheels calculated during the third step, at time k.

• le calcul d'une position du véhicule dans un repère, et
• le calcul d'une orientation du véhicule dans le repère, et
• le calcul d'une vitesse du véhicule, et
• le calcul d'une accélération longitudinale du véhicule, et
• le calcul d'une amplitude d'un mouvement de lacet.
  

The fifth stage may include:

• calculating a position of the vehicle in a frame, and
• calculating an orientation of the vehicle in the frame, and
• calculating a speed of the vehicle, and
• calculating a longitudinal acceleration of the vehicle, and
• calculating an amplitude of a yaw motion.
  

The fifth step can include solving the following system of equations:

in which :
X_(k+1) denotes an abscissa of the center of the rear wheel axle at time k+1,
X_k designates an abscissa of the center of the axis of the rear wheels at time k,
Y_(k+1) denotes an ordinate of the center of the rear wheel axle at time k+1,
Y_k designates an ordinate of the center of the axle of the rear wheels at time k,
T designates a period of time between instants k and k+1,
v_k designates the speed of the vehicle at time k,
v_(k+1) designates the speed of the vehicle at time k+1,
θ_k denotes an orientation of the vehicle in the reference frame at time k,
θ_(k+1) denotes an orientation of the vehicle in the reference frame at time k+1,
β^k denotes the slip angle of the vehicle at time k,
l_r designates a distance separating the axis of the rear wheels from the center of gravity of the vehicle,
ax_k denotes a longitudinal acceleration of the vehicle at time k,
ax_(k+1) denotes a longitudinal acceleration of the vehicle at time k+1,
ω^k denotes an amplitude of a yaw movement of the vehicle at time k,
ω^(k+1) denotes an amplitude of a yaw movement of the vehicle at instant k+1.

• une étape de détermination de la position et de la trajectoire d'un ensemble d'objets environnant le véhicule,
• une étape de vérification de l'adhérence du véhicule sur la route,
• une étape de mise en œuvre d'un procédé de détermination de la trajectoire du véhicule tel que défini précédemment, et
• une étape de calcul de la distance séparant le véhicule d'un objet positionné sur la trajectoire du véhicule.

The invention also relates to a method for determining the distance separating an object from a vehicle comprising two steered front wheels and two steered rear wheels, the method comprising:

• a step of determining the position and the trajectory of a set of objects surrounding the vehicle,
• a step of checking the grip of the vehicle on the road,
• a step of implementing a method for determining the trajectory of the vehicle as defined previously, and
• a step of calculating the distance separating the vehicle from an object positioned on the trajectory of the vehicle.

• une étape de mise en œuvre du procédé de détermination de la distance séparant un objet du véhicule tel que défini précédemment,
• une étape de régulation de la vitesse du véhicule en fonction de la distance séparant un objet du véhicule.

The invention also relates to a method for regulating the speed of a vehicle comprising two steered front wheels and two steered rear wheels, the method comprising:

• a step of implementing the method for determining the distance separating an object from the vehicle as defined above,
• a step of regulating the speed of the vehicle as a function of the distance separating an object from the vehicle.

The invention also relates to a speed regulation system, the system comprising hardware and/or software means implementing a method as defined above, in particular hardware and/or software elements designed to implement a method such than previously defined.

The invention also relates to a motor vehicle comprising a speed regulation system as defined previously.

Finally, the invention also relates to a computer program product comprising program code instructions recorded on a computer-readable medium, the program product comprising instructions which, when the program is executed by the computer, drive the it to implement a method as defined above.

Presentation of figures

These objects, characteristics and advantages of the present invention will be explained in detail in the following description of a particular embodiment given on a non-limiting basis in relation to the attached figures, among which:

Figure 1 is a schematic top view of a motor vehicle according to one embodiment of the invention.

Figure 2 is a schematic top view of a first motor vehicle equipped with only two steered wheels and of a second vehicle equipped with four steered wheels.

FIG. 3 is a block diagram of a method for regulating the speed of a vehicle according to one embodiment of the invention.

FIG. 4 is a graph illustrating the evolution of a steering angle formed by the rear wheels, of a saturation angle of the rear wheels, and of a yaw gain of the vehicle as a function of the speed of the vehicle.

Figure 5 is a top view of the vehicle in a benchmark.

Figure 6 is a schematic top view of a vehicle driving situation.

Figure 7 is a schematic view of a speed control system according to one embodiment of the invention.

detailed description

In the following description, the front and the rear are defined according to the direction of progression of a vehicle. In forward gear and in a straight line, the vehicle progresses from the rear to the front. Left and right are defined from the driver's point of view. The vehicle is assumed to rest on horizontal ground. The longitudinal axis designates an axis parallel to the axis along which the vehicle is moving in a straight line. The transverse axis designates an axis that is horizontal and perpendicular to the longitudinal axis.

FIG. 1 schematically illustrates a motor vehicle 1 according to one embodiment of the invention. The vehicle 1 can be of any kind. In particular, it may for example be a private vehicle, a utility vehicle, a truck or a bus. The vehicle 1 comprises four wheels 2f, 2r, including two front wheels 2f and two rear wheels 2r. The vehicle 1 also comprises a chassis which is supported by the wheels and which itself supports various equipment including a powertrain, a braking system and a steering unit. The two front wheels 2f and the two rear wheels 2r are steering wheels, that is to say their orientation can be modified to make the vehicle turn to the right or to the left. The four wheels of the vehicle are therefore capable of pivoting around a substantially vertical axis when the vehicle is resting on horizontal ground.

The vehicle further comprises a set of sensors A, B, C, D, F, G capable of detecting fixed or mobile objects positioned in the surroundings of the vehicle 1. These sensors can be, for example, telemetry sensors of the radar type, lidar, sonar or even cameras. They can detect other vehicles, pedestrians, cyclists or any type of obstacle within a given perimeter around the vehicle. The number and nature of the sensors can be arbitrary. According to the embodiment presented, the vehicle comprises a camera A located in the front position and capable of recording images in front of the vehicle. The vehicle further comprises a radar sensor B in a central position in front of the vehicle and four radar sensors C, D, F, G respectively at the front left, front right, rear left and rear right corners of the vehicle. Thus the vehicle can detect obstacles all around the vehicle.

The vehicle 1 also includes four wheel speed sensors H for each of the four wheels (or odometry sensor), a yaw sensor (or gyroscope) I, a steering wheel angle sensor K and a steering angle sensor steering of the rear wheels L. The wheel speed sensors H are capable of measuring the speed of rotation of each of the wheels and therefore make it possible to calculate the speed of the vehicle. The yaw sensor I is able to measure the yaw of the vehicle, i.e. its rotational movement around the vertical axis. The steering wheel angle sensor K is a sensor capable of measuring the angle formed by the steering wheel or by a steering column of the vehicle.

Furthermore, the vehicle also comprises a computer E equipped with a processor μP capable of performing calculations, a random access memory RAM, a read only memory ROM, analog-digital A/D converters, and various interfaces for input and/or output I/O. Computer E is directly or indirectly connected to sensors A, B, C, D, F, G, H, I, K, L and can therefore receive the signals delivered by these sensors. The computer E and the sensors A, B, C, D, F, G, H, I, K, L make up a speed regulation system 3 of the vehicle. The speed regulation system 3 is capable of sending control commands directly or indirectly to the braking system and to the powertrain to control the speed of the vehicle according to the objects detected in the environment of the vehicle.

In addition, the vehicle 1 also comprises a vehicle trajectory control unit, commonly referred to as ESP. This control unit can detect situations of loss of control of the vehicle such as for example situations where the vehicle skids. Then this unit can initiate the individual braking of each of the wheels to restore stability and control of the vehicle. Advantageously, when the ESP control unit detects a loss of control situation, it can deactivate the cruise control system 3.

In Figure 2, there is shown on the left a first vehicle equipped with only two steered wheels: the rear wheels of this vehicle remain in the longitudinal axis of the vehicle and their steering angle always remains zero. On the right, there is shown a second vehicle equipped with four steered wheels with the rear wheels turned to the right and the front wheels turned to the left. It is observed that, for an identical steering angle of the front wheels, the vehicle equipped with four steered wheels has a turning radius r2 smaller than the turning radius r1 of the vehicle equipped with only two steered wheels. It is therefore understood that by applying a modeling of the trajectory of the vehicle 1 based solely on the steering angle of the front wheels, it would not be possible to obtain a modeling of the correct trajectory of a vehicle equipped with four steered wheels.

For each wheel 2r, 2f, a rolling axis can be defined as the axis along which the wheel can roll. When the vehicle is moving in a straight line, the rolling axis of each wheel is parallel to the longitudinal axis. When the vehicle turns to the left, the rolling axis of the two front wheels is oriented to the left while the rolling axis of the two rear wheels can be oriented to the right as shown in particular in Figure 1 (the wheels rear are therefore steered in the opposite direction to the front wheels). As a variant, the rolling axis of the two rear wheels can also be oriented towards the left (the rear wheels are therefore turned in the same direction as the front wheels).

For each wheel, a steering angle δ can be defined as the angle formed between the longitudinal axis of the vehicle and the running axis of the wheel in question. This angle can also be defined as the angle formed between the transverse axis of the vehicle and the axis of rotation of the wheel considered. In a bend, the steering angle formed by the wheels on the inside of the bend of a vehicle is generally greater than the steering angle formed by the wheels on the outside of the bend. However, in the method which will be described, a single steering angle δf of the two front wheels is considered. This steering angle δf can be defined as the steering angle of a single virtual wheel 2f', interposed between the two front wheels 2f, and which would produce the same effect as the two front wheels 2f on the path of the vehicle. Similarly, a single steering angle δr of the two rear wheels is considered. This steering angle δr can be defined as the steering angle of a single virtual wheel 2r', interposed between the two rear wheels 2r, and which would produce the same effect as the two rear wheels 2r on the path of the vehicle. Thus, the modeling of the vehicle is a “bicycle” type modeling since it takes into account a single orientation for the two front wheels 2f and a single orientation for the two rear wheels 2r.

In other words, the angle δf is the angle formed by a single virtual wheel 2f' interposed halfway between the front left wheel and the front right wheel. The angle δr is the angle formed by a single virtual wheel 2r′ interposed halfway between the front left wheel and the front right wheel. These virtual wheels 2f', 2r' are represented in particular in FIG. 2 and in FIG. 5.

We will now describe a method for regulating the speed of vehicle 1 according to one embodiment of the invention with reference to the block diagram illustrated in FIG. 3.

In a first step E1, the position and the trajectory of the objects around the vehicle 1 are detected. This step can be implemented by a data fusion system which makes it possible to combine the detection data supplied by the set of sensors A , B, C, D, F, G. This system makes it possible to construct a model of all of the objects close to the motor vehicle, and in particular to precisely estimate their position and their speed. The data fusion system can operate as follows: Each sensor A, B, C, D, F, G can periodically transmit (at a period specific to it) to the computer E, all of the objects detected, as well as than their measured kinematic attributes (e.g. position and velocity). This list of measured objects can be compared with existing objects in memory in the computer E. By data association methods (for example by the method of the nearest neighbors), it is possible to check for each measured object whether it corresponds to one of the objects stored in memory. If this is the case, the kinematic attributes measured and stored in memory can be combined using temporal filtering techniques, for example using Kalman filters. A scoring system can then be used to weight each recorded object. If an object already stored in memory is detected again then its score may increase, and if an object stored in memory is not detected while it is in the field of view of the sensor then its score may decrease. Among the objects recorded in memory, only those which have a sufficiently high score can be selected and can be communicated to the speed regulation system 3. If one of the objects measured by the sensor does not correspond to any object kept in memory, then this measured object can be added to the list of objects stored by the computer, and a zero score can be assigned to it. At the end of this first step E1, there is therefore a list of objects surrounding the vehicle with their position and their trajectory.

In a second step E2, the grip of the vehicle on the road is checked. In particular, it is checked whether at least one of the wheels is skidding. This test can be carried out by the vehicle trajectory control unit (ESP), for example by comparing the speed of rotation of the four wheels of the vehicle and/or by comparing the yaw of the vehicle provided by the yaw sensor I before the steering wheel angle supplied by the steering wheel angle sensor K. If a loss of grip situation is detected, the cruise control system 3 can be deactivated, at least as long as the loss of grip is confirmed. If the vehicle 1 has good grip on the road, the speed regulation system 3 remains activated and it is possible to proceed to the next step. Thanks to this preliminary verification, the computer does not perform any trajectory calculation unnecessarily. Indeed, in the event of loss of control of the vehicle, the control commands delivered by the vehicle trajectory control unit have priority over the control commands delivered by the speed regulation system. This avoids performing unnecessary calculations with the calculator E.

In a third step E3, a method for determining the trajectory of the vehicle 1 according to one embodiment of the invention is implemented. The third step E3 can itself be broken down into five steps E31, E32, E33, E34 and E35.

The first step E31 is a step for calculating the speed v of the vehicle 1. The second step E32 is a step for calculating a steering angle formed by the front wheels. The third step E33 is a step for calculating a steering angle formed by the rear wheels. The fourth step E34 is a step of calculating a slip angle of the vehicle as a function of the steering angle formed by the front wheels, the steering angle formed by the rear wheels and the speed of the vehicle. The fifth step E35 is a step for calculating the trajectory of the vehicle as a function of the slip angle of the vehicle.

During the first step E31, the speed v of the vehicle 1 is calculated. This speed can in particular be calculated by means of the wheel speed sensors H. For example, the speed of the vehicle can be obtained by calculating the average of the speed of each wheel. The speed of each wheel can be calculated by multiplying its rotational speed by its developed (i.e. its perimeter).

During the second step E32, the steering angle of the front wheels δf is calculated thanks to the angle sensor at the steering wheel K. The angle of the steering wheel being mechanically linked to the front wheels via a steering system, a conversion table can allow the conversion of the signal delivered by the sensor K into a value of a steering angle of the front wheels δf.

During the third step E33, the steering angle of the rear wheels δr is calculated. The third step E33 first of all comprises a measurement of a first steering angle formed by the rear wheels δ_rs with the rear wheel angle sensor L. The rear wheel steering angle sensor L can for example be an angular position sensor linked to a vertical axis around which the rear wheels can pivot.

The third step E33 also includes the calculation of a second steering angle formed by the rear wheels δrswa as a function of a measurement of an angle at the steering wheel of the vehicle 1. In particular, the second steering angle formed by the rear wheels δ_r ,_swa can be calculated with the following formula:

in which :
δ_r,_SWA denotes the second steering angle,
sign designates a function whose result is equal to 1 when its argument is strictly greater than 0, whose result is equal to -1 when its argument is strictly less than 0, and whose result is equal to 0 when its argument is equal to 0,
T_gs denotes a yaw gain of the vehicle,
δ_f designates the steering angle formed by the front wheels,
sat denotes a saturation angle of the rear wheels, that is to say a maximum steering angle that the two rear wheels can take at a given vehicle speed.

As a side note, to simplify the formatting of this document, the "_" character refers to an inscription carried as a subscript and the character "^" refers to an inscription carried as a superscript. Occasionally, these characters can be omitted without affecting the understanding of the text. For example, the steering angle formed by the rear wheels could be referenced by δr as well as by δ_r.

The "T_gs" and "sat" parameters are vehicle-specific parameters. They depend in particular on the longitudinal speed of the vehicle and on a selected driving mode (in the case where the vehicle is configured to allow the user to choose from among several driving modes, for example a "comfort" mode, a "normal" and a "sport" mode). These parameters can be defined experimentally. FIG. 4 illustrates by way of example the evolution of the parameters "T_gs", "sat" and of the steering angle formed by the rear wheels δr as a function of the speed of the vehicle when the vehicle is used in comfort mode and with a constant steering wheel angle, for example 60°. As a side note, the gain T_gs is equal to 1 for a vehicle comprising only two steered wheels.

Finally, a second steering angle formed by the rear wheels δ_r,_swa is thus obtained which is calculated differently from the first steering angle δ_rs. In particular the second steering angle δ_r,_swa is not calculated as a function of the signal delivered by the rear wheel steering angle sensor L. Theoretically these two steering angles are equal. However, the inaccuracy of the rear wheel steering angle sensor L (which may be linked in particular to a non-linearity of the sensor L), and/or the inaccuracy of the steering wheel angle sensor K, and/or the inaccuracy of the model linking the second steering angle δ_r,_swa to the measurement of an angle at the steering wheel of vehicle 1 can lead to different values of the two steering angles δ_rs and δ_r,_swa

The third step E33 then comprises a first substep E331 of calculating the difference between the first steering angle δrs and the second steering angle δ_r,_swa of the rear wheels. This difference is then compared with a threshold value Δ. The threshold Δ can be dependent on the speed of the vehicle and the resolution of the steering wheel angle sensor K. The threshold Δ can be calculated using the following formula:

in which :
ξ denotes the steering wheel angle resolution K,
l is the wheelbase of the vehicle
vl is the maximum speed of the vehicle

For example, considering a maximum vehicle speed equal to 67m/s, a vehicle wheelbase equal to 2.5m and a steering wheel angle resolution K of 0.02rad/s, the threshold Δ can be set at a value of 0.04° .

Then, if the difference between the first steering angle δrs and the second steering angle δrswa is strictly less than the threshold Δ, the third step E33 then comprises a second sub-step E332 for calculating a weighted average of the first steering angle δrs and the second steering angle δrswa of the rear wheels. This weighted average can be calculated using the following formula:

with :
Pr,swa designating a first weighting coefficient,
Prs designating a second weighting coefficient,
δ_r^k designating the steering angle of the rear wheels at time k.

The two weighting coefficients Pr, swa, Prs can be estimated respectively from uncertainty data of the rear wheel steering angle sensor L and of the steering wheel angle sensor K. They can be obtained by calculating for example the standard deviation and the mean of a large set of data from each of these two sensors K, L. The first weighting coefficient Pr,swa is inversely proportional to the inaccuracy of the steering wheel angle sensor K. The second weighting coefficient Prs is inversely proportional to the inaccuracy of the rear wheel steering angle sensor L.

On the other hand, if the difference between the first steering angle δ_rs and the second steering angle δ_r,_swa is greater than or equal to the threshold Δ, the third step E33 then comprises a series of sub-steps E333 to E337 aimed at identifying the value inconsistent value and replacing it with a consistent value from a previous iteration of step E33.

More specifically, the third step E3 then comprises a third sub-step E333 of testing the consistency of the first steering angle with one or more values of the steering angle formed by the rear wheels calculated previously. This consistency test makes it possible to check whether the first steering angle δ_rs indicates a false value. It is possible for example to compare the first steering angle δ_rs with the last value of the steering angle calculated during the previous iteration of the third step E33. The consistency test can also be, for example, a so-called “Chi2” test, also called “Chi-squared test”.

If the consistency test is negative, in other words if the consistency test makes it possible to conclude that the first steering angle δ_rs calculated is not consistent with the value or values of the steering angle formed by the rear wheels calculated previously, the third step E33 then comprises a fourth sub-step E334 of replacing the value of the first steering angle δ_rs by a value of the steering angle δr(k-1) formed by the rear wheels calculated during the previous iteration of the third step E33.

The procedure is the same with the second steering angle δ_r,_swa. If the difference between the first steering angle δ_rs and the second steering angle δ_r,_swa is greater than or equal to the threshold Δ, the third step E33 then comprises a fifth sub-step E335 of consistency test of the second steering angle with a or several values of the steering angle formed by the rear wheels previously calculated. This second consistency test makes it possible to check whether the second steering angle δ_r,_swa indicates a false value. It is possible for example to compare the second steering angle δ_r,_swa with the last value of the steering angle calculated during the previous iteration of the third step E33. The second consistency test can for example be a so-called “Chi2” test, also called “Chi-squared test”.

If the second consistency test is negative, in other words if the consistency test makes it possible to conclude that the calculated second steering angle δ_r,_swa is not consistent with the value or values of the steering angle formed by the rear wheels calculated previously, the third step E33 then comprises a sixth sub-step E336 of replacing the value of the second steering angle δ_r,_swa by a value of the steering angle δr(k-1) formed by the rear wheels calculated during of the previous iteration of the third step E33.

Finally, the third step E33 then comprises a sub-step E337 of calculating a weighted average of the first steering angle δ_rs and of the second steering angle δ_r,_swa. This weighted average can be obtained by the following formula:

In which :
δ_r^k designates the steering angle of the rear wheels at time k,
δ_r^(k-1) designates the steering angle of the rear wheels at time k-1, that is to say during the previous iteration of step E33,
δ_c^k designates a value of the steering angle of the rear wheels from among the first steering angle or the second steering angle, having satisfied the consistency test,
p_1 designates a weighting coefficient which represents the confidence in the coherent value, provided by the rear wheel steering angle sensor L or by the steering wheel angle sensor K,
p_r^k designates a weighting coefficient.

The weighting coefficient p_r^k can be obtained by the following formula:

In which :
Pr,swa denotes the first weight, and
Prs designates the second weighting coefficient.

Finally, at the end of the third step E33, we therefore have a reliable value of the steering angle of the rear wheels since this is calculated by cross-checking both the data supplied directly by the angle sensor of the rear wheels and the data provided by other vehicle sensors, in particular the angle sensor on the steering wheel.

In the fourth step E34, a slip angle of the vehicle is calculated as a function of the steering angle formed by the front wheels, the steering angle formed by the rear wheels and the speed of the vehicle. The slip angle can be defined as the angle formed between the longitudinal axis of the vehicle and the axis defined by the direction in which the vehicle is heading at a given instant. The calculation of this angle, denoted by β^(k+1) in the formula below, may further depend on the slip angle β^k of the vehicle at a previous instant (i.e. calculated during a previous iteration of step E34) and an amplitude of a yaw movement of the vehicle. In particular, the slip angle of the vehicle can be calculated with the following formula:

in which :
β^(k+1) denotes the slip angle of the vehicle at time k+1,
c_f designates a coefficient of stiffness of the axis of the front wheels of the vehicle,
c_r designates a coefficient of stiffness of the axis of the rear wheels of the vehicle,
m is the total mass of the vehicle,
v denotes the speed of the vehicle,
T designates the period of time between instants k and k+1,
β^k denotes the slip angle of the vehicle at time k,
l_f designates the distance separating the axis of the front wheels from the center of gravity C of the vehicle,
l_r designates the distance separating the axis of the rear wheels from the center of gravity C of the vehicle,
ω^k designates the amplitude of a yaw movement of the vehicle at time k,
δ^k_f designates the steering angle of the front wheels calculated during the first step, at time k,
δ^k_r denotes the steering angle of the rear wheels calculated during the second step, at time k.

The intrinsic parameters of the vehicle 1 (the total mass of the vehicle m, the stiffness coefficients cr, cf, the distances lr, lf) can be estimated or calculated during a preliminary configuration step and be recorded once and for all in the computer ROM memory E.

The speed of the vehicle v can be calculated using the wheel speed sensors H. In particular, the speed of the front wheel can be calculated for example using the following formula:

With :
v_fl designating the rotational speed (in revolutions per minute) of the left front wheel,
v_fr designating the rotational speed (in revolutions per minute) of the right front wheel,
D designating the developed of the wheel.

In the fifth step E35, the trajectory of the vehicle is calculated as a function of the slip angle of the vehicle obtained at the end of the fourth step E34. To this end, it is possible to define an XY frame or frame of reference as represented in particular in FIG. 5. This XY frame includes an X axis on the abscissa and a Y axis on the ordinate. The XY mark is fixed and independent of the position or orientation of the vehicle. The angle θ is defined as the angle formed between the longitudinal axis of the vehicle and the axis X. The trajectory of vehicle 1 can then be defined by calculating:
- the position (X, Y) of the vehicle in the XY reference,
- the orientation θ of the vehicle in the reference (XY),
- the speed v of the vehicle,
- the longitudinal acceleration ax of the vehicle, and
- the amplitude of a yaw movement ω of the vehicle.

The kinematic model of the vehicle comprising the front virtual wheel 2f' and the rear steering wheel virtual wheel 2r' is used. This model corresponds to the kinematic model of a bicycle or a motorcycle having a steering wheel at the front and a steering wheel at the rear. The trajectory of the vehicle can then be defined by being calculated by solving the following system of equations:

in which :
X_(k+1) denotes the abscissa of the center of the rear wheel axle at time k+1
X_k designates the abscissa of the center of the axis of the rear wheels at time k
Y_(k+1) designates the ordinate of the center of the rear wheel axle at time k+1
Y_k designates the ordinate of the center of the rear wheel axle at time k
T designates the period of time between instants k and k+1,
v_k designates the speed of the vehicle at time k,
v_(k+1) designates the speed of the vehicle at time k+1,
θ_k denotes the angle formed between the longitudinal axis of the vehicle and the abscissa axis at time k,
θ_(k+1) denotes the angle formed between the longitudinal axis of the vehicle and the abscissa axis at time k+1,
β^k denotes the slip angle of the vehicle at time k,
l_r designates the distance separating the axis of the rear wheels from the center of gravity of the vehicle,
ax_k designates the longitudinal acceleration of the vehicle at time k,
ax_(k+1) denotes the longitudinal acceleration of the vehicle at time k+1,
ω^k designates the amplitude of a yaw movement of the vehicle at time k,
ω^(k+1) designates the amplitude of a yaw movement of the vehicle at time k+1.

At the end of the fifth step E35, the trajectory of the vehicle 1 has therefore been determined. This trajectory has been determined in particular using the slip angle β calculated during the fourth step E34.

In a fourth step E4, the distance separating the vehicle from an object positioned on the path of the vehicle is calculated. Among the detected during the first step E1, the object or objects on the path of the vehicle are selected. By knowing the objects surrounding the vehicle on the one hand and by knowing the trajectory of the vehicle on the other hand, it is possible to determine the distance separating the vehicle from the closest object positioned on the trajectory of the vehicle.

In a fifth step E5, the speed of the vehicle 1 is adapted according to the distance separating the vehicle 1 from the objects surrounding the vehicle and their trajectory. In particular, the fifth step can comprise a step of comparing the distance separating the vehicle from an object positioned on the trajectory of the vehicle with a reference value corresponding to a safety distance (typically of the order of 50 m to 100 m). Then, if the distance separating the vehicle from the object positioned on the trajectory of the vehicle is less than or equal to the reference value, the fifth step can comprise a step of automatic braking of the vehicle. Thanks to its output interfaces, the computer is suitable for transmitting instructions to the various parts of the vehicle to regulate the speed of the vehicle

FIG. 6 illustrates a driving situation in which the vehicle 1 is driving on a road, for example a highway, comprising three lanes. These lanes are delimited by dashed lines L1, L2 in FIG. 6. The vehicle 1 runs on the central lane without changing lanes. The road includes a turn to the left. A first vehicle v1 is also driving on the central lane, in front of vehicle 1. A second vehicle v2 is driving on the right lane. Thanks to the method which has just been described, the trajectory which has been determined corresponds to the trajectory T1 and not to the trajectory T2. The trajectory T2 could have been calculated by a model adapted to vehicles comprising only two steered wheels. The object identified as being on the trajectory of vehicle 1 is therefore indeed vehicle V1 and not vehicle V2. Thus, the speed of vehicle 1 can be adjusted according to the position and speed of vehicle V1 and not according to the position and speed of vehicle V2. If the vehicle V2 is slower than the vehicle V1, this prevents the vehicle 1 from braking unjustifiably.

The method which has just been described is converted into instructions stored in the read only memory ROM of the computer E. For each step of the method which has just been described, the speed regulation system 3 can comprise a module capable of implementing the corresponding step. In particular, the first step E31 can be implemented by a first module M1, the second step E32 can be implemented by a second module M2, the third step E33 can be implemented by a third module M3, the fourth step E34 can be implemented by a fourth module M4, the fifth step E35 can be implemented by a fifth module M5. These modules M1, M2, M3, M4, M5 can be in the form of code instructions stored in the ROM memory of the computer E. The execution by the processor μP of these instructions allows the computer to implement the process described. FIG. 7 schematically illustrates the speed regulation system 3, in particular the computer E in connection with the sensors A, B, C, D, F, G, H, I, K, L. The method can be repeated according to a period T possibly ranging between approximately 5 ms and 50 ms. This invention has the additional advantage of acting on a single processing block leaving the other algorithms or programs in memory in the computer E unchanged. This feature makes it possible to simplify the software development of the method.

Advantageously, the trajectory determination method can be implemented in other systems requiring an estimation of the trajectory such as in particular a parking assistance system or an emergency braking system. The method could also be used for determining the trajectory of an autonomous vehicle comprising four steered wheels. The method can even be used to determine the trajectory of a vehicle comprising only two steered wheels at the front (i.e. a vehicle whose two rear wheels are not steered). In this case, the angle δr is equal to 0°.

Claims (13)

Method for determining the trajectory of a vehicle (1) comprising two front wheels (2f) steered and two rear wheels (2r) steered, characterized in that it comprises:

• a first step (E31) of calculating a speed (v) of the vehicle,
• a second step (E32) of calculating a steering angle formed by the front wheels (δf),
• a third step (E33) of calculating a steering angle formed by the rear wheels (δr),
• a fourth step (E34) of calculating a slip angle (β) of the vehicle (1) as a function of:
  • the steering angle formed by the front wheels (δf),
  • the steering angle formed by the rear wheels (δr), and
  • the speed (v) of the vehicle,
• a fifth step (E35) of calculating the trajectory of the vehicle as a function of the sliding angle (β) of the vehicle (1).
  

Determination method according to the preceding claim, characterized in that the third step (E33) comprises:

• measuring a first steering angle (δrs) formed by the rear wheels by means of a rear wheel steering angle sensor (L), and
• calculating a second steering angle (δrswa) formed by the rear wheels as a function of a measurement of an angle at the steering wheel of the vehicle (1).
  

Determination method according to the preceding claim, characterized in that the second steering angle (δrswa) is calculated according to the formula:

in which :
δ_r, _SWA designates the second steering angle,
sign designates a function whose result is equal to 1 when its argument is strictly greater than 0, whose result is equal to -1 when its argument is strictly less than 0, and whose result is equal to 0 when its argument is equal to 0,
T_gs designates a gain in yaw of the vehicle,
δ_f indicates the steering angle formed by the front wheels calculated by means of an angle sensor at the steering wheel (K),
sat designates a saturation angle of the rear wheels.
Determination method according to one of Claims 2 or 3, characterized in that the third step (E33) comprises:

• a sub-step (E331) of calculating a difference between the first steering angle (δrs) and the second steering angle (δrswa), then
• if said difference is strictly less than a threshold (Δ), a sub-step (E332) of calculating a weighted average of the first steering angle (δrs) and of the second steering angle (δrswa),
• if said difference is greater than or equal to the threshold (Δ),
  • a substep (E333) for testing the consistency of the first steering angle (δrs) with one or more values of the steering angle (δr) formed by the rear wheels calculated during a previous iteration of the determination method, then if the consistency test is negative, a sub-step (E334) of replacing the value of the first steering angle (δrs) by a value of the steering angle (δr) formed by the rear wheels calculated during a previous iteration of the determination method,
  • a substep (E335) for testing the consistency of the second steering angle (δrswa) with one or more values of the steering angle (δr) formed by the rear wheels calculated during a previous iteration of the determination method, then if the consistency test is negative, a sub-step (E336) of replacing the value of the second steering angle (δrswa) by a value of the steering angle (δr) formed by the rear wheels calculated during a previous iteration of the determination method, then
  • a sub-step (E337) of calculating a weighted average of the first steering angle (δrs) and of the second steering angle (δrswa).
    

Determination method according to one of the preceding claims, characterized in that the fourth step (E34) comprises the calculation of a slip angle (β) of the vehicle (1) as a function, in addition, of a slip angle (β) of the vehicle (1) calculated during a previous iteration of the fourth step (E34) and as a function of an amplitude of a yaw movement (ω) of the vehicle (1).
Determination method according to one of the preceding claims, characterized in that the sliding angle (β) of the vehicle (1) is calculated according to the formula:

in which :
β ^ (k + 1) denotes a sliding angle of the vehicle at the instant k + 1,
c_f designates a transverse stiffness index of an axis of the front wheels of the vehicle,
c_r denotes a transverse stiffness index of an axis of the rear wheels of the vehicle,
m denotes the total mass of the vehicle,
v designates the speed of the vehicle,
T denotes a period of time between instants k and k + 1,
β ^ k denotes a sliding angle of the vehicle at time k,
l_f designates the distance separating the axis of the front wheels from a center of gravity (C) of the vehicle,
l_r designates the distance separating the axis of the rear wheels from the center of gravity (C) of the vehicle,
ω ^ k indicate an amplitude of a yaw movement of the vehicle at time k,
δ ^ k_f denote the steering angle of the front wheels calculated during the second step (E32), at time k,
δ ^ k_r denotes the steering angle of the rear wheels calculated during the third step (E33), at time k.
Determination method according to one of the preceding claims, characterized in that the fifth step (E35) comprises:

• the calculation of a position (X, Y) of the vehicle in a coordinate system (XY), and
• the calculation of an orientation (θ) of the vehicle in the frame (XY), and
• the calculation of a speed (v) of the vehicle, and
• the calculation of a longitudinal acceleration (ax) of the vehicle, and
• the calculation of an amplitude of a yaw movement (ω).
  

Determination method according to one of the preceding claims, characterized in that the fifth step (E35) comprises the resolution of the following system of equations:

in which :
X_ (k + 1) indicates an abscissa of the center of the axis of the rear wheels at the instant k + 1,
X_k indicate an abscissa of the center of the axis of the rear wheels at time k,
Y_ (k + 1) indicates an ordinate of the center of the axis of the rear wheels at the instant k + 1,
Y_k indicate an ordinate of the center of the axis of the rear wheels at time k,
T denotes a period of time between instants k and k + 1,
v_k indicate the speed of the vehicle at time k,
v_ (k + 1) indicates the speed of the vehicle at the instant k + 1,
θ_k designates an orientation of the vehicle in the reference frame of reference at time k,
θ_ (k + 1) designates an orientation of the vehicle in the reference frame of reference at the instant k + 1,
β ^ k denotes the angle of slip of the vehicle at time k,
l_r designates a distance separating the axis of the rear wheels from the center of gravity of the vehicle,
ax_k indicate a longitudinal acceleration of the vehicle at time k,
ax_ (k + 1) indicates a longitudinal acceleration of the vehicle at the instant k + 1,
ω ^ k indicate an amplitude of a yaw movement of the vehicle at time k,
ω ^ (k + 1) denotes an amplitude of a yawing movement of the vehicle at time k + 1.
Method for determining the distance separating an object (V1, V2) from a vehicle (1) comprising two front wheels (2f) steered and two rear wheels (2r) steered, characterized in that it comprises:

• a step (E1) of determining the position and the trajectory of a set of objects surrounding the vehicle,
• a step (E2) of checking the grip of the vehicle on the road,
• a step (E3) of implementing a method for determining the trajectory of the vehicle according to one of the preceding claims, and
• a step (E4) of calculating the distance separating the vehicle from an object (V1, V2) positioned on the path of the vehicle (1).
  

Method of regulating the speed of a vehicle (1) comprising two front wheels (2f) steered and two rear wheels (2r) steered, characterized in that it comprises:

• a step of implementing the method for determining the distance separating an object from the vehicle according to the preceding claim,
• a step (E5) of regulating the speed (v) of the vehicle as a function of the distance separating an object (V1, V2) from the vehicle (1).
  

Speed regulation system (3) characterized in that it comprises hardware means (A, B, C, D, E, F, G, H, I, K, L) and / or software implementing a method according to one of the preceding claims, in particular hardware elements (A, B, C, D, E, F, G, H, I, K, L) and / or software designed to implement a method according to one of the preceding claims.
Motor vehicle (1), characterized in that it comprises a speed regulation system (3) according to the preceding claim.
Computer program product comprising program code instructions recorded on a computer readable medium, characterized in that it comprises instructions which, when the program is executed by the computer, lead the latter to implement the method according to any one of claims 1 to 10.