METHOD FOR DETERMINING A SPEED PROFILE OF A MOTOR VEHICLE WITH NON-PREDETERMINED ACCELERATION

Abstract

A method for determining a speed profile to be followed by a vehicle, including acquiring event data including a distance from an event and a target speed at this event for the vehicle, and determining a speed profile to be followed as a function of time, between an initial speed and the target speed in three successive distinct phases, respectively a first phase in which the jerk is set constant at a predetermined maximum jerk value to reach an optimal target acceleration value, a second phase in which the optimal target acceleration value is kept constant, and a third phase in which the jerk is again set constant to reach a zero acceleration value at the end of the third phase. The optimal target acceleration value is such that the distance required to carry out the three phases of the profile is equal to the distance from the event.

Claims

1-10. (canceled)

11. A method for determining a speed profile to be followed by a motor vehicle, the method comprising: acquiring contextual information on a road environment of the vehicle via a multi-sensor system of the vehicle; extracting event data from the acquired contextual information, comprising at least one distance from an event in relation to said vehicle and a target speed for said vehicle at the event; providing a measured initial speed of said vehicle; determining a speed profile to be followed as a function of time, between said measured initial speed and said target speed in three successive distinct phases, respectively a first phase in which a jerk is set constant at a predetermined maximum jerk value in order to reach an optimal target acceleration value at an end of the first phase, a second phase in which said optimal target acceleration value is kept constant throughout a duration of the second phase, and a third phase in which the jerk is again set constant in order to reach a zero acceleration value at an end of the third phase; and determining said optimal target acceleration value during the second phase such that the distance required to carry out the three phases of said profile by applying said determined optimal target acceleration value is equal to said distance from the event.

12. The method as claimed in claim 11, wherein the distance required to carry out the three phases of said profile is calculated from a set of equations implemented for the calculation of the speed profile, the calculation steps of which comprise, for a set of fixed parameters comprising the initial speed and the initial acceleration of the vehicle when starting the speed profile, the target speed at the event and the predetermined maximum jerk value, and for an unfixed parameter comprising the optimal target acceleration to be reached in the second phase of the profile: calculating the duration of the phases and start and end times delimiting the phases, calculating the passage speeds at the start and end times delimiting the second phase, calculating the speed as a function of time for each of the phases, and calculating the distances traveled at the start and end times delimiting the phases.

13. The method as claimed in claim 11, wherein the determination of said optimal target acceleration value is carried out through iteration and bisection from a predetermined range bounded by a minimum acceleration value and a maximum acceleration value.

14. The method as claimed in claim 13, wherein, at each iteration, the distance required to produce the profile is calculated with an intermediate acceleration value, which is a barycenter of the minimum and maximum acceleration values.

15. The method as claimed in claim 11, wherein, in said third phase, the jerk is set constant at said predetermined maximum jerk value of the first phase.

16. The method as claimed in claim 11, wherein, in said third phase, the jerk is set constant at a predetermined maximum jerk value different from said predetermined maximum jerk value of the first phase.

17. The method as claimed in claim 11, wherein said predetermined maximum jerk value is different depending on whether the speed profile relates to a positive acceleration or to a negative acceleration of the vehicle.

18. The method as claimed in claim 11, further comprising transmitting said speed profile as an instruction to an adaptive speed control system fitted to the vehicle.

19. A device configured to be installed on board a motor vehicle for the implementation of the method as claimed in claim 11, the device comprising: a multi-sensor system configured to acquire contextual information on the road environment of a motor vehicle; a vehicle speed sensor; means for calculating said speed profile as a function of event data extracted from said acquired contextual information; and control means for applying said calculated speed profile to a vehicle adaptive speed control system.

20. A motor vehicle, comprising: the device as claimed in claim 19.

Description

[0022] FIG. 1 is a graph illustrating an example of a speed profile according to the invention as a function of time, with acceleration dependent on the distance from an event, allowing the vehicle to go from its initial speed to a target speed to be reached at the event, in a case where the target speed is lower than the initial speed;

[0023] FIG. 2 is a flowchart illustrating the bisection algorithm implemented in order to determine the acceleration required in the second phase of the speed profile;

[0024] FIG. 3 is a graph illustrating the various distance values required to produce the speed profile, as a function of the jerk and acceleration values chosen for the set initial speed and target speed values.

[0025] FIG. 4 is a set of graphs illustrating the speed of the vehicle according to the speed profile, distance from the event and acceleration of the vehicle.

[0026] The invention applies to a motor vehicle equipped with an adaptive speed control system and a multi-sensor perception system which are able to deliver contextual information relating to the events in the road scene ahead of the vehicle, for example approaching a roundabout, a bend, a traffic jam, a change in speed limit, etc. The data collected by the on-board sensors are sent to an electronic computer, which, by virtue of an environmental perception algorithm analyzing these data, constructs a description of the near environment of the vehicle and a configuration of the road scene. From this environment, the system is able to provide a (distance, speed) pair relating to a detected event, comprising the distance from this event D.sub.event and the speed to be reached V.sub.3 at this event, called the target speed. This detected event may, for example, be a speed limit sign.

[0027] The vehicle also comprises an on-board speed sensor, delivering information on its speed and its acceleration by processing the speed.

[0028] The speed profile described below is a speed profile determined from the measured speed of the vehicle and intended to be transmitted as an instruction to be followed to the adaptive speed control system of the vehicle so as to anticipate decelerations and accelerations when approaching an event. More specifically, the speed profile must allow the vehicle to go from its initial speed to the target speed while observing constraints in vehicle dynamics in terms of acceleration, which may be positive or negative (deceleration), depending on the type of profile, and jerk, i.e. the derivative of the acceleration. These last constraints will make it possible to optimize the performance in following this profile by the vehicle's adaptive speed control system.

[0029] The principle of the speed profile of the invention will now be illustrated starting from an example of a decreasing profile, as illustrated in FIG. 1, taking as the starting assumption a zero initial acceleration and a constant initial vehicle speed, denoted V.sub.0, and, as the ending assumption, a zero acceleration and a constant target vehicle speed V.sub.3, with V.sub.3<V.sub.0, since the speed profile here is decreasing.

[0030] The speed profile presented in FIG. 1 is defined according to the invention in three successive phases: [0031] a first phase, denoted Phase_1, extending between the start time to and end times t.sub.1 delimiting this phase, in which the jerk value is set at a predetermined maximum jerk value, of absolute value denoted J.sub.maxi, in order to reach an optimal target acceleration value at time t.sub.1, of absolute value denoted A.sub.target, [0032] a second phase, denoted Phase_2, extending between the start time t.sub.1 and end time t.sub.2 delimiting this phase, in which the target acceleration value reached at t.sub.1 is kept constant throughout the duration of the second phase, the jerk value then being zero, [0033] a third phase, denoted Phase_3, extending between the start time t.sub.2 and end time t.sub.3 delimiting this phase, in which the jerk value is again preferably set at the predetermined maximum jerk value J.sub.maxi, in order to return to a zero acceleration value at time t.sub.3.

[0034] The division of the speed profile according to the invention into three distinct successive phases is necessary in order to observe the constraints in vehicle dynamics in terms of jerk value in phases Phase_1 and Phase_3.

[0035] There is therefore the following set of fixed parameters:

[0036] V.sub.0: the initial speed when starting the speed profile;

[0037] V.sub.3: the target speed to be reached at the event;

[0038] A.sub.init: the acceleration of the vehicle when starting the speed profile, which might not be zero;

[0039] J.sub.maxi: the maximum jerk value defined for the profile.

[0040] The speed profile is expressed by two calculation functions actually used by the vehicle speed control system:

[0041] An instruction speed, V.sub.profil, to be followed as a function of time (t):

V.sub.profil(t)=f(t,V.sub.0V.sub.3,A.sub.init,J.sub.maxi)

[0042] The distance required to achieve the speed profile, denoted D.sub.profil

[0043] Following of the profile will be triggered as soon as the distance from the targeted event that it is sought to anticipate, D.sub.event, originating from the vehicle's multi-sensor perception system, becomes equal to D.sub.profil, for a given set of parameters.

[0044] It is desired to start the profile when the distance from the event D.sub.event and the speed to be reached V.sub.3 at the event are known, the following of the profile having to ensure a behavior adapted to the target speed desired at this event. For this type of profile, the acceleration to be used is not a constraint. This involves generating a speed profile with non-predetermined acceleration. It is therefore necessary to determine the acceleration before calculating the speed profile to be followed. The acceleration is determined by bisection.

[0045] The bisection method makes it possible to find an optimal target acceleration value A.sub.target such that:

[00001]$\{\begin{array}{c}{D}_{\mathrm{profil}}\left(V_0,V_3,J_{\mathrm{maxi}},A_{\mathrm{target}}\right)=D_{\mathrm{event}}\\ .Math.A_{\mathrm{target}}.Math.\le A_{\mathrm{maxi}}\end{array}$

[0046] The calculation steps for calculating this distance required to achieve the speed profile D.sub.profil will be detailed below.

[0047] The durations of the phases and the start and end times t.sub.0, t.sub.1, t.sub.2 and t.sub.3 delimiting phases Phase_1, Phase_2 and Phase_3 as defined in FIG. 1 are calculated.

[0048] The passage speeds V.sub.1 and V.sub.2 corresponding to the respective passage speeds at the start and end times t.sub.1 and t.sub.2 delimiting the second phase Phase_2 are calculated.

[0049] The behavior of the speed as a function of time for each of phases Phase_1, Phase_2 and Phase_3 is calculated.

[0050] The distances traveled as a function of time at each of times to, t.sub.1, t.sub.2 and t.sub.3 delimiting the different phases Phase_1, Phase_2 and Phase_3, denoted X.sub.0, X.sub.1, X.sub.2 and X.sub.3, respectively, are calculated. Thus, the distance required to achieve the profile is D.sub.profil=X.sub.3.

[0051] The results of these speed profile calculation steps are detailed below and will be demonstrated further on.

[0052] For the calculation of the start and end times to, t.sub.1, t.sub.2 and t.sub.3 delimiting phases Phase_1, Phase_2 and Phase_3, the following notation is used:

t.sub.0=0(by assumption)

t.sub.1=T.sub.01

t.sub.2=T.sub.01+T.sub.12

t.sub.3=T.sub.01+T.sub.12+T.sub.23

[0053] With T.sub.01, T.sub.12 and T.sub.23 the respective durations of phases Phase_1, Phase_2 and Phase_3 by integrating the speed between the various points:

[00002]$T_{01}=\frac{A_{\mathrm{target}}}{J_{\mathrm{maxi}}}{T}_{12}=\frac{V_0-V_3}{A_{\mathrm{target}}}-\frac{A_{\mathrm{target}}}{J_{\mathrm{maxi}}}{T}_{23}=\frac{A_{\mathrm{target}}}{J_{\mathrm{maxi}}}$

[0054] Regarding the various passage speeds of the phases, i.e. the speeds at times t.sub.0, t.sub.1, t.sub.2 and t.sub.3, denoted V.sub.0, V.sub.1, V.sub.2 and V.sub.3, respectively, they are expressed as follows:

[0055] V.sub.0, the initial speed of the profile, which is an imposed value, corresponding to the current measured speed of the vehicle when the profile is calculated,

[00003]$V_1=V_0-J_{\mathrm{maxi}}\times \frac{T_{01}^2}{2}{V}_2=V_3+\frac{T_{23}^2}{2}\times J_{\mathrm{maxi}}$

[0056] V.sub.3 is the target speed that it is desired to reach by following the speed profile and is also imposed, like the initial speed.

[0057] The equation for the speed profile v(t) for each of the phases is determined as a function of the elapsed time, as follows:

[00004]$\mathrm{Phase\_}1,\mathrm{for}0\le t\le t_1:V\left(t\right)=V_0-J_{\mathrm{maxi}}\times \frac{t^2}{2}\mathrm{Phase\_}2,\mathrm{for}{t}_1\le t\le t_2:V\left(t\right)=V_1-A_{\mathrm{target}}\times \left(t-t_1\right)\mathrm{Phase\_}3,\mathrm{for}{t}_2<=t<=t_3:V\left(t\right)=V_3+\frac{{\left(t-t_3\right)}^2}{2}\times J_{\mathrm{maxi}}$

[0058] The distances traveled as a function of time are calculated as follows:

[00005]$X_0=0\left(\mathrm{by}\mathrm{assumption}\right)X_1=X_0+T_{01}\times V_0-\frac{T_{01}^3}{6}\times J_{\mathrm{maxi}}{X}_2=X_1+T_{12}\times V_1-\frac{T_{12}^2}{2}\times A_{\mathrm{target}}{X}_3=X_2+T_{23}\times V_3+\frac{T_{23}^3}{6}\times J_{\mathrm{maxi}}$

[0059] The distance required to achieve the profile is D.sub.profil=X.sub.3. Thus, when the distance from the event is equal to X.sub.3, the following of the speed profile will be triggered by sending a speed instruction V(t) as defined above.

[0060] These results will now be demonstrated.

[0061] For phase Phase_1, for t such that t.sub.0≤t≤t.sub.1:

[0062] The jerk j.sub.01(t) of the profile over this first phase is set constant and has a value of: j.sub.01(t)=−J.sub.maxi

[0063] Since the initial acceleration A.sub.init is zero, the acceleration as a function of time, denoted A.sub.01(t) in this first phase, has a value of:

A.sub.01(t)=A.sub.init+∫.sub.0.sup.tJ(t)dt

A.sub.01(t)=−J.sub.maxi×t

[0064] Then deduced therefrom is the change in the speed as a function of time, denoted V.sub.01(t) in this first phase:

[00006]$V_{01}\left(t\right)=V_0+{\int }_0^t{A}_{01}\left(t\right)\mathrm{dt}{V}_{01}\left(t\right)=V_0-J_{\mathrm{maxi}}\times \frac{t^2}{2}$

[0065] Hence the distance traveled as a function of time X.sub.01(t) in the first phase

[0066] Phase_1:

[00007]$X_{01}\left(t\right)=X_0+{\int }_0^t{V}_{01}\left(t\right)\mathrm{dt}{X}_{01}\left(t\right)=t\times V_0-\frac{t^3}{6}\times J_{\mathrm{maxi}}$

[0067] For the second phase Phase_2, fort such that t.sub.1≤t≤t.sub.2:

[0068] The acceleration as a function of time, denoted A.sub.12 (t) in this second phase, is constant in this phase, namely:

A.sub.12=−A.sub.target

[0069] Therefore deduced therefrom is the change in the speed as a function of time in this second phase, denoted V.sub.12(t):

V.sub.12(t)=V.sub.1+∫.sub.t.sub.1.sup.t.sub.1A.sub.12(t)dt

V.sub.12=V.sub.1−A.sub.target×(t−t.sub.1)

[0070] Hence the distance traveled as a function of time X.sub.12 (t) in this second phase:

[00008]$X_{12}\left(t\right)=X_1+{\int }_{t_1}^t{V}_{12}\left(t\right)\mathrm{dt}{X}_{12}\left(t\right)=X_1+\left(t-t_1\right)\times V_1-\frac{{\left(t-t_1\right)}^2}{2}\times A_{\mathrm{target}}$

[0071] Lastly, for the third phase Phase_3, fort such that t.sub.2≤t≤t.sub.3:

[0072] The jerk J.sub.23(t) of the profile over this first phase is set constant and has a value of:

J.sub.23(t)=J.sub.maxi

[0073] Since the final acceleration in the third phase A.sub.final is zero, the acceleration as a function of time denoted A.sub.23 (t) in this phase has a value of:

A.sub.23(t)=A.sub.final+∫.sub.t.sub.3.sup.tJ.sub.23(t)dt

A.sub.23(t)=(t−t.sub.3)×J.sub.maxi

[0074] Then deduced therefrom is the change in the speed as a function of time in this third phase, denoted V.sub.23(t):

[00009]$V_{23}\left(t\right)=V_3+{\int }_{t_3}^t{A}_{23}\left(t\right)\mathrm{dt}{V}_{23}\left(t\right)=V_3+\frac{{\left(t-t_3\right)}^2}{2}\times J_{\mathrm{maxi}}$

[0075] Hence the distance traveled as a function of time X.sub.23 (t) in this phase:

[00010]$X_{23}\left(t\right)=X_3+{\int }_{t_3}^{t}V\left(t\right)\mathrm{dt}$$X_{23}\left(t\right)=X_3+\left(t-t_3\right)\times V_3+\frac{{\left(t-t_3\right)}^3}{6}\times J_{\mathrm{maxi}}$

[0076] For the expression of the respective durations of phases T.sub.01, T.sub.12 and T.sub.23 and of the start and end times delimiting the phases, it is recalled that the following notation is used:

t.sub.0=0(by assumption)

t.sub.1=T.sub.01

t.sub.2=T.sub.01+T.sub.12

t.sub.3=T.sub.01+T.sub.12+T.sub.23

[0077] The duration T.sub.01 of the first phase Phase_1 has a value of:

T.sub.01=t.sub.1−t.sub.0=t.sub.1

[0078] However, the acceleration is continuous between the first phase Phase_1 and the second phase Phase_2, i.e.:

A.sub.01(t.sub.1)=A.sub.12(t.sub.1)

[0079] Which is equivalent to:

[00011]$-J_{\mathrm{maxi}}\times t_1=-A_{\mathrm{target}}$$\mathrm{Hence}:T_{01}=t_1=\frac{A_{\mathrm{target}}}{J_{\mathrm{maxi}}}$

[0080] Thus, the speed V.sub.1 reached at time t.sub.1 (corresponding to the end of the first phase and to the start of the second phase) has a value of:

[00012]$V_1=V_{01}\left(t_1\right)=V_{01}\left(T_{01}\right)$$\mathrm{Namely}{V}_1=V_0-J_{\mathrm{maxi}}\times \frac{T_{01}^2}{2}$

[0081] Now starting from the duration T.sub.23 of the third phase Phase_3, it has a value of:

T.sub.23=t.sub.3t.sub.2

[0082] However, as between the first phase and the second phase, the acceleration is continuous between the second phase Phase_2 and the third phase Phase_3, i.e.:

A.sub.23(t.sub.2)=A.sub.12(t.sub.2)

[0083] Which is equivalent to:

[00013]$\left(t_2-t_3\right)\times J_{\mathrm{maxi}}=-T_{23}\times J_{\mathrm{maxi}}=-A_{\mathrm{target}}$$\mathrm{Hence}:T_{23}=\frac{A_{\mathrm{target}}}{J_{\mathrm{maxi}}}$

[0084] Thus, the speed V.sub.2 reached at time t.sub.2 (corresponding to the end of the second phase and to the start of the third phase) has a value of:

[00014]$V_2=V_{23}\left(t_2\right)=V_{23}\left(T_{23}\right)$$\mathrm{Hence}:V_2=V_3+J_{\mathrm{maxi}}\times \frac{T_{23}^2}{2}$

[0085] Now starting from the duration T.sub.12 of the second phase Phase_2, it has a value of:

T.sub.12=t.sub.2−t.sub.1

[0086] However, the speed at time t.sub.2 at the end of the second phase is denoted V.sub.2 and may be written as follows:

V.sub.12(t.sub.2)=V.sub.2

[0087] Which is equivalent to:

[00015]$V_1-A_{\mathrm{target}}\times \left(t_2-t_1\right)=V_1-A_{\mathrm{target}}\times T_{12}=V_2$$\mathrm{Thus}:T_{12}=\frac{V_1-V_2}{A_{\mathrm{target}}}$

[0088] By replacing the expressions of V.sub.1, V.sub.2, T.sub.01 and T.sub.23 developed previously, the following is deduced therefrom:

[00016]$T_{12}=\frac{V_0-V_3}{A_{\mathrm{maxi}}}-\frac{A_{\mathrm{target}}}{J_{\mathrm{maxi}}}$

[0089] It is apparent from the demonstration of the results of the calculation of the speed profile that although it is defined in 3 phases as a function of time, its implementation remains straightforward because it requires only simple mathematical operations (additions, multiplications, divisions) and simple logical checks. The computing power required is therefore limited.

[0090] Reference is now made to a more general speed profile, i.e. one that may be increasing or decreasing, with an initial acceleration value that might not be zero.

[0091] The starting assumption used here is therefore that of an initial acceleration A.sub.init that might not be zero and a constant initial vehicle speed V.sub.0 and, as the ending assumption, a zero acceleration and a constant target vehicle speed V.sub.3, with V.sub.3<V.sub.0 or V.sub.3>V.sub.0, depending on whether the speed profile is decreasing or increasing.

[0092] Like for the previous example, the speed profile is always defined according to the invention by the following three successive phases: [0093] the first phase Phase_1, where the jerk value is set to the maximum jerk value j.sub.maxi, in order to reach the optimal target acceleration value, dependent on the distance from the detected event, of absolute value denoted A.sub.target, [0094] the second phase Phase_2, where the acceleration is kept at the optimal target acceleration value, [0095] the third phase, at the maximum jerk value in order to return to a zero acceleration value.

[0096] In the same way as above, the distance required to achieve the speed profile is denoted D.sub.profil. Thus, the profile will be triggered when arriving at a distance D.sub.profil from the event.

[0097] Since the parameters A.sub.init and J.sub.maxi are absolute values, the following variables s and s1 are introduced to reflect the relative acceleration and jerk values.

[0098] The variable s is defined as follows:

[00017]$s=\{\begin{array}{c}1\mathrm{if}{V}_3>V_0\\ -1\mathrm{otherwise}\end{array}$

[0099] Thus, if the profile is increasing, i.e. V.sub.3>V.sub.0, then s will have a value of 1 and if it is decreasing, s will have a value of −1. In addition, in the first phase Phase_1 of the speed profile, the acceleration will change from A.sub.init to s×A.sub.target, in the second phase Phase_2, it will be kept at s×A.sub.target, and in the third phase Phase_3, it will change from s×A.sub.target to 0 m/s.sup.2.

[0100] In addition, the variable Si is defined as follows:

[00018]$s_1=\{\begin{array}{c}1\mathrm{if}s\times A_{\mathrm{target}}>A_{init}\\ -1\mathrm{otherwise}\end{array}$

[0101] This variable thus represents the direction of change in the acceleration in the first phase Phase_1, which changes from A.sub.int to s×A.sub.target. Thus, the jerk in this phase has a value of s.sub.1×J.sub.maxi

[0102] As explained with reference to the preceding example, the steps for calculating the speed profile are as follows:

[0103] The durations of the phases and the start and end times t.sub.0, t.sub.1, t.sub.2 and t.sub.3 delimiting phases Phase_1, Phase_2 and Phase_3 are calculated.

[0104] The passage speeds V.sub.1 and V.sub.2 corresponding to the respective passage speeds at the start and end times t.sub.1 and t.sub.2 delimiting the second phase Phase_2 are calculated.

[0105] The behavior of the speed as a function of time for each of phases Phase_1, Phase_2 and Phase_3 is calculated.

[0106] The distances traveled as a function of time at each of times t.sub.0, t.sub.1, t.sub.2 and t.sub.3 delimiting the different phases Phase_1, Phase_2 and Phase_3, denoted X.sub.0, X.sub.1, X.sub.2 and X.sub.3, respectively, are calculated.

[0107] The table below summarizes the change in the jerk, acceleration, speed and distance traveled variables in the various phases of the general speed profile:

TABLE-US-00001 TABLE 1 Phase_1 Phase_2 Phase_3 constant constant constant time jerk time acceleration time jerk time Time t t.sub.0 = 0 t.sub.0 ≤ t ≤ t.sub.1 t.sub.1 t.sub.1 ≤ t ≤ t.sub.2 t.sub.2 t.sub.2 ≤ t ≤ t.sub.3 t.sub.3 Jerk J(t) s.sub.1 × J.sub.maxi 0 s × J.sub.maxi Acceleration A(t) A.sub.init A.sub.init .fwdarw. s × A.sub.target s × A.sub.target s × A.sub.target s × A.sub.target s × A.sub.target .fwdarw. 0 0 Speed V(t) V.sub.0 V.sub.0 .fwdarw. V.sub.1 V.sub.1 V.sub.1 .fwdarw. V.sub.2 V.sub.2 V.sub.2 .fwdarw. V.sub.3 V.sub.3 Distance traveled X(t) X.sub.0 = 0 X.sub.0 .fwdarw. X.sub.1 X.sub.1 X.sub.1 .fwdarw. X.sub.2 X.sub.2 X.sub.2 .fwdarw. X.sub.3 X.sub.3

[0108] By following the same procedure as in the case of the previous example regarding a decreasing speed profile and zero initial acceleration, the parameters and speeds of the profile are defined as follows:

[0109] Regarding the start and end times of the first phase Phase_1, the following notation is used:

t.sub.0=0(by assumption)

t.sub.1=T.sub.01

[0110] With the respective durations of the first and third phases Phase_1 and Phase_3, which are stated as follows:

[00019]$T_{01}=s_1\times \frac{s\times A_{\mathrm{target}}-A_{init}}{J_{\mathrm{maxi}}}$$T_{23}=\frac{A_{\mathrm{target}}}{J_{\mathrm{maxi}}}$

[0111] The passage speeds of the phases are expressed as follows:

[0112] V.sub.0 is the imposed initial speed of the profile,

[00020]$V_1=V_0+T_{01}\times A_{init}+s_1\times J_{\mathrm{maxi}}\times \frac{T_{01}^2}{2}$$V_2=V_3-s\times J_{\mathrm{maxi}}\times \frac{T_{23}^2}{2}$

[0113] V.sub.3 is the imposed target speed.

[0114] The duration T.sub.12 of the second phase Phase_2 is defined as follows:

[00021]$T_{12}=s\times \frac{V_2-V_1}{A_{\mathrm{target}}}$

[0115] The times t.sub.2 and t.sub.3 delimiting the third phase Phase_3 are defined as follows:

t.sub.2=T.sub.01+T.sub.12

t.sub.3=T.sub.01+T.sub.12+T.sub.23

[0116] The equation for the speed profile v(t) for each of the phases is determined as a function of the elapsed time, as follows:

[00022]$\mathrm{Phase\_}1,\mathrm{for}0\le t\le t_1:V\left(t\right)=V_0+A_{init}\times t+s_1\times J_{\mathrm{maxi}}\times \frac{t^2}{2}$$\mathrm{Phase\_}2,\mathrm{for}{t}_1\le t\le t_2:V\left(t\right)=V_1+A_{\mathrm{target}}\times s\times \left(t-t_1\right)$$\mathrm{Phase\_}3,\mathrm{for}{t}_2<=t<=t_3:V\left(t\right)=V_3+\frac{{\left(t-t_3\right)}^2}{2}\times \left(-J_{\mathrm{maxi}}\times s\right)$

[0117] The distances traveled as a function of time are calculated as follows:

[00023]$X_0=0\left(\mathrm{by}\mathrm{assumption}\right)$$X_1=X_0+T_{01}\times V_0+\frac{T_{01}^2}{2}\times A_{init}+\frac{T_{01}^3}{6}\times s_1\times J_{\mathrm{maxi}}$$X_2=X_1+T_{12}\times V_1+\frac{T_{12}^2}{2}\times A_{\mathrm{target}}\times s$$X_3=X_2+T_{23}\times V_3-\frac{T_{23}^3}{6}\times J_{\mathrm{maxi}}\times s$

[0118] The distance required to achieve the profile is D.sub.profil=X.sub.3.

[0119] As a variant, the jerk values set in the first and third phases of the speed profile may be different.

[0120] As a further variant, provision could be made to have different jerk values depending on whether the profile relates to an acceleration or to a deceleration.

[0121] The acceleration A.sub.target required in the second phase Phase_2 of the profile is determined by bisection according to a bisection algorithm presented in FIG. 2. This bisection takes as a criterion the distance required to achieve the profile D.sub.profil which is calculated using the equations above and which should be equal to the distance from the event.

[0122] Advantageously, the speed profile is therefore generated from the following set of fixed parameters, comprising the initial speed V.sub.0 of the vehicle when starting the speed profile, the speed to be reached V.sub.3 at the event, the initial acceleration A.sub.init of the vehicle when starting the speed profile, the predetermined maximum jerk value and a non-predetermined parameter, in this case the target acceleration to be reached in the second phase of the profile A.sub.target. According to one particular feature of the invention, this last parameter takes an optimal value determined on completion of a search by bisection, said optimal acceleration value being chosen within a bounded range, such as the distance required to achieve the profile for the set of fixed parameters, and said optimal acceleration value is equal to the distance from the event D.sub.event.

[0123] The bisection algorithm will now be described in more detail with reference to FIG. 2. The objective is to determine the optimal acceleration value a.sub.optim chosen within a predetermined range that extends between a minimum acceleration value a.sub.min and a maximum acceleration value a.sub.max, such that the distance required to achieve the profile is equal to the distance from the event D.sub.event Note that the distance required to achieve the profile decreases as the acceleration increases.

[0124] Therefore, in a first, initialization step E0, these minimum and maximum acceleration values defining the range are set, namely:

a.sub.min=a.sub.min_init

a.sub.max=a.sub.max_init

[0125] In a step E1 there is calculated, using the equations described above, first the distance Da.sub.min, corresponding to the distance required to achieve the speed profile taking as the acceleration value required in the second phase of the profile the minimum acceleration valuea.sub.min and, second, the distance Da.sub.max, corresponding to the distance required to achieve the speed profile, taking as the acceleration value required in the second phase of the profile the maximum acceleration value a.sub.max.

[0126] A test step E2 is then implemented, which aims to check whether it is possible to determine an optimal acceleration value. In other words, it is checked whether the distance D.sub.event at which the event is located is between the distances required for the profile calculated with the maximum and minimum acceleration values a.sub.max and a.sub.min, respectively, namely:

D.sub.a.sub.min≥D.sub.event≥D.sub.a.sub.max

[0127] If the test is failed, the algorithm ends with step E20, meaning that no acceleration value can be found to achieve the profile such that the distance required to achieve the profile is equal to the distance from the event.

[0128] Conversely, if the test is passed, then the algorithm continues with a step E3, in which a loop iteration index NB.sub.iteration is initialized at 0.

[0129] Next, on each iteration, in a step E4, first determined is an intermediate value a.sub.bary within the range bounded by the predefined minimum and maximum acceleration values, which is a barycenter of the two values with a.sub.min and a.sub.max assigned respective coefficients δ and (1-δ):

a.sub.bary=6×a.sub.min+(1−δ)×a.sub.max

[0130] Next, in a step E5, still based on the equations described above, the distance D.sub.bary, corresponding to the distance required to achieve the speed profile is calculated, taking as the acceleration value required in the second phase of the profile the value a.sub.bary.

[0131] The distance values D.sub.bary and D.sub.event are then compared in a step E6. If the distance from the event D.sub.event is greater than or equal to the distance required for the profile calculated with a.sub.bary, then, in a step E7, the maximum acceleration value a.sub.max and the distance Da.sub.max required for the profile are set, calculated with a.sub.max as follows:

a.sub.max=a.sub.bary

Da.sub.max=D.sub.bary

[0132] Otherwise, in a step E8, the minimum acceleration value a.sub.min and the distance Da.sub.min required for the profile are set, calculated with aurin as follows:

a.sub.min=a.sub.bary

Da.sub.min=D.sub.bary

[0133] It is then checked in a step E9 whether the maximum number of iterations of the loop has been reached. If not, then the loop iteration index NB.sub.iteration is incremented in a step E30, namely:

NB.sub.iteration.sup.=NB.sub.iteration+1

[0134] And it loops back to step E4.

[0135] If the maximum number of iterations is reached in step E9, the algorithm provides as a result in a step E10 the optimal acceleration value a.sub.optim such that:

a.sub.optim=a.sub.min

[0136] The determination of the optimal acceleration value over the range [a.sub.min_init, a.sub.max_init] is therefore a process of searching by bisection with, on each iteration, a calculation of the distance required to achieve the profile with an intermediate acceleration value, which is a barycenter of the two values a.sub.min and a.sub.max assigned respective coefficients δ and (1-δ).

[0137] Since the jerk is set at the value J.sub.maxi, the method makes it possible to obtain the optimal acceleration A.sub.target=a.sub.optim ∈[a.sub.min_init, a.sub.max_init] such that:

D.sub.profil(a.sub.optim)=D.sub.event

[0138] In other words, this optimal acceleration value a.sub.optim is such that the distance required to achieve the profile, calculated with this value determined by bisection, is equal to the distance from the event.

[0139] This method for determining the optimal acceleration value in the second phase of the profile is particularly advantageous. First, the computational load required is predictable. Specifically, convergence is ensured for a fixed number of iterations. Second, it ensures good convergence. Thus, for a fixed iteration number N, and a coefficient δ=0.5, the accuracy of the result a.sub.optim is of the order of

[00024]$\frac{a_{\min }-a_{\max }}{2^N}.$

[0140] Taking a concrete exemplary application of the speed profile calculated according to the invention in the following case:

J.sub.maxi=0.6m/s.sup.3

A.sub.init=0m/s.sup.2

V.sub.0=22.2m/s=80km/h

V.sub.3=10m/s=36km/h

a.sub.min_init=0.5m.Math.s.sup.−2,a.sub.max_init=3.4m.Math.s.sup.−2

[0141] The following is obtained for D.sub.event=180 m:

a.sub.optim=2.1m.Math.s.sup.−2

[0142] FIG. 3 illustrates the various values taken by D.sub.profil as a function of the jerk and acceleration values chosen for the set values of V.sub.0 and V.sub.3. Here, since the value of the jerk is fixed, the sweep is therefore performed by accelerating along the arrow F.

[0143] The predetermined maximum jerk value in this case is therefore obtained by fixing at a value J.sub.maxi of 0.6 m/s.sup.3, but it could also have been predetermined differently, using the sweep technique. Specifically, the step of determination by bisection would then not have used an acceleration sweep along a straight line with constant y as in FIG. 3 but a sweep along an axis such as x=y for example, the jerk value J.sub.maxi would then have been predetermined as a function of its dependence on the acceleration and the two, optimal acceleration A.sub.target and jerk J.sub.maxi values would have been obtained in the bisection step in such a way that the distance D_profil required to achieve the three phases of said profile by applying said determined optimal target acceleration value and said jerk value is equal to said distance from the event D.sub.event.

[0144] The speed profile P in relation to these constraints, calculated according to the principles set out above, is illustrated in the first graph of FIG. 4. In the second graph of FIG. 4, the curve of the distance D.sub.event from the event is shown as a function of time. It may be seen in the first graph that the speed V measured for the vehicle, resulting from the following of the profile via the control law of longitudinal control for the vehicle, does indeed reach the target speed required at the event, i.e. V.sub.3, when the event is reached, namely when D.sub.event=0.

[0145] In the third graph of FIG. 4, the curve of the acceleration measured for the vehicle Ames is shown as a function of time. It may be seen that the acceleration of the vehicle is limited to 1.6 m/s.sup.2, which is much lower than the limit defined in the calculation constraints (a.sub.max_init=3.4 m.Math.s.sup.−2).

[0146] It therefore appears that the speed profile calculated according to the invention and transmitted as an instruction to the vehicle adaptive speed control system allows the vehicle to automatically reduce its speed behavior in order to gradually reach the target speed (36 km/h according to the example). This therefore makes it possible to adapt the speed of movement of the vehicle to contextual elements detected by the sensors of the vehicle. In particular, it makes it possible to reach the desired speed at the desired distance, i.e. only when reaching the event.

[0147] It has been seen above that the implementation of the speed profile requires only limited computing power, by virtue of the simple mathematical operations required. In addition, it does not require preliminary measurements on predetermined paths. In other words, it may be generalized for whenever an event ({distance, speed}) is received, by any means whatsoever.