METHOD FOR OPERATING A PARKING ASSISTANCE FUNCTION OF A MOTOR VEHICLE
20220348139 · 2022-11-03
Assignee
Inventors
Cpc classification
B60Q1/525
PERFORMING OPERATIONS; TRANSPORTING
B62D15/0285
PERFORMING OPERATIONS; TRANSPORTING
B60Q1/535
PERFORMING OPERATIONS; TRANSPORTING
B60W2552/53
PERFORMING OPERATIONS; TRANSPORTING
B60Q9/007
PERFORMING OPERATIONS; TRANSPORTING
B60W30/06
PERFORMING OPERATIONS; TRANSPORTING
B60Q2400/50
PERFORMING OPERATIONS; TRANSPORTING
B60W2554/80
PERFORMING OPERATIONS; TRANSPORTING
International classification
B60Q9/00
PERFORMING OPERATIONS; TRANSPORTING
B60Q1/50
PERFORMING OPERATIONS; TRANSPORTING
B60W30/06
PERFORMING OPERATIONS; TRANSPORTING
Abstract
A method for operating a parking assistance function of a motor vehicle is described, wherein the motor vehicle comprises at least one sensor for detecting the road surrounding the motor vehicle. The method includes the following steps: Finding and specifying a free parking space; Determining a trajectory for parking the motor vehicle in the parking space and a sequence of an at least partially automated parking process; Determining at least one outer boundary line of the road surface required for parking along the identified trajectory; Detecting at least one road user approaching the determined outer boundary line on the road by means of at least one sensor; Determining the distance of the road user approaching the determined outer boundary line from the outer boundary line; if the determined distance falls below a specified first threshold, outputting a warning signal to the approaching road user.
Claims
1. The method for operating a parking assistance function of a motor vehicle (1), wherein the motor vehicle (1) comprises at least one sensor for detecting the road (2) surrounding the motor vehicle, wherein the method includes the following steps: searching for and specifying a free parking space (11, 12), determining a trajectory for parking the motor vehicle in the parking space and a sequence of an at least partially automated parking process (12), determining at least one outer boundary line of the road surface required for parking along the determined trajectory (14), detecting at least one road user approaching the determined outer boundary line on the road by means of at least one sensor (16, 24), determining the distance between the road user approaching the determined outer boundary line and the outer boundary line (16, 26), and if the determined distance falls below a specified first threshold, outputting a warning signal to the approaching road user (18).
2. The method according to claim 1, wherein the probability that the detected road user will cross the outer boundary line (17) is determined and, if the determined probability exceeds a specified threshold, an adapted warning signal will be output to the approaching road user (18) and/or the course of the parking process will be adapted.
3. The method according to claim 1, wherein if the determined distance falls below a specified second threshold (27), the speed and/or acceleration of the approaching road user will be determined and if the determined speed exceeds a specified threshold and/or the determined acceleration exceeds a specified threshold, an adapted warning signal will be output to the approaching road user and/or the course of the parking process will be adapted.
4. The method according to claim 1, wherein the positions of the motor vehicle (1) and the detected road user (7, 8) are determined as a function of time and, if it is not ensured that if the detected road user (7, 8) reaches the at least one safety line (6), the motor vehicle (1) is in a position which allows the approaching road user to pass by (7, 8), a number of further steps of the method will be carried out, depending on whether the parking assistance function allows automated longitudinal control of the motor vehicle (28).
5. The method according to claim 4, wherein if the parking assistance function allows automated longitudinal control of the motor vehicle, it is checked whether the current movement of the motor vehicle is the first parking movement of the parking process (42), and wherein if it is the first parking movement, the minimum speed of the motor vehicle required to avoid a collision (33) with the approaching road user is calculated and a number of further steps of the method are carried out depending on whether the calculated minimum speed is lower than a maximum speed specified for the parking assistance function.
6. The method according to claim 4, wherein if the parking assistance function allows automated longitudinal control of the motor vehicle, it is checked whether the current movement of the motor vehicle is the first parking movement of the parking process (42), and wherein if it is not the first parking movement of the parking process and if the specified parking space is not a parking space arranged parallel to the road (47), the minimum speed required to avoid a collision with the approaching road user is calculated (49) and a number of further steps of the method are carried out depending on whether the calculated minimum speed is lower than a maximum speed specified for the parking assistance function (50).
7. The method according to claim 4, wherein if the parking assistance function does not allow automated longitudinal control of the motor vehicle, the minimum speed required to avoid a collision with the approaching road user (7, 8) is calculated (33) and a number of further steps of the method are carried out depending on whether the calculated minimum speed is lower than a maximum speed specified for the parking assistance function (34).
8. The method according to claim 7, wherein if the calculated minimum speed is less than the specified maximum speed, at least one signal is output to a user (35).
9. The method according to claim 7, wherein if the calculated minimum speed is not less than the specified maximum speed, a number of further steps of the method are carried out depending on whether the current movement of the motor vehicle is the first parking movement of the parking process (38).
10. The method according to claim 1, wherein at least one camera and/or at least one radar sensor and/or at least one lidar sensor and/or at least one ultrasonic sensor is used as a sensor.
11. A parking assistance device (57) for a motor vehicle (1), which comprises at least one sensor for detecting the vehicle surroundings, wherein the parking assistance device is designed to carry out the method according to claim 1.
12. A motor vehicle (1), which comprises a parking assistance device (57) according to claim 11.
13. A computer-implemented method including commands which, when the program is executed by a computer, cause it to carry out the method according to claim 1.
14. A computer program product, including commands which, when executed by a computer, cause it to carry out a method according to claim 1.
15. A computer-readable data carrier on which the computer program product according to claim 14 is stored.
16. A data carrier signal transmitting the computer program product according to claim 14.
Description
BRIEF DESCRIPTION OF THE FIGURES
[0024] The invention is explained in more detail below on the basis of exemplary embodiments with reference to the attached figures. Although the invention is illustrated and described in more detail by the preferred exemplary embodiments, the invention is not limited by the disclosed examples and other variations can be derived from this by the person skilled in the art without departing from the scope of protection of the invention.
[0025] The figures are not necessarily accurate in detail and true to scale and may be zoomed in or out to provide a better overview. Therefore, functional details disclosed here are not to be understood restrictively, but only as an illustrative basis which provides guidance to the person skilled in this field of technology to use the present invention in a variety of ways.
[0026] The term “and/or” used herein, when used in a series of two or more elements, means that each of the listed elements can be used alone, or any combination of two or more of the listed elements can be used. If, for example, a composition is described which contains the components A, B and/or C, the composition may contain A alone; B alone; C alone; A and B in combination; A and C in combination; B and C in combination; or A, B, and C in combination.
[0027]
[0028]
[0029]
[0030]
[0031]
[0032]
[0033]
[0034]
[0035]
[0036]
DETAILED DESCRIPTION
[0037] A first variant of a method according to the invention is explained in more detail below on the basis of
[0038] In step 12, the parking assistance system determines a suitable parking space, and the driver stops the vehicle at a suitable position. Individual user settings can be taken into account, for example desired road lighting or distances to neighboring vehicles. Corresponding user settings are indicated by the input block 13. The parking process is also started in step 12.
[0039] In this context, a planned trajectory has already been calculated. The start of the parking maneuver can be marked in various ways, for example, a reverse gear can be automatically engaged by the system, the driver can confirm the start of the maneuver via a human-machine interface (HMI) or via a dedicated input device, or the driver leaves the vehicle (in the case of remote parking variants). In the case of aborted or interrupted parking processes or parking maneuvers, it may be provided that no otherwise provided special road lighting is carried out to mark the maneuvering area.
[0040] In step 14, based on the trajectory already determined in step 12, the area required by the motor vehicle for the imminent movement is calculated. In step 15, the area outside the vehicle is illuminated, which is required for parking for the currently performed maneuver or the imminent movement of the motor vehicle. In the context of step 15, only the area required for the current movement is illuminated or displayed. Preferably, areas which were needed previously are no longer illuminated.
[0041] In step 16, other road users, preferably other vehicles, which will potentially intrude into the required maneuvering area, are identified or determined. This is preferably done by means of at least one sensor, for example a camera. Object recognition methods can be used here. In step 17 the probability of an intrusion of a vehicle determined in step 16 into the maneuvering area, as well as the speed at which the approaching vehicle is expected to cross the maneuvering area, are determined. In the context of the exemplary embodiments, vehicles are considered as approaching road users by way of example. The present invention can of course also be implemented accordingly for other road users.
[0042] In step 18, an indication to the approaching vehicle in the form of a light pattern is projected onto the road surface. This may be a warning symbol and/or appropriate information. These are preferably adapted to a reference scheme, which links the way of warning the approaching traffic to different warning levels, in particular to the speed and/or the distance of the approaching vehicle. Furthermore, as part of step 18, the motor vehicle can be braked automatically or stopped completely if another vehicle or road user reaches or exceeds the intended maneuvering area. In principle, the communication actions carried out in step 18, i.e. suitable lighting or the sending of warning information or automatic interventions in the planned movement of the vehicle, can be defined and individually specified by user input, for example via a suitable input menu 13.
[0043] In step 19, it is checked whether the following driving maneuver will change the direction of travel of the motor vehicle. If this is the case, the method jumps back to step 14. If this is not the case, it is checked in step 20 whether the parking maneuver is still ongoing. If this is the case, the method jumps back to step 14. If this is not the case, the method ends in step 21. In step 20, it can be checked in particular whether the parking process has ended or has been cancelled or interrupted.
[0044] A further variant of a method according to the invention is explained in more detail below on the basis of
[0045] The steps 10 to 13 of the method correspond to the steps explained in connection with
[0046] In step 25 a check is carried out as to whether there are other vehicles in the vicinity of the vehicle, for example whether other vehicles are present within a specified radius or within a specified distance on the road from the motor vehicle and are approaching the motor vehicle. If this is not the case, the method jumps back to step 24. If this is the case, in step 26 the distance between the individual other vehicles and the motor vehicle, their speed and acceleration, i.e. their change in speed over time, are determined. A distinction can be made here. For example, below a specified speed threshold of another road user, in particular a vehicle, only its distance from the motor vehicle may be determined and taken into account. Above a defined speed, which may be the aforementioned speed limit, the speed and acceleration of the other road user approaching the vehicle can also be determined and taken into account.
[0047] Following step 26, in step 27 a check is carried out as to whether the detected, in particular approaching road user, for example an approaching vehicle, is relevant for the current parking maneuver. In this context, account may be taken, in particular, of whether the other road user is moving away from or approaching the motor vehicle and/or whether it is moving on the side of the road of the motor vehicle or a different side.
[0048] If it is determined in step 27 that the detected road user is not relevant for the current parking maneuver, the method jumps back to step 24. If it is determined in step 27 that the detected road user is relevant for the current parking maneuver, it is checked in step 28 whether the parking assistance system used, i.e. the APA feature or the parking assistance system used, enables or supports longitudinal control of the vehicle. If this is the case, the method is continued according to the subroutine shown in
[0049] Following the selected subroutine, in step 29 a check is carried out as to whether the parking maneuver has ended or has been aborted. If this is not the case, the method jumps back to step 24. If this is the case, the method ends with step 30.
[0050] The subroutine shown in
[0051] If this is not the case, in step 33 the minimum speed of the motor vehicle required to avoid a conflict, in particular a collision, is calculated. In step 34, it is checked whether the calculated minimum speed is lower than the configured maximum permitted speed in the context of the parking assistance function. If this is the case, a notice and/or warning is output to the driver or user in step 35. This can be done visually and/or audibly. For example, the driver can be informed about the required speed for further maneuvers.
[0052] Following step 35, in step 36 it is checked whether the driver reacts to the information and/or warning provided in step 35. If this is the case, the method jumps to step 29 of the method shown in
[0053] If the check in step 34 shows that the calculated minimum speed is not less than the configured maximum speed, in step 38 it is checked whether the current parking process is a first movement to park the vehicle in a parallel parking space. If this is the case, the method is continued with step 37. If this is not the case, a trajectory for returning to the parking space is calculated in step 39. Then, in step 40, the driver is asked to return to the parking space according to the calculated trajectory. Following step 40, in step 41 waiting is carried out until the detected vehicle has moved away sufficiently. Following step 41, the method jumps to step 29 in
[0054] In
[0055] If the check in step 32 shows that the motor vehicle is in a safe position before another vehicle reaches it, the method jumps to step 29 of
[0056] If, in step 43, the calculated minimum speed is not lower than the intended maximum maneuvering speed, the motor vehicle is completely stopped in step 45. This can be done, for example, in various ways, for example by initiating full braking or by slowing down the motor vehicle slowly according to a configured acceleration profile and moving along the planned trajectory or by stopping the motor vehicle parallel to the parking space to signal that the parking space is occupied. In addition or alternatively, signals can be sent to other road users, for example by means of hazard warning lights, switching on the lighting, emitting acoustic signals (for example, honking signals) or by light projections on the road surface. Following step 45, in step 46 waiting is carried out until the relevant other road users, in particular the at least one vehicle, are outside the area required for parking.
[0057] If the check in step 42 shows that the current driving maneuver is not the first movement to park in a selected parking space, in step 47 it is checked whether the motor vehicle is parking in a parallel parking space. In the case of parking in a parallel parking space, it can be assumed that from the second parking movement all further movements take place in a spatial area, for example behind a defined safety line, in which there is no risk of a collision. If the check in step 47 shows that the motor vehicle is parking in a parallel parking space, the parking maneuver is continued in step 48 until the calculated final position is reached. Following step 48, the method jumps to step 29 of
[0058] If the check in step 47 shows that the motor vehicle is not parking in a parallel parking space, in step 49 the minimum speed of the motor vehicle required to avoid a collision with the approaching vehicle is determined. Then, in step 50, it is checked whether the calculated minimum speed is lower than the maximum maneuvering speed for which the parking assistance function is configured. If this is the case, the parking maneuver is continued in step 51 with an adapted speed profile. Following step 51, the method jumps to step 29 of
[0059] In
[0060] A parking process into a parallel parking space according to a method according to the invention is illustrated below on the basis of
[0061] Other motor vehicles using the road 2 are denoted by reference numbers 7 and 8. A motor vehicle 7 is moving in the direction of travel behind the motor vehicle 1 and a motor vehicle 8 is moving on the opposite lane opposite to the direction of travel of the motor vehicle 1.
[0062] Following the calculation of the trajectory 5 and the at least one safety line 6, the road area 9 required for parking is illuminated by suitable lighting devices of the motor vehicle 1 before the start of the parking process. This is shown schematically in
[0063]
[0064] The calculation of the course of the safety line 6 is explained below on the basis of
[0065] The motor vehicle 1 has a width I.sub.vw. The distance between the front axle 62 and the rear axle 61 is denoted by I.sub.wb. The distance between the front axle 62 and the front of the vehicle 55 is denoted by I.sub.ot. The distance between the rear axle 61 and the tail end of the vehicle 56 is denoted by I.sub.or.
[0066] The left-side extreme left-side front point of the motor vehicle 1 resulting from the length and width of the motor vehicle 1 is denoted by reference number 64. Analogously, the extreme left-side rear point is denoted by the reference number 65. For both the extreme left-side front point 64 and the extreme left-side rear point 65, the trajectories of points 64 and 65 resulting during the parking process are calculated on the basis of the calculated and already known trajectory 5. The geometry of the motor vehicle 1 and its dimensions are taken into account here. The trajectory of the extreme left-side front point 64 is denoted by line 66. The trajectory of the extreme left-side rear point 65 is denoted by the trajectory 67. The safety line 6 is calculated from trajectories 66 and 67. Already when determining the coordinates of points 64 and 65, a safety distance in the y-direction d.sub.offset_y and/or a safety distance in the x-direction d.sub.offset_x can be added. Alternatively, a safety line 6 resulting from the trajectories 66 and 67 can first be calculated and a safety distance can be added to this in the x-direction and/or in the y-direction. The safety line 6 is derived from the trajectories 66 and 67 in such a way that for each x-value the maximum y-value, i.e. the larger value of the trajectories 66 and 67, is used to form the safety line 6.
[0067] The image section 68 in
x.sub.0=x.sub.v+(I.sub.wb+I.sub.of+d.sub.offset_X*(1−sin(α))*cos(ϕ)−sin(ϕ)*(½*I.sub.vw+d.sub.offset_Y*(1−sin(α))
y.sub.0=y.sub.v+(I.sub.wb+I.sub.of+d.sub.offset_X*(1−sin(α))*sin(ϕ)+cos(ϕ)*(½*I.sub.vw+d.sub.offset_Y*(1−sin(α))
α denotes the steering angle of the front wheels when moving along the trajectory 5.
[0068]
x.sub.FR=x.sub.v+(I.sub.wb+I.sub.of)*cos(ϕ)+½*sin(ϕ)*I.sub.vw
y.sub.FR=y.sub.v+(I.sub.wb+I.sub.of)*sin(ϕ)−½*cos(ϕ)*I.sub.vw
x.sub.FL=x.sub.v+(I.sub.wb+I.sub.of)*cos(ϕ)−½*sin(ϕ)*I.sub.vw
y.sub.FL=y.sub.v+(I.sub.wb+I.sub.of)*sin(ϕ)+½*cos(ϕ)*I.sub.vw
x.sub.RR=x.sub.v−(I.sub.wb+I.sub.of)*cos(ϕ)+½*sin(ϕ)*I.sub.vw
y.sub.RR=y.sub.v−(I.sub.wb+I.sub.of)*sin(ϕ)−½*cos(ϕ)*I.sub.vw
x.sub.RL=x.sub.v−(I.sub.wb+I.sub.of)*cos(ϕ)−½*sin(ϕ)*I.sub.vw
y.sub.RL=y.sub.v−(I.sub.wb+I.sub.of)*sin(ϕ)+½*cos(ϕ)*I.sub.vw
[0069] An implementation variant is described below on the basis of
[0070] Furthermore, the distance d.sub.E2SB of the motor vehicle 1 in the x-direction from the safety point SB is calculated. In addition, the distance
and the speed of the vehicle V1 or 7 on reaching the parking space
is calculated. If the distance d.sub.slowdown is smaller than the distance d.sub.v2SB (d.sub.slowdown<d.sub.V2SB), a first warning signal is projected onto the road surface in front of the vehicle 7, for example an encircled green thumb. If the speed v.sub.enterparkzone is between 0 and a specified threshold speed v.sub.warn, a second warning signal is projected onto the road surface, for example an orange exclamation mark. If the speed v.sub.enterparkzone of the vehicle 7 is greater than or equal to the threshold speed, a third warning symbol is projected onto the road surface, for example an exclamation mark marked in red. In other words, depending on the distance, speed, and acceleration of the approaching vehicle 7, an adapted warning signal is output, which can be output visually and/or acoustically.
[0071] A further variant is explained in more detail below on the basis of
[0072] In addition, a distance d.sub.V2SL along the second safety line 78 was defined in
[0073] Furthermore, in the context of the variant shown in
[0074] In
[0075] Furthermore, based on the speed and the acceleration of the approaching vehicle 8, the distance d.sub.v1 is calculated according to d.sub.v1(t.sub.dXOP2NSL)=v.sub.v1*t.sub.dXOP2NSL+½*a v1*t.sub.dXOP2NSL+½*a.sub.v1*t.sub.dXOP2SLN.sup.2, which must be less than or equal to the distance d.sub.V2NSL to avoid a collision. This is the possible distance for stopping the vehicle 8 for the current speed v.sub.1 and the acceleration a.sub.v1. If the distance d.sub.v1(t.sub.dXOP2NSL) is greater than d.sub.V2NSL, the time t.sub.dXOP2NSL is recalculated to meet the aforementioned condition. The speed v.sub.E is adapted taking into account a maximum possible speed v.sub.Emax during the parking process.
[0076] Another variant is shown in
REFERENCE CHARACTER LIST
[0077] 1 Motor vehicle [0078] 2 Road [0079] 3 Parking space [0080] 4 Motor vehicle [0081] 5 Trajectory [0082] 6 Outer safety line [0083] 7 Motor vehicle [0084] 8 Motor vehicle [0085] 9 Road area required for parking [0086] 10 Start [0087] 11 Finding a parking space [0088] 12 Determine parking space, stop vehicle, determine trajectory, start parking process [0089] 13 Enter user settings [0090] 14 Calculate maneuvering area [0091] 15 Illuminate the road surface required for parking for the currently performed maneuver or the imminent movement of the motor vehicle [0092] 16 Determine vehicles which will potentially intrude into the required maneuvering area [0093] 17 Probability of an intrusion of a detected vehicle into the maneuvering area and predicted excess speed at the time of intrusion [0094] 18 Outputting an indication in the form of a light pattern [0095] 19 Will the following maneuver change the direction of travel of the motor vehicle? [0096] 20 Is the parking maneuver still ongoing? [0097] 21 End [0098] 24 Monitoring the surroundings of the motor vehicle [0099] 25 Are there other vehicles in the surroundings of the vehicle? [0100] 26 Determine the distance between the individual other vehicles and the motor vehicle, their speed and acceleration [0101] 27 Is the approaching vehicle relevant for the current parking maneuver? [0102] 28 Is longitudinal control of the vehicle possible? [0103] 29 Parking maneuver completed or agreed? [0104] 30 End [0105] 31 Compare distances travelled depending on the time of the motor vehicle and the detected vehicle [0106] 32 Is the motor vehicle in a safe position before the detected vehicle reaches the motor vehicle? [0107] 33 Calculate the minimum speed of the motor vehicle required to avoid a conflict, in particular a collision [0108] 34 Is the calculated minimum speed less than the configured maximum speed? [0109] 35 Output an indication to the user [0110] 36 Did the user respond to an indication? [0111] 37 Braking intervention [0112] 38 Is this the first movement to park the vehicle in a parallel parking space? [0113] 39 Calculate trajectory to return to the parking space [0114] 40 Request to driver to drive the motor vehicle back into the parking space in accordance with the calculated trajectory [0115] 41 Waiting [0116] 42 Is the current driving maneuver the first movement to park in the selected parking space? [0117] 43 Is the calculated minimum speed less than the maximum maneuvering speed provided by the assistance function? [0118] 44 Continue parking maneuver with an adapted speed profile [0119] 45 Stop the motor vehicle [0120] 46 Waiting [0121] 47 Parking the motor vehicle in a parallel parking space? [0122] 48 Continue parking maneuver [0123] 49 Determining the minimum speed of the motor vehicle required to avoid a collision with the approaching vehicle [0124] 50 Is the calculated minimum speed less than the maximum maneuvering speed for which the parking assistance function is configured? [0125] 51 Continue parking maneuver with an adapted speed profile [0126] 52 Calculate the trajectory into the parking space [0127] 53 Moving the motor vehicle into the parking space according to the calculated trajectory [0128] 54 Waiting [0129] 55 Front of vehicle [0130] 56 Rear of vehicle [0131] 57 Parking assistance device [0132] 60 Indication sign [0133] 61 Rear axle [0134] 62 Front axle [0135] 63 Longitudinal axis [0136] 64 Left-side extreme front point of the motor vehicle [0137] 65 Left-side extreme rear point of the motor vehicle [0138] 66 Trajectory of the left-side extreme front point [0139] 67 Trajectory of the left-side extreme rear point [0140] 68 Image detail [0141] 74 Right-side extreme front point of the motor vehicle [0142] 75 Right-side extreme rear point of the motor vehicle [0143] 76 Trajectory of the right-side extreme front point [0144] 77 Trajectory of the right-side extreme rear point [0145] 78 Second safety line [0146] 79 Determined region of safety line 6 located in the area of the road surface of the opposite lane [0147] 80 Opposite lane [0148] 81 First position [0149] 82 Second position [0150] 83 Third position [0151] Y yes [0152] N no [0153] x.sub.w Directional vector [0154] y.sub.w Directional vector [0155] x Directional vector [0156] y Directional vector [0157] I.sub.vw Width of the subject vehicle [0158] I.sub.wb Distance between the front axle and the rear axle [0159] I.sub.ot Distance between the front axle and the front of the vehicle [0160] I.sub.or Distance between the rear axle and the rear of the vehicle [0161] d.sub.offset_y Safety distance in y-direction [0162] d.sub.offset_x Safety distance in x-direction [0163] v.sub.v1 Speed of another road user [0164] a.sub.v1 Acceleration of another road user [0165] d.sub.E2V Distance between subject vehicle and another road user [0166] d.sub.v2SB Distance of the vehicle 7 from a point SB on the safety line [0167] SB Point on the safety line [0168] d.sub.E2SB Distance of the motor vehicle 1 in x-direction from the point SB [0169] dY.sub.OP2SL Distance between the extreme front point 64 and the second safety line, and between the extreme rear point 65 and the second safety line [0170] d.sub.v2SL Distance of the extreme front point of an approaching vehicle along the second safety line [0171] d.sub.V2NSL Distance of the approaching vehicle until reaching a point on the safety line where there would potentially be a collision between the approaching vehicle and the motor vehicle [0172] dX.sub.OP2NSL Distance the motor vehicle must travel to reach the potential collision point [0173] ϕ Yaw angle