Patent Publication Number: US-2017349213-A1

Title: System And Method For Displaying A Forward Drive Trajectory, Providing A Jackknifing Warning And Providing A Trailer Turn Aid

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Application No. 62/334,740, filed on Jun. 3, 2016. The disclosure of the above application is incorporated herein by reference in its entirety. 
    
    
     FIELD 
     The present disclosure relates to systems and methods for displaying a forward drive trajectory, providing a jackknifing warning and providing a trailer turn aid. 
     BACKGROUND 
     The background description provided here is for the purpose of generally presenting the context of the disclosure. Work of the presently named inventors, to the extent it is described in this background section, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the present disclosure. 
     When a vehicle towing a trailer makes a turn while moving forward, the trailer may follow a different path or trajectory than the path or trajectory that the vehicle follows. For a given turning radius of the vehicle, the difference between the trailer trajectory and the vehicle trajectory may be greater when the vehicle is travelling at low speeds relative to when the vehicle is travelling at high speeds. If a driver of the vehicle does not account for the difference between the trailer trajectory and the vehicle trajectory, the trailer may run over an outer lane boundary (e.g., a curb) extending alongside the road adjacent to the turn. If the driver overcompensates for the difference between the trailer trajectory and the vehicle trajectory, the vehicle may run over the centerline of the road onto which the vehicle is turning. 
     In some cases, the driver does not account for the difference between the trailer trajectory and the vehicle trajectory because the driver forgets that the vehicle is towing a trailer. In other cases, the driver is unable to comprehend the width of the trailer and/or the trajectory of the trailer. 
     SUMMARY 
     A first example of a system according to the principles of the present disclosure includes an expected trajectory module and an electronic display. The expected trajectory module determines an expected forward drive trajectory of a vehicle and determines an expected forward drive trajectory of a trailer being towed by the vehicle. The electronic display displays the expected forward drive trajectories of the vehicle and the trailer. 
     A second example of a system according to the principles of the present disclosure includes an expected trajectory module, a target trajectory module, and at least one of a user interface device and a steering control module. The expected trajectory module determines an expected trajectory of a vehicle and determines an expected trajectory of a trailer being towed by the vehicle. The target trajectory module determines a target trajectory of the vehicle during a turn based on the expected vehicle trajectory, the expected trailer trajectory, and at least one road parameter. The user interface device guides a driver of the vehicle through the turn based on the target vehicle trajectory. The steering control module controls a steering actuator of the vehicle based on the target vehicle trajectory. 
     Further areas of applicability of the present disclosure will become apparent from the detailed description, the claims and the drawings. The detailed description and specific examples are intended for purposes of illustration only and are not intended to limit the scope of the disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present disclosure will become more fully understood from the detailed description and the accompanying drawings, wherein: 
         FIG. 1  is a functional block diagram of an example vehicle system according to the present disclosure, the vehicle system including a vehicle and a trailer being towed by the vehicle; 
         FIG. 2  is a functional block diagram of an example control system according to the present disclosure; 
         FIG. 3  is a flowchart illustrating an example method for displaying a forward drive trajectory of a vehicle and a trailer and providing a jackknifing warning according to the present disclosure; 
         FIGS. 4 through 7  are example images on an electronic display and an example graph displaying a forward drive trajectory of a vehicle and a trailer; 
         FIG. 8  includes example images on an electronic display displaying a forward drive trajectory of a vehicle and a trailer and providing a jackknifing warning according to the present disclosure; 
         FIG. 9  is a flowchart illustrating an example method for providing a turn aid for a driver of a vehicle towing a trailer according to the present disclosure; 
         FIGS. 10 through 14  are top views of an example vehicle system making a turn according to the present disclosure; and 
         FIGS. 15 and 16  include an example image on an electronic display and an example view of a driver of a vehicle towing a trailer illustrating a turn aid for the driver according to the present disclosure. 
     
    
    
     In the drawings, reference numbers may be reused to identify similar and/or identical elements. 
     DETAILED DESCRIPTION 
     A system and method according to the present disclosure determines the trajectories of a vehicle and a trailer as the vehicle is moving forward through a turn and displays the trajectories in view of a driver of the vehicle. Thus, the driver may use the trajectories displayed to identify whether the trailer will run over an outer lane boundary or the vehicle will run over the centerline of the road onto which the vehicle is turning. In addition, the system and method may determine when jackknifing is likely to occur and display a jackknifing warning in view of the driver when jackknifing is likely to occur. 
     In various implementations, the system and method determines a target trajectory of the vehicle when the vehicle is about to make a turn and guides the driver through the turn based on the target vehicle trajectory. In one example, the system and method guides the driver through the turn by displaying a curve representing the target vehicle trajectory. In another example, the system and method determines a target steering wheel position based on the target vehicle trajectory and displays an arrow representing the target steering wheel position. The system and method may display the target vehicle trajectory and/or the target steering wheel position on an electronic display and/or a windshield of the vehicle. 
     Thus, in addition to informing the driver of a potential problem with the current vehicle trajectory, the system and method may provide a solution to that problem via the target vehicle trajectory. Further, in various implementations, the system and method controls a steering actuator to automatically steer the vehicle through a turn based on the target vehicle trajectory. When the vehicle steering is automatically controlled, the driver may continue to control the throttle of the vehicle and the brakes of the vehicle. 
     Referring now to  FIG. 1 , a vehicle system  10  includes a vehicle  12  and a trailer  14 . The vehicle  12  includes a frame or body  15 , a front axle  16 , a rear axle  18 , a left front wheel  20 , a right front wheel  21 , a left rear wheel  22 , a right rear wheel  23 , a steering system  24 , and a trailer hitch  26  having a distal end or ball  28 . The steering system  24  is operable to turn the left and right front wheels  20  and  21  and thereby turn the vehicle  12 . 
     The steering system  24  includes a steering wheel  30 , a steering column  32 , a steering linkage  34 , and a steering actuator  36 . A driver rotates the steering wheel  30  to turn the vehicle  12  left or right. The steering column  32  is coupled to the steering wheel  30  so that the steering column  32  rotates when the steering wheel  30  is rotated. The steering column  32  may also be coupled to the steering linkage  34  so that rotation of the steering column  32  causes translation of the steering linkage  34 . The steering linkage  34  is coupled to the left and right front wheels  20  and  21  so that translation of the steering linkage  34  turns the left and right front wheels  20  and  21 . 
     The steering actuator  36  is coupled to the steering linkage  34  and is operable to translate the steering linkage  34  and thereby turn the left and right front wheels  20  and  21 . The steering actuator  36  may be a hydraulic and/or electric actuator. If the steering column  32  is coupled to the steering linkage  34 , the steering actuator  36  may reduce the amount of effort that the driver must exert to turn the vehicle  12  left or right. In various implementations, the steering column  32  may not be coupled to the steering linkage  34 , and the steering actuator  36  may translate the steering linkage  34  in response to an electronic signal that is generated based on the position of the steering wheel  30 . When the steering actuator  36  is electronically controlled in this way, the steering system  24  may be referred to as a steer-by-wire system. 
     The trailer  14  includes a frame or body  38 , an axle  40 , a left wheel  42 , a right wheel  43 , and a tongue  44  having a distal end  46 . Although the trailer  14  is depicted as a two-wheel trailer, the principles of the present application apply to a trailer having more than two wheels. The distal end  46  of the tongue  44  may be placed onto the ball  28  of the trailer hitch  26  of the vehicle  12  to couple the trailer  14  to the vehicle  12 . 
     The vehicle  12  further includes a steering angle sensor  48 , a wheel speed sensor  49 , a front camera  50 , a rear camera  52 , a left side camera  54 , a right side camera  56 , a control module  58 , and a user interface device  60 . The steering angle sensor  48  measures a steering angle of the vehicle  12  or another parameter that indicates the steering angle, such as the angular position of the steering column  32 . The steering angle of the vehicle  12  may be an average value of a steering angle  62  of the left front wheel  20  and a steering angle  64  of the right front wheel  21 . The steering angle sensor  48  may be mounted on the steering column  32  as shown or at another location in the steering system  24  between the steering wheel  30  and the left and right front wheels  20  and  21 . The steering angle sensor  48  may include a Hall effect sensor. 
     The wheel speed sensor  49  measures the speed of a wheel of the vehicle  12 . Although the wheel speed sensor  49  is shown mounted to the right front wheel  21  of the vehicle  12 , the wheel speed sensor  49  may measure the speed of another wheel of the vehicle  12 . In various implementations, the vehicle  12  may include multiple wheel speed sensors to measure the speeds of multiple wheels of the vehicle. 
     The front camera  50  captures an image of the environment in front of the vehicle  12 . The rear camera  52  captures an image of the environment to the rear of the vehicle  12 . The left side camera  54  captures an image of the environment on the left side of the vehicle  12 . The right side camera  56  captures an image of the environment on the right side of the vehicle  12 . 
     The control module  58  determines a forward drive trajectory of the vehicle  12  and a forward drive trajectory of the trailer  14  and controls the user interface device  60  to display the forward drive trajectories of the vehicle  12  and the trailer  14 . In addition, the control module  58  determines when jackknifing is likely to occur, and controls the user interface device  60  to provide a jackknifing warning when jackknifing is likely to occur. Further, the control module  58  determines a target trajectory of the vehicle  12  when the vehicle  12  is about to make a turn and controls the user interface device  60  to display the target trajectory. In various implementations, the control module  58  may also control the steering actuator  36  based on the target trajectory of the vehicle  12 . 
     The user interface device  60  may include an electronic display (e.g., a touch display) that displays the images captured by the cameras  50 - 56 . In addition, the electronic display may display the forward drive trajectories of the vehicle  12  and the trailer  14  and/or the target trajectory of the vehicle  12 , for example, as lines or curves that are overlaid onto the images captured by the cameras  50 - 56 . 
     In addition to or instead of the electronic display, the user interface device  60  may include one or more vibrators mounted to, for example, the steering wheel  30  to provide haptic feedback to the driver regarding whether the vehicle  12  is following the target trajectory. For example, when the vehicle  12  is to the right of the target trajectory, the vibrators may vibrate the left side of the steering wheel  30  to direct the driver to turn the steering wheel  30  counterclockwise and thereby turn the vehicle  12  left. In another example, when the vehicle  12  is to the left of the target trajectory, the vibrators may vibrate the right side of the steering wheel  30  to direct the driver to turn the steering wheel  30  clockwise and thereby turn the vehicle  12  right. 
     The vehicle  12  has a mass center  66  that turns on a first circle having a radius  68 , which is a function of the steering angle of the vehicle  12 . The trailer  14  has a longitudinal centerline  70  that turns on a second circle having a radius  72 . The first and second circles may have a common center at a point  74 . The longitudinal centerline  70  of the trailer  14  is oriented at an angle  76  relative to a longitudinal centerline  78  of the vehicle  12 . The angle  76  may be referred to as a hitch angle. 
     The mass center  66  of the vehicle  12  is located a distance  80  from the front axle  16  and a distance  82  from the rear axle  18 . The ball  28  of the trailer hitch  26  is located a distance  84  from the rear axle  18 . The axle  40  of the trailer  14  is located a distance  86  from the distal end  46  of the tongue  44  of the trailer  14 . 
     Referring now to  FIG. 2 , an example implementation of the control module  58  includes an actual steering angle module  102 , a hitch angle module  104 , an environment mapping module  106 , an expected trajectory module  108 , and a jackknifing identification module  110 . The actual steering angle module  102  determines the actual steering angle of the vehicle  12  and outputs the actual steering angle. The actual steering angle module  102  may determine the steering angle of the vehicle  12  based on an input from the steering angle sensor  48 . 
     In one example, the steering angle sensor  48  includes a first sensor that measures the steering angle  62  of the left front wheel  20  and a second sensor that measures the steering angle  64  of the right front wheel  21 . The actual steering angle module  102  may determine the steering angle of the vehicle  12  based on the steering angles  62  and  64  of the left and right front wheels  20  and  21 . For example, the actual steering angle module  102  may determine the steering angle of the vehicle  12  using a relationship such as 
     
       
         
           
             
               
                 
                   
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     where δ is the steering angle of the vehicle  12 , δ o  is the steering angle  62  of the left front wheel  20 , and δ i  is the steering angle of the right front wheel  21 . 
     In another example, the steering angle sensor  48  measures the angular position of the steering column  32 , and the actual steering angle module  102  determines the steering angle of the vehicle  12  based on the steering column position. In another example, the steering angle sensor  48  measures the angular position of the steering wheel  30 , and the actual steering angle module  102  determines the steering angle of the vehicle  12  based on the steering wheel position. 
     The hitch angle module  104  determines the hitch angle (i.e., the angle  76  between the longitudinal centerline  70  of the trailer  14  and the longitudinal centerline  78  of the vehicle  12 ) and outputs the hitch angle. The hitch angle module  104  may determine the hitch angle based on an input from the rear camera  52 , which may include an image of the environment to the rear of the vehicle  12 . Additionally or alternatively, the hitch angle module  104  may determine the hitch angle based on an input from a Hall effect or ultrasonic sensor that measures the hitch angle. 
     The environment mapping module  106  determines one or more parameters of a road on which the vehicle  12  is travelling, the position of the vehicle  12  on the road, and/or whether any obstacles lie in the expected trajectory of the vehicle  12 . Briefly referring to  FIG. 10 , the road parameters may include an outer lane boundary  88  that extends alongside a first road  90  on which the vehicle  12  is currently travelling and a second road  92  onto which the vehicle  12  is turning. The outer lane boundary  88  may be a curb or a lane marking. The road parameters may also include a centerline  94  of the second road  92 . 
     Referring again to  FIG. 2 , the environment mapping module  106  may determine the road parameters based on the image captured by the front camera  50 . Additionally or alternatively, the environment mapping module  106  may receive the road parameters from a vehicle-to-everything (V2X) communication network  96  and/or a satellite communication network  98 . The environment mapping module  106  may also determine the position of the vehicle  12  by communicating with the V2X communication network  96  and/or the satellite communication network  98 . The environment mapping module  106  may include an antenna and/or a global positioning system (GPS) for wirelessly communicating with the V2X communication network  96  and/or the satellite communication network  98 . 
     The environment mapping module  106  may determine whether any obstacles lie in the expected trajectory of the vehicle  12  based on the expected vehicle trajectory and the image captured by the front camera  50 . Additionally or alternatively, the environment mapping module  106  may determine whether any obstacles lie in the expected trajectory of the vehicle  12  by communicating with the V2X communication network  96  and/or the satellite communication network  98 . 
     In addition, the environment mapping module  106  may generate a top view of the vehicle  12  and at least part of the trailer  14  based on the images from the cameras  50 - 56 . The environment mapping module  106  outputs the road parameters, the vehicle position, and/or the location of any obstacles that lie in the expected trajectory of the vehicle  12 . Further, the environment mapping module  106  may generate one or more sets of gridlines representing the surface(s) of the first road on which the vehicle  12  is travelling and/or the second road onto which the vehicle  12  is turning. Each set of gridlines may correspond to one of the images captured by the cameras  50 - 56  or the top view generated by the environment mapping module  106 . For example, a first set of gridlines may represent the road surface in the image captured by the front camera  50 , and a second set of gridlines may represent the road surface in the top view. 
     The expected trajectory module  108  determines an expected trajectory of the vehicle  12  and an expected trajectory of the trailer  14 . The expected trajectory module  108  outputs the expected trajectories of the vehicle  12  and the trailer  14 . The expected vehicle trajectory may include one or more points and/or a curve representing a path through which one or more points on the vehicle  12  are expected to move. For example, the expected vehicle trajectory may include two curves representing the paths through which the left and right front wheels  20  and  21  are expected to move. In another example, the expected vehicle trajectory may include four curves representing the paths through which the four corners of the vehicle  12  are expected to move. 
     Similarly, the expected trailer trajectory may include one or more points and/or a curve representing a path through which the trailer  14  is expected to move. For example, the expected vehicle trajectory may include two curves representing the paths through which the left and right wheels  42  and  43  are expected to move. In another example, the expected vehicle trajectory may include four curves representing the paths through which the four corners of the trailer  14  are expected to move. 
     The expected trajectory module  108  may determine the expected trajectories of the vehicle  12  and the trailer  14  when the vehicle  12  and the trailer  14  are moving forward. In this case, the expected vehicle trajectory may be referred to as an expected forward drive trajectory of the vehicle  12 , and the expected trailer trajectory may be referred to as an expected forward drive trajectory of the trailer  14 . The expected trajectory module  108  may also determine the expected vehicle trajectory and the expected trailer trajectory when the vehicle  12  and the trailer  14  are moving rearward. 
     The expected trajectory module  108  may determine the expected vehicle trajectory based on the steering angle of the vehicle  12  and/or one or more parameters of the vehicle  12 . The vehicle parameters may include a current position of the vehicle  12 , the speed of the vehicle  12 , a wheelbase of the vehicle  12 , a wheel track of the vehicle  12 , and/or the distance  82  between the mass center  66  of the vehicle  12  and the rear axle  18 . The expected trajectory module  108  may receive the current vehicle position from the environment mapping module  106 . The expected trajectory module  108  may determine the speed of the vehicle  12  based on the wheel speed from the wheel speed sensor  49 . The vehicle wheelbase, the vehicle wheel track, and the distance  82  may be predetermined and stored in the expected trajectory module  108 . 
     The expected trajectory module  108  may determine one or more radii of turning paths that the vehicle  12  is expected to follow and determine the expected vehicle trajectory based on the radii. In one example, the expected trajectory module  108  determines the turning radius  68  of the mass center  66  of the vehicle  12  based on the distance  82 , the wheelbase of the vehicle  12 , and the steering angle of the vehicle  12  using a relationship such as 
         R =√{square root over ( a   2   2   +l   2  cot 2  δ)},  (2)
 
     where R is the turning radius  68 , a 2  is the distance  82 , l is the wheelbase of the vehicle, and δ is the steering angle of the vehicle  12 . 
     The expected trajectory module  108  may determine the expected trajectories of other points on the vehicle  12  based on predetermined geometric relationships between the mass center  66  and the other points. The other points may include the left front wheel  20 , the right front wheel  21 , and/or the four corners of the vehicle  12 . In one example, the expected trajectory module  108  determines the turning radius of the left front wheel  20  based on the wheelbase of the vehicle  12 , the steering angle of the vehicle  12 , and the wheel track of the vehicle  12  using a relationship such as 
     
       
         
           
             
               
                 
                   
                     
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     where R i  is the turning radius of the left front wheel  20 , l is the wheelbase of the vehicle  12 , δ is the steering angle of the vehicle  12 , and w is the wheel track of the vehicle  12 . 
     In another example, the expected trajectory module  108  determines the turning radius of the right front wheel  21  based on the wheelbase of the vehicle  12 , the steering angle of the vehicle  12 , and the wheel track of the vehicle  12  using a relationship such as 
     
       
         
           
             
               
                 
                   
                     
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     where R o  is the turning radius of the right front wheel  21 , l is the wheelbase of the vehicle  12 , δ is the steering angle of the vehicle  12 , and w is the wheel track of the vehicle  12 . 
     Relationships (3) and (4) may be used to determine the turning radii of the left and right front wheels  20  and  21 , respectively, when the vehicle  12  is taking a left turn at shown in  FIG. 1 . However, when the vehicle  12  is taking a right turn, the relationships used to determine the turning radii of the left and right front wheels  20  and  21  may be switched. In other words, relationships (3) and (4) may be used to determine the turning radii of the right and left front wheels  21  and  20 , respectively. 
     The expected trajectory module  108  may determine the expected trailer trajectory based on the steering angle of the vehicle  12 , the hitch angle, one or more parameters of the vehicle  12 , and/or one or more parameters of the trailer  14 . The vehicle parameters may include the wheelbase of the vehicle  12 , the wheel track of the vehicle  12 , the current position of the vehicle  12 , the speed of the vehicle  12 , and/or the distance  84  between the rear axle  18  and the ball  28  of the trailer hitch  26 . The trailer parameters may include a wheel track of the trailer  14  and/or the distance  86  between the distal end  46  of the tongue  44  and the axle  40  of the trailer  14 . The trailer wheel track and the distances  84  and  86  may be predetermined. 
     The expected trajectory module  108  may determine one or more radii of turning paths that the trailer  14  is expected to follow and determine the expected trailer trajectory based on the radii. In one example, the expected trajectory module  108  determines the turning radius  72  of the longitudinal centerline  70  of the trailer  14  based on the distances  84  and  86 , the wheelbase of the vehicle  12 , the steering angle of the vehicle  12 , and the hitch angle using a relationship such as 
     
       
         
           
             
               
                 
                   
                     
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     where R t  is the turning radius  72 , b 1  is the distance  84 , b 2  is the distance  86 , l is the wheelbase of the vehicle  12 , δ is the steering angle of the vehicle  12 , and θ is the hitch angle. 
     In another example, the expected trajectory module  108  determines the turning radius  72  based on the vehicle wheelbase, the steering angle  62  of the left front wheel  20 , the vehicle wheel track, and the distances  84  and  86  using a relationship such as 
     
       
         
           
             
               
                 
                   
                     
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     where R t  is the turning radius  72 , l is the vehicle wheelbase, δ i  is the steering angle  62  of the left front wheel  20 , w is the vehicle wheel track, b 1  is the distance  84 , and b 2  is the distance  86 . 
     The expected trajectory module  108  may determine the expected trajectories of other points on the trailer  14  based on predetermined geometric relationships between the longitudinal centerline  70  and the other points. The other points may include the left wheel  42 , the right wheel  43 , and/or the four corners of the trailer  14 . The driver may use the user interface device  60  to provide the dimensions of the trailer  14 , and the expected trajectory module  108  may determine the geometric relationships between the longitudinal centerline  70  and the four corners of the trailer  14  based thereon. In one example, the expected trajectory module  108  determines the turning radius of the left wheel  42  by subtracting one-half of the trailer wheel track from turning radius  72 . In another example, the expected trajectory module  108  determines the turning radius of the right wheel  43  by adding one-half of the vehicle wheel track to the turning radius  72 . 
     The user interface device  60  displays one or more of the images captured by the cameras  50 - 56  and/or the top view generated by the environment mapping module  106 . In addition, the user interface device  60  may display the expected trajectories of the vehicle  12  and the trailer  14 . The user interface device  60  may do this by overlaying the expected trajectories of the vehicle  12  and the trailer  14  onto one or more of the images from the cameras  50 - 56  and/or the top view generated by the environment mapping module  106 . 
     The jackknifing identification module  110  identifies when the vehicle  12  and the trailer  14  are likely to jackknife based on the expected trajectories of the vehicle  12  and the trailer  14 . The jackknifing identification module  110  may identify that the vehicle  12  and the trailer  14  are likely to jackknife when the expected trajectories of the vehicle  12  and the trailer  14  indicate that any portion of the trailer  14  other than the tongue  44  will contact the vehicle  12 . For example, the jackknifing identification module  110  may identify that the vehicle  12  and the trailer  14  are likely to jackknife when the expected trajectories of the vehicle  12  and the trailer  14  indicate that the body  38  of the trailer  14  will contact a rear bumper of the vehicle  12 . The rear bumper may be part of the body  15  of the vehicle. 
     The user interface device  60  displays a jackknifing warning when the jackknifing identification module  110  identifies that the vehicle  12  and the trailer  14  are likely to jackknife. The jackknifing warning indicates that the vehicle  12  and the trailer  14  are likely to jackknife. The jackknifing warning may include text such as “jackknife imminent” and a symbol such as an exclamation mark. 
     The example implementation of the control module  58  shown in  FIG. 2  further includes a turn identification module  112 , a target steering angle module  114 , a target trajectory module  116 , and a steering control module  118 . The turn identification module  112  identifies when the vehicle  12  is going to make a turn. The turn identification module  112  may identify when the vehicle  12  is going to make a turn based on the position of the vehicle  12  and a predetermined route of the vehicle  12 . For example, the turn identification module  112  may identify that the vehicle  12  is going to make a turn when the vehicle position indicate that the vehicle  12  is approaching an intersection and the predetermined route includes a turn at that intersection. The driver may use the user interface device  60  to upload the predetermined route to the turn identification module  112  before making a trip. 
     Additionally or alternatively, the turn identification module  112  may identify when the vehicle  12  is going to make a turn based on the position of the vehicle  12  and a position of a turn signal switch. For example, the turn identification module  112  may identify that the vehicle  12  is going to make a turn when the vehicle position indicate that the vehicle  12  is approaching an intersection and the turn signal switch is on. The turn signal switch may be part of or separate from the user interface device  60 . 
     The target steering angle module  114  determines a target steering angle of the vehicle  12  during a turn and outputs the target steering angle. The target steering angle module  114  may determine the target steering angle when the turn identification module  112  identifies that the vehicle  12  is going to make the turn. The target steering angle module  114  may determine the target steering angle based on the expected trajectories of the vehicle  12  and the trailer  14 , the outer lane boundary  88  that extends along the first and second roads  90  and  92 , and the centerline  94  of the second road  92 . 
     When determining the expected trajectories for use in determining the target steering angle, the expected trajectory module  108  may determine the expected trajectories based on a possible steering angle for the turn instead of the current steering angle. If the expected trajectories satisfy predetermined criteria, the target steering angle module  114  may set the target steering angle equal to the possible steering angle. Otherwise, the expected trajectory module  108  may select another possible steering angle, and the target steering angle module  114  may determine whether that possible steering angle satisfies the predetermined criteria. 
     The target steering angle module  114  may determine the target steering angle based on a relationship between the expected trajectory of the trailer  14  and the outer lane boundary  88 . For example, referring briefly to  FIG. 11 , an expected trajectory  120  of the left front wheel  20  and an expected trajectory  122  of the right front wheel  21  are shown as the vehicle  12  makes a right turn from the first road  90  to the second road  92 . The target steering angle module  114  may determine the target steering angle based on a distance  124  between the expected trajectory  122  and the outer lane boundary  88 . 
     The target steering angle module  114  may determine the target steering angle based on a relationship between the expected trajectory of the vehicle  12  and the centerline  94 . For example, referring briefly to  FIG. 12 , an expected trajectory  126  of the left wheel  42  and an expected trajectory  128  of the right wheel  43  are shown as the trailer  14  makes a right turn from the first road  90  to the second road  92 . The target steering angle module  114  may determine the target steering angle based on a distance  130  between the expected trajectory  126  and the centerline  94 . 
     The target steering angle module  114  may determine the target steering angle in a way that maximizes the distances  124  and  130 . For example, the target steering angle module  114  may determine the target steering angle using a relationship such as 
         I =max{∫ t1   t2   [W   1 ( S   v ( t )− S   v   infra ) 2   +W   2 ( S   tr ( t )− S   tr   infra ) 2   ]dt},   (7)
 
     where I is a cost of a possible steering angle, S v (t) is the expected vehicle trajectory for the possible steering angle as a function of time t, S v   infra  is the centerline  94 , and W 1  is a weighting value associated with a difference between the expected vehicle trajectory and the centerline  94 . Similarly, S tr (t) is the expected trailer trajectory for the possible steering angle as a function of time t, S tr   infra  is the outer lane boundary  88 , and W 2  is a weighting value associated with a difference between the expected trailer trajectory and the centerline  94 . 
     The target steering angle module  114  determines the cost of the possible steering angle by integrating the right side of relationship (7) with respect to time. More specifically, the target steering angle module  114  determines the cost of the possible steering angle by performing the integration over a period from a time t 1  to a time t 2 . The target steering angle module  114  then determines whether the possible steering angle maximizes the cost for that period. If the possible steering angle maximizes the cost for that period, the target steering angle module  114  sets the target steering angle for that period equal to the possible steering angle. Otherwise, the expected trajectory module  108  selects another possible steering angle, and the target steering angle module  114  determine whether that possible steering angle maximizes the cost. Thus, the target steering angle module  114  may determine the target steering angle in an iterative manner. The target steering angle module  114  may determine the target steering angle using relationship (7) and an iterative problem solving approach such as the Hamilton-Jacobi-Bellman equation. The expected trajectory module  108  may initially select a possible steering angle that achieves a vehicle turning radius that is offset from the outer lane boundary  88 , and then adjust the possible steering angle incrementally as iterations are performed. 
     The target steering angle module  114  may determine the target steering angle in the manner described above for a plurality of periods within an overall period that it takes the vehicle  12  and the trailer  14  to complete the turn. In one example, each period may be a few milliseconds. As a result, the target steering angle module  114  may generate a plurality of target steering angles corresponding to a plurality of periods within an overall period of a single turn. 
     The target trajectory module  116  determines a target trajectory of the vehicle  12  based on the target steering angle and outputs the target vehicle trajectory. The target trajectory module  116  may determine the target vehicle trajectory in the same manner that the expected trajectory module  108  determines the expected vehicle trajectory. However, instead of using the current steering angle or a possible steering angle, the target trajectory module  116  may use the target steering angle to determine the target vehicle trajectory. The target vehicle trajectory may include one or more points and/or a curve representing a target path for one or more points on the vehicle  12 . In one example, the target vehicle trajectory includes a curve representing a target path for a point midway between the left and right front wheels  20  and  21 . The target trajectory module  116  may adjust the target vehicle trajectory to avoid any obstacles in the path of the vehicle  12  and/or the trailer  14 . 
     The user interface device  60  displays the target vehicle trajectory by, for example, overlaying the target vehicle trajectory on the image captured by the front camera  50  and/or the top view generated by the environment mapping module  106 . In various implementations, the control module  58  may include a target steering wheel position module (not shown) that determines a target steering wheel position, and the user interface device  60  may display the target steering wheel position. The target steering wheel position module may determine the target steering wheel position based on the target steering angle using, for example, a predetermined relationship between the steering wheel position and the steering angle. 
     The steering control module  118  may control the steering actuator  36  based on the actual position of the steering wheel  30  when the steering system  24  is a steer-by-wire system. Additionally or alternatively, the steering control module  118  may control the steering actuator  36  based on the target steering angle. The steering control module  118  may control the steering actuator  36  based on the target steering angle instead of or in addition to the user interface device  60  displaying the target vehicle trajectory and/or the target steering wheel position. When the steering control module  118  controls the steering actuator  36  based on the target steering angle, the driver may control a throttle (not shown) of the vehicle  12  and brakes (not shown) of the vehicle  12 . 
     Referring now to  FIG. 3 , a method for displaying forward drive trajectories of a vehicle and a trailer and providing a jackknifing warning begins at  202 . The method is described in the context of the modules of  FIG. 2 . However, the particular modules that perform the steps of the method may be different than the modules mentioned below and/or the method may be implemented apart from the modules of  FIG. 2 . 
     At  204 , the actual steering angle module  102  determines the actual steering angle of the vehicle  12 . At  206 , the turn identification module  112  determines whether the vehicle  12  is making a turn while moving forward. If the vehicle  12  is making a turn while moving forward, the method continues at  208 . Otherwise, the method returns to  204 . 
     The turn identification module  112  may determine that the vehicle  12  is making a turn when the steering angle is greater than a predetermined angle. The turn identification module  112  may determine whether the vehicle is moving forward based on the wheel speed from the wheel speed sensor  49  and/or the position of a shift lever. For example, the turn identification module  112  may determine that the vehicle is moving forward when the wheel speed is greater than a predetermined speed and the shift lever is in a forward gear position. The shift lever may be part of or separate from the user interface device  60 . 
     At  208 , the hitch angle module  104  determines the hitch angle. At  210 , the expected trajectory module  108  determines the expected trajectory of the vehicle  12 . At  212 , the expected trajectory module  108  determines the expected trajectory of the trailer  14 . At  214 , the user interface device  60  displays the expected trajectories of the vehicle  12  and the trailer  14 . 
     As discussed above, the user interface device  60  may overlay the expected trajectories of the vehicle  12  and the trailer  14  onto the image captured by the front camera  50  and/or the top view generated by the environment mapping module  106 . Referring briefly to  FIGS. 4-7 , an overview of the process will now be explained.  FIG. 4  shows an example of a top view  402  of the vehicle  12  and the trailer  14  generated by the environment mapping module  106 , and an example of an image  404  captured by the front camera  50 . 
       FIG. 5  shows an example of a first set of gridlines  502  representing the road surface in the top view  402 , and an example of a second set of gridlines  504  representing the road surface in the image  404 .  FIG. 6  shows an example trajectory  602  of the left front wheel  20 , an example trajectory  604  of the right front wheel  21 , an example trajectory  606  of the left wheel  42 , and an example trajectory  608  of the right wheel  43 . The user interface device  60  plots the example trajectories  602 - 608  relative to the first set of gridlines  502 .  FIG. 6  also shows an example trajectory  610  of the left front wheel  20 , an example trajectory  612  of the right front wheel  21 , an example trajectory  614  of the left wheel  42 , and an example trajectory  616  of the right wheel  43 . The user interface device  60  plots the example trajectories  610 - 616  relative to the second set of gridlines  504 . 
       FIG. 7  shows the trajectories  602 - 608  overlaid onto the top view  402  and the trajectories  610 - 616  overlaid onto the image  404 . The trajectories  610 - 616  correspond to the trajectories  602 - 608 , respectively. However, the trajectories  610 - 616  appear differently to account for the different perspectives shown in the top view  402  and the image  404 . The gridlines  502  and  504  enable the user interface device  60  to adjust the appearance of the trajectories  602 - 616  based on the different perspectives shown in the top view  402  and the image  404 . 
     Referring again to  FIG. 3 , at  216 , the jackknifing identification module  110  determines whether the vehicle  12  and the trailer  14  are likely to jackknife. If the vehicle  12  and the trailer  14  are likely to jackknife, the user interface device  60  displays the jackknifing warning at  218  and then the method continues at  220 . Otherwise, the method continues directly to  220 . 
     Referring briefly to  FIG. 8 , the jackknifing identification module  110  may determine that the vehicle  12  and the trailer  14  are likely to jackknife when the trailer left wheel trajectory intersects the vehicle left front wheel trajectory as indicated at  802 . In addition, the jackknifing identification module  110  may determine that the vehicle  12  and the trailer  14  are likely to jackknife when the trailer right wheel trajectory intersects the vehicle right front wheel trajectory as indicated at  804 . 
     Further, an example of a jackknifing warning includes a symbol  806  and a text box  808 . The symbol  806  may include an exclamation mark as shown, and the text box  808  may include text such as “jackknife imminent.” The user interface device  60  overlaid the symbol  806  onto the top view  402 , and overlaid the symbol  806  and the text box  808  onto the image  404 . 
     Referring again to  FIG. 3 , at  220 , the turn identification module  112  determines whether the vehicle  12  and the trailer  14  have competed the turn. The turn identification module  112  may determine that the vehicle  12  and the trailer  14  have competed the turn when the steering angle is less than a predetermined angle. If the vehicle  12  and the trailer  14  have competed the turn, the method continues at  222 . At  222 , the user interface device  60  stops displaying the expected trajectories of the vehicle  12  and the trailer  14 . Also, at  222 , the user interface device  60  may stop displaying the top view generated by the environment mapping module  106  and the view captured by the front camera  50 . If the vehicle  12  and the trailer  14  have not competed the turn, the method returns to  208 . Before the method returns to  208 , the actual steering angle module  102  may determine the actual steering angle of the vehicle  12  once again. 
     Referring now to  FIG. 9 , an example method for providing a turn aid for a driver of a vehicle towing a trailer begins at  902 . The method is described in the context of the modules of  FIG. 2 . However, the particular modules that perform the steps of the method may be different than the modules mentioned below and/or the method may be implemented apart from the modules of  FIG. 2 . 
     At  904 , the environment mapping module  106  determines the position of the vehicle  12 . At  906 , the turn identification module  112  determines whether the vehicle  12  is going to make a turn. If the vehicle  12  is going to make a turn, the method continues at  908 . Otherwise, the method returns to  904 . 
     At  908 , the expected trajectory module  108  selects a possible steering angle of the vehicle  12  during the turn. At  910 , the expected trajectory module  108  determines the expected trajectory of the vehicle  12 . At  912 , the expected trajectory module  108  determines the expected trajectory of the trailer  14 . At  914 , the environment mapping module  106  determines the road parameters. At  916 , the environment mapping module  106  identifies any objects or obstacles in the expected trajectories of the vehicle  12  and the trailer  14 . 
     At  918 , the target steering angle module  114  determines the distance  124  between the expected trajectory  122  and the outer lane boundary  88 . The distance  124  may be the minimum distance between the expected trajectory  122  and the outer lane boundary  88  as shown in  FIG. 11 . At  920 , the target steering angle module  114  determines the distance  130  between the expected trajectory  126  and the centerline  94 . The distance  130  may be the minimum distance between the expected trajectory  126  and the centerline  94  as shown in  FIG. 12 . 
     At  922 , the target steering angle module  114  determines the cost of the possible steering angle using relationship (7). At  924 , the target steering angle module  114  determines whether the possible steering angle maximizes the cost. If the possible steering angle maximizes the cost, the method continues at  926 . Otherwise, the method continues at  928 . 
     At  928 , the target trajectory module  116  determines the target vehicle trajectory. At  930 , the steering wheel position module determines the target steering wheel position. At  932 , the user interface device  60  guides the driver through the turn based on the target vehicle trajectory. 
     Referring briefly to  FIG. 13 , the user interface device  60  may guide the driver through the turn by displaying an arrow  132  indicating the direction in which the vehicle  12  should move in order to follow the target vehicle trajectory. The user interface device  60  may display the arrow  132  in a top view  134  of the vehicle  12  and the trailer  14 . Additionally or alternatively, briefly referring to  FIG. 15 , the user interface device  60  may display a curve  136  representing the target vehicle trajectory in a top view  138  of the vehicle  12  and the trailer  14 . Additionally or alternatively, briefly referring to  FIG. 16 , the user interface device  60  may display a curve  140  representing the target vehicle trajectory and/or an arrow  142  representing the target steering wheel position. The user interface device  60  may display the curve  140  and/or the arrow  142  on a windshield  144  of the vehicle  12 , in which case the user interface device  60  may include a projector. 
     At  934 , the steering control module  118  controls the steering actuator  36  based on the target steering angle. At  936 , the turn identification module  112  determines whether the turn is complete. The turn identification module  112  may determine whether the turn is complete based on the position of the vehicle  12 . For example, referring briefly to  FIG. 14 , the turn identification module  112  may determine that the turn is complete when the vehicle position indicates that the vehicle  12  and the trailer  14  are on the second road  92  as shown. If the turn is complete, the method continues at  938 . Otherwise, the method returns to  908  and the expected trajectory module  108  selects another possible steering angle. Before returning to  908 , the environment mapping module  106  may determine the actual position of the vehicle  12  once again. 
     At  938 , the user interface device  60  stops guiding the driver through the turn based on the target steering angle and the steering control module  118  stops controlling the steering actuator  36  based on the target steering angle. Also, at  938 , the user interface device  60  may stop displaying the top view generated by the environment mapping module  106  and the view captured by the front camera  50 . 
     The foregoing description is merely illustrative in nature and is in no way intended to limit the disclosure, its application, or uses. The broad teachings of the disclosure can be implemented in a variety of forms. Therefore, while this disclosure includes particular examples, the true scope of the disclosure should not be so limited since other modifications will become apparent upon a study of the drawings, the specification, and the following claims. It should be understood that one or more steps within a method may be executed in different order (or concurrently) without altering the principles of the present disclosure. Further, although each of the embodiments is described above as having certain features, any one or more of those features described with respect to any embodiment of the disclosure can be implemented in and/or combined with features of any of the other embodiments, even if that combination is not explicitly described. In other words, the described embodiments are not mutually exclusive, and permutations of one or more embodiments with one another remain within the scope of this disclosure. 
     Spatial and functional relationships between elements (for example, between modules, circuit elements, semiconductor layers, etc.) are described using various terms, including “connected,” “engaged,” “coupled,” “adjacent,” “next to,” “on top of,” “above,” “below,” and “disposed.” Unless explicitly described as being “direct,” when a relationship between first and second elements is described in the above disclosure, that relationship can be a direct relationship where no other intervening elements are present between the first and second elements, but can also be an indirect relationship where one or more intervening elements are present (either spatially or functionally) between the first and second elements. As used herein, the phrase at least one of A, B, and C should be construed to mean a logical (A OR B OR C), using a non-exclusive logical OR, and should not be construed to mean “at least one of A, at least one of B, and at least one of C.” 
     In the figures, the direction of an arrow, as indicated by the arrowhead, generally demonstrates the flow of information (such as data or instructions) that is of interest to the illustration. For example, when element A and element B exchange a variety of information but information transmitted from element A to element B is relevant to the illustration, the arrow may point from element A to element B. This unidirectional arrow does not imply that no other information is transmitted from element B to element A. Further, for information sent from element A to element B, element B may send requests for, or receipt acknowledgements of, the information to element A. 
     In this application, including the definitions below, the term “module” or the term “controller” may be replaced with the term “circuit.” The term “module” may refer to, be part of, or include: an Application Specific Integrated Circuit (ASIC); a digital, analog, or mixed analog/digital discrete circuit; a digital, analog, or mixed analog/digital integrated circuit; a combinational logic circuit; a field programmable gate array (FPGA); a processor circuit (shared, dedicated, or group) that executes code; a memory circuit (shared, dedicated, or group) that stores code executed by the processor circuit; other suitable hardware components that provide the described functionality; or a combination of some or all of the above, such as in a system-on-chip. 
     The module may include one or more interface circuits. In some examples, the interface circuits may include wired or wireless interfaces that are connected to a local area network (LAN), the Internet, a wide area network (WAN), or combinations thereof. The functionality of any given module of the present disclosure may be distributed among multiple modules that are connected via interface circuits. For example, multiple modules may allow load balancing. In a further example, a server (also known as remote, or cloud) module may accomplish some functionality on behalf of a client module. 
     The term code, as used above, may include software, firmware, and/or microcode, and may refer to programs, routines, functions, classes, data structures, and/or objects. The term shared processor circuit encompasses a single processor circuit that executes some or all code from multiple modules. The term group processor circuit encompasses a processor circuit that, in combination with additional processor circuits, executes some or all code from one or more modules. References to multiple processor circuits encompass multiple processor circuits on discrete dies, multiple processor circuits on a single die, multiple cores of a single processor circuit, multiple threads of a single processor circuit, or a combination of the above. The term shared memory circuit encompasses a single memory circuit that stores some or all code from multiple modules. The term group memory circuit encompasses a memory circuit that, in combination with additional memories, stores some or all code from one or more modules. 
     The term memory circuit is a subset of the term computer-readable medium. The term computer-readable medium, as used herein, does not encompass transitory electrical or electromagnetic signals propagating through a medium (such as on a carrier wave); the term computer-readable medium may therefore be considered tangible and non-transitory. Non-limiting examples of a non-transitory, tangible computer-readable medium are nonvolatile memory circuits (such as a flash memory circuit, an erasable programmable read-only memory circuit, or a mask read-only memory circuit), volatile memory circuits (such as a static random access memory circuit or a dynamic random access memory circuit), magnetic storage media (such as an analog or digital magnetic tape or a hard disk drive), and optical storage media (such as a CD, a DVD, or a Blu-ray Disc). 
     The apparatuses and methods described in this application may be partially or fully implemented by a special purpose computer created by configuring a general purpose computer to execute one or more particular functions embodied in computer programs. The functional blocks, flowchart components, and other elements described above serve as software specifications, which can be translated into the computer programs by the routine work of a skilled technician or programmer. 
     The computer programs include processor-executable instructions that are stored on at least one non-transitory, tangible computer-readable medium. The computer programs may also include or rely on stored data. The computer programs may encompass a basic input/output system (BIOS) that interacts with hardware of the special purpose computer, device drivers that interact with particular devices of the special purpose computer, one or more operating systems, user applications, background services, background applications, etc. 
     The computer programs may include: (i) descriptive text to be parsed, such as HTML (hypertext markup language) or XML (extensible markup language), (ii) assembly code, (iii) object code generated from source code by a compiler, (iv) source code for execution by an interpreter, (v) source code for compilation and execution by a just-in-time compiler, etc. As examples only, source code may be written using syntax from languages including C, C++, C#, Objective C, Haskell, Go, SQL, R, Lisp, Java®, Fortran, Perl, Pascal, Curl, OCaml, Javascript®, HTML5, Ada, ASP (active server pages), PHP, Scala, Eiffel, Smalltalk, Erlang, Ruby, Flash®, Visual Basic®, Lua, and Python®. 
     None of the elements recited in the claims are intended to be a means-plus-function element within the meaning of 35 U.S.C. §112(f) unless an element is expressly recited using the phrase “means for,” or in the case of a method claim using the phrases “operation for” or “step for.”