Patent Publication Number: US-9849878-B2

Title: System and method for providing a corrected lane following path through a curve for trailering vehicles

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     This invention relates generally to a system and method for providing lateral control for lane centering, lane keeping and/or lane changing purposes in an autonomously driven or semi-autonomously driven vehicle that is towing a trailer and, more particularly, to a system and method for providing lateral control for lane centering, lane keeping and/or lane changing purposes in an autonomously driven or semi-autonomously driven vehicle that is towing a trailer, where the system provides a corrected vehicle steering path if the trailer will cross out of the vehicle lane when traveling through a curve if the vehicle follows a current path. 
     Discussion of the Related Art 
     The operation of modern vehicles is becoming more autonomous, i.e., vehicles are able to provide driving control with less driver intervention. Cruise control systems have been on vehicles for a number of years where the vehicle operator can set a particular speed of the vehicle, and the vehicle will maintain that speed without the driver operating the throttle. Adaptive cruise control systems have been recently developed in the art where not only does the system maintain the set speed, but also will automatically slow the vehicle down in the event that a slower moving preceding vehicle is detected using various sensors, such as radar and cameras. Certain modern vehicles also provide autonomous parking where the vehicle will automatically provide the steering control for parking the vehicle. Some vehicle systems provide automatic braking to prevent rear-end collisions. As vehicle systems improve, they will become more autonomous with the goal being a completely autonomously driven vehicle, where future vehicles may employ autonomous systems for lane changing, passing, turns away from traffic, turns into traffic, etc. 
     U.S. Pat. No. 8,170,739 issued May 1, 2012 to Lee, titled, Path Generation Algorithm for Automated Lane Centering and Lane Changing Control System, assigned to the Assignee of this application and herein incorporated by reference, discloses a system for providing vehicle path generation for automated lane centering and/or lane keeping purposes. The system detects lane markings on the roadway, generates a desired vehicle path in the travel lane, and provides automatic steering that maintains the vehicle in the lane. 
     Although the system and method for providing path generation for automated lane centering and lane keeping purposes disclosed in the &#39;739 patent is effective for steering the vehicle to stay in the travel lane, the system and method is not applicable for maintaining a towed vehicle in the lane even though the towing vehicle stays in the lane when the vehicle travels around a curve. 
     SUMMARY OF THE INVENTION 
     The present disclosure describes a system and method for providing vehicle steering control in an autonomously driven or semi-autonomously driven vehicle that is towing a trailer so as to prevent the trailer from crossing out of a travel lane through a curve that the vehicle is traveling along. The method determines a radius of curvature of road, a lane width of the travel lane, a length of the trailer, and a current steering angle of the vehicle. The method determines a current turn radius of the vehicle for traveling through the curve using the current steering angle and determines a turn radius of the trailer using the current turn radius of the vehicle. The method determines that the trailer will cross out of the travel lane based on the curvature of the curve and the turn radius of the trailer. The method calculates a start turn radius of the vehicle for a start location of the curve, an end turn radius of the vehicle for an end location of the curve, and a turn end point proximate the end location or a turn start point proximate the start location. The method provides initial and boundary conditions for determining a desired path of the vehicle through the curve that prevents the trailer from crossing out of the lane and determines the desired path based on the initial and boundary conditions by solving a polynomial equation. 
     Additional features of the present invention will become apparent from the following description and appended claims, taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an illustration of a vehicle towing a trailer and approaching a curve in a travel lane; 
         FIG. 2  is an illustration showing the vehicle and the trailer traveling through the curve; 
         FIG. 3  is a flow chart diagram showing a process for warning a vehicle driver that the trailer may cross out of the lane when traveling through a curve; 
         FIG. 4  is a flow chart diagram similar to the flow chart diagram shown in  FIG. 3 , and including providing turning recommendations for the driver so that the trailer does not cross out of the travel lane; 
         FIG. 5  is an illustration of a vehicle towing a trailer and traveling through a curve along a wide turn radius; 
         FIG. 6  is an illustration of a vehicle towing a trailer and traveling through a curve along a narrow turn radius; 
         FIG. 7  is a block diagram of a path prediction system for providing automated vehicle steering; 
         FIG. 8  is a flow chart diagram showing a process for providing a path for the vehicle to follow for the wide turn radius; and 
         FIG. 9  is a flow chart diagram showing a process for providing a path for a vehicle to follow for the narrow turn radius. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     The following discussion of the embodiments of the invention directed to a system and method for providing lateral control for lane centering, lane keeping and/or lane changing purposes in an autonomously driven or semi-autonomously driven vehicle that is towing a trailer is merely exemplary in nature, and is in no way intended to limit the invention or its applications or uses. 
       FIG. 1  is an illustration  10  showing a vehicle  14  towing a trailer  16  by a hitch  18  and traveling in a travel lane  12  of a roadway. The trailer  16  is shown merely for representation purposes in that it can be any vehicle being towed by the vehicle  14 , such as boats, mobile homes, etc. The vehicle  14  is approaching a curve  20  in the lane  12  and is following along a travel path  22  at the center of the lane  12  that causes the vehicle  14  to stay within the lane  12 . The vehicle  14  includes suitable sensors  24 , such as cameras, radar, lidar, etc., that may be applicable to detect lane markings, objects, the curve  20 , etc., consistent with the discussion herein. The vehicle  14  also includes a map database  26 , a display  30 , a GPS unit  34  and a controller  28 . The controller  28  is intended to represent all of the various modules, controllers, processors, electronic control units (ECUs), etc. that are necessary to perform and operate the various algorithms and processes discussed herein. The map database  26  stores map information at any level of detail that is available, such as the number of travel lanes, travel lane patterns, etc. The travel path  22  can be displayed on the display  30 . The vehicle  14  and the trailer  16  are shown in phantom in the illustration  10  when traveling around the curve  20  along the path  22  to show that the vehicle  14  may stay within the travel lane  12 , but the trailer  16  may cross out of the lane  12 . 
     As is well understood, vehicles and trailers have a variety of sizes and lengths each possibly having a different wheel base l, trailer length, trailer width, hitch length, etc. that define the turn radius of the vehicle  14  and trailer  16  when going around the curve  20 . Further, vehicle roadways may have different widths and roadway curves have different radius of curvatures. 
     The present invention proposes identifying the predicted path of the vehicle  14  through the curve  20 , whether the vehicle  14  is being autonomously driven, semi-autonomously driven and/or mechanically driven, before the vehicle  14  enters the curve  20  to determine whether the trailer  16  will cross out of the lane  12 , and if so, provide one or more remedial actions. In one embodiment, if the controller  28  determines that the predicted path of the vehicle  14  will cause the trailer  16  to cross out of the lane  12 , then the controller  28  will provide a suitable warning, such as an icon on the display  30 , haptic seat, haptic steering wheel, warning chimes, etc., prior to the vehicle  14  reaching the curve  20 , such as about 5 seconds before. The display  30  may illustrate the predicted path of the vehicle  14  and the trailer  16 . In another embodiment, the controller  28  may not only warn the vehicle driver that the trailer  16  may cross out of the lane  12 , but also may show a path on the display  30  that the vehicle  14  should follow so that the trailer  16  does not cross out of the lane  12  when traveling through the curve  20  so as to provide a desired steering path for the driver. In another embodiment, where the vehicle  14  is being autonomously driven, the system will cause the vehicle  14  to be steered along a corrected lane following path or lane keeping path to prevent the trailer  16  from crossing out of the lane  12  in the curve  20 . 
       FIG. 2  is an illustration  34  showing the vehicle  14  and the trailer  16  traveling through the curve  20 . In the illustration  34 , for a particular vehicle steering angle δ and for a particular wheel base l of the vehicle  14 , the turn radius R f  at the front of the vehicle  14  through the curve  20  can be calculated as: 
     
       
         
           
             
               
                 
                   
                     R 
                     f 
                   
                   = 
                   
                     
                       l 
                       δ 
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     Once the turn radius R f  of the vehicle  14  is known, the turn radius R b  at the rear wheels of the vehicle  14 , the turn radius R l  at the hitch point of the trailer  16 , and the turn radius R t  at the rear of the trailer  16  can be calculated as:
 
 R   b =√{square root over ( R   f   2 −( l+a   1 ) 2 )},  (2)
 
 R   l =√{square root over ( R   f   2 −( l+a   1 ) 2   +b   1   2 )},  (3)
 
 R   t =√{square root over ( R   f   2 −( l+a   1 ) 2   +b   1   2   −b   2   2 )},  (4)
 
where a 1  is the distance between the front wheels and the front bumper of the vehicle  14 , b 1  is the length of the hitch  18 , and b 2  is the length of the trailer  16 , which would be known or could be calculated from a suitable sensor (not shown). It is noted that the turn radius R t  of the trailer&#39;s end point is smaller than the turn radius R f  of the vehicle  14 , and the turn radius R t  gets smaller as the length of the trailer  16  gets longer.
 
     In order to determine whether the trailer  16  will cross out of the travel lane  12  when in the curve  20 , the radius of curvature of the curve  20  and the width of the trailer  16  need to be known. The radius of curvature of the curve  20  can be obtained from cameras, the map database  26 , information from the GPS unit  32 , or otherwise, and the turn radius R f  is obtained by equation (1). Using these two radius values, the width of the trailer  16 , the width of the lane  12  and equation (4), the controller  28  can determine whether part of the trailer  16  will cross out of the lane  12  in the curve  20  within some predetermined tolerance, such as +/−20 cm. For example, if the width of the lane  12  is 3.5 m, the curve  20  has a 200 m radius of curvature, l is 2.9464 m, a 1  is 1.105 m, b 1  is 0.55 m, b 2  is 14.63 m, and the trailer width is 2.5908 m, the controller  28  can determine using equation (4) that the turn radius R t  at a center of the trailer&#39;s end is 199.443 m, which is less than the radius of curvature of the curve  20 . By knowing the width of the trailer  16  and the width of the lane  12 , the controller  28  can then determine that the end of the trailer  16  will cross out of the travel lane  12 , where the controller  28  can then provide a warning to the vehicle driver in advance. 
       FIG. 3  is a flow chart diagram  40  showing a process for determining whether to warn the vehicle driver that the trailer  16  will cross out of the lane  12  when traveling through the curve  20  along the current vehicle path as discussed above. At box  42 , the algorithm identifies a curve in the roadway at some predetermined time before the vehicle  14  reaches the curve  20 , such as 5 seconds, and also, identifies the radius of the curve  20  and the lane width of the curve  20  at a certain sample time. The algorithm identifies the length of the trailer  16  at box  44  and determines the vehicle steering angle δ at box  46 . The algorithm calculates the trailer&#39;s turn radius R t  at box  48  in the manner discussed above. The algorithm then compares the trailer&#39;s turn radius R t  with the radius of the curve  20  at box  50 , and then determines whether the trailer  16  will cross out of the lane  12  using the width of the lane  12  and the width of the trailer  16  at decision diamond  52  within the predetermined tolerance. If the trailer  16  will not cross out of the lane  12  at the decision diamond  52 , then the algorithm does not provide a warning and continues to monitor the vehicle path at box  54 , and the algorithm ends at box  56 . If the algorithm determines that the trailer  16  will cross out of the lane  12  at the decision diamond  52 , then the algorithm determines how soon the vehicle  14  will enter the curve  20  at box  58 , and provide the warning at box  60  if the vehicle  14  will enter the curve  20  within some predetermined period of time, such as 5 seconds. The algorithm can also show the predicted trailer path on the display  30  at box  62  before the vehicle  14  enters the curve  20 . 
     In addition to warning the vehicle driver that the trailer  16  may cross out of the travel lane  12  for the current vehicle path, the algorithm can also provide recommendations for steering, such as display a vehicle path that the vehicle driver can steer along, to prevent the trailer  16  from crossing out of the travel lane  12 . In order to perform this feature, the algorithm determines a desired steering angle δ desired  that will maintain the trailer  16  within the lane  12  once the vehicle  14  has entered the curve  20  as: 
     
       
         
           
             
               
                 
                   
                     δ 
                     desired 
                   
                   = 
                   
                     
                       
                         2 
                         ⁢ 
                         l 
                       
                       
                         
                           3 
                           ⁢ 
                           
                             R 
                             f 
                           
                         
                         - 
                         
                           R 
                           t 
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     The algorithm then compares the desired steering angle δ desired  with the current steering angle δ current  when the vehicle  14  has entered the curve  20 , and if the desired steering angle δ desired  is different than the current steering angle δ current  outside of some tolerance, then the algorithm will display a change in the vehicle steering path to allow the driver to steer the vehicle  14  along the desired path to prevent the trailer  16  from crossing out of the lane  12 . Alternately, or in addition to, the vehicle systems can provide audible instructions to provide more or less left or right turning to maintain the desired steering angle δ desired . 
       FIG. 4  is a flow chart diagram  70  showing this embodiment of the invention, where like boxes to the flow chart diagram  40  are identified by the same reference number. In the diagram  70 , after the algorithm warns the driver that the trailer  16  may travel outside of the lane  12 , the algorithm will determine whether the vehicle  14  has entered the curve  20  at decision diamond  72 , and if not, return to the box  60  to continue warning the driver. If the vehicle  14  has entered the curve  20  at the decision diamond  72 , then the algorithm calculates the desired steering angle δ desired  to maintain the trailer  16  within the travel lane  12  through the curve  20  at box  74 , and then determines whether the difference between the desired steering angle δ desired  and the current steering angle δ current  is within the tolerance at decision diamond  76 , where the algorithm ends at box  56  if it is. If the difference between the desired steering angle δ desired  and the current steering angle δ current  is outside of the tolerance at the decision diamond  76 , then the algorithm provides instructions for the driver for a different steering angle at box  78 , and shows the trailer path at the box  62 . 
     In a second aspect of the invention, the vehicle  14  is being driven autonomously or semi-autonomously, where the vehicle is being controlled by determining the desired vehicle path and automatically steering the vehicle  14  along that path. In this embodiment, in order to prevent the trailer  16  from crossing out of the lane  12  along the curve  20 , the algorithm generates a corrected lane following or lane keeping path, if necessary, for the vehicle  14  to be steered along through the curve  20  considering the trailer&#39;s turn radius R t , the road curvature ρ, i.e., the road radius, the lane width, the trailer length b 2 , the vehicle wheel base l, etc., as discussed above. 
     The lane following or lane keeping algorithm may provide two different path planning approaches for navigating through the curve  20 . In a first turning approach, the algorithm calculates a vehicle path that provides a wide turn through the curve  20 , where the turn starts at the beginning of the curve. This approach is illustrated in  FIG. 5  by illustration  80  showing the vehicle  14  as it enters the curve  20  and in phantom in the curve  20 . In this approach, the vehicle  14  begins its turn from the current path  22  to a wide turn path  82  at the very beginning of the curve  20  identified by a turn start point  84 . Because this is a wider turn through the curve  20 , the turn will end at point  86  before the end of the curve  20 , where the vehicle  14  will begin traveling straight. In this embodiment, the start turn radius of the vehicle  14  at the point  84  is R f , which is 200 m in the example above, the end turn radius of the vehicle  14  at the point  86  is 
                   3   ⁢     R   f       -     R   t       2     ,         
which is 200.28 m in the example above, and the turn end point before the end of the curve  20  is:
 
                         R   f   2     -       (         R   f     +     R   t       2     )     2         ,           (   6   )               
which is 10.55 m before the end of the curve  20  in the example above.
 
     A second turning approach provides a narrow turn from the path  22 , but having a later turn start while the vehicle  14  is in the curve  20 . This approach is illustrated in  FIG. 6  by illustration  90  showing the vehicle  14  as it enters the curve  20  and in phantom in the curve  20 . In this approach, the vehicle  14  begins its turn from the current path  22  to a narrow turn path  92  after the beginning of the curve  20  identified by a turn start point  94 . Because this is a narrower turn through the curve  20 , the turn will end at point  96  at the very end of the curve  20  where the vehicle  14  will begin traveling straight. In this embodiment, the start turn radius of the vehicle  14  at the point  94  is 
                   3   ⁢     R   f       -     R   t       2     ,         
which is 200.28 m in the example above, the end turn radius of the vehicle  14  at the point  96  is R f , which is 200 m in the example above, and the turn start point after the beginning of the curve  20  is:
 
                         R   f   2     -       (         R   f     +     R   t       2     )     2         ,           (   7   )               
which is 10.55 m after the beginning of the curve  20  in the example above.
 
       FIG. 7  is a schematic block diagram of a system  100  that provides autonomous path control for a vehicle when changing lanes, either on a straight road or a curved road, and lane centering in an autonomous or semi-autonomous vehicle system. The discussion below is a general discussion of providing a desired path in an autonomously driven or semi-autonomously driven vehicle as more specifically discussed in the &#39;739 patent. The system  100  includes a desired path generation processor  102  that generates a desired steering path for the vehicle  14 . For any purpose, such as lane changing, curve navigation, object avoidance, etc., the desired steering path is represented as a series of lateral offsets, heading angles and longitudinal distances over a time period that the steering change will take place. 
     The system  100  uses measured roadway parameters, such as vehicle lateral offset y r , roadway curvature ρ and vehicle yaw angle φ r  with respect to the vehicle&#39;s centered coordinate system at the path generation processor  102 . The roadway is modeled as a second order polynomial equation as:
 
 y   r ( x )= Ax   2   +Bx+C, 0&lt; X&lt;x   range   (8)
 
where x range  represents the range of a forward vision camera on the vehicle  14 .
 
     From the geometric relationship between the roadway and the roadway representation of equation (8), the coefficients of equation (8) with the measured roadway parameters y r , ρ and φ r  can be related as: 
                     A   =     ρ   2       ,           (   9   )                 B =tan φ r ,  (10)
 
 C=y   r (0).  (11)
 
     Using the roadway lateral offset y r , the heading angle φ r  and the roadway curvature ρ, the path generation processor  102  generates a smooth desired path by solving a fifth order polynomial equation provided as:
 
 y   d ( t )= a   5   x   d   5 ( t )+ a   4   x   d   4 ( t )+ a   3   x   d   3 ( t )+ a   2   x   d   2 ( t )+ a   1   x   d   1 ( t )+ a   0 .  (12)
 
     The fifth order polynomial path generation captures the roadway parameters y r , ρ and φ r  at the beginning and the end of the path and guarantees the smoothness of the path up to the second order path derivatives. In addition, the path can be obtained by a few simple algebraic computations using the road geometry measurement, thus it does not require heavy computing power. 
     This path information including state variable x d , lateral position y d , and heading angle φ d  is provided to a comparator  104  that receives a signal identifying a predicted vehicle path from a path prediction processor  106 , discussed below, and provides an error signal between the desired path and the predicted path. The lateral speed v y , the yaw angle φ and the lateral position y r  of the vehicle  14  are predicted or estimated over the turn change completion time. After the roadway model of equation (8) is obtained, the roadway lateral position y r  and the yaw angle φ r  can be predicted at the path prediction processor  106  using a vehicle dynamic model:
 
 {dot over (x)}   r   =A   r   x   r   +B   r   δ+G   r ρ,  (13)
 
 z   r   =c   r   x   r ,  (14)
 
with:
 
 x   r   =[y   r  φ r    v   y    r]   T ,  (15)
 
                       B   r     =       [         0       0           C   f     m             aC   f     I           ]     T       ,           (   16   )                   C   r     =     [         1       0       0       0           0       1       0       0         ]       ,           (   17   )                 G   r =[0  v   x  0 0] T ,  (18)
 
                       A   r     =     [         0         v   x           -   1         0           0       0       0         -   1             0       0         -         C   f     +     C   r         mv   x                     bC   r     -     aC   f         mv   x       -     v   x               0       0             bC   r     -     aC   f         Iv   x             -           a   2     ⁢     C   f       +       b   2     ⁢     C   r           Iv   x               ]       ,           (   19   )               
where c f  and c r  are the concerning stiffnesses of the front wheels and rear wheels of the vehicle  14 , respectively, a and b are the distances from the center of gravity of the vehicle  14  to the front and rear axles, respectively, m is the vehicle mass, δ is the steering angle and I z  is the moment of inertia around the center of mass of the vehicle  14  perpendicular to the plane where the vehicle  14  is located.
 
     The error signal from the comparator  104  is sent to a lane change controller  108  that provides a steering angle command signal δ cmd  for path steering that minimizes the error signal. The lane change controller  108  generates a sequence of future steering angle commands δ cmd  that minimize the orientation and offset errors between the desired vehicle path and the predicted vehicle path. A lateral motion control algorithm in the controller  108  compares the predicted vehicle path to the vehicle&#39;s desired path (x d ,y d ), and calculates the steering angle command signal δ cmd  by minimizing the path difference, where the steering angle command signal δ cmd  is obtained by: 
                         δ   cmd     ⁡     (   k   )       =         ∑     i   =   0       N   -   1       ⁢         (         z   d     ⁡     (     k   +   i   +   1     )       -       CA     i   +   1       ⁢     x   ⁡     (   k   )           )     T     ⁢     Q   ⁡     (     k   +   i   +   1     )       ⁢     (       CA   i     ⁢   B     )               ∑     i   =   0       N   -   1       ⁢       (       CA   i     ⁢   B     )     ⁢     Q   ⁡     (     k   +   i   +   1     )       ⁢     (       CA   i     ⁢   B     )         +     R   ⁡     (   k   )             ,           (   20   )               
and where x=[y φ v y  r] T , z d (k)=[y d  φ d ] T , Q and R are weighting matrices used in the minimization with the system matrices definitions
 
               A   =     e       A   r     ⁢     t   s           ,     B   =       ∫   0     t   s       ⁢       e       A   r     ⁢   α       ⁢     B   r     ⁢   d   ⁢           ⁢   α               
and
 
     
       
         
           
             C 
             = 
             
               
                 [ 
                 
                   
                     
                       1 
                     
                     
                       0 
                     
                     
                       0 
                     
                     
                       0 
                     
                   
                   
                     
                       0 
                     
                     
                       1 
                     
                     
                       0 
                     
                     
                       0 
                     
                   
                 
                 ] 
               
               . 
             
           
         
       
     
     The steering angle command signal δ cmd  is sent to a steering system  110  that provides the steering control for a vehicle system  112 . The steering system  110  receives the steering angle command signal δ cmd  and provides a steering torque command signal τ cmd  to achieve the desired steering angle δ desired  as commanded. 
     As the vehicle  14  turns, various sensors on the vehicle  14 , such as a steering angle sensor, speedometer and yaw rate sensor, provide measured signals of the motion of the vehicle  14 . These measured vehicle motion signals are sent from the vehicle system  112  to the desired path generation processor  102 . Inertial sensors, such as a speedometer, a rate gyro and a steering angle sensor, can be used to measure vehicle states, such as longitudinal speed v x , longitudinal acceleration a x , lateral acceleration a y , yaw rate r and steering angle δ. The lateral speed v y  is estimated as: 
                       [             v     ^   .       y               r     ^   .             ]     =         [           -         C   f     +     C   r         mv   x                     bC   r     -     aC   f         mv   x       -     v   x                     bC   r     -     aC   f         Iv   x             -           a   2     ⁢     C   f       +       b   2     ⁢     C   r           Iv   x               ]     ·     [             v   ^     y               r   ^           ]       +       [             C   f     m                 aC   f     I           ]     ·   δ     +     K   ·     [         0             r   -     r   ^             ]           ,           (   21   )               
where r is a measured vehicle yaw rate, {circumflex over (v)} y  and {circumflex over (r)} are the estimated lateral speed and the vehicle yaw rate, respectively, and K is a yaw rate observer gain.
 
     The vehicle motion information is also provided to a vehicle state estimation processor  114  that provides estimated vehicle state signals, namely, lateral offset y, yaw angle φ, vehicle lateral speed v y  and vehicle yaw rate r. The vehicle state estimation processor  114  uses a vehicle model to filter the estimated vehicle state signals. The state signals are sent to the path prediction processor  106  that predicts the vehicle path for the next few instances in time based on that information as discussed above. The path prediction processor  106  estimates the vehicle future path based on the current vehicle speed v x , yaw rate r and steering angle δ. 
     The camera signals and the filtered sensor signals from the vehicle system  112  are also provided to a lane mark detection processor  116  that corrects the parameters of the lane markings based on the motion of the vehicle  14 . The lane mark detection processor  116  recognizes the lane markings in the roadway and represents them with the parameters of lane curvature, tangential angle and lateral offset, where the output of the lane mark detection processor  116  is the yaw angle φ r , the lateral position y r , the curvature ρ of the roadway and a rate of change in the roadway curvature Δρ of the roadway. The position of the lane markings relative to the vehicle  14  is then sent to the desired path generation processor  102  through a roadway estimation processor  120  to provide the desired path generation updating. 
     When the curve  20  is detected, the present invention proposes correcting the desired steering path to prevent the trailer  16  from crossing out of the lane  12  as it travels around the curve  20 . More particularly, the path control algorithm revises the roadway curvature ρ and the rate of change in the roadway curvature Δρ with a new roadway curvature ρ new  and a new rate of change in roadway curvature Δρ new  in a path correction processor  118  that is then used by the road estimation processor  120 . If no curve is detected, then the roadway curvature ρ and the rate of change in the roadway curvature Δρ pass unchanged through the processor  118 . Specifically, for the wide turn path approach the processor  118  calculates the new roadway curvature ρ new  and the new rate of change in roadway curvature Δρ new  as: 
                       ρ   new     =     1     R   f         ,           (   22   )                   Δρ   new     =     2     D   ⁡     (       R   f     -     R   t       )           ,           (   23   )               
and for the narrow turn approach the processor  118  calculates the new roadway curvature ρ new  and the new rate of change in roadway curvature Δρ new  as:
 
                       ρ   new     =     2       3   ⁢     R   f       -     R   t           ,           (   24   )                   Δρ   new     =     2     D   ⁡     (       R   f     -     R   t       )           ,           (   25   )               
where D is a tuning parameter to adjust for driver aggressiveness.
 
     When the lane centering or lane keeping algorithm identifies the curve  20 , the algorithm uses the start point, the end point and the rate of change in the roadway curvature Δρ new  in combination with the path generation operation in the path generation processor  102  for either the wide turn approach or the narrow turn approach, where the algorithm will be previously programmed with one or the other of the wide turn approach or the narrow turn approach. For both of these approaches, the fifth order polynomial of equation (12) is solved with different initial and boundary conditions by first normalizing the polynomial trajectory as:
 
 y   n ( x   n )= a   0   +a   1   x   n   +a   2   x   n   2   +a   3   x   n   3   +a   4   x   n   4   +a   5   x   n   5 ,  (26)
 
                       0   ≤     x   n       =       x       v   x     ⁢   Δ   ⁢           ⁢   T       ≤   1       ,           (   27   )                 y   n   =y/L,   (28)
 
     where L is the lane width and ΔT is the time for the vehicle  14  to travel through the lane  12 . 
     For the wide turn approach, initial conditions for the start point  84  are given as:
 
 y   n (0)=0,  (29)
 
 y′   n (0)=0,  (30)
 
                         y   n   ″     ⁡     (   0   )       =         (       v   x     ⁢   Δ   ⁢           ⁢   T     )     2         R   f     ⁢   L         ,           (   31   )               
and boundary conditions for the end point  86  are given as:
 
                         y   n     ⁡     (   1   )       =           y   lane     ⁡     (       v   x     ⁢   Δ   ⁢           ⁢   T     )       +   L     L       ,           (   32   )                     y   n   ′     ⁡     (   1   )       =         y   lane   ′     ⁡     (       v   x     ⁢   Δ   ⁢           ⁢   T     )       ·         v   x     ⁢   Δ   ⁢           ⁢   T     L         ,           (   33   )                     y   n   ″     ⁡     (   1   )       =       2   ⁢       (       v   x     ⁢   Δ   ⁢           ⁢   T     )     2           (       3   ⁢     R   f       -     R   t       )     ⁢   L         ,           (   34   )               where:   y   lane   =c   3   x   3   c   2   x   2   c   1   x+c   0 ,  (35)
 
and where c 0 , c 1 , c 2  and c 3  are measured values from a front camera.
 
     For the narrow turn approach, different initial and boundary conditions are used to solve the polynomial equation (26), where the initial conditions for the start point  94  are given as:
 
 y   n (0)=0,  (36)
 
 y′   n (0)=0,  (37)
 
                         y   n   ″     ⁡     (   0   )       =       2   ⁢       (       v   x     ⁢   Δ   ⁢           ⁢   T     )     2           (       3   ⁢     R   f       -     R   t       )     ⁢   L         ,           (   38   )               
and the boundary conditions for the end point  96  are given as:
 
     
       
         
           
             
               
                 
                   
                     
                       
                         y 
                         n 
                       
                       ⁡ 
                       
                         ( 
                         1 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           
                             y 
                             lane 
                           
                           ⁡ 
                           
                             ( 
                             
                               
                                 v 
                                 x 
                               
                               ⁢ 
                               Δ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               T 
                             
                             ) 
                           
                         
                         + 
                         L 
                       
                       L 
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   39 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         y 
                         n 
                         ′ 
                       
                       ⁡ 
                       
                         ( 
                         1 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           y 
                           lane 
                           ′ 
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               v 
                               x 
                             
                             ⁢ 
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             T 
                           
                           ) 
                         
                       
                       · 
                       
                         
                           
                             v 
                             x 
                           
                           ⁢ 
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           T 
                         
                         L 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   40 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       y 
                       n 
                       ″ 
                     
                     ⁡ 
                     
                       ( 
                       1 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         2 
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 v 
                                 x 
                               
                               ⁢ 
                               Δ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               T 
                             
                             ) 
                           
                           2 
                         
                       
                       
                         
                           R 
                           f 
                         
                         ⁢ 
                         L 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   41 
                   ) 
                 
               
             
           
         
       
     
       FIG. 8  is a flow chart diagram  130  showing a process for calculating the path  82  for the wide turn approach when the vehicle  14  enters the curve  20  as discussed above. At box  132 , the algorithm obtains the roadway curvature ρ, the lane width, and the necessary measurements from the map database  26  and the forward looking camera on the vehicle  14 . The algorithm obtains the length of the trailer  16  at box  134  and obtains the vehicle steering angle δ at box  136 . The algorithm then calculates the trailer&#39;s turn radius R t  at box  138  and determines whether based on the current path of the vehicle  14  the trailer  16  will cross out of the lane  12  in the curve  20  at decision diamond  140 . If the trailer  16  will not cross out of the lane  12  during the turn through the curve  20  at the decision diamond  140 , then the algorithm will cause the vehicle  14  to continue along its current path at box  142 , and the algorithm will end at box  144 . If the trailer  16  will cross out of the lane  12  for the current vehicle path at the decision diamond  140 , then the algorithm calculates the start turn radius R f  of the vehicle  14  at box  146 , calculates the end turn radius 
                 3   ⁢     R   f       -     R   t       2         
of the vehicle  14  at box  148 , and calculates the turn end point  86  from equation (6) before the end of the curve  20  at box  150 . The algorithm will then update the initial boundary and conditions for the path generation problem from equations (29)-(34) at box  152  and use those conditions for the path generation operation in the processor  92  at box  154 . The algorithm will then provide the necessary turning commands for the new path at box  156  and report the new trailer path to the driver at box  158 .
 
       FIG. 9  is a flow chart diagram  160  showing a process for calculating the path  92  for the narrow turn approach when the vehicle  14  enters the curve  20 , as discussed above, that is the same as the steps in the flow chart diagram  130 , except that the algorithm calculates the turn start point from equation (7) at box  162  instead of the end point of the turn at the box  150 . Further, the start turn radius is 
                 3   ⁢     R   f       -     R   t       2         
at the box  146 , the end turn radius is R f  at the box  148  and the initial and boundary conditions at the box  152  are obtained from equations (36)-(41).
 
     As will be well understood by those skilled in the art, the several and various steps and processes discussed herein to describe the invention may be referring to operations performed by a computer, a processor or other electronic calculating device that manipulate and/or transform data using electrical phenomenon. Those computers and electronic devices may employ various volatile and/or non-volatile memories including non-transitory computer-readable medium with an executable program stored thereon including various code or executable instructions able to be performed by the computer or processor, where the memory and/or computer-readable medium may include all forms and types of memory and other computer-readable media. 
     The foregoing discussion discloses and describes merely exemplary embodiments of the present invention. One skilled in the art will readily recognize from such discussion and from the accompanying drawings and claims that various changes, modifications and variations can be made therein without departing from the spirit and scope of the invention as defined in the following claims.