Patent Publication Number: US-9896126-B2

Title: Jackknife detection for vehicle reversing a trailer

Description:
FIELD OF THE INVENTION 
     The present invention generally relates to trailer motion and parameter estimation and condition detection, and more particularly to the detection of a hitch angle approaching an unknown jackknife angle based on dynamic characteristics of the hitch angle. 
     BACKGROUND OF THE INVENTION 
     Reversing a vehicle while towing a trailer can be challenging for many drivers, particularly for drivers that drive with a trailer on an infrequent basis or with various types of trailers. Systems used to assist a driver with backing a trailer frequently measure or estimate the position of the trailer relative to the vehicle with a sensor that determines a hitch angle. Among uses of this detected or estimated hitch angle is the determination of the hitch angle relative to a jackknife angle of the trailer relative to the vehicle. In general, a jackknife angle represents the maximum angle at which a change in direction of the trailer relative to the vehicle can be made with a maximum steering input in either direction, while the vehicle is still reversing. If a vehicle is reversed in a jackknife condition, in which the hitch angle is greater than the jackknife angle, the trailer will approach the vehicle, which could lead to a collision therebetween. Accordingly, the accuracy and reliability of hitch angle detection or estimation relative to the jackknife angle can be critical to the operation of the backup assist system. 
     SUMMARY OF THE INVENTION 
     According to one aspect of the present invention, a backup assist system for a vehicle reversing a trailer includes a hitch angle sensor providing a measured hitch angle of the trailer. The system also includes a controller determining a position of the measured hitch angle in relation to an unknown jackknife angle, which is generally dependent on vehicle and trailer dimensions, by monitoring a predetermined dynamic hitch angle characteristic derived from the measured hitch angle for a corresponding jackknife indicating characteristic. 
     According to another aspect of the present invention, a vehicle includes a steering system and a hitch angle detector. The vehicle also includes a control system coupled with the steering system and implementing a backup mode for reversing a trailer including controlling the steering system to maintain the trailer along a path. The controller is further coupled with the hitch angle detector for determining a relationship between a measured hitch angle and an unknown jackknife angle by monitoring a predetermined dynamic hitch angle characteristic for development of a jackknife indicator, which develops in a manner determined by the actual jackknife angle. 
     According to another aspect of the present invention, a method for assisting reversing of a vehicle with a trailer includes controlling a steering angle of a vehicle steering system to maintain the trailer along a user-selected reversing curvature path, continuously measuring a hitch angle of the trailer relative to the vehicle, and monitoring a predetermined dynamic hitch angle characteristic for development of a jackknife indicator. The method further includes determining a relationship between the measured hitch angle and an unknown jackknife angle based on development of the jackknife indicator. 
     These and other aspects, objects, and features of the present invention will be understood and appreciated by those skilled in the art upon studying the following specification, claims, and appended drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the drawings: 
         FIG. 1  is a top perspective view of a vehicle attached to a trailer with one embodiment of a hitch angle sensor for operating a trailer backup assist system; 
         FIG. 2  is a block diagram illustrating one embodiment of the trailer backup assist system having a steering input device, a curvature controller, and a trailer braking system; 
         FIG. 3  is a schematic diagram that illustrates the geometry of a vehicle and a trailer overlaid with a two-dimensional x-y coordinate system, identifying variables used to determine a kinematic relationship of the vehicle and the trailer for the trailer backup assist system, according to one embodiment; 
         FIG. 4  is a schematic block diagram illustrating portions of a curvature controller, according to an additional embodiment, and other components of the trailer backup assist system, according to such an embodiment; 
         FIG. 5  is a schematic block diagram of the curvature controller of  FIG. 5 , showing the feedback architecture and signal flow of the curvature controller, according to such an embodiment; 
         FIG. 6  is a schematic diagram showing a relationship between a hitch angle and a steering angle of the vehicle as it relates to curvature of the trailer and a jackknife angle; 
         FIG. 7  is a top view showing a trailer positioned with respect to a vehicle at varying hitch angles at varying distances from a jackknife angle; 
         FIGS. 8A, 8B, and 8C  are graphic representations of oscillation profiles of the trailer of  FIG. 7  corresponding to the varying positions of the trailer shown therein; 
         FIG. 9  is a graphical representation of a hitch angle rate of change during reversing of the vehicle of  FIG. 7  for varying lengths of the corresponding trailer; 
         FIG. 10  is a plan view of a steering input device having a rotatable knob for operating the trailer backup assist system, according to one embodiment; 
         FIG. 11  is a plan view of another embodiment of a rotatable knob for selecting a desired curvature of a trailer and a corresponding schematic diagram illustrating a vehicle and a trailer with various trailer curvature paths correlating with desired curvatures that may be selected; 
         FIG. 12  is a schematic diagram showing a backup sequence of a vehicle and a trailer implementing various curvature selections with the trailer backup assist system, according to one embodiment; and 
         FIG. 13  is a flow diagram illustrating a method of operating a trailer backup assist system using an operating routine for steering a vehicle reversing a trailer with normalized control of the desired curvature, according to one embodiment. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     For purposes of description herein, the terms “upper,” “lower,” “right,” “left,” “rear,” “front,” “vertical,” “horizontal,” “interior,” “exterior,” and derivatives thereof shall relate to the invention as oriented in  FIG. 1 . However, it is to be understood that the invention may assume various alternative orientations, except where expressly specified to the contrary. It is also to be understood that the specific devices and processes illustrated in the attached drawing, and described in the following specification are simply exemplary embodiments of the inventive concepts defined in the appended claims. Hence, specific dimensions and other physical characteristics relating to the embodiments disclosed herein are not to be considered as limiting, unless the claims expressly state otherwise. Additionally, unless otherwise specified, it is to be understood that discussion of a particular feature of component extending in or along a given direction or the like does not mean that the feature or component follows a straight line or axis in such a direction or that it only extends in such direction or on such a plane without other directional components or deviations, unless otherwise specified. 
     Referring to  FIGS. 1-5 , reference numeral  10  generally designates a trailer backup assist system for controlling a backing path of a trailer  12  attached to a vehicle  14  by allowing a driver of the vehicle  14  to specify a desired curvature  26  of the backing path of the trailer  12 . In one embodiment, the trailer backup assist system  10  automatically steers the vehicle  14  to guide the trailer  12  on the desired curvature or backing path  26  as a driver uses the accelerator and brake pedals to control the reversing speed of the vehicle  14 . The system  10 , as shown in  FIGS. 6-9 , further includes functionality related to determining whether an angle of the trailer  12  relative to the vehicle  14 , referred to as the hitch angle γ, is approaching a jackknife angle γ(j) that may not be known within system  10 . In an embodiment, to implement such functionality, the system may include a hitch angle sensor  44  providing a measured hitch angle γ of the trailer  12 . A controller  28  determines a position of the measured hitch angle γ in relation to the unknown jackknife γ(j) angle by monitoring a predetermined hitch angle characteristic derived from the measured hitch angle γ for a corresponding jackknife angle indicating characteristic. 
     With respect to the general operation of the trailer backup assist system  10 , as illustrated in the system diagram of  FIG. 2 , a steering input device  18  may be provided, such as a rotatable knob  30  (also shown in  FIGS. 10 and 11 ), for a driver to provide the desired curvature  26  ( FIG. 11 ) of the trailer  12 . As such, the steering input device  18  may be operable between a plurality of selections, such as successive rotated positions of a knob  30 , that each provide an incremental change to the desired curvature  26  of the trailer  12 . With reference to the embodiment of the trailer backup assist system  10  shown in  FIG. 2 , the trailer backup assist system  10  receives vehicle and trailer status-related information from various sensors and devices. This information includes positioning information from a positioning device  56 , which may include a global positioning system (GPS) on the vehicle  14  or a handheld device, to determine a coordinate location of the vehicle  14  and the trailer  12  based on the location of the positioning device  56  with respect to the trailer  12  and/or the vehicle  14 . The positioning device  56  may additionally or alternatively include a dead reckoning system for determining the coordinate location of the vehicle  14  and the trailer  12  within a localized coordinate system based at least on vehicle speed, steering angle, and hitch angle γ. Other vehicle information received by the trailer backup assist system  10  may include a speed of the vehicle  14  from a speed sensor  58  and a yaw rate of the vehicle  14  from a yaw rate sensor  60 . It is contemplated that in additional embodiments, a hitch angle sensor  44 , a proximity sensor, and other vehicle sensors and devices may provide sensor signals or other information, such as successive images of the trailer  12 , that the controller of the trailer backup assist system  10  may process with various routines to determine an indicator of the hitch angle γ, such as a range of hitch angles. 
     As further shown in  FIG. 2 , one embodiment of the trailer backup assist system  10  is in communication with a power assist steering system  62  of the vehicle  14  to operate the steered wheels  64  ( FIG. 1 ) of the vehicle  14  for moving the vehicle  14  in such a manner that the trailer  12  reacts in accordance with the desired curvature  26  of the trailer  12 . In the illustrated embodiment, the power assist steering system  62  is an electric power-assisted steering (“EPAS”) system that includes an electric steering motor  66  for turning the steered wheels  64  to a steering angle based on a steering command, whereby the steering angle may be sensed by a steering angle sensor  67  of the power assist steering system  62 . The steering command may be provided by the trailer backup assist system  10  for autonomously steering during a backup maneuver and may alternatively be provided manually via a rotational position (e.g., steering wheel angle) of a steering wheel  68  ( FIG. 1 ). However, in the illustrated embodiment, the steering wheel  68  of the vehicle  14  is mechanically coupled with the steered wheels  64  of the vehicle  14 , such that the steering wheel  68  moves in concert with steered wheels  64 , preventing manual intervention with the steering wheel  68  during autonomous steering. More specifically, a torque sensor  70  is provided on the power assist steering system  62  that senses torque on the steering wheel  68  that is not expected from autonomous control of the steering wheel  68  and therefore indicative of manual intervention, whereby the trailer backup assist system  10  may alert the driver to discontinue manual intervention with the steering wheel  68  and/or discontinue autonomous steering. 
     In alternative embodiments, some vehicles have a power assist steering system  62  that allows a steering wheel  68  to be partially decoupled from movement of the steered wheels  64  of such a vehicle. Accordingly, the steering wheel  68  can be rotated independent of the manner in which the power assist steering system  62  of the vehicle controls the steered wheels  64  (e.g., autonomous steering as commanded by the trailer backup assist system  10 ). As such, in these types of vehicles where the steering wheel  68  can be selectively decoupled from the steered wheels  64  to allow independent operation thereof, the steering wheel  68  may be used as a steering input device  18  for the trailer backup assist system  10 , as disclosed in greater detail herein. 
     With continued reference to  FIG. 2 , the power assist steering system  62  provides the controller  28  of the trailer backup assist system  10  with information relating to a rotational position of steered wheels  64  of the vehicle  14 , including a steering angle. The controller  28  in the illustrated embodiment processes the current steering angle, in addition to other vehicle  14  and trailer  12  conditions to guide the trailer  12  along the desired curvature  26 . It is conceivable that the trailer backup assist system  10 , in additional embodiments, may be an integrated component of the power assist steering system  62 . For example, the power assist steering system  62  may include a trailer backup assist algorithm for generating vehicle steering information and commands as a function of all or a portion of information received from the steering input device  18 , the hitch angle sensor  44 , the power assist steering system  62 , a vehicle brake control system  72 , a powertrain control system  74 , and other vehicle sensors and devices. 
     As also illustrated in  FIG. 2 , the vehicle brake control system  72  may also communicate with the controller  28  to provide the trailer backup assist system  10  with braking information, such as vehicle wheel speed, and to receive braking commands from the controller  28 . For instance, vehicle speed information can be determined from individual wheel speeds as monitored by the brake control system  72 . Vehicle speed may also be determined from the powertrain control system  74 , the speed sensor  58 , and the positioning device  56 , among other conceivable means. In some embodiments, individual wheel speeds can also be used to determine a vehicle yaw rate, which can be provided to the trailer backup assist system  10  in the alternative or in addition to the vehicle yaw rate sensor  60 . The trailer backup assist system  10  can, further, provide vehicle braking information to the brake control system  72  for allowing the trailer backup assist system  10  to control braking of the vehicle  14  during backing of the trailer  12 . For example, the trailer backup assist system  10  in some embodiments may regulate speed of the vehicle  14  during backing of the trailer  12 , which can reduce the potential for unacceptable trailer backup conditions, as described further below. Examples of unacceptable trailer backup conditions include, but are not limited to, a vehicle  14  over-speed condition, a high hitch angle rate, potentially uncontrollable trailer angle dynamic instability, a calculated theoretical trailer jackknife condition (defined by a maximum vehicle steering angle, drawbar length, tow vehicle wheelbase, and an effective trailer length), or physical contact jackknife limitation (defined by an angular displacement limit relative to the vehicle  14  and the trailer  12 ), and the like, as also described further below. It is disclosed herein that the trailer backup assist system  10  can issue an alert signal corresponding to a notification of an actual, impending, and/or anticipated unacceptable trailer backup condition. 
     The powertrain control system  74 , as shown in the embodiment illustrated in  FIG. 2 , may also interact with the trailer backup assist system  10  for regulating speed and acceleration of the vehicle  14  during backing of the trailer  12 . As mentioned above, regulation of the speed of the vehicle  14  may be necessary to limit the potential for unacceptable trailer backup conditions such as, for example, jackknifing and trailer angle dynamic instability. Similar to high-speed considerations as they relate to unacceptable trailer backup conditions, high acceleration and high dynamic driver curvature requests can also lead to such unacceptable trailer backup conditions. 
     With continued reference to  FIG. 2 , the trailer backup assist system  10  in the illustrated embodiment may communicate with one or more devices, including a vehicle alert system  76 , which may prompt visual, auditory, and tactile warnings. For instance, vehicle brake lights  78  and vehicle emergency flashers may provide a visual alert and a vehicle horn  79  and/or speaker  81  may provide an audible alert. Additionally, the trailer backup assist system  10  and/or vehicle alert system  76  may communicate with a human machine interface (HMI)  80  for the vehicle  14 . The HMI  80  may include a vehicle display  82 , such as a center-stack mounted navigation or entertainment display ( FIG. 2 ). Further, the trailer backup assist system  10  may communicate via wireless communication with another embodiment of the HMI  80 , such as with one or more handheld or portable devices, including one or more smartphones. The portable device may also include the display  82  for displaying one or more images and other information to a user. For instance, the portable device may display one or more images of the trailer  12  and an indication of the estimated hitch angle on the display  82 . In addition, the portable device may provide feedback information, such as visual, audible, and tactile alerts. 
     As further illustrated in  FIG. 2 , the trailer backup assist system  10  includes a steering input device  18  that is connected to the controller  28  for allowing communication of information therebetween. It is disclosed herein that the steering input device  18  can be coupled to the controller  28  in a wired or wireless manner. The steering input device  18  provides the trailer backup assist system  10  with information defining the desired backing path of travel of the trailer  12  for the controller  28  to process and generate steering commands. More specifically, the steering input device  18  may provide a selection or positional information that correlates with a desired curvature  26  of the desired backing path of travel of the trailer  12 . Also, the trailer steering commands provided by the steering input device  18  can include information relating to a commanded change in the path of travel, such as an incremental change in the desired curvature  26 , and information relating to an indication that the trailer  12  is to travel along a path defined by a longitudinal centerline axis of the trailer  12 , such as a desired curvature value of zero that defines a substantially straight path of travel for the trailer. As will be discussed below in more detail, the steering input device  18  according to one embodiment may include a movable control input device for allowing a driver of the vehicle  14  to command desired trailer steering actions or otherwise select and alter a desired curvature. For instance, the moveable control input device may be a rotatable knob  30 , which can be rotatable about a rotational axis extending through a top surface or face of the knob  30 . In other embodiments, the rotatable knob  30  may be rotatable about a rotational axis extending substantially parallel to a top surface or face of the rotatable knob  30 . Furthermore, the steering input device  18 , according to additional embodiments, may include alternative devices for providing a desired curvature  26  or other information defining a desired backing path, such as a joystick, a keypad, a series of depressible buttons or switches, a sliding input device, various user interfaces on a touch-screen display  82 , a vision based system for receiving gestures, a control interface on a portable device, and other conceivable input devices as generally understood by one having ordinary skill in the art. It is contemplated that the steering input device  18  may also function as an input device for other features, such as providing inputs for other vehicle features or systems. 
     Still referring to the embodiment shown in  FIG. 2 , the controller  28  is configured with a microprocessor  84  to process logic and routines stored in memory  86  that receive information from the sensor system  16 , including the trailer sensor module  20 , the hitch angle sensor  44 , the steering input device  18 , the power assist steering system  62 , the vehicle brake control system  72 , the trailer braking system, the powertrain control system  74 , and other vehicle sensors and devices. The controller  28  may generate vehicle steering information and commands as a function of all or a portion of the information received. Thereafter, the vehicle steering information and commands may be provided to the power assist steering system  62  for affecting steering of the vehicle  14  to achieve a commanded path of travel for the trailer  12 . The controller  28  may include the microprocessor  84  and/or other analog and/or digital circuitry for processing one or more routines. Also, the controller  28  may include the memory  86  for storing one or more routines, including a hitch angle estimation routine  130 , an operating routine  132 , and a curvature routine  98 . It should be appreciated that the controller  28  may be a stand-alone dedicated controller or may be a shared controller integrated with other control functions, such as integrated with the sensor system  16 , the power assist steering system  62 , and other conceivable onboard or off-board vehicle control systems. 
     With reference to  FIG. 3 , we now turn to a discussion of vehicle and trailer information and parameters used to calculate a kinematic relationship between a curvature of a path of travel of the trailer  12  and the steering angle of the vehicle  14  towing the trailer  12 , which can be desirable for a trailer backup assist system  10  configured in accordance with some embodiments, including for use by a curvature routine  98  of the controller  28  in one embodiment. To achieve such a kinematic relationship, certain assumptions may be made with regard to parameters associated with the vehicle/trailer system. Examples of such assumptions include, but are not limited to, the trailer  12  being backed by the vehicle  14  at a relatively low speed, wheels of the vehicle  14  and the trailer  12  having negligible (e.g., no) slip, tires of the vehicle  14  having negligible (e.g., no) lateral compliance, tires of the vehicle  14  and the trailer  12  having negligible (e.g., no) deformation, actuator dynamics of the vehicle  14  being negligible, and the vehicle  14  and the trailer  12  exhibiting negligible (e.g., no) roll or pitch motions, among other conceivable factors with the potential to have an effect on controlling the trailer  12  with the vehicle  14 . 
     As shown in  FIG. 3 , for a system defined by a vehicle  14  and a trailer  12 , the kinematic relationship is based on various parameters associated with the vehicle  14  and the trailer  12 . These parameters include:
         δ: steering angle at steered front wheels of the vehicle;   α: yaw angle of the vehicle;   β: yaw angle of the trailer;   γ: hitch angle (γ=β−α);   W: wheel base of the vehicle;   L: drawbar length between hitch point and rear axle of the vehicle;   D: distance (trailer length) between hitch point and axle of the trailer or effective axle for a multiple axle trailer; and   r 2 : curvature radius for the trailer.       

     In one example, a kinematic relationship between trailer path radius of curvature r 2  at the midpoint of an axle of the trailer  12 , steering angle δ of the steered wheels  64  of the vehicle  14 , and the hitch angle γ can be expressed in the equation provided below. As such, if the hitch angle γ is provided, the trailer path curvature κ 2  is can be controlled based on regulating the steering angle δ (where {dot over (β)} is trailer yaw rate and {dot over (η)} is trailer velocity). 
     
       
         
           
             
               κ 
               2 
             
             = 
             
               
                 1 
                 
                   r 
                   2 
                 
               
               = 
               
                 
                   
                     β 
                     . 
                   
                   
                     η 
                     . 
                   
                 
                 = 
                 
                   
                     
                       
                         ( 
                         
                           W 
                           + 
                           
                             
                               KV 
                               2 
                             
                             g 
                           
                         
                         ) 
                       
                       ⁢ 
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       γ 
                     
                     + 
                     
                       L 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       cos 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       γ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       tan 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       δ 
                     
                   
                   
                     D 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             ( 
                             
                               W 
                               + 
                               
                                 
                                   KV 
                                   2 
                                 
                                 g 
                               
                             
                             ) 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           γ 
                         
                         - 
                         
                           L 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           γ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           tan 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           δ 
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     This relationship can be expressed to provide the steering angle δ as a function of trailer path curvature κ 2  and hitch angle γ. 
     
       
         
           
             δ 
             = 
             
               
                 
                   tan 
                   
                     - 
                     1 
                   
                 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         ( 
                         
                           W 
                           + 
                           
                             
                               KV 
                               2 
                             
                             g 
                           
                         
                         ) 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               κ 
                               2 
                             
                             ⁢ 
                             D 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             cos 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             γ 
                           
                           + 
                           
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             γ 
                           
                         
                         ] 
                       
                     
                     
                       
                         DL 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           κ 
                           2 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         γ 
                       
                       + 
                       
                         L 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         γ 
                       
                     
                   
                   ) 
                 
               
               = 
               
                 F 
                 ⁡ 
                 
                   ( 
                   
                     γ 
                     , 
                     
                       κ 
                       2 
                     
                     , 
                     K 
                   
                   ) 
                 
               
             
           
         
       
     
     Accordingly, for a particular vehicle and trailer combination, certain parameters (e.g., D, W and L) of the kinematic relationship are constant and assumed known. V is the vehicle longitudinal speed and g is the acceleration due to gravity. K is a speed dependent parameter which when set to zero makes the calculation of steering angle independent of vehicle speed. For example, vehicle-specific parameters of the kinematic relationship can be predefined in an electronic control system of the vehicle  14  and trailer-specific parameters of the kinematic relationship can be inputted by a driver of the vehicle  14 , determined from sensed trailer behavior in response to vehicle steering commands, or otherwise determined from signals provided by the trailer  12 . Trailer path curvature κ 2  can be determined from the driver input via the steering input device  18 . Through the use of the equation for providing steering angle, a corresponding steering command can be generated by the curvature routine  98  for controlling the power assist steering system  62  of the vehicle  14 . 
     Additionally, an assumption may be made by the curvature routine  98  that a longitudinal distance L between the pivoting connection and the rear axle of the vehicle  14  is equal to zero for purposes of operating the trailer backup assist system  10  when a gooseneck trailer or other similar trailer is connected with the a hitch ball or a fifth wheel connector located over a rear axle of the vehicle  14 . The assumption essentially assumes that the pivoting connection with the trailer  12  is substantially vertically aligned with the rear axle of the vehicle  14 . When such an assumption is made, the controller  28  may generate the steering angle command for the vehicle  14  as a function independent of the longitudinal distance L between the pivoting connection and the rear axle of the vehicle  14 . It is appreciated that the gooseneck trailer mentioned generally refers to the tongue configuration being elevated to attach with the vehicle  14  at an elevated location over the rear axle, such as within a bed of a truck, whereby embodiments of the gooseneck trailer may include flatbed cargo areas, enclosed cargo areas, campers, cattle trailers, horse trailers, lowboy trailers, and other conceivable trailers with such a tongue configuration. 
     Yet another example of the curvature routine  98  of the trailer backup assist system  10  is illustrated in  FIG. 4 , showing the general architectural layout whereby a measurement module  88 , a hitch angle regulator  90 , and a curvature regulator  92  are routines that may be stored in the memory  86  of the controller  28 . In the illustrated layout, the steering input device  18  provides a desired curvature κ 2  value to the curvature regulator  92  of the controller  28 , which may be determined from the desired backing path  26  that is input with the steering input device  18 . The curvature regulator  92  computes a desired hitch angle γ(d) based on the current desired curvature κ 2  along with the steering angle δ provided by a measurement module  88  in this embodiment of the controller  28 . The measurement module  88  may be a memory device separate from or integrated with the controller  28  that stores data from sensors of the trailer backup assist system  10 , such as the hitch angle sensor  44 , the vehicle speed sensor  58 , the steering angle sensor, or alternatively the measurement module  88  may otherwise directly transmit data from the sensors without functioning as a memory device. Once the desired hitch angle γ(d) is computed by the curvature regulator  92  the hitch angle regulator  90  generates a steering angle command based on the computed desired hitch angle γ(d) as well as a measured or otherwise estimated hitch angle γ(m) and a current velocity of the vehicle  14 . The steering angle command is supplied to the power assist steering system  62  of the vehicle  14 , which is then fed back to the measurement module  88  to reassess the impacts of other vehicle characteristics impacted from the implementation of the steering angle command or other changes to the system. Accordingly, the curvature regulator  92  and the hitch angle regulator  90  continually process information from the measurement module  88  to provide accurate steering angle commands that place the trailer  12  on the desired curvature κ 2  and the desired backing path  26 , without substantial overshoot or continuous oscillation of the path of travel about the desired curvature κ 2 . 
     As also shown in  FIG. 5 , the curvature routine  98  shown in  FIG. 4  is illustrated in a control system block diagram. Specifically, entering the control system is an input, κ 2 , which represents the desired curvature  26  of the trailer  12  that is provided to the curvature regulator  92 . The curvature regulator  92  can be expressed as a static map, ρ(κ 2 , δ), which in one embodiment is the following equation: 
     
       
         
           
             
               p 
               ⁡ 
               
                 ( 
                 
                   
                     κ 
                     2 
                   
                   , 
                   δ 
                 
                 ) 
               
             
             = 
             
               
                 tan 
                 
                   - 
                   1 
                 
               
               ⁡ 
               
                 ( 
                 
                   
                     
                       
                         κ 
                         2 
                       
                       ⁢ 
                       D 
                     
                     + 
                     
                       L 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         tan 
                         ⁡ 
                         
                           ( 
                           δ 
                           ) 
                         
                       
                     
                   
                   
                     
                       
                         κ 
                         2 
                       
                       ⁢ 
                       DL 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         tan 
                         ⁡ 
                         
                           ( 
                           δ 
                           ) 
                         
                       
                     
                     - 
                     W 
                   
                 
                 ) 
               
             
           
         
       
         
         
           
             where, 
             κ 2  represents the desired curvature of the trailer  12  or 1/r 2  as shown in  FIG. 3 ; 
             δ represents the steering angle; 
             L represents the distance from the rear axle of the vehicle  14  to the hitch pivot point; 
             D represents the distance from the hitch pivot point to the axle of the trailer  12 ; and 
             W represents the distance from the rear axle to the front axle of the vehicle  14 . 
           
         
       
    
     With further reference to  FIG. 5 , the output hitch angle of ρ(κ 2 , δ) is provided as the reference signal, γ ref , for the remainder of the control system, although the steering angle δ value used by the curvature regulator  92  is feedback from the non-linear function of the hitch angle regulator  90 . It is shown that the hitch angle regulator  90  uses feedback linearization for defining a feedback control law, as follows: 
     
       
         
           
             
               g 
               ⁡ 
               
                 ( 
                 
                   u 
                   , 
                   γ 
                   , 
                   v 
                 
                 ) 
               
             
             = 
             
               δ 
               = 
               
                 
                   tan 
                   
                     - 
                     1 
                   
                 
                 ( 
                 
                   
                     W 
                     
                       v 
                       ⁡ 
                       
                         ( 
                         
                           1 
                           + 
                           
                             
                               L 
                               D 
                             
                             ⁢ 
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 γ 
                                 ) 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       u 
                       - 
                       
                         
                           v 
                           D 
                         
                         ⁢ 
                         
                           sin 
                           ⁡ 
                           
                             ( 
                             γ 
                             ) 
                           
                         
                       
                     
                     ) 
                   
                 
                 ) 
               
             
           
         
       
     
     As also shown in  FIG. 5 , the feedback control law, g(u, γ, ν), is implemented with a proportional integral (PI) controller, whereby the integral portion substantially eliminates steady-state tracking error. More specifically, the control system illustrated in  FIG. 4  may be expressed as the following differential-algebraic equations: 
     
       
         
           
             
               
                 
                   γ 
                   . 
                 
                 ⁡ 
                 
                   ( 
                   t 
                   ) 
                 
               
               = 
               
                 
                   
                     
                       v 
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     It is contemplated that the PI controller may have gain terms based on trailer length D because shorter trailers will generally have faster dynamics. In addition, the hitch angle regulator  90  may be configured to prevent the desired hitch angle γ(d) to reach or exceed a jackknife angle γ(j), as computed by the controller or otherwise determined by the trailer backup assist system  10 , as disclosed in greater detail herein. 
     Referring now to  FIG. 6 , in the illustrated embodiments of the disclosed subject matter, it is desirable to limit the potential for the vehicle  14  and the trailer  12  to attain a jackknife angle (i.e., the vehicle/trailer system achieving a jackknife condition). A jackknife angle γ(j) refers to a hitch angle γ that, while vehicle  14  is backing, cannot be overcome by the maximum steering input for a vehicle such as, for example, the steered front wheels of the vehicle  14  being moved to a maximum steered angle δ at a maximum rate of steering angle change. The jackknife angle γ(j) is a function of a maximum wheel angle for the steered wheels of the vehicle  14 , the wheel base W of the vehicle  14 , the distance L between hitch point and the rear axle of the vehicle  14 , and the trailer length D between the hitch point and the axle of the trailer  12  or the effective axle when the trailer  12  has multiple axles. When the hitch angle γ for the vehicle  14  and the trailer  12  achieves or exceeds the jackknife angle γ(j), the vehicle  14  may be pulled forward to reduce the hitch angle γ. Conversely, under continued backing of vehicle  14 , the hitch angle γ will continue to increase, regardless of the steering input, toward a collision angle at which point trailer  12  may come into contact with vehicle  14 . Thus, for limiting the potential for a vehicle/trailer system attaining a jackknife angle, it is preferable to control the yaw angle of the trailer  12  while keeping the hitch angle γ of the vehicle/trailer system relatively small. 
     In one aspect, a kinematic model representation of the vehicle  14  and the trailer  12  can be used to determine a jackknife angle for the vehicle-trailer combination when the vehicle  14  is moving forward (i.e. towing the trailer  12 ). Accordingly, with reference to  FIGS. 3 and 6 , a steering angle limit for the steered front wheels requires that the hitch angle γ cannot exceed the jackknife angle γ(j), which is also referred to as a critical hitch angle γ. Thus, under the limitation that the hitch angle γ cannot exceed the jackknife angle γ(j), the jackknife angle γ(j) is the hitch angle γ that maintains a circular motion for the vehicle/trailer system when the steered wheels  64  are at a maximum steering angle δ(max). The steering angle for circular motion with hitch angle γ is defined by the following equation. 
     
       
         
           
             
               tan 
               ⁢ 
               
                   
               
               ⁢ 
               
                 δ 
                 max 
               
             
             = 
             
               
                 w 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 sin 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   γ 
                   max 
                 
               
               
                 D 
                 + 
                 
                   L 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   cos 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     γ 
                     max 
                   
                 
               
             
           
         
       
     
     Solving the above equation for hitch angle γ can allow the jackknife angle γ(j) to be determined. This solution, which is shown in the following equation, can, in some instances, be used in implementing trailer backup assist functionality in accordance with the disclosed subject matter for monitoring hitch angle γ in relation to jackknife angle. 
     
       
         
           
             
               cos 
               ⁢ 
               
                   
               
               ⁢ 
               
                 γ 
                 _ 
               
             
             = 
             
               
                 
                   - 
                   b 
                 
                 ± 
                 
                   
                     
                       b 
                       2 
                     
                     - 
                     
                       4 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       ac 
                     
                   
                 
               
               
                 2 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 a 
               
             
           
         
       
         
         
           
             where,
 
 a=L   2  tan 2  δ(max)+ W   2 ;
 
 b= 2  LD  tan 2  δ(max); and
 
 c=D   2  tan 2  δ(max)− W   2 .
 
As can be seen above, equations based solely on a vehicle-trailer kinematic model require the distance D from the hitch  42  to the front axle of trailer  12  trailer be known prior to calculating γ(j). As discussed above, other dimensions used in these equations, such as the vehicle wheelbase W and the distance to hitch L, are specific to vehicle  14  and can be stored in memory  86  by the manufacturer or dealer. The trailer length D, however, is dependent on the particular trailer  12  coupled with vehicle  14  and, as discussed above, may require measurement and input into memory  86  (such as by HMI  80 ) by a user. Such a scheme for obtaining a value for trailer length D may be difficult or burdensome for a user and may introduce inaccuracy into the kinematic model that may affect the accuracy of determining the jackknife angle γ(j) in a manner that may adversely affect the system. In one example, if a measurement or other inaccuracy causes the estimated or calculated γ(j) to be too large, trailer  12  may move into a jackknife condition at a point where system  10  believes such a condition to not yet have been reached. Without an intervening control operation, system  10  may continue to reverse, moving trailer  12  toward or into contact with vehicle  14 . Such a situation may be more likely to occur with certain trailer configuration or lengths, where shorter trailers approach and move into a jackknife condition more rapidly than longer trailers, and some geometries independent of trailer length D may position the collision angle particularly close to the jackknife angle γ(j), making intervention in such a situation difficult. Further, as mentioned above, must be calculated during forward movement of the vehicle  14  and trailer  12  combination, as the inherently instability of the arrangement during reversing will not result in the above-described circular path, the trailer  12 , during reversing, tending to move increasingly closer to vehicle  14 , absent corrective steering inputs.
 
           
         
       
    
     To reduce or remove the dependence on a measured trailer length D from the ability of system  10  to determine whether trailer  12  is approaching jackknife angle γ(j), system  10  may monitor the trailer angle γ, such as by using a hitch angle sensor  44  or the like, for one or more jackknife indicating characteristic. In particular, there are particular ways in which trailer  12  behaves as it is approaching a jackknife condition that may be observable via the hitch angle γ. With reference to  FIG. 7 , a vehicle  14  is shown in various states of reversing a trailer  12 , which can include backing thereof along various different curvature paths κ 2  that correspond with or otherwise result in various positions of trailer  12 . In particular, a first position  140  is shown, in which the corresponding hitch angle γ 1  is relatively low (i.e. close to zero or less than 10°). A second position  142  is also shown in which the hitch angle γ 2  is larger than γ 1 , but is still within a generally controllable distance from the jackknife angle γ(j) (absent a particularly significant adverse condition or the like). Finally, trailer  12  is shown in  FIG. 7  in a third position  144  in which the hitch angle γ 2  is approaching the jackknife angle γ(j). It is noted that, while the jackknife angle γ(j) is shown in the schematic view of  FIG. 7 , the actual angle γ(j) may be unknown to or unidentified by system  10  through positions  140  and  142 . By the time trailer  12  reaches position  144 , system  10  may still not precisely know the value for jackknife angle γ(j), but may be able to detect that hitch angle γ 3  is approaching the jackknife angle γ(j). 
     In one embodiment, a condition in which the hitch angle γ is approaching a jackknife angle γ(j) can be identified by monitoring hitch angle γ for a particular response to vehicle yaw. In general, the system shown in  FIGS. 3 and 7 , in which vehicle  14  is reversing trailer  12 , is unstable, such that in any of the positions  140 ,  142 , and  144  of trailer  12  depicted in  FIG. 7 , trailer  12  will tend to move to increase the hitch angle γ under a constant steering angle δ. This instability, in general, may require near constant adjustment of the steering angle δ to maintain a particular hitch angle γ or to maintain trailer  12  along a particular curvature path, as discussed above. Such control is possible because, in normal conditions, various steering inputs to change the steering angle δ can cause a change in the hitch angle in either direction (i.e. to increase or decrease the hitch angle γ). However, as discussed above, once the jackknife angle γ(j) is crossed, trailer will move so as to increase the hitch angle γ, regardless of steering input. As shown in  FIGS. 8A, 8B, and 8C , the change in hitch angle γ in response to varying steering angle δ changes in proportion to an overall increase in hitch angle γ in a manner that can be used to identify a potential jackknife condition before occurrence thereof. 
     As shown in  FIG. 8A , for a trailer position  140  including a low hitch angle γ 1 , a series of successive changes in direction of vehicle yaw by the same amount induce similar changes in hitch angle γ 1  wherein the hitch angle γ 1  oscillates by moving in opposite directions at similar magnitudes, meaning that the hitch angle γ 1  will generally remain close to the initial value. As illustrated in  FIG. 8A , the small movements of trailer  12  to the right  146  are of a similar magnitude to the movements to the left  148  with such successive movements of similar magnitude keeping the hitch angle γ near the initial hitch angle γ 1 . Such successive changes in direction of vehicle yaw may be implemented by alternately braking the wheels on opposite sides (left and right) of vehicle  14 , such as by causing alternate brake pulses thereof, and thereby causing the vehicle to wiggle, a corresponding wiggle being induced in trailer  12  such that hitch angle γ responds similarly (such as by the movement shown in  FIG. 8A ). Such braking can be implemented by system  10  outputting a particular signal to the brake control system  72 . Alternatively, vehicle wiggle can be added to the steering input of system  10  to EPAS  62  that is used to maintain trailer  12  along the desired curvature path, as further discussed below. In either case, vehicle wiggle can be caused by system  10  at regular intervals (such as at predetermined times or within a certain time from a change in curvature demand) or constantly during operation of system  10  and, depending on the sensitivity of hitch angle sensor  46 , can be implemented in a manner that is imperceptible or, at least, tolerable by a user. 
     Turning to  FIG. 8B  it is shown that when a similar trailer wiggle is implemented with trailer  12  positioned such that the initial hitch angle γ 2  is larger than γ 1  but still less than the jackknife angle γ(j), including outside of a predetermined critical range from jackknife angle γ(j), the oscillations  146 , 148  may still occur in both the left and right directions. However, the oscillations  146  in the direction toward the jackknife angle γ(j) may be larger than the oscillations  148  away from the jackknife angle γ(j), leading an aggregate trailer wiggle direction to tend toward the overall hitch angle γ to increase from the initial hitch angle γ 1 . However, because the trailer wiggle is still indicating responses to steering input in both directions, such a condition may indicate that the initial hitch angle γ 2  is not yet approaching the jackknife angle γ(j) and that trailer  12  can be maintained along the selected curvature κ 2  that lead to the particular angle γ 2 . Further, after the induced wiggle of trailer  12  has been completed, which can correspond to system  10  obtaining data through a sufficient number of oscillations to determine a hitch angle γ below the jackknife angle γ(j), system  10  can adjust the steering input δ to return the hitch angle γ to the initial hitch γ 2  angle or as otherwise needed to maintain the selected curvature κ 2  for trailer  12 . 
     As shown in  FIG. 8C , when trailer wiggle is induced with an even larger initial hitch angle γ 3 , the comparative magnitude of oscillations  146  toward jackknife angle γ(j) becomes even greater than the magnitude of oscillations  148  away from jackknife angle γ(j) than shown in  FIG. 8B  and described above. Accordingly, system  10  can be calibrated to identify a hitch angle γ that is determined to be too close in approaching jackknife angle γ(j) such that intervention is required. In particular, system  10  can compare the oscillations toward jackknife angle γ(j) (i.e. increasing hitch angle γ) to those away from jackknife angle γ(j) (i.e. decreasing hitch angle) and determine if a threshold convergence toward jackknife angle γ(j) (based on, for example, the aggregate trailer wiggle direction) has been met or exceeded. For example, system  10  can monitor oscillations  146  and  148  during induced trailer wiggle for oscillations  148  away from jackknife angle γ(j) (and, accordingly, away from vehicle  14 ) that are below a predetermined threshold of, for example 10% or less than the magnitude of corresponding oscillations  146  toward jackknife angle γ(j). In another example, oscillations  148  away from jackknife angle γ(j) that are 5% or less the magnitude of adjacent oscillations  146  toward jackknife angle γ(j) (i.e. toward the vehicle  14  itself) can be used to indicate a trailer angle γ that is approaching the jackknife angle γ(j). In either example, system  10  can be configured to identify a hitch angle γ that is approaching the jackknife angle γ(j) at a sufficient distance therefrom for system  10  to take action to prevent the jackknife angle γ(j) from being reached. This can include altering the curvature κ 2  of trailer, or changing the steering input δ to reduce the jackknife angle indicating characteristic, which may include increasing the comparative magnitude of oscillations  148  away from jackknife angle γ(j) to adjacent oscillations  146  toward jackknife angle γ(j). 
     In certain instances of backing the trailer  12 , a jackknife enabling condition can arise based on current operating parameters of the vehicle  14  in combination with a corresponding hitch angle γ. This condition can be indicated when one or more specified vehicle operating thresholds are met while a particular hitch angle γ is present. For example, although the particular hitch angle γ is not currently at the jackknife angle for the vehicle  14  and attached trailer  12 , certain vehicle operating parameters can lead to a rapid (e.g., uncontrolled) transition of the hitch angle γ to the jackknife angle for a current commanded trailer curvature and/or can reduce an ability to steer the trailer  12  away from the jackknife angle. One reason for a jackknife enabling condition is that trailer curvature control mechanisms (e.g., those in accordance with the disclosed subject matter) generally calculate steering commands at an instantaneous point in time during backing of a trailer  12 . However, these calculations will typically not account for lag in the EPAS  62  of the vehicle  14  (e.g., lag in a steering EPAS controller or the like). Another reason for the jackknife enabling condition is that trailer curvature control mechanisms generally exhibit reduced steering sensitivity and/or effectiveness when the vehicle  14  is at relatively high speeds and/or when undergoing relatively high acceleration. 
     Jackknife determining information may be received by the controller  28 , according to, for example, the embodiment discussed above, to process and characterize a jackknife enabling condition of the vehicle-trailer combination at a particular point in time (e.g., at the point in time when the jackknife determining information was sampled, including an instance of induced trailer wiggle). Examples of information that may lead to or increase a jackknife enabling condition include, but are not limited to, information characterizing a vehicle accelerator pedal transient state, information characterizing a speed of the vehicle  14 , information characterizing longitudinal acceleration of the vehicle  14 , information characterizing a brake torque being applied by a brake system of the vehicle  14 , information characterizing a powertrain torque being applied to driven wheels of the vehicle  14 , and information characterizing the magnitude and rate of driver requested trailer curvature. In this regard, such information may be continually monitored. Such information may be used to modify the response of system  10  to the above described comparisons of trailer wiggle oscillation magnitude to allow system  10  to have adequate time to respond to a potential convergence toward jackknife angle γ(j), as needed depending on particular circumstances. For example, the threshold percentage magnitude of oscillations  148  away from jackknife angle γ(j) to oscillations  146  toward jackknife angle γ(j) may be increased with increasing vehicle speed V, as increased vehicle speed V may speed convergence of hitch angle γ toward the jackknife angle γ(j). Similar adjustments can be made with respect to other characteristics of vehicle  14  or trailer  12 . In a further example, the threshold percentage magnitude of oscillations  148  away from jackknife angle γ(j) to oscillations  146  toward jackknife angle γ(j) may be increased with shorter trailer length D (should such a parameter be presently available for system  10 ), as increased vehicle speed V may speed convergence of hitch angle γ toward the jackknife angle γ(j). 
     As discussed above, such a scheme for determining if hitch angle γ is approaching a jackknife angle γ(j) can be carried out without knowing the particular jackknife angle γ(j) for the given trailer  12  and vehicle  14  combination. Further, the scheme can be executed without knowing, for example, the distance D between the hitch and axle of trailer  12 . Accordingly, after a certain number of instances of system  10  determining that hitch angle γ has reached a certain threshold distance of the corresponding jackknife angle γ(j), system can use the hitch angles γ in such instances, in light of the factor or distance relating those angles γ to the jackknife angle γ(j) to derive an estimate (such as by averaging) jackknife angle γ(j). The above-discussed equation: 
               tan   ⁢           ⁢     δ   max       =       W   ⁢           ⁢   sin   ⁢           ⁢     γ   max         D   +     L   ⁢           ⁢   cos   ⁢           ⁢     γ   max                 
can then be solved for D to derive an estimated distance D using the estimated jackknife angle γ(j) for γ max .
 
     Turning now to  FIG. 9 , an alternative embodiment of a process for system  10  to identify potential convergence of hitch angle γ to an unidentified jackknife angle is described. In particular, instead of (or in combination with) inducing trailer wiggle, as described above, system  10  can monitor, along with hitch angle γ itself, the rate of change of hitch angle {dot over (γ)}. In one example, the rate of change of hitch angle {dot over (γ)} can be determined using the following equation: 
     
       
         
           
             
               
                 γ 
                 . 
               
               = 
               
                 
                   
                     - 
                     
                       ( 
                       
                         
                           V 
                           W 
                         
                         + 
                         
                           VL 
                           
                             WD 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             cos 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             γ 
                           
                         
                       
                       ) 
                     
                   
                   ⁢ 
                   tan 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   δ 
                 
                 - 
                 
                   
                     V 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     γ 
                   
                   D 
                 
               
             
             ; 
           
         
       
         
         
           
             where: 
             {dot over (γ)} is the rate of change of the measured hitch angle; 
             γ is the measured hitch angle; 
             V is a vehicle longitudinal speed; 
             W is a wheelbase of the vehicle; 
             L is a hitch length of the vehicle; and 
             D is the distance between the hitch and a front axle of the trailer.
 
The behavior of a trailer  12  being reversed by a vehicle  14  is known to be such that trailer turns about the hitch at a speed that increases toward a maximum at the jackknife angle before slowing again as the hitch angle continues to increase. In other words, the rate of change {dot over (γ)} of the hitch angle γ will increase to a peak value (i.e. an absolute value, regardless of whether a particular direction is measured as negative relative to a second positive direction) at the jackknife angle γ(j). This knowledge can be used in a number of ways to evaluate the rate of change {dot over (γ)} of hitch angle γ to determine if the hitch angle γ is approaching an unidentified jackknife angle γ(j). In one example, given a known trailer length D, system  10  can look for a particular rate of change {dot over (γ)}, such as a threshold rate of between about 0.6 and 0.65 for a trailer  12  of about 2 m in length D, a threshold rate of between about 0.45 and 0.47 for a trailer  12  of about 3 m in length D, or a threshold rate of between about 0.36 and 0.38 for a trailer  12  of about 4 m in length.
 
           
         
       
    
     In another example, system  10  can look at a further rate of change {umlaut over (γ)} of the rate of change {dot over (γ)} itself, according to the following equation: 
               γ   ¨     =       -       LV   ⁢           ⁢   tan   ⁢           ⁢     δ   ·   sin     ⁢           ⁢   γ       W   ⁢           ⁢   δ   ⁢           ⁢     cos   2     ⁢   γ         -         V   ⁢           ⁢   cos   ⁢           ⁢   γ     δ     .             
The result for {umlaut over (γ)} can indicate whether, for a constant steering input d and vehicle velocity V, the rate of change {dot over (γ)} of the hitch angle γ is approaching a peak velocity, which may correspond to hitch angle γ approaching the jackknife angle γ(j). Accordingly, system  10  can monitor the rate of change {umlaut over (γ)} of the rate of change {dot over (γ)} to determine if {umlaut over (γ)} is sufficiently close to zero to require intervention to prevent a jackknife condition from being reached. In one example, system  10  can monitor for {umlaut over (γ)} reaching a value of less than 1, or in another example, less than 0.5, or in a further example, less than 0.1 to determine that intervention is needed to prevent hitch angle γ from reaching the jackknife angle γ(j). As discussed above, system  10  can vary the jackknife indicating threshold value of {umlaut over (γ)} depending on various vehicle characteristics that may influence the speed at which the hitch angle γ approaches a jackknife angle γ(j) or the ability of system  10  to intervene to prevent a jackknife condition from being reached.
 
     As previously disclosed with reference to the illustrated embodiments, during operation of the trailer backup assist system  10 , a driver of the vehicle  14  may be limited in the manner in which steering inputs may be made with the steering wheel  68  of the vehicle  14  due to the power assist steering system  62  being directly coupled to the steering wheel  68 . Accordingly, the steering input device  18  of the trailer backup assist system  10  may be used for inputting a desired curvature  26  of the trailer  12 , thereby decoupling such commands from being made at the steering wheel  68  of the vehicle  14 . However, additional embodiments of the trailer backup assist system  10  may have the capability to selectively decouple the steering wheel  68  from movement of steerable wheels of the vehicle  14 , thereby allowing the steering wheel  68  to be used for commanding changes in the desired curvature  26  of a trailer  12  or otherwise selecting a desired backing path during such trailer backup assist. 
     Referring now to  FIG. 10 , one embodiment of the steering input device  18  is illustrated disposed on a center console  108  of the vehicle  14  proximate a shifter  110 . In this embodiment, the steering input device  18  includes a rotatable knob  30  for providing the controller  28  with the desired backing path of the trailer  12 . More specifically, the angular position of the rotatable knob  30  may correlate with a desired curvature κ 2 , such that rotation of the knob to a different angular position provides a different desired curvature with an incremental change based on the amount of rotation and, in some embodiments, a normalized rate, as described in greater detail herein. 
     The rotatable knob  30 , as illustrated in  FIGS. 10 and 11 , may be biased (e.g., by a spring return) to a center or at-rest position P(AR) between opposing rotational ranges of motion R(R), R(L). In the illustrated embodiment, a first one of the opposing rotational ranges of motion R(R) is substantially equal to a second one of the opposing rotational ranges of motion R(L), R(R). To provide a tactile indication of an amount of rotation of the rotatable knob  30 , a force that biases the knob toward the at-rest position P(AR) can increase (e.g., non-linearly) as a function of the amount of rotation of the rotatable knob  30  with respect to the at-rest position P(AR). Additionally, the rotatable knob  30  can be configured with position indicating detents such that the driver can positively feel the at-rest position P(AR) and feel the ends of the opposing rotational ranges of motion R(L), R(R) approaching (e.g., soft end stops). The rotatable knob  30  may generate a desired curvature value as function of an amount of rotation of the rotatable knob  30  with respect to the at-rest position P(AR) and a direction of movement of the rotatable knob  30  with respect to the at-rest position P(AR). It is also contemplated that the rate of rotation of the rotatable knob  30  may also be used to determine the desired curvature output to the controller  28 . The at-rest position P(AR) of the knob corresponds to a signal indicating that the vehicle  14  should be steered such that the trailer  12  is backed along a substantially straight backing path  114  (zero trailer curvature request from the driver), as defined by the longitudinal direction  22  of the trailer  12  when the knob was returned to the at-rest position P(AR). A maximum clockwise and anti-clockwise position of the knob (i.e., limits of the opposing rotational ranges of motion R(R), R(L)) may each correspond to a respective signal indicating a tightest radius of curvature (i.e., most acute trajectory or smallest radius of curvature) of a path of travel of the trailer  12  that is possible without the corresponding vehicle  14  steering information causing a jackknife condition. 
     As shown in  FIGS. 10 and 11 , a driver can turn the rotatable knob  30  to provide a desired curvature  26  while the driver of the vehicle  14  backs the trailer  12 . In the illustrated embodiment, the rotatable knob  30  rotates about a central axis between a center or middle position  114  corresponding to a substantially straight backing path  26  of travel, as defined by the longitudinal direction  22  of the trailer  12 , and various rotated positions  116 ,  118 ,  120 ,  122  on opposing sides of the middle position  114 , commanding a desired curvature  26  corresponding to a radius of the desired backing path  26  of travel for the trailer  12  at the commanded rotated position. It is contemplated that the rotatable knob  30  may be configured in accordance with embodiments of the disclosed subject matter and omit a means for being biased to an at-rest position P(AR) between opposing rotational ranges of motion. Lack of such biasing may allow a current rotational position of the rotatable knob  30  to be maintained until the rotational control input device is manually moved to a different position. It is also conceivable that the steering input device  18  may include a non-rotational control device that may be configured to selectively provide a desired curvature  26  and to override or supplement an existing curvature value. Examples of such a non-rotational control input device include, but are not limited to, a plurality of depressible buttons (e.g., curve left, curve right, and travel straight), a touch screen on which a driver traces or otherwise inputs a curvature for path of travel commands, a button that is translatable along an axis for allowing a driver to input backing path commands, or a joystick type input and the like. 
     Referring to  FIG. 12 , an example of using the steering input device  18  for dictating a curvature of a desired backing path of travel (POT) of the trailer  12  while backing up the trailer  12  with the vehicle  14  is shown. In preparation of backing the trailer  12 , the driver of the vehicle  14  may drive the vehicle  14  forward along a pull-thru path (PTP) to position the vehicle  14  and trailer  12  at a first backup position B 1 . In the first backup position B 1 , the vehicle  14  and trailer  12  are longitudinally aligned with each other such that a longitudinal centerline axis L 1  of the vehicle  14  is aligned with (e.g., parallel with or coincidental with) a longitudinal centerline axis L 2  of the trailer  12 . It is disclosed herein that such alignment of the longitudinal axis L 1 , L 2  at the onset of an instance of trailer backup functionality is not a requirement for operability of a trailer backup assist system  10 , but may be done for calibration. 
     After activating the trailer backup assist system  10  (e.g., before, after, or during the pull-thru sequence), the driver begins to back the trailer  12  by reversing the vehicle  14  from the first backup position B 1 . So long as the rotatable knob  30  of the trailer backup steering input device  18  remains in the at-rest position P(AR) and no other steering input devices  18  are activated, the trailer backup assist system  10  will steer the vehicle  14  as necessary for causing the trailer  12  to be backed along a substantially straight path of travel, as defined by the longitudinal direction  22  of the trailer  12 , specifically the centerline axis L 2  of the trailer  12 , at the time when backing of the trailer  12  began. When the trailer  12  reaches the second backup position B 2 , the driver rotates the rotatable knob  30  to command the trailer  12  to be steered to the right (i.e., a knob position R(R) clockwise rotation). Accordingly, the trailer backup assist system  10  will steer the vehicle  14  for causing the trailer  12  to be steered to the right as a function of an amount of rotation of the rotatable knob  30  with respect to the at-rest position P(AR), a rate movement of the knob, and/or a direction of movement of the knob with respect to the at-rest position P(AR). Similarly, the trailer  12  can be commanded to steer to the left by rotating the rotatable knob  30  to the left. When the trailer  12  reaches backup position B 3 , the driver allows the rotatable knob  30  to return to the at-rest position P(AR) thereby causing the trailer backup assist system  10  to steer the vehicle  14  as necessary for causing the trailer  12  to be backed along a substantially straight path of travel as defined by the longitudinal centerline axis L 2  of the trailer  12  at the time when the rotatable knob  30  was returned to the at-rest position P(AR). Thereafter, the trailer backup assist system  10  steers the vehicle  14  as necessary for causing the trailer  12  to be backed along this substantially straight path to the fourth backup position B 4 . In this regard, arcuate portions of a path of travel POT of the trailer  12  are dictated by rotation of the rotatable knob  30  and straight portions of the path of travel POT are dictated by an orientation of the centerline longitudinal axis L 2  of the trailer  12  when the knob is in/returned to the at-rest position P(AR). 
     In the embodiment illustrated in  FIG. 12 , in order to activate the trailer backup assist system  10 , the driver interacts with the trailer backup assist system  10  and the automatically steers as the driver reverses the vehicle  14 . As discussed above, the driver may command the trailer backing path  26  by using a steering input device  18  and the controller  28  may determine the vehicle steering angle to achieve the desired curvature  26 , whereby the driver controls the throttle and brake while the trailer backup assist system  10  controls the steering. As discussed above, the control of the steering by the system  10  can include adjusting the desired curvature  26  and/or the corresponding steering input δ to prevent the steering angle γ from approaching a jackknife angle γ(j), according to one or more of the detection schemes discussed above. 
     With reference to  FIG. 13 , a method of operating one embodiment of the trailer backup assist system  10  is illustrated, shown as one embodiment of the operating routine  132  ( FIG. 2 ). At step  134 , the method is initiated by the trailer backup assist system  10  being activated. It is contemplated that this may be done in a variety of ways, such a making a selection on the display  82  of the vehicle HMI  80 . The next step  136 , then determines the kinematic relationship between the attached trailer  12  and the vehicle  14 . To determine the kinematic relationship, various parameters of the vehicle  14  and the trailer  12  must be sensed, input by the driver, or otherwise determined for the trailer backup assist system  10  to generate steering commands to the power assist steering system  62  in accordance with the desired curvature or backing path  26  of the trailer  12 . As disclosed with reference to  FIGS. 3-6 , the kinematic parameters to define the kinematic relationship include a length of the trailer  12 , a wheel base of the vehicle  14 , a distance from a hitch connection to a rear axle of the vehicle  14 , and a hitch angle γ between the vehicle  14  and the trailer  12 , among other variables and parameters as previously described. Accordingly, after the kinematic relationship is determined, the trailer backup assist system  10  may proceed at step  160  to determine the current hitch angle such as by use of hitch angle sensor  44  or the like. 
     Subsequently, at step  162 , the position and rate of change is received from the steering input device  18 , such as the angular position and rate of rotation of the rotatable knob  30 , for determining the desired curvature  26 . At step  164 , steering commands may be generated based on the desired curvature, correlating with the position and rate of change of the steering input device  18 . The steering commands and actuation commands generated may be generated in conjunction with processing of the curvature routine  98 , as previous discussed, and including any necessary intervention or adjustment to prevent the hitch angle γ from reaching the jackknife angle γ(j), as also discussed above. At step  166 , the steering commands and actuation commands have been executed to guide the trailer  12  on the desired curvature provided by the steering input device  18 . 
     It is to be understood that variations and modifications can be made on the aforementioned structure without departing from the concepts of the present invention, and further it is to be understood that such concepts are intended to be covered by the following claims unless these claims by their language expressly state otherwise.