# Patent

## Title
Vehicle and method of advising a driver therein

## Abstract

A vehicle may include a driver interface and at least one controller operatively arranged with the interface. The at least one controller may be configured to determine a speed and acceleration of the vehicle, to predict a time until a future speed of the vehicle exceeds a predefined speed based on the predefined speed and the speed and acceleration of the vehicle, and to issue an alert via the interface if the time is less than a predefined time.

## Background
CROSS-REFERENCE TO RELATED APPLICATION
This application is a U.S. national phase of PCT Application No. PCT/US2009/062724, filed Oct. 30, 2009, which claims the benefit of U.S. provisional Application Ser. No. 61/109,584, filed Oct. 30, 2008, the disclosures of which are hereby incorporated by reference in their entirety.


BACKGROUND
Operating a vehicle at speeds above posted speed limits may increase the chances of being involved in a road accident. Furthermore, it may reduce the time available to react to varying driving conditions.
SUMMARY
A method for advising a driver of a vehicle may include predicting an acceleration of the vehicle, determining whether the predicted acceleration is greater than a threshold acceleration, and generating an alert for the driver before an acceleration of the vehicle exceeds the threshold acceleration if the predicted acceleration is greater than the threshold acceleration.
A method for advising a driver of a vehicle may include determining a speed and acceleration of the vehicle, and generating an alert for the driver before the speed of the vehicle exceeds a predefined speed based on the speed and acceleration of the vehicle and the predefined speed.
While example embodiments in accordance with the invention are illustrated and disclosed, such disclosure should not be construed to limit the invention. It is anticipated that various modifications and alternative designs may be made without departing from the scope of the invention.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of an embodiment of a vehicle control system.
FIG. 2 is a plot of example vehicle speed, traction and braking profiles.
FIGS. 3A through 3C are plots of example vehicle motion states of yaw rate and sideslip angle.
FIGS. 4A through 4C are plots of example yawing, longitudinal, and sidesliping handling limit margins.
FIG. 5 is a plot of example vehicle speed, traction and braking profiles.
FIGS. 6A through 6C are plots of example vehicle motion states of yaw rate and sideslip angle.
FIGS. 7A through 7C are plots of example yawing, longitudinal, and sidesliping handling limit margins.
FIG. 8 is a plot of example membership functions characterizing four driver categories based on handling risk factor.
FIGS. 9A, 10A and 11A are plots of example final handling limit margins and risk.
FIGS. 9B, 10B and 11B are plots of example probabilities of driver style.
FIG. 12 is a plot of example determinants of smooth and abrupt driving behaviors.
FIGS. 13A and 13B are plots of example mean gap times for aggressive and cautious driving respectively.
FIGS. 14A and 14B are plots of example standard deviations of accelerator pedal rate for aggressive and cautious driving respectively.
FIGS. 15A and 15B are plots of example standard deviations of brake pedal rate for aggressive and cautious driving respectively.
FIGS. 16A and 16B are plots of example driver indices for aggressive and cautious driving respectively.
FIG. 17 is a plot of an example relative range, range-error and longitudinal acceleration between a leading and following car for aggressive driving.
FIG. 18 is a plot of select example parameters characterizing the aggressive driving of FIG. 17.
FIG. 19 is a plot of an example relative range, range-error and longitudinal acceleration between a leading and following car for cautious driving.
FIG. 20 is a plot of select example parameters characterizing the cautious driving of FIG. 19.
FIG. 21 is a block diagram of an embodiment of a driver advisory system.
FIG. 22 is a plot of example vehicle speed versus sample time.
FIGS. 23 and 24 are plots of expanded portions of FIG. 22.



DETAILED DESCRIPTION
I. Introduction
An objective of existing vehicle electronic control systems is to facilitate the driving task by identifying driver intent and aiding the driver by controlling the vehicle to achieve the driver intent safely, robustly, and smoothly. The control effectiveness of electronic control systems may be significantly increased when the driver and the electronic control system work together towards the same accident avoidance goal and maximize the accident avoidance capability of the driver-in-the-loop vehicle as a system. One approach to achieve this is to provide timely clear and transparent advisory information to a driver such that a responsible driver can respond accordingly. Such advisory information can be gathered or computed from sensors normally found on a vehicle, which implement a bilateral closed-loop control between the driver and the electronic control. The electronic control follows the driver intent and the driver responds to the advisory information from the electronic control to modify his drive inputs (such as dropping throttle, easing steering inputs, etc.) In this way, a seamless coordination between the driver and the electronic control system is possible and is likely to minimize the effect of potential safety hazards due to driver errors.
Here, we consider, inter alia, warnings that are issued in advance of violating a speed or acceleration limit. This may be part of a cluster of warning functions that may be defined as an Intelligent Personal Minder (IPM) system. Generally speaking, the intelligence computed for the IPM system can be sent to warn or advise a driver through various devices including a haptic pedal, a heads-up-display, an audio warning device, a voice system, etc.
FIG. 1 depicts the interaction of an embodiment of an IPM system 10 with other components/subsystems 12 of a vehicle 14. The other components/subsystems 12 may include vehicle sensors 16, 18 (e.g., a yaw rate sensor, steering angle sensor, lateral acceleration sensor, longitudinal acceleration sensor, wheel speed sensor, brake pressure sensor, etc.), actuators 20 and one or more controllers 22. The one or more controllers 22 may include stability control 24, arbitration logic 26 and other controllers/systems 28 (e.g., anti-lock braking system, traction control system, etc.)
For any control system, the plant model may play a role in designing an effective control strategy. Similarly, a driver model is important for generating effective and appropriate driver advisory signals. Hence, driving style characterization may be needed. We discuss methods of identifying a driver's characteristics based on his or her vehicle handling capability. While driver modeling and driver behavior characterization have been studied, we suggest an approach in which the driving behavior/style and/or the driving experience level may be deduced, for example, based on the frequency and duration of driving close to the handling limit (as well as other techniques). Such driver characterization information may be used in a variety of applications, some of which are discussed below.
II. A Brief Discussion of Vehicle Stability Controls
A vehicle's handling determines the vehicle's ability to corner and maneuver. The vehicle needs to stick to the road with its four tire contact patches in order to maximize its handling capability. A tire which exceeds its limit of adhesion is either spinning, skidding or sliding. A condition where one or more tires exceed their limits of adhesion may be called a limit handling condition and the adhesion limit may be called a handling limit. Once a tire reaches its handling limit, the average driver is usually no longer in control. In the so-called understeer case, the car under performs a driver's steering input, its front tires pass their handling limit, and the vehicle continues going straight regardless of the driver's steering request. In the so-called oversteer case, the car over performs the driver's steering inputs, its rear tires pass their handling limit, and the vehicle continues spinning. For safety purposes, most vehicles are built to understeer at their handling limits.
In order to compensate vehicle control in case a driver is unable to control the vehicle at or beyond the handling limit, electronic stability control (ESC) systems are designed to redistribute tire forces to generate a moment that can effectively turn the vehicle consistent with the driver's steering request. Namely, to control the vehicle to avoid understeer and oversteer conditions.
Since its debut in 1995, ESC systems have been implemented in various platforms. Phasing in during model year 2010 and achieving full installation by model year 2012, Federal Motor Vehicle Safety Standard 126 requires ESC systems on any vehicle with a gross weight rating below 10,000 lb. ESC systems may be implemented as an extension of anti-lock braking systems (ABS) and all-speed traction control systems (TCS). They may provide the yaw and lateral stability assist to the vehicle dynamics centered around the driver's intent. It may also proportion brake pressure (above or below the driver applied pressure) to individual wheel(s) so as to generate an active moment to counteract the unexpected yaw and lateral sliding motions of the vehicle. This leads to enhanced steering control at the handling limits for any traction surface during braking, accelerating or coasting. More specifically, current ESC systems compare the driver's intended path to the actual vehicle response which is inferred from onboard sensors. If the vehicle's response is different from the intended path (either understeering or oversteering), the ESC controller applies braking at selected wheel(s) and reduces engine torque if required to keep the vehicle on the intended path and to minimize loss of control of the vehicle.
A limit handling condition can be detected using data already existing in ESC systems, so new sensors may not be required. Consider, for example, a vehicle equipped with an ESC system using a yaw rate sensor, a steering wheel sensor, a lateral accelerometer, a wheel speed sensors, a master cylinder brake pressure sensor, a longitudinal accelerometer, etc. The vehicle motion variables are defined in the coordinate systems as defined in ISO-8855, where a frame fixed on the vehicle body has its vertical axis up, longitudinal axis along the longitudinal direction of the vehicle body, and a lateral axis pointed from the passenger side to the driver side.
Generally speaking, vehicle level feedback controls can be computed from individual motion variables such as yaw rate, sideslip angle, or their combination together with arbitrations among other control commands such as driver braking, engine torque request, ABS and TCS. Vehicle level control commands are discussed in the following.
The well-known bicycle model captures the vehicle dynamics, its yaw rate ωz along the vertical axis of the vehicle body and its sideslip angle βr defined at its rear axle, and obeys the following equations

Iz{dot over (ω)}z=−bfcf(βr+bωztvx−1−δ)+brcrβr+Mz 

M({dot over (v)}xβr+vx{dot over (β)}r+br{dot over (ω)}z+ωzvx)=−cf(βr+bωzvx−1−δ)−crβr  (1)

where vx is the vehicle's travel speed, M and Iz are the total mass and the yaw moment of inertia of the vehicle, cf and cr are the cornering stiffness of the front and rear tires, bf and br are the distances from the center of gravity of the vehicle to the front and rear axles, b=bf+br, Mz is the active moment applied to the vehicle, and δ is the front wheel steering angle.

A target yaw rate ωzt and a target sideslip angle βrt used to reflect the driver's steering intent can be calculated from (1) using the measured steering wheel angle δ and the estimated travel velocity vx as the inputs. In such a computation, we assume that the vehicle is driven on a road of normal surface condition (e.g., high friction level with nominal cornering stiffness cf and cr). Signal conditioning, filtering and nonlinear corrections for steady state limit cornering may also be performed in order to fine tune the target yaw rate and the target sideslip angle. These calculated target values characterize the driver's intended path on a normal road surface.
The yaw rate feedback controller is essentially a feedback controller computed from the yaw error (the difference between the measured yaw rate and the target yaw rate). If the vehicle is turning left and ωz≧ωzt+ωzdbos (where ωzdbos is a time varying deadband), or the vehicle is turning right and ωz≦ωrt−ωzdbos, the vehicle is oversteering and activating the oversteer control function in ESC. For instance, the active torque request (applied to the vehicle for reducing the oversteer tendency) might be computed as in the following

during a left turn: Mz=min(0,−kos(ωz−ωzt−ωzdbos))

during a right turn: Mz=max(0,−kos(ωz−ωzt+ωzdbos))  (2)

where kos is a speed dependent gain which might be defined as in the following





  
    
      
        
          k
          os
        
        =
        
          
            k
            0
          
          +
          
            
              (
              
                
                  v
                  x
                
                -
                
                  v
                  xdbl
                
              
              )
            
            ⁢
            
              
                
                  k
                  dbu
                
                -
                
                  k
                  dbl
                
              
              
                
                  v
                  xdbu
                
                -
                
                  v
                  xdbl
                
              
            
          
        
      
    
    
      
        (
        3
        )
      
    
  




with parameters k0, kdbl, kdbu, vxdbl, vxdbu being tunable.

If ωz≦ωz−ωzdbus (where ωzdbus is a time varying deadband) when the vehicle is turning left or ωz≧ωz+ωzdbus when the vehicle is turning right, the understeer control function in ESC is activated. The active torque request can be computed as in the following

during a left turn: Mz=max(0,−kus(ωz−ωzt+ωzdbus))

during a right turn: Mz=min(0,−kus(ωz−ωzt−ωzdbus))  (4)

where kus is a tunable parameter.

The sideslip angle controller is a supplementary feedback controller to the aforementioned oversteer yaw feedback controller. It compares the sideslip angle estimation βr to the target sideslip angle βrt. If the difference exceeds a threshold βrdb, the sideslip angle feedback control is activated. For instance, the active torque request is calculated as in the following
during a left turn,

βr≧0:Mz=min(0,kss(βr−Brt−Brdb)−ksscmp{dot over (β)}rcmp)  (5)

during a right turn,

βr<0:Mz=max(0,kss(β−Brt+Brdb)−ksscmp{dot over (β)}rcmp)

where kss and ksscmp are tunable parameters and {dot over (β)}rcmp is a compensated time derivative of the sideslip angle.

Other feedback control terms based on variables such as yaw acceleration and sideslip gradient can be similarly generated. When the dominant vehicle motion variable is either the yaw rate or the sideslip angle, the aforementioned active torque can be directly used to determine the necessary control wheel(s) and the amount of brake pressures to be sent to corresponding control wheel(s). If the vehicle dynamics are dominated by multiple motion variables, control arbitration and prioritization will be conducted. The final arbitrated active torque is then used to determine the final control wheel(s) and the corresponding brake pressure(s). For example, during an oversteer event, the front outside wheel is selected as the control wheel, while during an understeer event, the rear inside wheel is selected as the control wheel. During a large side-slipping case, the front outside wheel is always selected as the control wheel. When both the side slipping and oversteer yawing happen simultaneously, the amount of brake pressure may be computed by integrating both yaw error and the sideslip angle control commands.
Besides the above cases where the handling limit is exceeded due to the driver's steering maneuvers, a vehicle can reach its limit handling condition in its longitudinal motion direction. For example, braking on a snowy and icy road can lead to locked wheels, which increases the stopping distance of the vehicle. Open throttling on a similar road can cause the drive wheels to spin without moving the vehicle forward. For this reason, the handling limit may also be used for these non-steering driving conditions. That is, the conditions where the tire longitudinal braking or driving forces reach their peak values may also be included in a definition of the handling limit.
The ABS function monitors the rotational motion of the individual wheels in relation to the vehicle's travel velocity, which can be characterized by the longitudinal slip ratios λi, with i=1, 2, 3, 4 for the front-left, front-right, rear-left and rear-right wheels, computed as in the following




  
    
      
        
          
            λ
            1
          
          =
          
            
              
                
                  κ
                  1
                
                ⁢
                
                  ω
                  1
                
              
              
                max
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            -
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            2
          
          =
          
            
              
                
                  κ
                  2
                
                ⁢
                
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                    2
                    ⁢
                    
                      
                    
                  
                
              
              
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                ⁡
                
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              λ
              3
            
            =
            
              
                
                  
                    κ
                    3
                  
                  ⁢
                  
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                    3
                  
                
                
                  max
                  ⁡
                  
                    (
                    
                      
                        
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              -
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              λ
              4
            
            =
            
              
                
                  
                    κ
                    4
                  
                  ⁢
                  
                    ω
                    
                      4
                      ⁢
                      
                        
                      
                    
                  
                
                
                  max
                  ⁡
                  
                    (
                    
                      
                        
                          v
                          x
                        
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                            z
                          
                          ⁢
                          
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        (
        6
        )
      
    
  




where tf and tr are the half tracks for the front and rear axles, ωi is the ith wheel speed sensor output, κi is the ith wheel speed scaling factor, vy is the lateral velocity of the vehicle at its e.g. location, and vmin is a preset parameter reflecting the allowable minimum longitudinal speed. Notice that (6) is only valid when the vehicle is not in the reverse driving mode. When the driver initiated braking generates too much slip (e.g., −λi≧λbp=20%) at a wheel, the ABS module will release the brake pressure at that wheel. Similarly, during a large throttle application causing a large slip on the ith driven wheel, the TCS module will request engine torque reduction and/or brake pressure applied to the opposite wheel at the same axle. Consequently, ABS or TCS activations can be predicted by monitoring how close λis are from λbp and λtp.

III. Handling Limit Driving Style Characterization

While the aforementioned ESC (including ABS and TCS) is effective in achieving its safety goal, further enhancement is still possible. For example, augmentation of ESC systems may be desirable for roll stability control. The appropriate correction which ESC tries to make, however, may be counteracted by the driver or ambient conditions. A speeding vehicle, whose tire forces go far beyond the traction capability of the road and the tires, might not be able to avoid an understeer accident even with ESC intervention.
We introduce an integration of the driver and ESC system such that they may work cooperatively towards an enhanced control performance of the driver-in-the-loop system. In certain embodiments, the proposed Handling Limit Minder (HLM) determines how close the current driving condition is to the handling limit.
Generally speaking, accurate determination of the handling limit conditions would involve direct measurements of road and tire characteristics or very intensive information from many related variables if direct measurements are not available. Currently, both of these methods are not mature enough for real-time implementation.
Due to their feedback feature, ESC systems may be configured to determine the potential limit handling conditions through monitoring the motion variables of a vehicle such as those described in the last section. When the motion variables deviate from their reference values by a certain amount (e.g., beyond certain deadbands), the ESC systems may start to compute differential braking control command(s) and determine control wheel(s). The corresponding brake pressure(s) is then sent to the control wheel(s) to stabilize the vehicle. The starting point of the ESC activation can be thought of as the beginning of the handling limit.
More specifically, we may define a relative handling limit margin hx as in the following




  
    
      
        
          h
          x
        
        =
        
          {
          
            
              
                
                  
                    
                      x
                      _
                    
                    -
                    x
                  
                  
                    x
                    _
                  
                
              
              
                
                  
                    if
                    ⁢
                    
                      
                    
                    ⁢
                    0
                  
                  ≤
                  x
                  ≤
                  
                    x
                    _
                  
                
              
            
            
              
                
                  
                    x
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                      x
                      _
                    
                  
                  
                    x
                    _
                  
                
              
              
                
                  
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                    ⁢
                    
                      
                    
                    ⁢
                    
                      x
                      _
                    
                  
                  ≤
                  x
                  <
                  0
                
              
            
            
              
                0
              
              
                otherwise
              
            
          
        
      
    
    
      
        (
        8
        )
      
    
  




where x is the deviation of a motion variable from its reference value and [x,x] defines the deadband interval within which x falls without initiating the ESC, ABS or TCS. x can be any of the control variables defined in the last section (or any other suitable control variable).

The benefit of hx defined in (8) is that the driving condition can be quantitatively characterized into different categories. For instance, when hx≦10%, the driving condition may be categorized as a red zone condition where the driver needs to have special attention or take some special actions (e.g., slowing down the vehicle); when 10%<hx<40%, the driving condition may be categorized as a yellow zone condition which needs some level of special attention from the driver; when 40%<hx≦100%, the driving condition may be characterized as a normal condition. In the normal condition, the driver need only to maintain his normal driving attention. Of course, other ranges may also be used.
Various audible and/or visual warnings may be activated to alert a driver about the handling limit margin. When hx≦10% for example, a warning light/haptic device may activate to inform the driver that they need to slow down. Alternatively, a voice enabled display system may instruct the driver to take particular action. When 10%<hx<40%, an audible tone or display may inform the driver that they are approaching unstable driving conditions, etc.
More specifically, let us use the control variables computed in the last section to discuss the computation of hxs. The vehicle's yaw handling limit margin during oversteer situations hOS (where ωz>ωzt when the vehicle is turning to the left and ωz>ωzt when the vehicle is turning to the right) can be computed from (8) by setting x=ωz−ωzt and x=ωzdbos=−x, where ωzdbos is the oversteer yaw rate deadband as defined in (2).
Similarly, the vehicle's yaw handling limit hUS for understeer situations can be computed from (8) by setting x=ωz−ωzt and x=ωzdbus=−x, where ωzdbus is the understeer yaw rate deadband as defined in (4). Notice that the aforementioned deadbands might be functions of the vehicle speed, the magnitude of the target yaw rate, the magnitude of the measured yaw rate, etc. The deadbands for the understeer situation (x<0) and the oversteer situation (x>0) are different and they are tunable parameters.
The vehicle's sideslip handling limit margin hSSRA can be computed from (8) by setting x=βr−βrt and x=βrdb=−x.
The longitudinal handling limits of the vehicle involve the conditions when either the driving or braking force of the tires approach the handling limit. The traction control handling limit margin for the ith driven wheel hTCSi can be computed from (8) by setting x=λi, x=0, and x=λtb. The ABS handling limit margin for the ith wheel hABSi can also be computed from (8) by setting x=λi, x=λbp, and x=0. The final traction and braking handling limit margins may be defined as




  
    
      
        
          
            h
            
              AB
              ⁢
              
                
              
              ⁢
              S
            
          
          =
          
            
              min
              
                i
                ∈
                
                  {
                  
                    1
                    ,
                    2
                    ,
                    3
                    ,
                    4
                  
                  }
                
              
            
            ⁢
            
              h
              
                AB
                ⁢
                
                  
                
                ⁢
                
                  S
                  i
                
              
            
          
        
        ,
        
          
            h
            TCS
          
          =
          
            
              min
              
                i
                ∈
                
                  {
                  
                    1
                    ,
                    2
                    ,
                    3
                    ,
                    4
                  
                  }
                
              
            
            ⁢
            
              h
              
                TCS
                i
              
            
          
        
      
    
    
      
        (
        9
        )
      
    
  




Notice that further screening conditions may be used in computing the aforementioned handling limit margins. For instance, one of the following or the combination of some of the following conditions might be used to set the handling limit margin as 0: a magnitude of the target yaw rate is beyond a certain threshold; a magnitude of the measured yaw rate is greater than a certain threshold; a driver's steering input exceeds a certain threshold; or, extreme conditions such as the vehicle's cornering acceleration is greater than 0.5 g, the vehicle's deceleration is greater than 0.7 g, the vehicle is driven at a speed beyond a threshold (e.g., 100 mph), etc.
In order to test the aforementioned handling limit margin computations and verify their effectiveness with respect to known driving conditions, a vehicle equipped with a research ESC system developed at Ford Motor Company was used to conduct vehicle testing.
For the driving condition profiled by the vehicle speed, throttling, and braking depicted in FIG. 2, the measured and computed vehicle motion variables are shown in FIGS. 3A through 3C. The corresponding individual handling limit margins hUS, hOS, hTCS, hABS, and hSSRA are shown in FIGS. 4A through 4c. This test was conducted as a free form slalom on a snow pad with all ESC computations running. The brake pressure apply was turned off in order for the vehicle to approach the true limit handling condition.
For another test, the vehicle was driven on a road surface with high friction level. The vehicle speed, traction and braking profiles for this test are depicted in FIG. 5. The vehicle motion states are shown in FIGS. 6A through 6C. The corresponding individual handling limit margins hUS, hOS, hTCS, hABS, and hSSRA are shown in FIGS. 7A and 7B.
An envelope variable of all the individual handling limit margins is defined as

henv=min{hOS,hUS,hTCS,hABS,hSSRA}  (10)

Considering that sudden changes in the envelope handling limit margin might be due to signal noises, a low-pass filter F(z) is used to smooth henv so as to obtain the final handling limit margin

h=F(z)henv  (11)

For the vehicle test data shown on FIG. 2 and FIGS. 3A through 3C, the final handling limit margin is depicted in FIG. 9A, while for the vehicle test data shown on FIG. 5 and FIGS. 6A through 6C, the final handling limit margin is depicted in FIG. 10A.

We may now use the final handling limit margin computed in (11) to characterize vehicle handling related driving conditions and driving style. We introduce the concept of a Handling Risk Factor (HRF) as the measure of how a driving condition is related to the handling limit. The handling risk factor r is defined as the complement of the final handling limit margin h, i.e.,

r=1−h  (12)

The handling risk factor is minimal (r=0) when the final handling limit margin h is maximal (h=1) and vice versa. The HRF may be further used to develop a probabilistic model describing different categories of driving styles which are reflected by the current driving conditions with respect to the handling limit.
Generally speaking, a cautious driver usually drives without frequent aggressiveness, i.e., fast changes of steering, speed and acceleration. Hence, it is reasonable to characterize a cautious driver as one who constantly avoids using extreme driving inputs and getting close to the maximal handling risk. An average driver likely exhibits a higher level of HRF than a cautious driver. An expert driver might be more skilful in controlling the vehicle, i.e., he can drive with a relatively high level of HRF for a long duration without having the vehicle pass the maximal handling limit. A reckless driver exhibits a careless handling behavior which is unpredictable and could induce fast changes. The reckless driver is expected to drive with a handling risk factor that might approach the maximum (r=1) very briefly from time to time, thus causing frequent triggering of the related safety systems (e.g., ABS, TCS, ESC).
Notice that the difference between the expert driver and the reckless driver is that the former can hold a driving condition at a relatively high HRF level for long duration, while the latter can only hold at the similar level for a short duration before causing the vehicle to pass the maximal handling limit due to the driver's poor control capability. Since the handling risk factor ranges defining, for example, cautious, average, expert and reckless driving behavior (with respect to the limit handling conditions) may not be well defined, we use fuzzy subsets to quantify the four categories of drivers. We further evaluate those categories probabilistically based on a specific driver style. The fuzzy subsets associated with the categories of cautious, average, expert and reckless drivers may be described by the following membership functions

μc(r),μe(r),μa(r),μr(r)

defined over the HRF universe [0, 1]. FIG. 8 shows the relationship between the degrees of membership for each of those categories and the HRF.

The membership functions in FIG. 8 can be assigned to any event that is represented by a specific HRF with value rk using a four dimensional vector

Dk=[μc(rk)μe(rk)μa(rk)μr(rk)]T 

of its degree of membership to each of the four example categories: cautious, average, expert and reckless. For example, a HRF value rk=0.4 (corresponding to handling limit margin value hk=0.6) will translate to the degrees of membership to the cautious, average, expert and reckless categories

μc(0.4)=0.46, μe(0.4)=0.85

μa(0.4)=0.09, μr(0.4)=0.22

The membership grades encode the possibilities that the event characterized by a HRF with value r=0.4 (or the handling limit margin h=0.6) might be associated with any of the four example partitions. The vector of membership values dk makes the association between a single driving event and the possible driver characterization with respect to the HRF of that event. In order to characterize the long term behavior of the driver, we need a probabilistic interpretation of the possibilities that are generated by multiple events. By adding the membership values for each event, we essentially aggregate the overall possibilities that a specific driver can be categorized as cautious, average, expert and reckless, i.e., the vector




  
    
      
        
          d
          *
        
        =
        
          
            ∑
            
              k
              =
              1
            
            N
          
          ⁢
          
            
              [
              
                
                  
                    μ
                    c
                  
                  ⁡
                  
                    (
                    
                      r
                      k
                    
                    )
                  
                
                ⁢
                
                  
                    μ
                    e
                  
                  ⁡
                  
                    (
                    
                      r
                      k
                    
                    )
                  
                
                ⁢
                
                  
                    μ
                    r
                  
                  ⁡
                  
                    (
                    
                      r
                      k
                    
                    )
                  
                
              
              ]
            
            T
          
        
      
    
    
      
        (
        13
        )
      
    
  




where N is the number of samples. The aggregated possibilities can be considered as frequencies (sometimes referred to as fuzzy frequencies) since they reveal how frequently and to what degree the HRFs for the multiple events can be cascaded to the four example categories. The alternative to aggregating the possibilities, i.e., adding the membership functions, is to add 1 if the specific membership grade μi(rk), iε{c,a,e,r} is greater than a prescribed threshold value, e.g., 0.8, or 0 otherwise, resulting in calculating the conventional frequency of the four example categories. From the aggregated possibilities, we can calculate the probabilities of the cautious, average, expert and reckless driver style





  
    
      
        
          p
          i
        
        =
        
          
            
              d
              i
              *
            
            (
            
              
                ∑
                
                  j
                  ∈
                  
                    {
                    
                      c
                      ,
                      a
                      ,
                      e
                      ,
                      r
                    
                    }
                  
                
              
              ⁢
              
                d
                j
                *
              
            
            )
          
          
            -
            1
          
        
      
    
    
      
        (
        14
        )
      
    
  




where iε{c,a,e,r}. The probabilities are calculated from the aggregated possibilities (fuzzy frequencies) and can be considered fuzzy probabilities. The reason for the fuzziness here is the lack of certainty in characterizing the relationship between the four example categories and the HRF. For the special case of crisply defined categories (represented by intervals rather than fuzzy subsets), the possibilities transform to Boolean values, their aggregated values become frequencies, and consequently the fuzzy probabilities are translated to conventional probabilities.

The most likely driver category i* is the one that is characterized with the highest probability, i.e.,




  
    
      
        
          i
          *
        
        =
        
          
            arg
            
              i
              ∈
              
                {
                
                  c
                  ,
                  a
                  ,
                  e
                  ,
                  r
                
                }
              
            
          
          ⁢
          
            
          
          ⁢
          
            max
            ⁡
            
              (
              
                p
                i
              
              )
            
          
        
      
    
    
      
        (
        15
        )
      
    
  




The frequencies based calculation of the probabilities can be expressed in terms of the average frequencies




  
    
      
        
          p
          i
        
        =
        
          
            d
            i
            *
          
          /
          
            
              N
              (
              
                
                  ∑
                  
                    j
                    ∈
                    
                      {
                      
                        c
                        ,
                        a
                        ,
                        e
                        ,
                        r
                      
                      }
                    
                  
                
                ⁢
                
                  
                    d
                    j
                    *
                  
                  /
                  N
                
              
              )
            
            
              -
              1
            
          
        
      
    
    
      
        (
        16
        )
      
    
  




Alternatively, it can be expressed through the exponentially weighted average frequencies where the higher weights are assigned to the possibilities that are associated with the most recent events. Numerically, the process of generating a weighted average with higher weights corresponding to the recent observation can be accomplished by applying a low pass filter implementing the exponential smoothing algorithm in the time domain

d*new=(1−α)d*old+αdk=d*old+α(dk−d*old)  (17)

where the constant forgetting factor 0<α≦1 controls the rate of updating the mean d* by assigning a set of exponentially decreasing weights to the older observations. For a constant forgetting factor α, expression (17) recursively generates a vector of positive weights

W=[(1−α)kα(1−α)k−1α(1−α)k−2 . . . α]  (18)

with a unit sum. Vector W delineates a weighted average type aggregating operator with exponentially decreasing weights that are parameterized by the forgetting factor α. Parameter α defines the memory depth (the length of the moving window) of the weighted averaging aggregating operator. Therefore, the filtered value d* of the membership grade vector in (17) represents the weighted averages of the individual possibilities over the weights W. Since all of the aggregated possibilities are calculated over the same moving window of length Kα=1/α, we can consider them as representations of the frequencies of the associations with each of the four concepts. Weighted average (17) is calculated over the events with indexes belonging to a soft interval

sε{k−Kα+1,k]  (19)

where symbol {indicates a soft lower bound that includes values with lower indexes than (k−Kα) with relatively low contribution. Consequently, the aggregated possibilities that form the vector d* can be converted to probabilities according to expression (14).

In certain embodiments, α a may be selectable so that a characterization for a desired period of time is achieved. For example, a user may supply input related to a such that every half hour, a characterization is made. Other scenarios are also possible.
For the vehicle testing depicted by FIGS. 2, 3A through 3C and 4A through 4C, the individual pi's are shown on FIG. 9B indicating that for most of the driving, the driver exhibited a reckless driving behavior, which is consistent with the large value of the sideslip angle in FIG. 3C (peak magnitude of the sideslip angle exceeds 10 degrees). For vehicle testing depicted by FIGS. 5 through 7C, the individual pi's are shown in FIG. 10B, indicating that the driver initially exhibited an average driver behavior and then transitioned to a reckless driver behavior.
The calculated probabilities define the most likely HRF based characterization of a driver for the time window that is specified by the forgetting factor α. By modifying the moving window, we can learn and summarize the long and short term characterization for a specific driver based on the HRF.
In order to predict the impact of the changes in HRF on the driver's characterization, we introduce the notion of transitional probabilities. The Markov model P probabilistically describes the set of transitions between the current and the predicted value of the driver category:




  
    
  
  ⁢
  
    
      
        p
        j
      
      ⁡
      
        (
        
          k
          +
          1
        
        )
      
    
    ->
    
      

    
    ⁢
    
      
        
          
            
          
        
        
          
            p
            11
          
        
        
          
            p
            12
          
        
        
          
            p
            13
          
        
        
          
            p
            14
          
        
      
      
        
          
            
              p
              i
            
            ⁡
            
              (
              k
              )
            
          
        
        
          
            p
            21
          
        
        
          
            p
            22
          
        
        
          
            p
            23
          
        
        
          
            p
            24
          
        
      
      
        
          
            
          
        
        
          
            p
            31
          
        
        
          
            p
            32
          
        
        
          
            p
            33
          
        
        
          
            p
            34
          
        
      
      
        
          
            
          
        
        
          
            p
            41
          
        
        
          
            p
            42
          
        
        
          
            p
            43
          
        
        
          
            p
            44
          
        
      
    
  




where pij is the probability of switching from category i at time k to category j at time k+1, and pii=max(pi) is the probability that is associated with the dominating category i at time k, i,jε{c,a,e,r}. The transitional probabilities pij are derived from the transitional aggregated possibilities that are updated only if i=arg max(p1) at time k and j=arg max(p1), lε{c,a,e,r}.





  
    
      
        
          d
          
            if
            ,
            new
          
          *
        
        =
        
          {
          
            
              
                
                  
                    
                      (
                      
                        1
                        -
                        α
                      
                      )
                    
                    ⁢
                    
                      d
                      
                        if
                        ,
                        old
                      
                      *
                    
                  
                  +
                  
                    α
                    ⁢
                    
                      
                    
                    ⁢
                    
                      d
                      
                        i
                        ,
                        k
                      
                    
                  
                
              
              
                
                  
                    if
                    ⁢
                    
                      
                    
                    ⁢
                    j
                  
                  =
                  
                    
                      arg
                      
                        l
                        ∈
                        
                          {
                          
                            c
                            ,
                            a
                            ,
                            e
                            ,
                            r
                          
                          }
                        
                      
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      max
                      ⁡
                      
                        (
                        
                          p
                          l
                        
                        )
                      
                    
                  
                
              
            
            
              
                
                  
                    (
                    
                      1
                      -
                      α
                    
                    )
                  
                  ⁢
                  
                    d
                    
                      if
                      ,
                      old
                    
                    *
                  
                
              
              
                otherwise
              
            
          
          }
        
      
    
    
      
        (
        20
        )
      
    
  




The transitional probabilities are then calculated by converting the aggregated transitional possibilities to the probabilities. The maximal transitional probability pij determines the transition from category i to category j as the most likely transition.

FIGS. 11A and 11B use a driving vehicle test to verify long term driving behavior characterization. The driver generally shows a cautious driving style (which could be a novice, average or expert driver). At around 190 seconds, the vehicle was turned with some degree of aggressiveness which can be seen from the peak at the HRF plot, and the driving style transitioned to the average category. Since no major HRF events were further identified, this category was carried out for the rest of the driving cycle in conjunction with the concept of the long term characterization.
As mentioned above, various audible and/or visual warnings may be activated to alert a driver about the handling limit margin. The margin thresholds that define whether (and/or what type) of warning is to be issued may be altered (or suspended) based on the driver characterization. For example, if it is determined that the driver is an expert driver, the warning threshold may be reduced from hx≦10% to hx≦2%, or the warnings regarding the handling limit margin may be suspended (an expert driver may not need the warnings).
IV. Unsupervised Driving Style Characterization
During a normal driving maneuver, a driver's long term longitudinal vehicle control may be used to determine driving behavior regardless of the vehicle's dynamic response. For instance, a driver may exhibit a specific longitudinal control pattern during driving on a highway for a long period of time. His pattern of acceleration pedal activation can be smooth or abrupt even in the absence of emergency conditions. The variability of the pedal and its rate change can be used to differentiate between smooth and abrupt application. Such a smooth or abrupt application exhibits strong correlation with fuel economy and acceleration performance when driving conditions are unconstrained. Identifying such driving behaviors can be used, for example, to implement a fuel economy advisor.
Anomaly detection can be used to estimate major changes in the overall variability of the control actions indicating changes in corresponding behaviors. Anomaly detection is a technique that puts a major emphasis on the continuous monitoring, machine learning, and unsupervised classification to identify a trend of departure from a normal behavior and predict potential significant change. The determinant of the covariance matrix of the population of a driver's actions may be used as a measure of the generalized variance (spread) of the population, and hence as an indicator for a change in the driver's behavior.
The feature space of driving torque request τd and its derivative is spanned by the vector y=[τd{dot over (τ)}d]. The determinant D of the covariance matrix of the population can be recursively calculated as

Dk+1=(1−α)k−1Dk(1−α+(yk−vk)Qk(yk−vk)T)  (21)

with

vk+1=(1−α)vk+αyk 

Qk+1=(I−Gk(yk−vk))Qk(1−α)−1 

Gk+1=Qk(yk−vk)Tα(1−α+α(yk−vk)Qk(yk−vk)T)−1  (22)

where vk is a filtered version of yk, Qk is the estimated inverse covariance matrix, and α is a constant which reflects the forgetting factor related to the filter memory depth.

Dk thus computed in (21) has initial means and standard deviations for abrupt and smooth type behaviors. The instantaneous behavior is classified as abrupt if its value is higher than a control limit labrupt and is classified as smooth if its value is lower than a control limit usmooth. labrupt and usmooth are defined as labrupt=μabrupt−3σabrupt, usmooth=μsmooth+3σsmooth where μabrupt and σabrupt are the mean and standard deviation of the abrupt behavior class. μsmooth and σsmooth are similarly defined for the smooth behavior class. If the current behavior is classified as either abrupt or smooth, the corresponding mean and standard deviation of the matching behavior are recursively updated

wk+1=(1−β)wk+βDk+1 

Hk+1=(1−β)Hk+(β−β2)(Dk+1−wk)T(Dk+1−wk)

σk+1=(Hk+1)1/2  (23)

where w and H are the estimated mean and variance, and β is another forgetting factor.

FIG. 12 shows the determinant of the covariance matrix from the vector of acceleration pedal position and its rate change for 8 runs of vehicle tests. The 4 runs with solid lines of determinant were for abrupt acceleration pedal applications. These determinants show a large value, for example, greater than 7. The 4 runs with dotted lines of determinant were for smooth acceleration pedal applications. These determinants show a small value, for example, less than 4. Hence, the size of the determinant reveals the unique informative patterns which can be used to distinguish smooth driving behavior from abrupt driving behavior.
Since interactions between the driver and the driving environment include frequent vehicle stops with varied durations, suspension of the continual updating may be required to prevent numerical problems during recursive computation. The following suspension conditions may be used: (i) If vehicle speed is less than 1 mph, vehicle speed and acceleration related recursive calculations are suspended. (ii) If the accelerator pedal position is less than 1%, pedal related recursive calculations are suspended.
Although the above deviation focuses on the acceleration pedal, it can be easily applied to the braking case. Since sudden aggressive braking can happen during emergency situations (which are not necessarily indicative of the driver's general behavior), quasi-steady state driving where braking is not at its extreme may be used for computational screening.
During transient acceleration and deceleration, certain wheels of the vehicle may experience large longitudinal slip, and the tire longitudinal forces of those wheels may reach their peak values. Such conditions can be identified through monitoring the rotational motion of the individual wheels in relation to the vehicle's travel velocity, and consequently the driver behavior during transient maneuvers can be determined as discussed above.
V. Semi-Supervised Driving Style Characterization
All driver inputs may not be accessible by electronic control systems. Certain variables, however, may construct an input-output pair that may be used to deduce driver control structure. For example, during a car-following maneuver, the relative distance between the leading and following car and the driver's braking and throttle requests are usually well coordinated. Here we consider using a Tagaki-Sugeno (TS) model to relate the variance of the driver's braking and throttling commands to the relative range and velocity between the leading and following car.
A fuzzy system may utilize the signal conditioned mean driving headway (gap-time) relative to the other vehicle, as well as the standard deviation of the rate changes of the accelerator pedal and brake pedal to determine whether the driver is aggressive or cautious. The driver index value from fuzzy computation and rule evaluation may determine the aggressiveness of the driver based on car following, vehicle speed and the driver's control actions on acceleration and deceleration.
For real-time vehicle implementation, the recursive estimation of the mean and variance of a variable of interest is applied. The signal conditioned average mean gap-time at sample time k can be computed as

gk=gk−1+α(Δsk/vfk−gk−1)  (24)

where Δsk is the relative distance between the leading and following vehicle, and vfk is the velocity of the following vehicle. α is a filter coefficient similar to the one used in (22). FIGS. 13A and 13B show the mean gap-times computed from two runs of vehicle testing: one for aggressive driving and the other for cautious driving.

The acceleration pedal rate mean can be computed as

ρk=ρk−1+α((ρk−ρk−1)/ΔT−pk−1)  (25)

where ρ is the acceleration pedal mean and ΔT is the sample time. The corresponding variance can be computed as

νkανk−1+(1−α)(ρk−ρk)2  (26)

and the standard deviation is obtained from the square-root of the variance. FIGS. 14A and 14B show the standard deviations of two runs of test data for aggressive and cautious driving.

Similar to (25) and (26), the mean and variance of the brake pedal rate change can be computed. FIGS. 15A and 15B show the standard deviations of two runs of test data for aggressive and cautious driving. The variables are first normalized before presenting them to the fuzzy inference system. The fuzzy sets and membership functions were determined for the features to transform the crisp inputs into fuzzy terms. The mean gap-time fuzzy set Gs is defined by

Gs={(g,μ(g))|gεG}  (27)

where G is given by the bounded collection of gap-times g in the vehicle path. The gap-time membership function μ is chosen to be a Gaussian function.

A zero-order TS model was used to compute the driver index level. A normalized output scale from 0-1.0 represented the levels from cautious, to less aggressive, to aggressive driving behavior. The driver index is obtained from fuzzy computation and rule evaluation. Table 1 shows the rules used. Notice that a higher gap-time is relatively more safety conscious compared to a lower gap-time.







TABLE 1







Rules for driving behavior characterization













If accel
If brake




If gap-time
pedal rate
pedal rate
Then driver



is
STD is
STD is
index is







Low
Low
Low
Less






Aggressive



High
Low
Low
Cautious



Low
High
Low
Aggressive



Low
Low
High
Aggressive



Low
High
High
Aggressive



High
High
High
Less






Aggressive



High
Low
High
Cautious



High
High
Low
Less






Aggressive










FIGS. 16A and 16B show the driver index computed from two runs of vehicle testing data: one for aggressive driving with a driver index greater than 0.8 and the other for cautious driving with a driver index less than 0.2.
VI. Supervised Driving Style Characterization
The car-following task requires the driver to maintain with the leading vehicle one of the following (i) a zero speed difference; (ii) a constant relative distance; and (iii) a constant relative gap-time defined by the division of the relative distance by the relative velocity.
A human driver may be modeled as a PD feedback controller. The closed loop system during a car following maneuver may be expressed as

({umlaut over (x)}l−{umlaut over (x)}f−{umlaut over (x)}g)=−cv({dot over (x)}l−{dot over (x)}f−{dot over (x)}g)−cs(xl−xf−xg)  (28)

where xl and xf are the leading and the following vehicle travel distance and xg is the gap offset reference. Due to the implementation of radar used in vehicles equipped with adaptive cruise control function, the relative distance and velocity are measured and defined as

Δs=xl−xf,Δv={dot over (x)}l−{dot over (x)}f  (29)

A vehicle equipped with stability controls has a longitudinal accelerometer with output αx, which measures {umlaut over (x)}f. (28) can be further expressed as

αx=cv(Δv−{dot over (x)}g)+cs(Δs−xg)+({umlaut over (x)}l−{umlaut over (x)}g)  (30)

The unknown parameters cv and cs in (30) can be used to characterize a driver's control structure during a car following. Using the low-pass filtered Δs and Δv to replace the gap offset reference xg and its derivative {dot over (x)}g, and considering the time delays, we have the following equations





  
    
      
        
          α
          
            x
            
              k
              +
              i
            
          
        
        =
        
          
            
              
                c
                v
              
              ⁡
              
                [
                
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    
                      s
                      k
                    
                  
                  -
                  
                    
                      μ
                      k
                    
                    ⁡
                    
                      (
                      
                        Δ
                        ⁢
                        
                          
                        
                        ⁢
                        s
                      
                      )
                    
                  
                
                ]
              
            
            +
            
              
                c
                s
              
              ⁡
              
                [
                
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    
                      v
                      k
                    
                  
                  -
                  
                    
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                    ⁡
                    
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                        ⁢
                        
                          
                        
                        ⁢
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                ]
              
            
            +
            
              w
              ⁢
              
                

              
              [
              
                
                  
                    
                      
                        μ
                        k
                      
                      ⁡
                      
                        (
                        
                          Δ
                          ⁢
                          
                            
                          
                          ⁢
                          s
                        
                        )
                      
                    
                  
                
                
                  
                    
                      
                        μ
                        k
                      
                      ⁡
                      
                        (
                        
                          Δ
                          ⁢
                          
                            
                          
                          ⁢
                          v
                        
                        )
                      
                    
                  
                
              
              ]
            
          
          =
          
            
              
                (
                
                  1
                  -
                  α
                
                )
              
              ⁡
              
                [
                
                  
                    
                      
                        
                          μ
                          
                            k
                            -
                            1
                          
                        
                        ⁡
                        
                          (
                          
                            Δ
                            ⁢
                            
                              
                            
                            ⁢
                            s
                          
                          )
                        
                      
                    
                  
                  
                    
                      
                        
                          μ
                          
                            k
                            -
                            1
                          
                        
                        ⁡
                        
                          (
                          
                            Δ
                            ⁢
                            
                              
                            
                            ⁢
                            v
                          
                          )
                        
                      
                    
                  
                
                ]
              
            
            +
            
              α
              ⁡
              
                [
                
                  
                    
                      
                        Δ
                        ⁢
                        
                          
                        
                        ⁢
                        
                          s
                          k
                        
                      
                    
                  
                  
                    
                      
                        Δ
                        ⁢
                        
                          
                        
                        ⁢
                        
                          v
                          k
                        
                      
                    
                  
                
                ]
              
            
          
        
      
    
    
      
        (
        31
        )
      
    
  




where subscript i in αxk+i reflects the time delay between the driver's braking/throttling actuation and the measured relative distance and velocity, and acceleration, α is a low-pass filter coefficient similar to the one used in (22), and w is a high frequency uncertain signal that may be treated as white noise. Using a conditional least square identification algorithm, cv and cs can be identified in real-time from (31). The response time tp and the damping ratio ζ of the driver-in-the-loop system can be related to Cv and cs as

tp=2πcs/√{square root over (4cs−cc2,)} ζ=cv/2√{square root over (cs)}  (32)

which can be used to deduce the driver's driving behavior: (i) for a normal driver, it is desired that the transient response of the driver-in-the-loop system be fast (sufficiently small tp, e.g., less than 0.5 s) and damped (sufficiently large ζ); (ii) for an aged or driver with physical limitation, tp may be large; (iii) for an aggressive driver, ζ is likely to show a small value, such as one less than 0.5, and the system response is likely to exhibit excessive overshoot; (iv) for a cautious driver, ζ is likely to show a reasonably large value, such as one greater than 0.7.

A least-square parameter identification was implemented for calculating cv and cs. Two runs of vehicle testing were conducted. In the 1st run, the driver in the following car tried to use aggressive throttling and braking to achieve a constant relative gap-time between his vehicle and a leading vehicle, which led to larger range error Δsk−μk(Δs). See, FIG. 17. The identified cv is around 0.2 and identified cs around 0.05. See, FIG. 18. The damping ratio thus computed from (32) showed a value less than 0.5, which is an indication of a light damping driver-in-the-loop system, hence corresponding to aggressive driving behavior.
In the 2nd run, the driver was using cautious throttle and brake application to achieve car following, the relative range error Δsk−μk(Δs) in FIG. 19 had less magnitude in comparison with the one shown in FIG. 17. The identified cv and cs are depicted in FIG. 20. The damping ratio showed a value greater than 0.8 except during the first 150 seconds. See, FIG. 20. This is an indication of a heavy damping driver-in-the-loop system, hence corresponding to cautious driving behavior.
VII. Speed and Acceleration Limit Minder
Certain embodiments described herein provide a vehicle speed and/or acceleration limit minder that may issue warnings through, for example, a haptic accelerator pedal or display in advance of the vehicle violating a speed/acceleration limit. Certain algorithms may, for example, determine whether a driver's acceleration profile exhibits a tendency to exceed a speed and/or an acceleration limit. If so, the acceleration of the vehicle with respect to a given maximal acceleration profile may be limited or constrained (without braking). This maximal acceleration profile may be retrieved from an on-board/off-board navigation database or defined by the driver.
An acceleration model for a vehicle may be approximated by the linear function

Accs(t+Δt)=a0+a1APs(t)+a2APs(t)2  (33)

where,

Accs(t+Δt) is the instantaneous acceleration of the vehicle at time t+Δt;
APs(t) is the instantaneous accelerator pedal position at time t; and
a0, a1, and a2 are coefficients that are calculated continuously using known recursive techniques.
Accs(t+Δt) and APs(t) may be exponentially smoothed and calculated as

Xs(t)=α*Xs(t−1)+(1−α)*X(t)  (34)

where,

XS(t) is either Accs(t+Δt) or APs(t); and
α is a tuning constant.
Smoothing the signals may facilitate approximation through a linear model with de-noised information and provide warnings that are more stable and not significantly influenced by inherently noisy data from driver pedal maneuvers and driving conditions.
Given the linear relationship between vehicle acceleration, Accs, and accelerator pedal position, APs, in (1), the following recursive least squares learning algorithm may be applied to approximate the function parameters in real-time




  
    
      
        
          InCot
          ⁡
          
            (
            
              t
              +
              1
            
            )
          
        
        =
        
          
            
              InCov
              ⁡
              
                (
                t
                )
              
            
            -
            
              (
              
                
                  α
                  *
                
                ⁢
                
                  
                    InCov
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                  *
                
                ⁢
                
                  x
                  *
                
                ⁢
                
                  
                    x
                    ′
                  
                  *
                
                ⁢
                
                  InCov
                  ⁡
                  
                    (
                    t
                    )
                  
                
              
              )
            
          
          
            (
            
              1
              +
              
                
                  α
                  *
                
                ⁢
                
                  
                    x
                    ′
                  
                  *
                
                ⁢
                
                  
                    InCov
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                  *
                
                ⁢
                x
              
            
            )
          
        
      
    
    
      
        (
        35
        )
      
    
  
  
    
      
        
          Par
          ⁡
          
            (
            
              t
              +
              1
            
            )
          
        
        =
        
          
            Par
            ⁡
            
              (
              t
              )
            
          
          +
          
            (
            
              
                
                  InCov
                  ⁡
                  
                    (
                    
                      t
                      +
                      1
                    
                    )
                  
                
                *
              
              ⁢
              
                
                  x
                  *
                
                ⁡
                
                  (
                  
                    y
                    -
                    
                      
                        x
                        
                          ′
                          *
                        
                      
                      ⁢
                      Par
                    
                  
                  )
                
              
            
            )
          
        
      
    
    
      
        (
        36
        )
      
    
  




where,

InCov is the inverse covariance matrix of Kc*eye(r)
where,
Kc is 1000, and
r is the dimensionality of Par;
Par is the linear function parameters [a0,a1,a2] initialized to [0, 0, 0];
α is a tuning constant;
x is the input vector [1,APs(t),APs(t)2]; and
y is the measured acceleration of the vehicle.
The above parameters associate accelerator pedal position and vehicle acceleration in smoothed data space in real-time. At a given driver initiated accelerator pedal position, the algorithm will produce a predicted near term acceleration, ap(t)

ap(t)=[1,APs(t),APs(t)2]*Par  (37)

Of course, vehicle acceleration may be determined in any suitable fashion. For example, acceleration may be determined via an accelerometer or based on a change in vehicle speed over time.

The time, T(t), until the vehicle reaches a speed limit, L, may be determined based on the speed limit, speed of the vehicle, S(t), and the acceleration of the vehicle, ap(t)




  
    
      
        
          T
          ⁡
          
            (
            t
            )
          
        
        =
        
          
            (
            
              L
              -
              
                S
                ⁡
                
                  (
                  t
                  )
                
              
            
            )
          
          
            
              a
              p
            
            ⁡
            
              (
              t
              )
            
          
        
      
    
    
      
        (
        38
        )
      
    
  




The speed limit may be set, for example, by the driver via an input switch/interface or determined in a known fashion via a navigation system based on a location of the vehicle. For example, a navigation system may provide road speed limit information, e.g., 65 mph, based on the vehicle's geographic location. The speed of the vehicle may be determined in any known/suitable fashion, such as by way of a speed sensor, etc.

In certain embodiments, if the acceleration, ap(t), is positive, the time, T(t), is less than a predefined threshold time, such as 2 seconds, etc., and the vehicle is not in a state of braking, a warning may be generated to advise the driver of the impending speed limit violation. (Whether the vehicle is in a state of braking may be determined in any known/suitable fashion. For example, brake pedal position may be used to determine whether the vehicle is in a state of braking.)
In other embodiments, a time need not be calculated. A table of speed limit versus vehicle speed versus vehicle acceleration, for example, may be used to determine whether to issue warnings. If, under a given set of circumstances, the speed limit, vehicle speed and vehicle acceleration achieve some value (or range of values) a warning may be generated.
In still other embodiments, if the acceleration, ap(t), is positive and the speed of the vehicle, S(t), falls within some range of speeds that is less than the speed limit, a warning may be generated to advise the driver of the impending speed limit violation. For example, if the vehicle is accelerating and the vehicle speed is within 3 mph of the speed limit, a warning may be generated.
Alternatively, a warning may be generated if the acceleration, ap(t), exceeds a predefined threshold. For example, if ap(t) (the predicted acceleration) is greater than 3 m/s2, a warning may be generated as described herein. The predefined threshold may have a default value, be input by a driver, or selected based on driver type as discussed below.
Referring to FIG. 21, an embodiment of a driver advisory system 30 for a vehicle 32 including an accelerator pedal 34, powertrain system 36 and navigation system 38 may include position and speed sensors 40, 42, one or more controllers 44 and an audio, visual and/or haptic interface 46. The position sensor 40 detects a position of the accelerator pedal 34. The speed sensor 42 detects a speed associated with the vehicle 32. The interface 46 may be any suitable/known driver interface such as a display screen, speaker arrangement, haptic accelerator pedal, etc.
The one or more controllers 44 may receive accelerator pedal position information from the sensor 40, vehicle speed information from the sensor 42, and local speed limit information from the navigation system 38. Using the algorithms discussed above, the one or more controllers 44 may predict an acceleration of the vehicle 32, predict a time until a future vehicle speed exceeds the speed limit, and issue an audio, visual and/or haptic alert via the interface 46 if this time is less than some default threshold (e.g., 3 seconds). This default threshold may be, for example, preset by the vehicle manufacturer or input by the driver via any suitable interface (including the interface 46). Using the algorithms discussed above, the one or more controllers 44 may alternatively predict an acceleration of the vehicle 32, determine whether the predicted acceleration is greater than a threshold acceleration, and issue an audio, visual and/or haptic alert via the interface 46 if the predicted acceleration is greater than the threshold acceleration. Other scenarios are also contemplated.
The one or more controllers 44 may characterize/categorize driver behavior using the algorithms discussed above and alter/select the thresholds based on the characterization/categorization. As an example, if the one or more controllers 44 determine the driver to be “expert,” the default threshold time may be decreased (or eliminated). As another example, if the one or more controllers 44 determine the driver to be “reckless,” the default threshold time may be increased and/or the default threshold acceleration may be decreased, etc. As yet another example, several different threshold values may be held in a table. Each of these threshold values may be linked with a different characterization/categorization. A particular threshold value may thus be selected based on the characterization/categorization via the table.
VIII. Experimental Results
A vehicle equipped with a haptic accelerator pedal and configured with an advisory system similar to the advisory system 30 was tested with limits of 40 mph and 60 mph. Referring to FIGS. 22, 23 and 24, a driver set the first speed limit of 40 mph for samples 1 to 5000 and a navigation system provided a second speed limit of 60 mph after sample 5000. For both limits, the algorithms predicted a near term acceleration (given then current accelerator pedal position) that lead to the vehicle speed exceeding the speed limit. Alerts were generated via activation of the haptic accelerator pedal prior to actual violation (as indicated by “*” on FIGS. 22, 23 and 24.)
As apparent to those of ordinary skill, the algorithms disclosed herein may be deliverable to a processing device, which may include any existing electronic control unit or dedicated electronic control unit, in many forms including, but not limited to, information permanently stored on non-writable storage media such as ROM devices and information alterably stored on writeable storage media such as floppy disks, magnetic tapes, CDs, RAM devices, and other magnetic and optical media. The algorithms may also be implemented in a software executable object. Alternatively, the algorithms may be embodied in whole or in part using suitable hardware components, such as Application Specific Integrated Circuits (ASICs), state machines, controllers or other hardware components or devices, or a combination of hardware, software and firmware components.
While embodiments of the invention have been illustrated and described, it is not intended that these embodiments illustrate and describe all possible forms of the invention. The words used in the specification are words of description rather than limitation, and it is understood that various changes may be made without departing from the spirit and scope of the invention.

## Claims

1. A method for advising a driver of a vehicle comprising:
generating a categorization of a driver's dynamic control of the vehicle;
predicting an acceleration of the vehicle;
determining whether the predicted acceleration is greater than a threshold acceleration; and
activating a haptic interface before an acceleration of the vehicle exceeds the threshold acceleration when the predicted acceleration is greater than the threshold acceleration, wherein the threshold acceleration is based on the categorization.

2. The method of claim 1 wherein the vehicle includes an accelerator pedal and wherein predicting an acceleration of the vehicle includes determining a position of the accelerator pedal.

3. A method for advising a driver of a vehicle comprising:
generating a categorization of a driver's dynamic control of the vehicle; and
in response to a predicted acceleration of the vehicle being greater than a threshold acceleration that is based on the categorization, generating an alert for the driver before an acceleration of the vehicle exceeds the threshold acceleration.

4. The method of claim 3 wherein the predicted acceleration is based on an accelerator pedal position.

5. The method of claim 3 wherein generating an alert for the driver includes activating a haptic interface.

6. A vehicle comprising:
an interface; and
a controller configured to generate a categorization of a driver's dynamic control of the vehicle, and in response to a predicted acceleration of the vehicle being greater than a threshold acceleration that depends on the categorization, to generate an alert via the interface before an acceleration of the vehicle exceeds the threshold acceleration.

7. The vehicle of claim 6 further comprising an accelerator pedal, wherein the predicted acceleration is based on a position of the accelerator pedal.

8. The vehicle of claim 6 wherein the interface is a haptic interface.