Patent Publication Number: US-2022234556-A1

Title: Automatic Emergency Braking Using a Time-to-Collision Threshold Based on Target Acceleration

Description:
BACKGROUND 
     Driver-assistance technologies are increasingly implemented in vehicles to increase safety. Automatic emergency braking (AEB) is one driver-assistance technology that enables vehicles to automatically slow to avoid collisions with other vehicles or objects. For example, a vehicle may determine that a collision with another vehicle is imminent and apply a braking force in an attempt to avoid the collision. 
     Traditional AEB systems are based on non-linear ideal braking profiles of the respective vehicles (e.g., maximum decelerations in ideal conditions). The non-linearity of the ideal braking profiles makes determining accurate time-to-collision (TTC) thresholds for activation of AEB systems difficult. Furthermore, actual braking performances of vehicles often deviate from their ideal braking profiles. 
     SUMMARY 
     Apparatuses and techniques enabling automatic emergency braking (AEB) using a time-to-collision (TTC) threshold based on target acceleration are described below. Some aspects described below include a method of AEB performed by a vehicle. The method determines, based on sensor data received from one or more sensors that are local to the vehicle, a target acceleration of a target object proximate to the vehicle. Based on the target acceleration, the method determines a TTC with the target object and a TTC threshold for the target object. The method further establishes that the TTC meets or is lower than the TTC threshold and causes a braking system of the vehicle to apply a braking force effective to avoid a collision with the target object. 
     Other aspects described below also include a system for performing AEB of a vehicle. The system comprises one or more sensors configured to produce sensor data indicating attributes of the vehicle and a target object proximate to the vehicle, a braking system configured to apply braking forces effective to slow the vehicle in conjunction with or in lieu of driver input, at least one processor, and at least one computer-readable storage medium comprising instructions that, when executed by the processor, cause the system to determine, based on the sensor data, a target acceleration of the target object. The instructions further cause the processor to determine, based on the target acceleration, a TTC with the target object and a TTC threshold for the target object. The instructions also cause the processor to establish that the TTC meets or is lower than the TTC threshold and cause, based on the establishment that the TTC has met or is lower than the TTC threshold, the braking system to apply a braking force effective to avoid a collision with the target object. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Apparatuses and techniques enabling automatic emergency braking (AEB) using a time-to-collision (TTC) threshold based on target acceleration are described with reference to the following drawings. The same numbers are used throughout the drawings to reference like features and components: 
         FIG. 1  illustrates an example environment where AEB using a TTC threshold based on target acceleration may be used; 
         FIG. 2  illustrates an example AEB system configured to perform AEB using a TTC threshold based on target acceleration; 
         FIG. 3  illustrates an example data flow and actions for AEB using a TTC threshold based on target acceleration; 
         FIG. 4  illustrates example look-up tables used to determine a TTC threshold based on target acceleration; and 
         FIG. 5  illustrates an example method of AEB using a TTC threshold based on target acceleration. 
     
    
    
     DETAILED DESCRIPTION 
     Overview 
     Automatic emergency braking (AEB) systems enable vehicles to determine that collisions with objects are imminent and provide braking forces in order to avoid the collisions. AEB systems generally calculate time-to-collision (TTC) estimates for targets and compare them with TTC thresholds to determine when to apply braking forces. Often times, however, these systems (or portions thereof) determine TTC thresholds based on ideal braking profiles and velocities of the vehicles and the targets. While these systems may work in many situations, there are situations where they may fail to apply braking forces soon enough to avoid a collision. For example, a system tuned for a moderate breaking of a front-traveling vehicle may be unable to stop when that front-traveling vehicle brakes aggressively. Accordingly, traditional AEB systems often produce non-optimal braking results in many situations. 
     Techniques and systems are described that enable AEB using a TTC threshold that is based on target acceleration. More specifically, the TTC threshold may be based on a vehicle velocity, a relative velocity between the vehicle and the target object, an acceleration of the target, and a distance between the vehicle and the target object. By accounting for target acceleration, the techniques and systems described herein are able to compensate for aggressive stopping of the target, thereby allowing AEB to function as planned in more situations. 
     Example Environment 
       FIG. 1  is an example environment  100  where AEB using a time-to-collision threshold based on target acceleration may be used. The environment contains a vehicle  102  (e.g., host vehicle) that includes an AEB system  104 , which is discussed further in regard to  FIG. 2 , and a target  106  (e.g., target object or target vehicle) that is in a path of travel of the vehicle  102 . Although shown as automobiles, the vehicle  102  may be any type of system with autonomous braking ability (car, truck, motorcycle, e-bike, boat, etc.), and the target  106  may be any type of moving object (another car, truck, motorcycle, e-bike, or boat, pedestrian, cyclist, boulder, etc.). 
     In the illustrated example, the vehicle  102  is traveling with a vehicle velocity  108  and accelerating with a vehicle acceleration  110 . The target  106  is traveling with a target velocity  112  and accelerating with a target acceleration  114 . A distance  116  exists between the vehicle  102  and the target  106 . A relative velocity  118  exists that is based on a difference between the target velocity  112  and the vehicle velocity  108 , and a relative acceleration  120  exists that is based on a difference between the target acceleration  114  and the vehicle acceleration  110 . 
     In the illustrated example, a positive velocity has a direction of up the page, and a negative velocity has a direction down the page. The vehicle velocity  108  is positive (because it gives a reference direction), and the target velocity  112  can be either positive or negative depending on whether it is traveling in the same direction as the vehicle  102 . As such, the relative velocity  118  is negative when the target  106  has a lower speed than the vehicle  102  or is traveling in the opposite direction (e.g., is headed towards the vehicle  102 ). 
     Similarly, a positive acceleration has a direction of up the page, and a negative acceleration has a direction of down the page. The accelerations are positive when the respective entities are accelerating in the direction of the vehicle velocity  108  and negative when the respective entities are decelerating in the direction of the vehicle velocity  108 . 
     The magnitudes of the respective vectors are shown for illustration purposes only. For example, in the illustrated example, the target acceleration  114  is less than the vehicle acceleration  110  (e.g., the target  106  is decelerating faster than the vehicle  102 ). Furthermore, the conventions used may differ without departing from the scope of the disclosure. 
     Based on the above, the vehicle  102  is traveling faster than the target  106  and in a same direction. Also, the target  106  is decelerating more aggressively than the vehicle  102 . The example illustration may be indicative of a panic stop by the target  106 , e.g., to avoid its own collision. 
     By utilizing the techniques described herein, the vehicle  102  is able to determine a more accurate TTC threshold for the example environment  100 . In doing so, the vehicle  102  may be able to avoid colliding with the target  106 , which may not be possible with traditional AEB systems. 
     Example System 
       FIG. 2  is an example illustration  200  of the AEB system  104  in which AEB using a time-to-collision threshold based on target acceleration can be implemented. As shown underneath, the AEB system  104  of the vehicle  102  includes at least one processor  202 , at least one computer-readable storage medium  204 , one or more sensors  206 , a power-braking system  208 , and an AEB module  210 . 
     The processor  202  (e.g., an application processor, microprocessor, digital-signal processor (DSP), or controller) executes instructions  212  (e.g., code) stored within the computer-readable storage medium  204  (e.g., a non-transitory storage devices such as a hard drive, SSD, flash memory, read-only memory (ROM), EPROM, or EEPROM) to cause the AEB system  104  to perform the techniques described herein. The instructions  212  may be part of an operating system and/or one or more applications of the AEB system  104 . 
     The instructions  212  cause the AEB system  104  to act upon (e.g., create, receive, modify, delete, transmit, or display) data  214  (e.g., application data, module data, sensor data  216  from sensors  206 , or I/O data). Although shown as being within the computer-readable storage medium  204 , portions of the data  214  may be within a random-access memory (RAM) or a cache of the AEB system  104  (not shown). Furthermore, the instructions  212  and/or the data  214  may be remote to the AEB system  104 . 
     The AEB module  210  (or portions thereof) may be comprised by the computer-readable storage medium  204  or be a stand-alone component (e.g., executed in dedicated hardware in communication with the processor  202  and computer-readable storage medium  204 ). For example, the instructions  212  may cause the processor  202  to implement or otherwise cause the AEB module  210  to receive the sensor data  216  and implement AEB, as described below. 
     The sensors  206  provide the sensor data  216  that enables the determination of the attributes described in  FIG. 1  (e.g., distance  116 , vehicle velocity  108 , vehicle acceleration  110 , target velocity  112 , target acceleration  114 , relative velocity  118 , and relative acceleration  120 ). For example, the sensors  206  may comprise a ranging sensor to indicate the distance  116 , the target velocity  112 , and the target acceleration  114 . A speedometer may be implemented to indicate the vehicle velocity  108 , and an accelerometer may be implemented to indicate the vehicle acceleration  110 . 
     In some implementations, the sensors  206  may comprise instructions that interface with another module or system of the vehicle  102  to determine the attributes described in  FIG. 1 . For example, the sensors  206  may comprise instructions to receive the vehicle acceleration  110  from an airbag module or vehicle dynamics module that contains an accelerometer. 
     Furthermore, in some implementations, the sensors  206  may comprise instructions to receive information from the target  106  via a communication system (not shown). For example, a vehicle-to-vehicle communication system may be used to obtain the target velocity  112  and the target acceleration  114 . 
     The power-braking system  208  may be any type of system known by those of ordinary skill in the art. For example, the power-braking system may be a hydraulic, pneumatic, or electric braking system or some combination thereof. Regardless of implementation, the power-braking system  208  provides braking forces to the vehicle that are effective to slow the vehicle  102 . 
     By determining the TTC threshold for the target  106  using the techniques described herein, the power-braking system  208  may apply the braking forces earlier than traditional AEB systems. In doing so, the AEB system  104  is able to mitigate front-end collisions with better efficacy. 
     Example Data Flow 
       FIG. 3  is an example illustration  300  of a data flow and actions for AEB using a TTC threshold based on target acceleration. The example illustration  300  is generally comprised by the AEB module  210 . Various other entities, however, may perform one or more of the actions described below. 
     The example illustration  300  starts with the sensor data  216  being received at an input to an attribute module  302  of the AEB module  210 . The attribute module  302  uses the sensor data  216  to determine attributes  304  of the vehicle  102  and the target  106 , including those discussed in regard to  FIG. 1 . For example, the attributes  304  may comprise the vehicle velocity  108 , the vehicle acceleration  110 , the target velocity  112 , the target acceleration  114 , the distance  116 , the relative velocity  118 , and the relative acceleration  120 . Some of the attributes  304  may be directly determined from the sensor data  216  (e.g., the vehicle velocity  108  determined from a speedometer output), and some of the attributes  304  may be derived from the sensor data  216  (e.g., the relative velocity  118  determined from a speedometer output and a ranging sensor output). Regardless of how the attributes  304  are determined, derived, or calculated, the attribute module  302  is configured to output the attributes  304  to a TTC threshold module  306  and a TTC module  308  of the AEB module  210 . 
     The TTC threshold module  306  and the TTC module  308  receive the attributes  304  as inputs, or otherwise have access to a shared memory that stores the attributes  304 . For example, the attribute module  302  may allocate a shared memory space as registers for containing the attributes  304 , e.g., within computer readable storage medium  204 . The TTC threshold module  306  and/or the TTC module  308  can access the registers in order to determine a TTC threshold  310  and/or a TTC  312  for the target  106 . 
     The TTC threshold module  306  may use the vehicle velocity  108 , the relative velocity  118 , the target acceleration  114 , and the distance  116  to determine the TTC threshold  310  for the target  106 . The TTC module  308  may use the relative acceleration  120 , the relative velocity  118 , and the distance  116  to determine the TTC  312  for the target  106 . The TTC  312  is an estimated time-to-collision with the target  106 , and the TTC threshold  310  is a threshold for the target  106  that is used to activate AEB once the TTC  312  crosses the determined TTC threshold  310 . 
     The TTC module  308  calculates the TTC  312  for the target  106  by solving the quadratic equation of Equation 1 for t (TTC  312 ): 
       ½ a   r   t   2   +v   r   t+s= 0  (1)
 
     where a r  is the relative acceleration  120 , v r  is the relative velocity  118 , and s is the distance  116 . The TTC module  308  outputs the TTC  312  to a comparison module  318 . 
     The TTC threshold module  306  determines the TTC threshold  310  for the target  106  based on a sum of a one of first TTC sub-thresholds  314  and a one of second TTC sub-thresholds  316 . By using two sub-thresholds, the TTC threshold module  306  is able to factor the target acceleration  114  into the determination of the TTC threshold  310 . The TTC threshold  310  determination is discussed below in regard to  FIG. 4 . The TTC threshold module  306  outputs the TTC threshold  310  to the comparison module  318 . 
     The TTC threshold  310  and the TTC  312  for the target  106  are received by the comparison module  318  of the AEB module  210 , which determines if the TTC  312  has met or is lower than the TTC threshold  310 . The TTC threshold  310  and the TTC  312  may be constantly or intermittently calculated and updated for receipt by the comparison module  318 . As such, the comparison module  318  may evaluate the TTC threshold  310  against the TTC  312  constantly or intermittently, as well. If or when the TTC  312  for the target  106  has met or is lower than the TTC threshold  310  for the target  106 , the comparison module  318  sends an activation signal  320  to the power-braking system  208  to apply a braking force to stop the vehicle  102 . 
     By utilizing the target acceleration  114  for the TTC threshold  310  determination for the target  106 , the AEB module  210  is able to compensate for situations where the target  106  is decelerating aggressively. In this way, the AEB module  210  is able to cause the vehicle  102  to avoid collisions more effectively than traditional AEB systems. 
     TTC Threshold Determination 
       FIG. 4  is an example illustration  400  of look-up tables that may be used to determine the TTC threshold  310  for the target  106 . As stated above, the TTC threshold  310  for the target  106  may be a sum of a determined one of first TTC sub-thresholds  314  and a determined one of second TTC sub-thresholds  316 . The one of the TTC sub-thresholds  314  is selected based on the vehicle velocity  108  and the relative velocity  118 . The one of the second TTC sub-thresholds  316  is selected based on the target acceleration  114  and the distance  116 . By basing the TTC threshold  310  on the sum of the first and second TTC sub-thresholds  314 ,  316 , proportionate weighting may be given to the target acceleration  114  and the distance  116  relative to the vehicle velocity  108  and the relative velocity  118 . 
     As illustrated, the first TTC sub-thresholds  314  and the second TTC sub-thresholds  316  are organized into respective two-dimensional look-up tables. Accordingly, the one of the first TTC sub-thresholds  314  for the target  106  is at an intersection of the vehicle velocity  108  and the relative velocity  118 . Similarly, the one of the second TTC sub-thresholds  316  for the target  106  is at an intersection of the target acceleration  114  and the distance  116 . 
     Consider an example where the vehicle velocity  108  is c, the relative velocity  118  is 1, the target acceleration  114  is h, and the distance  116  is 7. By using the illustrated look-up tables, the first TTC sub-threshold for the target  106  would be c1 (e.g., first TTC sub-threshold  402 ), and the second TTC sub-threshold for the target  106  would be h7 (e.g., second TTC sub-threshold  404 ). Accordingly, the TTC threshold  310  for the target  106  would be a sum of the first TTC sub-threshold  402  and the second TTC sub-threshold  404  (e.g., c1+h7). 
     The first TTC sub-thresholds  314  (e.g., values within the upper look-up table) are pre-determined based on Equation 2: 
     
       
         
           
             
               
                 
                   
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     where d ideal  is an ideal braking distance based on an ideal braking profile of the vehicle  102 . 
     The ideal braking distance is calculated based on Equation 3: 
         d   safe   +v   h   t   delay +∫∫ 0   t     req     a ( t ) d   2   t   (3)
 
     where d safe  is a desired minimum safe distance between the vehicle  102  and the target  106  after stopping, t delay  is a delay between the AEB system  104  activating and the power-braking system  208  applying braking forces, and a(t) is a time-based ideal braking profile with maximum acceleration of the vehicle achieved by the AEB system  104  (either single or multiple stage), and t req  is a required time to brake the vehicle  102  from the relative velocity  118  to zero. 
     The t req  is based on solving Equation 4 for t req : 
         v   r =∫ 0   t     req     a ( t ) dt   (4)
 
     The first TTC sub-thresholds  314  may be adjusted based on empirical data for the vehicle  102 , another vehicle, or many vehicles. For example, the above equations may be used to provide baseline values, and the empirical data may be used to “tune” the first TTC sub-thresholds  314 . For example, initial values may be established based on the above equations. Actual braking performance for each of the input pairs (vehicle velocity/relative velocity pairs) may be determined, and any differences may be used to adjust the values. 
     The second TTC sub-thresholds  316  (e.g., values within the lower look-up table) may be pre-determined based on empirical data for the vehicle  102 , another vehicle, or for many vehicles. For example, test scenarios may be set up for each of the input pairs (target acceleration/distance pairs) and used to determine values that produce the desired braking. Real-world or simulated data associated with each of the test scenarios may be fed into a machine learning model to determine the second TTC sub-thresholds  316 . 
     In some implementations, modeling equations known by those of ordinary skill in the art may be used instead of, or in conjunction with, the empirical data to determine the values. Although described in terms of target acceleration/distance inputs, the second TTC sub-thresholds  316  may be based on other attributes. 
     Although the example illustration  400  shows a sum of values from two two-dimensional look-up tables, a single four-dimensional look-up table may be used with vehicle velocity, relative velocity, target acceleration, and distance as the respective dimensions. The TTC threshold  310 , in such a case, would become a value within the four-dimensional look-up table that corresponds to the vehicle velocity  108 , the relative velocity  118 , the target acceleration  114 , and the distance  116 . 
     The look-up tables (e.g., the first TTC sub-thresholds  314  and the second TTC sub-thresholds  316 ) may be stored within the computer-readable storage medium  204 , e.g., as data  212 . By doing so, the TTC threshold module  306  may determine the first TTC sub-threshold  402  and the second TTC sub-threshold  404  for the target  106  quickly without having to solve the equations above. It should be noted, however, that one or more of the look-up tables may not be used in some implementations. For example, one or more of the first TTC sub-threshold  314  and the second TTC sub-threshold  316  for the target  106  may be calculated in real-time by the TTC threshold module  306  using the above equations and techniques. 
     Example Method 
       FIG. 5  illustrates an example method  500  for AEB using a TTC threshold based on target acceleration. Method  500  may be implemented utilizing the previously described examples, such as the environment  100 , the AEB system  104 , the process flow of illustration  300 , and determination of the TTC threshold  310  of illustration  400 . Operations  502  through  510  may be performed by one or more entities of a vehicle (e.g., portions of the AEB system  104 ). The order in which the operations are shown and/or described is not intended to be construed as a limitation, and any number or combination of the operations can be combined in any order to implement the method  500  or an alternate method. 
     At  502 , a target acceleration of a target object proximate to a vehicle is determined based on sensor data received from one or more sensors that are local to the vehicle. For example, the attribute module  302  may receive the sensor data  216  and determine the target acceleration  114 . Other attributes  304  may also be determined by the attribute module  302 , such as the vehicle velocity  108 , the vehicle acceleration  110 , the target velocity  112 , the distance  116 , the relative velocity  118 , and the relative acceleration  120 . Using the example of  FIG. 1 , the vehicle  102  may be approaching the target  106  that is decelerating aggressively. 
     At  504 , a TTC is determined for the target object based on the target acceleration  114 . For example, the TTC module  308  may receive the relative acceleration  120  (which is based on the target acceleration  114 ) from the attribute module  302  and determine the TTC  312 . The TTC  312  may further be based on the relative velocity  118  and the distance  116 . Continuing with the example of  FIG. 1 , consider that the TTC  312  is determined to be 2 seconds. 
     At  506 , a TTC threshold is determined for the target object based on the target acceleration  114 . For example, the TTC threshold module  306  may receive the target acceleration  114  and determine the first TTC sub-threshold  402  for the target  106  and the second TTC sub-threshold  404  for the target  106 . The first TTC sub-threshold  402  may be based on the vehicle velocity  108  and the relative velocity  118 . The second TTC sub-threshold  404  may be based on the target acceleration  114  and the distance  116 . The first and second TTC sub-thresholds  402 , 404  may be added by the TTC threshold module  306  to determine the TTC threshold  310 . Continuing with the example of  FIG. 1 , consider that the first TTC sub-threshold  402  is determined to be 1.8 seconds and that the second TTC sub-threshold  404  is determined to be 0.3 seconds. 
     At  508 , an establishment is made that the TTC meets or is lower than the TTC threshold. For example, the comparison module  318  may receive the TTC threshold  310  and the TTC  312  and determine if the TTC  312  is less than or equal to the TTC threshold  310 . 
     Consider again the example of  FIG. 1 . Without utilizing the second TTC sub-threshold  404 , the comparison module  318  would receive the first TTC sub-threshold  402  as the TTC threshold  310 . As such, the comparison module  318  would fail to provide an activation signal  320  because 1.8 seconds is less than 2 seconds. However, by incorporating the second TTC sub-threshold  402 , the TTC threshold  310  becomes 1.1 seconds (0.8+0.3). As such, the comparison module  318  does provide the activation signal  320 . 
     At  510 , a braking system is caused to apply a braking force. For example, the comparison module  318  may provide the activation signal  320  to the power-braking system  208  that is effective to slow the vehicle to avoid the target  106 . By activating the braking system  208  based on a combination of the first and second TTC sub-thresholds, the AEB module  210  is able to mitigate a collision that may not have been mitigated by conventional AEB systems. 
     EXAMPLES 
     Example 1: A method of automatic emergency braking (AEB) performed by a vehicle, the method comprising: determining, based on sensor data received from one or more sensors that are local to the vehicle, a target acceleration of a target object proximate to the vehicle; determining, based on the target acceleration, a time to collision (TTC) with the target object; determining, based on the target acceleration, a TTC threshold for the target object; establishing that the TTC meets or is lower than the TTC threshold; and causing, based on the establishing that the TTC has met or is lower than the TTC threshold, a braking system of the vehicle to apply a braking force effective to avoid a collision with the target object. 
     Example 2: The method as recited in example 1, further comprising: determining, based on the sensor data, a relative acceleration, a relative velocity, and a distance between the target object and the vehicle, wherein the TTC is based further on the relative acceleration, the relative velocity, and the distance. 
     Example 3: The method as recited in example 2, wherein the determining the TTC comprises solving a quadratic equation. 
     Example 4: The method as recited in example 1, further comprising: determining, based on the sensor data, a vehicle velocity of the vehicle, a relative velocity between the target object and the vehicle, and a distance between the target object and the vehicle, wherein the TTC threshold is based further on the vehicle velocity, the relative velocity, the target acceleration, and the distance. 
     Example 5: The method as recited in example 4, wherein the TTC threshold is further based on one or more values within one or more sets of values. 
     Example 6: The method as recited in example 5, wherein: the sets of values comprise first and second sets of values; and the TTC threshold is a sum of a first TTC sub-threshold determined from the first set of values and a second TTC sub-threshold determined from the second set of values. 
     Example 7: The method as recited in example 6, wherein the first and second sets of values comprise first and second two-dimensional look-up tables. 
     Example 8: The method as recited in example 7, wherein: the vehicle velocity and the relative velocity correspond to respective dimensions of the first two-dimensional look-up table; and the target acceleration and the distance correspond to respective dimensions of the first two-dimensional look-up table the second two-dimensional look-up table. 
     Example 9: The method as recited in example 8, wherein the first sets of values within the first two-dimensional look-up table are based on an ideal braking profile of the vehicle. 
     Example 10: The method as recited in example 8, wherein the second sets of values within the second two-dimensional look-up table are based on empirical data. 
     Example 11: A system for automatic emergency braking (AEB) of a vehicle, the system comprising: one or more sensors configured to produce sensor data indicating attributes of the vehicle and a target object proximate to the vehicle; a braking system configured to apply braking forces effective to slow the vehicle in conjunction with or in lieu of driver input; at least one processor; and at least one computer-readable storage medium comprising instructions that, when executed by the processor, cause the system to: determine, based on the sensor data, a target acceleration of the target object; determine, based on the target acceleration, a time to collision (TTC) with the target object; determine, based on the target acceleration, a TTC threshold for the target object; establish that the TTC meets or is lower than the TTC threshold; and cause, based on the establishment that the TTC has met or is lower than the TTC threshold, the braking system to apply a braking force effective to avoid a collision with the target object. 
     Example 12: The system as recited in example 11, wherein the instructions further cause the processor to: determine, based on the sensor data, a relative acceleration, a relative velocity, and a distance between the target object and the vehicle, wherein the TTC is based further on the relative acceleration, the relative velocity, and the distance. 
     Example 13: The system as recited in example 12, wherein the determination of the TTC comprises solving a quadratic equation. 
     Example 14: The system as recited in example 12, wherein the instructions further cause the processor to: determine, based on the sensor data, a vehicle velocity of the vehicle, a relative velocity between the target object and the vehicle, and a distance between the target object and the vehicle, wherein the TTC threshold is based further on the vehicle velocity, the relative velocity, the target acceleration, and the distance. 
     Example 15: The system as recited in example 14, wherein the TTC threshold is further based on one or more values within one or more sets of values stored within the computer-readable storage medium. 
     Example 16: The system as recited in example 15, wherein: the sets of values comprise first and second sets of values; and the TTC threshold is a sum of a first TTC sub-threshold determined from the first set of values and a second TTC sub-threshold determined from the second set of values. 
     Example 17: The system as recited in example 16, wherein the first and second sets of values comprise first and second two-dimensional look-up tables. 
     Example 18: The system as recited in example 17, wherein: the vehicle velocity and the relative velocity correspond to respective dimensions of the first two-dimensional look-up table; and the target acceleration and the distance correspond to respective dimensions of the first two-dimensional look-up table the second two-dimensional look-up table. 
     Example 19: The system as recited in example 18, wherein the first sets of values within the first two-dimensional look-up table are based on an ideal braking profile of the vehicle. 
     Example 20: The system as recited in example 18, wherein the second sets of values within the second two-dimensional look-up table are based on empirical data. 
     CONCLUSION 
     While various embodiments of the disclosure are described in the foregoing description and shown in the drawings, it is to be understood that this disclosure is not limited thereto but may be variously embodied to practice within the scope of the following claims. From the foregoing description, it will be apparent that various changes may be made without departing from the spirit and scope of the disclosure as defined by the following claims. 
     The use of “or” and grammatically related terms indicates non-exclusive alternatives without limitation unless the context clearly dictates otherwise. As used herein, a phrase referring to “at least one of” a list of items refers to any combination of those items, including single members. As an example, “at least one of: a, b, or c” is intended to cover a, b, c, a-b, a-c, b-c, and a-b-c, as well as any combination with multiples of the same element (e.g., a-a, a-a-a, a-a-b, a-a-c, a-b-b, a-c-c, b-b, b-b-b, b-b-c, c-c, and c-c-c or any other ordering of a, b, and c).