Patent Publication Number: US-2023150485-A1

Title: Vehicle path adjustment

Description:
BACKGROUND 
     Computers can provide commands to operate vehicles autonomously or semi-autonomously. Other vehicles, both moving and non-moving, as well as other moving and/or non-moving objects, e.g., a bicycle, a pedestrian, etc., may be present in an area where a first or host vehicle operates. Planning a path for the host vehicle, especially when taking into account possible paths of other moving objects, can be challenging. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a diagram showing an example vehicle with a virtual boundary. 
         FIG.  2    is a diagram showing the vehicle of  FIG.  1    and a target object. 
         FIG.  3    is a diagram showing another example of a virtual boundary of the vehicle of  FIG.  1   . 
         FIG.  4    is a flowchart of an exemplary process for navigating a vehicle. 
     
    
    
     DETAILED DESCRIPTION 
     Introduction 
     Disclosed herein is a system for detecting a road surface, comprising a processor and a memory. The memory stores instructions executable by the processor to determine a virtual boundary for a vehicle body based on a shape of the vehicle body, to identify one or more objects based on vehicle sensor data, based on the identified one or more objects, the determined virtual boundary, and an input to at least one of propulsion, steering, or braking, to determine at least one of a braking override or a steering override, and based on the determination, to perform at least one of adjusting a vehicle steering and a vehicle speed. 
     The instructions to determine the virtual boundary may further include instructions to specify the virtual boundary by specifying a function that determines lengths of virtual lines from a reference point inside the virtual boundary and a point on the virtual boundary at respective orientations of the virtual line relative to a reference line. 
     The instructions to determine the at least one of the braking override or the steering override may include instructions to perform optimization operation on a control barrier function including a distance function and a derivative of the distance function, wherein the distance function is defined, at an orientation of a line extending from a reference point of the virtual boundary to the one or more objects, based on a length of the line from the one or more objects to an intersection with the virtual boundary. 
     The instructions may further include instructions to determine the derivative of the distance function based on a derivative of distance of a virtual line extending from the virtual boundary to the one or more objects and a derivative of the orientation of the virtual line relative to a virtual reference line. 
     The instructions may further include instructions to determine the braking override further based on a maximum allowed deceleration. 
     The instructions may further include instructions to determine the steering override further based on a maximum allowed steering. 
     The input to at least one of propulsion, steering, or braking may be received from at least one of a vehicle operator or an autonomous vehicle control system. 
     Further disclosed herein is a method for detecting a road surface including determining a virtual boundary for a vehicle body based on a shape of the vehicle body, identifying one or more objects based on vehicle sensor data, based on the identified one or more objects, the determined virtual boundary, and an input to at least one of propulsion, steering, or braking, determining at least one of a braking override or a steering override, and based on the determination, performing at least one of adjusting a vehicle steering and a vehicle speed. 
     Determining the virtual boundary may further include specifying the virtual boundary by specifying a function that determines lengths of virtual lines from a reference point inside the virtual boundary and a point on the virtual boundary at respective orientations of the virtual line relative to a reference line. 
     Determining the at least one of the braking override or the steering override may further include performing optimization operation on a control barrier function including a distance function and a derivative of the distance function, wherein the distance function is defined, at an orientation of a line extending from a reference point of the virtual boundary to the one or more objects, based on a length of the line from the one or more objects to an intersection with the virtual boundary. 
     The method may further include determining the derivative of the distance function based on a derivative of distance of a virtual line extending from the virtual boundary to the one or more objects and a derivative of the orientation of the virtual line relative to a virtual reference line. 
     The method may further include determining the braking override further based on a maximum allowed deceleration. 
     The method may further include determining the steering override further based on a maximum allowed steering. 
     The method may further include receiving the input to at least one of propulsion, steering, or braking from at least one of a vehicle operator or an autonomous vehicle control system. 
     Further disclosed is a computing device programmed to execute any of the above method steps. 
     Yet further disclosed is a computer program product, comprising a computer-readable medium storing instructions executable by a computer processor, to execute any of the above method steps. 
     Exemplary System Elements 
     A vehicle may traverse a path by actuating vehicle propulsion, braking, and/or steering. The vehicle may be operated by a human operator and/or a computer based on a variety of data, e.g., data about a presence and/or movement of other objects such as vehicles, bicycles, pedestrians, etc. To address technical challenges arising in planning and/or executing a path for a vehicle, a vehicle computing device can include programming to determine a virtual boundary for a vehicle body based on a shape of the vehicle body, identify one or more objects based on vehicle sensor data, and then, based on the detected one or more objects, the determined virtual boundary, and an input to at least one of propulsion, steering, or braking, to determine at least one of a braking override, acceleration override, or a steering override, and further, based on the determination, can perform at least one of adjusting a vehicle steering and a vehicle speed. 
       FIG.  1    illustrates an example vehicle  100 . The vehicle  100  may be powered in a variety of ways, e.g., with an electric motor and/or internal combustion engine. The vehicle  100  may be a land vehicle such as a car, truck, etc. A vehicle  100  may include a computer  110 , actuator(s)  120 , sensor(s)  130 , and a human-machine interface (HMI  140 ). A reference point  150  can be defined with respect to the vehicle  100 , e.g., the illustrated reference point  150  is within the space defined by a vehicle  100  body  160 , and is a geometrical center point, i.e., a point at which respective longitudinal and lateral center axes of the vehicle  100  intersect. 
     The computer  110  includes a processor and a memory such as are known. The memory includes one or more forms of computer-readable media, and stores instructions executable by the computer  110  for performing various operations, including as disclosed herein. 
     The computer  110  may operate the vehicle  100  in an autonomous or a semi-autonomous mode. For purposes of this disclosure, an autonomous mode is defined as one in which each of vehicle  100  propulsion, braking, and steering are controlled by the computer  110 ; in a semi-autonomous mode the computer  110  controls one or two of vehicles  100  propulsion, braking, and/or steering. 
     The computer  110  may include programming to operate one or more of land vehicle brakes, propulsion (e.g., control of acceleration in the vehicle by controlling one or more of an internal combustion engine, electric motor, hybrid engine, etc.), steering, climate control, interior and/or exterior lights, etc., as well as to determine whether and when the computer  110 , as opposed to a human operator, is to control such operations. Additionally, the computer  110  may be programmed to determine whether and when a human operator is to control such operations. As discussed below, the computer can include programming to override a human operator or an autonomous vehicle control system, e.g., by actuating a brake, propulsion, and/or steering actuator. For example, the computer  110  may be programmed to execute instructions of an autonomous vehicle control system to operate the vehicle and additionally be programmed based on the techniques disclosed herein to override an operation of the autonomous vehicle control system programmed based on specified conditions, as discussed below. In another example, a first computer  110  may be programmed to operate the vehicle autonomously and a second computer  110  may be programmed to override actuation of the first computer  110  when specific conditions are satisfied. In yet another example, a first computer  110  may operate the vehicle based on inputs received from a human operator and a second computer  110  may be programmed based on the techniques herein to override human user actuation commands when specific conditions are satisfied. 
     The computer  110  may include or be communicatively coupled to (e.g., via a vehicle  100  communications bus as described further below) more than one processor, e.g., controllers or the like included in the vehicle for monitoring and/or controlling various vehicle controllers, e.g., a powertrain controller, a brake controller, a steering controller, etc. The computer  110  is generally arranged for communications on a vehicle communication network that can include a bus in the vehicle such as a controller area network (CAN) or the like, and/or other wired and/or wireless mechanisms. 
     Via the vehicle  100  network, the computer  110  may transmit messages to various devices in the vehicle and/or receive messages from the various devices, e.g., an actuator  120 , an HMI  140 , etc. Alternatively or additionally, in cases where the computer  110  actually comprises multiple devices, the vehicle  100  communication network may be used for communications between devices represented as the computer  110  in this disclosure. Further, as mentioned below, various controllers and/or sensors may provide data to the computer  110  via the vehicle communication network. 
     In addition, the computer  110  may be configured for communicating through a wireless vehicular communication interface with other traffic objects (e.g., vehicles, infrastructure, pedestrian, etc.), e.g., via a vehicle-to-vehicle communication network and/or a vehicle-to-infrastructure communication network. The vehicular communication network represents one or more mechanisms by which the computers  110  of vehicles  100  may communicate with other traffic objects, and may be one or more of wireless communication mechanisms, including any desired combination of wireless (e.g., cellular, wireless, satellite, microwave and radiofrequency) communication mechanisms and any desired network topology (or topologies when multiple communication mechanisms are utilized). Exemplary vehicular communication networks include cellular, Bluetooth®, IEEE 802.11, dedicated short-range communications (DSRC), and/or wide area networks (WAN), including the Internet, providing data communication services. 
     The vehicle  100  actuators  120  are implemented via circuits, chips, or other electronic and or mechanical components that can actuate various vehicle subsystems in accordance with appropriate control signals as is known. The actuators  120  may be used to control braking, acceleration, and steering of the vehicles  100 . The computer  110  may be programmed to actuate the vehicle  100  actuators  120  including propulsion, steering, and/or braking actuators  120  based on the planned acceleration. 
     The sensors  130  may include a variety of devices known to provide data to the computer  110 . For example, the sensors  130  may include object detection sensors  130  such as Light Detection And Ranging (LIDAR) sensor(s)  130  disposed on a top of the vehicle  100  that provide relative locations, sizes, and shapes of one or more targets  200  (or objects) surrounding the vehicle  100 , e.g., second vehicles, bicycles, pedestrians, robots, drones, etc., traveling next to, ahead, or behind of the vehicle  100 . As another example, one or more radar sensors  130  fixed to vehicle  100  bumpers may provide locations of the target(s)  200  relative to the location of the vehicle  100 . 
     The object detection sensors  130  may include camera sensor(s)  130 , e.g. to provide a front view, side view, etc., providing images from an area surrounding the vehicle  100 . For example, the computer  110  may be programmed to receive image data from a camera sensor(s)  130  and to implement image processing techniques to detect a road, infrastructure elements, etc. The computer  110  may be further programmed to determine a current vehicle  100  location based on location coordinates, e.g., GPS coordinates, received from a vehicle  100  location (e.g., GPS) sensor  130 . 
     The HMI  140  may be configured to receive input from a user during operation of the vehicle  100 . Moreover, an HMI  140  may be configured to provide output to the user. The HMI  140  is typically located in the passenger compartment of the vehicle  100 . In one example, the computer  110  may be programmed to receive destination a destination location, from the HMI  140 . The destination location can be specified according to geocoordinates or the like, e.g., according to map data stored in the vehicle  100 . 
       FIG.  2    shows an example operating scenario of the vehicle  100  and a target object, or target  200 , e.g., a second vehicle, a pedestrian, etc., within an area  210 . An area  210 , in the present context, means a portion of a ground surface, e.g., a two-dimensional (2D) area on the surface of the earth. Location coordinates of vehicle(s)  100 , target(s)  200 , etc., may be defined by global positioning system (GPS) coordinates. Boundaries or edges of an area  210 , e.g., defined by connecting vertices of a triangular or rectangular area, specifying a radius from a center of a circular area, etc., may be specified by GPS coordinates. An area  210  may have any suitable dimensions and/or shape, e.g., rectangular, oval, circular, irregularly shaped, etc. An area  210  may include a section of a road, an intersection, etc. An area  210  may be defined by a detection range of a sensor  130 , i.e., locations within a predetermined distance, e.g., 200 meters (m), from the sensor  130 . 
     In addition to a vehicle  100 , target(s)  200  such as other vehicles, pedestrians, bicycles, etc. may be present in the area. The locations of the vehicle  100  and the target(s)  200  may be specified in a two-dimensional Cartesian coordinate system  240 , e.g., having X, Y axes, as shown in  FIG.  2   . For example, the location coordinates of the vehicle  100  and/or the targets  200  may be defined according to one or more of GPS location coordinates, a coordinate system defined with respect to the vehicle  100 , e.g., the reference point150, a coordinate system defined for a locale or area in which the vehicle  100  is operating, etc. 
     The computer  110  may navigate the vehicle  100 , e.g., based on data received from the HMI  140 . For example, the received data may include GPS location coordinates of a destination specified according to user input. 
     A vehicle  100  can operate on a roadway by determining a path polynomial to traverse a vehicle path. A computer  110  can determine a path polynomial including path coefficients based on vehicle  100  sensor data and/or data received from a remote computer, etc. In the present context, a path is a straight and/or curved line that describes successive locations (i.e., locations at different times) of an object, e.g., a vehicle  100 , a target  200 , etc., on a two-dimensional (2D) plane parallel to the surface of a roadway upon which the object moves. 
     The computer  110  may be programmed to actuate vehicle  100  actuators  120 , e.g., propulsion, braking, and/or steering actuators  120 . In one example, the computer  110  may actuate the vehicle  100  actuators  120  based on input received from a vehicle  100  operator via a vehicle HMI  140 , e.g., brake pedal, steering wheel, gas pedal, etc. Additionally or alternatively, the computer  110  may be programmed to operate the vehicle  100  in an autonomous mode by actuating vehicle  100  actuators  120  to navigate the vehicle  100  to a destination while avoiding a collision with other target(s)  200  within the area  210 . The vehicle  100  computer  110  can be programmed to determine an acceleration command u p  and a steering command δp for the vehicle  100  based on the vehicle  100  destination and sensor  130  data. The computer  110  may be programmed to actuate propulsion and/or braking actuator(S)  120  based on the determined acceleration command u p  and actuate a steering actuator  120  based on the determined steering command δp. 
     As disclosed herein, a vehicle computer  110  can detect a road surface, i.e., characteristics or attributes of a ground surface on which a vehicle  100  is operating. and can then, based on the detected road surface, intervene in vehicle  100  operation of propulsion, steering, and/or braking. For example, the vehicle computer  110  could override a vehicle  100  operator input and/or a command generating by a virtual driver program or the like, i.e., a command generated in a vehicle computer  110  to control the vehicle  100  based at least in part on data from one or more vehicle sensors  130 . For example, a vehicle  100  computer  110  can be programmed to determine a virtual boundary  170  for a vehicle  100  body  160  based on a shape of the vehicle  100  body  160 , to identify target(s)  200  based on vehicle sensor data, based on the detected target(s)  200 , the determined virtual boundary  170 , and an input to at least one of propulsion, steering, or braking, determine at least one of a braking override, acceleration override, or a steering override, and based on the determination, perform at least one of adjusting a vehicle  100  steering and a vehicle  100  speed. 
     In the present context, a steering override δ̅̅, and an acceleration override u̅ are respective commands to deviate from a steering command δp or acceleration command u p  determined based on user input and/or by a vehicle computer  110 . Acceleration override u̅ may be an array including propulsion override and braking override. 
       FIG.  3    shows another example of a virtual boundary  170  for the vehicle  100  defined as an area on a ground surface around the vehicle  100 , e.g., defined based on an exterior shape of the vehicle  100  in a horizontal plane. Typically the virtual boundary  170  is defined as a projection of the vehicle  100  body  160  on the ground surface including accessories such as exterior mirrors, bumpers, etc., which may be at different heights (i.e., distances from a ground surface). That is, a top-down view of an outline of a vehicle  100  body  160  could be projected onto a ground surface to define a 2D virtual boundary  170 . Thus, a virtual boundary  170  defines an area around the vehicle  100  enclosing the body  160  of the vehicle  100 . An area of a virtual boundary  170  can be mathematically specified as {(r, θ R ) ∈ [0, ∞) × [0, 2π) | r ≤ Γ(θ R )}. In one example, each point on the virtual boundary  170  is defined to be spaced from a nearest point of the vehicle  100   body  160  by a specified distance, e.g., 10 centimeters (cm). With reference to Equation (1) and  FIG.  2    below, the computer  110  may be programmed to specify the virtual boundary  170  by implementing a function Γ(θ R ) that determines a distance from the reference point  150  within the virtual boundary to a point  230  on the virtual boundary at an angle θ R  angle between a virtual line  220  and reference line x h . In other words, the function Γ(θ R ) can specify various shapes of virtual boundaries as the distance of a point  230  on the virtual boundary  170  and the angle θ R  vary. The virtual line  220  is an imaginary line extending from the vehicle  100 , e.g., a reference point  150 , to a target  200 . 
     The computer  110  may be programmed to operate based on a control barrier function (as discussed below with respect to Expressions (2)-(4)) that determines a barrier distance h along a virtual line  220  extending from the vehicle  100 , e.g., a reference point  150 , to a target  200 . The relative distance h is defined as a distance (or length) along the line  220  from a point  230  on the virtual boundary  170  at respective orientations of a virtual line  220  to the target  200 . The point  230  is at an intersection of the virtual line  220  with the virtual boundary  170 . A distance h is defined as a distance from the virtual boundary  170  of the vehicle  100  to a target  200 . Additionally or alternatively, as discussed below, h may represent a relative motion between the vehicle  100  and a target  200  taking into account various physical parameters such as relative distance, relative acceleration, relative speed between the vehicle  100  and the target  200 . When other physical parameters. such as speed or acceleration. are taken into account, a visualization of distance h and boundary  170  may need to include a third dimension z (not shown). Alternatively, level sets may be used to illustrate the boundary in the plane. A level-set is an embedding of a higher-dimensional geometric object into a lower-dimensional subspace by fixing one of the independent variables. Examples include visualizing horizontal cut-outs of 3D geometric objects. For example, dimensions of the boundary around the vehicle  100  may either increase or decrease in size depending on a sign of the relative velocity of the vehicle  100  and target  200 . For example, if the relative velocity is negative (indicating the vehicle  100  is approaching the target  200 ), then the virtual boundary  170  would be enlarged. Alternatively, if the relative velocity is positive, the virtual boundary  170  may shrink in size. Lines x h , y h  illustrated in  FIG.  2    are axes of a coordinate system defined with respect to the vehicle  100 , i.e., a Cartesian coordinate system having an origin at the reference point  150 . Parameters r, Γ, ν H , ν T , θ R , θ T,  represent, respectively, (i) a distance between the target  200  and the virtual boundary reference point  150 , (ii) a distance of the virtual boundary  170  from the point  230  and the reference point  150 , (iii) a velocity vector of the vehicle  100 , (iv) a velocity vector (i.e., a vector specifying a direction and magnitude of speed) of the target  200 , (v) an angle between the virtual line  220  and reference line x h , and (vi) an angle between the velocity vector ν T  of the target  200  and the reference line x h . Expression 1 below thus illustrates a mathematical function for determining the relative distance h. 
     
       
         
           
             h 
             
               
                 r 
                 , 
                 
                   θ 
                   R 
                 
                 , 
                 
                   θ 
                   T 
                 
                 , 
                 
                   v 
                   H 
                 
                 , 
                 
                   v 
                   T 
                 
               
             
             = 
             r 
             − 
             Γ 
             
               
                 
                   θ 
                   R 
                 
               
             
           
         
       
     
     A Control Barrier Function, herein, is an expression, i.e., a mathematical relationship, such as Expressions (2)-(4), which define a constraint to be satisfied. A Control Barrier Function (CBF) is a barrier function where for every state x(t) ∈ X, there exists a control input u(t) ∈ U such that (2) is true. Note that defining a control barrier is based on a mathematical model for a system, e.g., ẋ = f(x) + g(x)u to specify a state of a system including the vehicle  100  and the target  200 . Thus, Expression (1) defines the CBF, Expression (2) may be used to define a set of x that satisfy the CBF, and Expression (3) defines a dynamic constraint to be enforced via a control input u. With reference to Expression (2) below, the computer  110  may be programmed to operate the vehicle  100  such that the barrier function h(x)is greater than or equal 0 (zero), i.e., avoiding that a target 20 enters the virtual boundary  170 . x(t) represents a location of the vehicle  100  at a time t. The time t is a time at which the vehicle  100  is operated using control barrier function to avoid the target  200  entering the virtual boundary  170  of the vehicle  100 . 
     
       
         
           
             h 
             
               
                 x 
                 
                   t 
                 
               
             
             ≥ 
             0 
           
         
       
     
     The computer  110  may determine the propulsion and/or braking override u̅ by performing an optimization operation on a control barrier function (e.g., as shown in example Expressions (2), (3), or (4) including a relative distance function h and a derivative of the relative distance function h. With reference to Expression (3), which specifies a constraint providing an improved approach to avoid a target  200  entering the virtual boundary  200 , the computer  110  may be programmed to determine the derivative of the distance function based on a derivative of a distance of a virtual line  220  extending from the virtual boundary  170  to the one or more targets  200  and a derivative of the orientation of the virtual line  220  relative to a virtual reference line x H . Expression (3) further depends on a control input u(t), e.g., actuation of steering and acceleration of the vehicle  100 . Thus, control function u(t) or a range for the control function u(t) may be identified which satisfies the Expression (3). A function ḣ((x(t), u(t)) is a temporal derivative of function h based on location x(t) of the vehicle  100  and the control input u(t). 
     
       
         
           
             
               h 
               ˙ 
             
             
               
                 
                   
                     x 
                     
                       t 
                     
                     ,u 
                     
                       t 
                     
                   
                 
               
             
             + 
             λ 
             h 
             
               
                 x 
                 
                   t 
                 
                 ≥ 
                 0 
               
             
           
         
       
     
     In some examples, to compensate for uncertainty, a margin for the uncertainty may be built into the control barrier function, e.g., as shown in Expression (4). Uncertainty is a measure of potential inaccuracy, i.e., specifies a level of expected precision or accuracy, in data from sensors  130 . For example, there may be uncertainty in determining the relative distance or relative motion h based on data received from the sensors  130 . For example, an object detection sensor  130  determining a distance from a target  200  may have in the inaccuracy of 1 meter. 
     
       
         
           
             
               h 
               ˙ 
             
             
               
                 
                   
                     x 
                     
                       t 
                     
                     ,u 
                     
                       t 
                     
                   
                 
               
             
             + 
             λ 
             h 
             
               
                 x 
                 
                   t 
                 
                 − 
                 ε 
                 ≥ 
                 0 
               
             
           
         
       
     
     Equations (5)-(6b), shows other examples of defining relative motion h and a derivative of relative motion ḣ. Function γ is a spatial gradient with respect to a relative heading angle of the vehicle  100 , as shown in Expression (6b). 
     
       
         
           
             h 
             
               
                 r 
                 , 
                 
                   θ 
                   R 
                 
                 , 
                 
                   r 
                   ˙ 
                 
               
             
             = 
             r 
             − 
             Γ 
             
               
                 
                   θ 
                   R 
                 
               
             
           
         
       
     
     
       
         
           
             
               h 
               ˙ 
             
             
               
                 r 
                 , 
                 
                   θ 
                   R 
                 
               
             
             = 
             
               r 
               ˙ 
             
             − 
             γ 
             
               
                 
                   θ 
                   R 
                 
               
             
             
               
                 θ 
                 ˙ 
               
               R 
             
           
         
       
     
     
       
         
           
             γ 
             
               
                 
                   θ 
                   R 
                 
               
             
             : 
             = 
               
             
               ∂ 
               
                 ∂ 
                 
                   θ 
                   R 
                 
               
             
             Γ 
             
               
                 
                   θ 
                   R 
                 
               
             
           
         
       
     
     The computer  110  may be programmed to determine (i) an override of propulsion, (ii) a combination of overriding propulsion and steering, (ii) an override of steering only, (iii) an override of steering and an override of braking, or any other combination of overriding propulsion, steering, and braking. The computer  110  may be programmed to determine steering override δ̅ and acceleration override u̅ using an optimization technique, e.g., Quadratic Programming. Quadratic programming (QP) is a type of non-linear programming for solving mathematical optimization problems involving quadratic functions; QP can be used to optimize (minimize or maximize) a multivariate quadratic function subject to linear constraints on the variables. For example, the computer  110  may be programmed to identify optimized minimum overrides  δ , u̅ for Expression (3) based on min operation (7). Operation (7) returns minimum values for overrides  δ , u̅ based on, e.g., Expression (3). Thus, based on solving the optimization problem expressed in Expression (7) subject to the constraint given in (3), only certain combinations of steering/braking will be satisfying Expression (3). Based on the result of optimization, then, a minimum “amount” of steering/braking is taken to actuate the vehicle  100  actuators  120 . The computer  110  may be programmed to determine adjusted actuation commands based on the planned values and override values. For example, with reference to Equation (8), the computer  110  may be programmed to determine an adjusted steering actuation δ adj  based on the determined steering actuation δ p  (e.g., determined by a human operator or an autonomous vehicle control system) and the determined steering override  δ . With reference to Equation (9), the computer  110  may be programmed to determine an adjusted acceleration actuation u adj  based on the determined acceleration actuation u p  (e.g., determined by human operator or autonomous vehicle control system) and the determined acceleration override u̅. 
     
       
         
           
             min 
             
               
                 
                   δ 
                   ¯ 
                 
                   
                 
                   u 
                   ¯ 
                 
               
             
             H 
             
               
                 
                   
                     
                       
                         δ 
                         ¯ 
                       
                     
                   
                   
                     
                       
                         u 
                         ¯ 
                       
                     
                   
                 
               
             
           
         
       
     
     
       
         
           
             
               δ 
               
                 adj 
               
             
             = 
             
               δ 
               p 
             
             + 
             
               δ 
               ¯ 
             
           
         
       
     
     
       
         
           
             
               u 
               
                 adj 
               
             
             
               
                 =u 
               
               p 
             
             + 
             
               u 
               ¯ 
             
           
         
       
     
     The technique disclosed herein can simultaneously be applied to more than one target  200 . Expression (10) specifies a first barrier function h 1  for a first target  200  and Expression (11) specifies a second barrier function h 2  for a second target  200 . The computer  110  may be programmed to identify overrides  δ , u̅ while simultaneously satisfying the Expressions (10)-(11). 
     
       
         
           
             
               
                 h 
                 ˙ 
               
               1 
             
             
               
                 
                   
                     x 
                     
                       t 
                     
                     ,u 
                     
                       t 
                     
                   
                 
               
             
             + 
             λ 
             
               h 
               1 
             
             
               
                 x 
                 
                   t 
                 
               
             
             ≥ 
             0 
           
         
       
     
     
       
         
           
             
               
                 h 
                 ˙ 
               
               2 
             
             
               
                 
                   
                     x 
                     
                       t 
                     
                     ,u 
                     
                       t 
                     
                   
                 
               
             
             + 
             λ 
             
               h 
               2 
             
             
               
                 x 
                 
                   t 
                 
               
             
             ≥ 
             0 
           
         
       
     
     Based on, e.g., physical characteristics of vehicle  100  actuators  120 , road conditions, etc., maximum allowed acceleration, deceleration, and/or steering actuation limits may be specified. For example, a maximum braking deceleration may be determined based on braking actuator  120  characteristics, e.g., a friction coefficient of brake pads, a vehicle  100  weight, a vehicle  100  aerodynamic resistance, etc., and/or a road condition, e.g., a coefficient of friction, rain, snow, ice, etc. Equations (12)-(13) show examples of the relative motion function h that further includes maximum allowed deceleration. The operator “sgn” is a function returning 1 (one) for positive input, -1 (minus one) for negative input and 0 (zero) for a 0 (zero) input. A maximum acceleration is computed defined as d in the denominator of Expression (12). When vehicle  100  is heading straight toward the target  200 , and can only use deceleration, the value of the function h will be negative if more deceleration is needed than the amount given by d. This is found via kinematic expressions for constant deceleration, i.e. if an initial relative velocity and distance from the target  200  are known, then a constant deceleration will result in a fixed amount of distance traveled. If the actual distance is less than the distance needed, then the vehicle  100  may hit the target  200 . The function h is then positive if there is enough distance to stop assuming maximum deceleration. Note that there is no encoding of maximum steering. Additionally or alternatively, an additional constraint such as |δ adj | ≤ δ max  may be added to Expressions (10)-(11). 
     
       
         
           
             h 
             
               
                 r 
                 , 
                 
                   θ 
                   R 
                 
                 , 
                 
                   r 
                   ˙ 
                 
               
             
             = 
             r 
             − 
             Γ 
             
               
                 
                   θ 
                   R 
                 
               
             
             + 
             sgn 
             
               
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       FIG.  4    is a flowchart of an example process  400  for controlling vehicle  100  operation. The computer  110  may be programmed to execute blocks of the process  400 . 
     The process  400  begins in a block  410 , in which the computer  110  determines or receives a predetermined virtual boundary  170  of the vehicle  100 . For example, as discussed with respect to  FIG.  2   , the computer  110  may be programmed to determine and store a function Γ(θ R ) that returns a distance from a reference point  150  of the virtual boundary  170  to a point on the virtual boundary  170  for each given angle specified location θ R . Alternatively, the computer  110  may store, and/or receive from a remote computer, a default virtual boundary  170  definitions 
     Next, in a decision block  420 , the computer  110  determines whether one or more targets  200 , e.g., other vehicles, pedestrians, buildings, vegetation, etc., is or are detected. The computer  110  may be programmed to identify a target  200  based on data received from a vehicle  100  sensor  130 , a remote computer, etc., according to any suitable means. If the computer  110  determines that one or more targets  200  are detected, then the process  400  proceeds to a decision block  430 ; otherwise the process  400  returns to the decision block  420 . 
     In the decision block  430 , the computer  110  determines whether an actuation input is received. The computer  110  may be programmed to an actuation input from a human operator, e.g., via HMI  140 , and/or from an autonomous vehicle control system, e.g., a second program stored in the computer  110  memory, an FPGA communicating with the computer  110  via a vehicle  100  network, etc. For example, actuation inputs may include acceleration or deceleration actuation u p  and/or steering actuation δ p . If the computer  110  determines that actuation input is received, then the process  400  proceeds to a decision block  440 ; otherwise the process  400  returns to the decision block  430 . 
     In the decision block  440 , the computer  110  determines whether a control barrier function, e.g., as specified in Expression (3), is satisfied. In another example, if more than one target  200  is identified, the computer  110  may be programmed to determine whether each of the respective barrier functions, e.g., as shown in Expressions (10)-(11) are satisfied. If the barrier function(s) associated with detected target(s)  200  are satisfied, then the process  400  proceeds to a block  450 ; otherwise the process  400  proceeds to a block  460 . 
     In the block  450 , the computer  110  applies the received actuation inputs of the block  430 . Following the block  450 , the process  400  ends, or alternatively returns to the block  410 , although not shown in  FIG.  1   . 
     In the block  460 , the computer  110  determines one or both of actuation overrides  δ , u. The computer  110  may be programmed to perform an optimization technique to identify propulsion or braking override u̅, and/or steering override  δ  based on a respective Expression (3). In another example, when multiple targets  200  are identified, the computer  110  may identify override actuation  δ , u̅ while satisfying multiple Expressions, e.g., Expressions (10)-(11). 
     Next, in a block  470 , the computer  110  applies adjusted actuation commands δ adj , u adj  to the vehicle  100  actuators  120 . The computer  110  may be programmed, based on Equations (8)-(9), to determine the adjusted actuation commands δ adj , u adj  based on the received actuation input δ p , u p , and the determined overrides  δ , u̅. Following the block  470 , the process  400  ends, or alternatively returns to the block  410 , although not shown in  FIG.  1   . 
     Computing devices as discussed herein generally each includes commands executable by one or more computing devices such as those identified above, and for carrying out blocks or steps of processes described above. Computer-executable instructions may be compiled or interpreted from computer programs created using a variety of programming languages and/or technologies, including, without limitation, and either alone or in combination, Java™, C, C++, Visual Basic, Java Script, Perl, HTML, etc. In general, a processor (e.g., a microprocessor) receives instructions, e.g., from a memory, a computer-readable medium, etc., and executes these instructions, thereby performing one or more processes, including one or more of the processes described herein. Such instructions and other data may be stored and transmitted using a variety of computer-readable media. A file in the computing device is generally a collection of data stored on a computer readable medium, such as a storage medium, a random-access memory, etc. 
     A computer-readable medium includes any medium that participates in providing data (e.g., instructions), which may be read by a computer. Such a medium may take many forms, including, but not limited to, non-volatile media, volatile media, etc. Non-volatile media include, for example, optical or magnetic disks and other persistent memory. Volatile media include dynamic random-access memory (DRAM), which typically constitutes a main memory. Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD, any other optical medium, paper tape, any other physical medium with patterns of holes, a RAM, a PROM, an EPROM, a FLASH, an EEPROM, any other memory chip or cartridge, or any other medium from which a computer can read. 
     With regard to the media, processes, systems, methods, etc. described herein, it should be understood that, although the steps of such processes, etc. have been described as occurring according to a certain ordered sequence, such processes could be practiced with the described steps performed in an order other than the order described herein. It further should be understood that certain steps could be performed simultaneously, that other steps could be added, or that certain steps described herein could be omitted. In other words, the descriptions of systems and/or processes herein are provided for the purpose of illustrating certain embodiments, and should in no way be construed so as to limit the disclosed subject matter. 
     Accordingly, it is to be understood that the present disclosure, including the above description and the accompanying figures and below claims, is intended to be illustrative and not restrictive. Many embodiments and applications other than the examples provided would be apparent to those of skill in the art upon reading the above description. The scope of the invention should be determined, not with reference to the above description, but should instead be determined with reference to claims appended hereto and/or included in a non-provisional patent application based hereon, along with the full scope of equivalents to which such claims are entitled. It is anticipated and intended that future developments will occur in the arts discussed herein, and that the disclosed systems and methods will be incorporated into such future embodiments. In sum, it should be understood that the disclosed subject matter is capable of modification and variation.