Patent Publication Number: US-11377112-B2

Title: Low-speed, backward driving vehicle controller design

Description:
TECHNICAL FIELD 
     Embodiments of the present disclosure relate generally to operating autonomous vehicles. More specifically, the present disclosure is related to determining a more efficient and more accurate control effort for controlling the ADV when controlling the ADV in either forward or reverse driving direction, and in low speed environments. 
     BACKGROUND 
     Vehicles operating in an autonomous mode (e.g., driverless) can relieve occupants, especially the driver, from some driving-related responsibilities. When operating in an autonomous mode, the vehicle can navigate to various locations using onboard sensors, allowing the vehicle to travel with minimal human interaction or in some cases without any passengers. 
     Motion planning and control are critical operations in autonomous driving. However, conventional motion planning operations estimate the difficulty of completing a given path mainly from its curvature and speed, without considering the differences in features for different types of vehicles. Same motion planning and control is applied to all types of vehicles, which may not be accurate and smooth under some circumstances. 
     Certain driving scenarios, such as low speed driving that require driving in reverse, are very difficult to model. Forward driving often uses the “bicycle model” as a dynamic model for driving forward over a wide variety of speeds. Some prior art solutions to modeling driving in reverse use a forward dynamic model and simply reverse the sign and/or orientation of algorithms and obstacles to the ADV. However, as is well-known to human drivers, the dynamics of any vehicle are different in reverse than in forward driving due, in part, to imperfect center of mass of the vehicle, whether the steering wheels are in front or the rear of the vehicle, whether the driving wheels are in front or the rear of the vehicle, the location of the engine, camber and caster of the steering wheels at the limits of the vehicle&#39;s turning radius, state of the tread wear and alignment of the steering wheels, and the like. 
     These dynamics are often more pronounced in slow speed driving. Slow speed driving is typically used for open-space driving scenarios such as autonomous parking in a parking lot, 3-point turns, U-turns, and other low-speed, tight turning radius driving scenarios. These tight turning scenarios frequently require that the vehicle turn to its maximum turning angle, which adversely affects the friction force offered by the wheels and tires of the vehicle. For at least these reasons, conventional autonomous driving dynamic models do not provide sufficient control accuracy for open-space driving scenarios that require tight turning and both forward and reverse driving at low speeds. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments of the disclosure are illustrated by way of example and not limitation in the figures of the accompanying drawings in which like references indicate similar elements. 
         FIG. 1  is a block diagram illustrating a networked system according to one embodiment. 
         FIG. 2  is a block diagram illustrating an example of an autonomous vehicle according to one embodiment. 
         FIGS. 3A-3B  are block diagrams illustrating an example of a perception and planning system used with an autonomous vehicle according to one embodiment. 
         FIG. 4  is a block diagram illustrating architecture of an autonomous driving system according to one embodiment. 
         FIGS. 5A and 5B  are block diagrams illustrating an example of a predicting a lateral error and heading error in forward driving ( FIG. 5A ) and reverse driving ( FIG. 5B ) scenarios, according to one embodiment. 
         FIG. 6  illustrates a method of controlling an autonomous driving vehicle, according to one embodiment. 
         FIG. 7  illustrates a method of controlling an autonomous driving vehicle, according to one embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Various embodiments and aspects of the disclosures will be described with reference to details discussed below, and the accompanying drawings will illustrate the various embodiments. The following description and drawings are illustrative of the disclosure and are not to be construed as limiting the disclosure. Numerous specific details are described to provide a thorough understanding of various embodiments of the present disclosure. However, in certain instances, well-known or conventional details are not described in order to provide a concise discussion of embodiments of the present disclosures. 
     Reference in the specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in conjunction with the embodiment can be included in at least one embodiment of the disclosure. The appearances of the phrase “in one embodiment” in various places in the specification do not necessarily all refer to the same embodiment. 
     According to a first aspect, a method of controlling an autonomous driving vehicle (ADV) using a model-switching method includes determining a gear position of the ADV. The gear position can be a forward driving gear position or a reverse driving gear position. A driving model and a predictive feedback model are selected, based upon the gear position. In the forward driving gear position, the driving model can be a dynamic model, such as the “bicycle” model or other dynamic model, and the predictive feedback model can be a look-ahead model. In the reverse driving gear position, the driving model can be a hybrid dynamic and kinematic model, described herein, and the predictive feedback model can be a “look-back” model. Using the selected driving model, a current lateral error and current heading error of the ADV are determined. Using the selected predictive feedback model, a predicted lateral error and predicted heading error of the ADV are determined. The current and predicted lateral errors and heading errors can be provided to a linear quadratic regulator (LQR) to produce a first control effort, based on the current and predicted lateral errors and heading errors. In an embodiment, an augmented control effort, based on a Fourier Transform analysis, in the frequency domain, of a lateral and/or heading error signal of the ADV, can be added to the LQR control effort output to produce a final control effort sent to a control module of the ADV to control the ADV driving. 
     In an embodiment, any/all of the above method functionality can be implemented by a processing system, comprising one or more hardware processors coupled to a memory programmed with executable instructions that, when executed by the processing system, cause a computing system to implement the claimed functionality. In an embodiment, the memory can be a non-transitory computer-readable medium or other type of memory. 
       FIG. 1  is a block diagram illustrating an autonomous vehicle network configuration according to one embodiment of the disclosure. Referring to  FIG. 1 , network configuration  100  includes autonomous vehicle  101  that may be communicatively coupled to one or more servers  103 - 104  over a network  102 . Although there is one autonomous vehicle shown, multiple autonomous vehicles can be coupled to each other and/or coupled to servers  103 - 104  over network  102 . Network  102  may be any type of networks such as a local area network (LAN), a wide area network (WAN) such as the Internet, a cellular network, a satellite network, or a combination thereof, wired or wireless. Server(s)  103 - 104  may be any kind of servers or a cluster of servers, such as Web or cloud servers, application servers, backend servers, or a combination thereof. Servers  103 - 104  may be data analytics servers, content servers, traffic information servers, map and point of interest (MPOI) servers, or location servers, etc. 
     An autonomous vehicle refers to a vehicle that can be configured to in an autonomous mode in which the vehicle navigates through an environment with little or no input from a driver. Such an autonomous vehicle can include a sensor system having one or more sensors that are configured to detect information about the environment in which the vehicle operates. The vehicle and its associated controller(s) use the detected information to navigate through the environment. Autonomous vehicle  101  can operate in a manual mode, a full autonomous mode, or a partial autonomous mode. 
     In one embodiment, autonomous vehicle  101  includes, but is not limited to, perception and planning system  110 , vehicle control system  111 , wireless communication system  112 , user interface system  113 , and sensor system  115 . Autonomous vehicle  101  may further include certain common components included in ordinary vehicles, such as, an engine, wheels, steering wheel, transmission, etc., which may be controlled by vehicle control system  111  and/or perception and planning system  110  using a variety of communication signals and/or commands, such as, for example, acceleration signals or commands, deceleration signals or commands, steering signals or commands, braking signals or commands, etc. 
     Components  110 - 115  may be communicatively coupled to each other via an interconnect, a bus, a network, or a combination thereof. For example, components  110 - 115  may be communicatively coupled to each other via a controller area network (CAN) bus. A CAN bus is a vehicle bus standard designed to allow microcontrollers and devices to communicate with each other in applications without a host computer. It is a message-based protocol, designed originally for multiplex electrical wiring within automobiles, but is also used in many other contexts. 
     Referring now to  FIG. 2 , in one embodiment, sensor system  115  includes, but it is not limited to, one or more cameras  211 , global positioning system (GPS) unit  212 , inertial measurement unit (IMU)  213 , radar unit  214 , and a light detection and range (LIDAR) unit  215 . GPS system  212  may include a transceiver operable to provide information regarding the position of the autonomous vehicle. IMU unit  213  may sense position and orientation changes of the autonomous vehicle based on inertial acceleration. Radar unit  214  may represent a system that utilizes radio signals to sense objects within the local environment of the autonomous vehicle. In some embodiments, in addition to sensing objects, radar unit  214  may additionally sense the speed and/or heading of the objects. LIDAR unit  215  may sense objects in the environment in which the autonomous vehicle is located using lasers. LIDAR unit  215  could include one or more laser sources, a laser scanner, and one or more detectors, among other system components. Cameras  211  may include one or more devices to capture images of the environment surrounding the autonomous vehicle. Cameras  211  may be still cameras and/or video cameras. A camera may be mechanically movable, for example, by mounting the camera on a rotating and/or tilting a platform. 
     Sensor system  115  may further include other sensors, such as, a sonar sensor, an infrared sensor, a steering sensor, a throttle sensor, a braking sensor, and an audio sensor (e.g., microphone). An audio sensor may be configured to capture sound from the environment surrounding the autonomous vehicle. A steering sensor may be configured to sense the steering angle of a steering wheel, wheels of the vehicle, or a combination thereof. A throttle sensor and a braking sensor sense the throttle position and braking position of the vehicle, respectively. In some situations, a throttle sensor and a braking sensor may be integrated as an integrated throttle/braking sensor. 
     In one embodiment, vehicle control system  111  includes, but is not limited to, steering unit  201 , throttle unit  202  (also referred to as an acceleration unit), and braking unit  203 . Steering unit  201  is to adjust the direction or heading of the vehicle. Throttle unit  202  is to control the speed of the motor or engine that in turn controls the speed and acceleration of the vehicle. Braking unit  203  is to decelerate the vehicle by providing friction to slow the wheels or tires of the vehicle. Note that the components as shown in  FIG. 2  may be implemented in hardware, software, or a combination thereof. 
     Referring back to  FIG. 1 , wireless communication system  112  is to allow communication between autonomous vehicle  101  and external systems, such as devices, sensors, other vehicles, etc. For example, wireless communication system  112  can wirelessly communicate with one or more devices directly or via a communication network, such as servers  103 - 104  over network  102 . Wireless communication system  112  can use any cellular communication network or a wireless local area network (WLAN), e.g., using WiFi to communicate with another component or system. Wireless communication system  112  could communicate directly with a device (e.g., a mobile device of a passenger, a display device, a speaker within vehicle  101 ), for example, using an infrared link, Bluetooth, etc. User interface system  113  may be part of peripheral devices implemented within vehicle  101  including, for example, a keyboard, a touch screen display device, a microphone, and a speaker, etc. 
     Some or all of the functions of autonomous vehicle  101  may be controlled or managed by perception and planning system  110 , especially when operating in an autonomous driving mode. Perception and planning system  110  includes the necessary hardware (e.g., processor(s), memory, storage) and software (e.g., operating system, planning and routing programs) to receive information from sensor system  115 , control system  111 , wireless communication system  112 , and/or user interface system  113 , process the received information, plan a route or path from a starting point to a destination point, and then drive vehicle  101  based on the planning and control information. Alternatively, perception and planning system  110  may be integrated with vehicle control system  111 . 
     For example, a user as a passenger may specify a starting location and a destination of a trip, for example, via a user interface. Perception and planning system  110  obtains the trip related data. For example, perception and planning system  110  may obtain location and route information from an MPOI server, which may be a part of servers  103 - 104 . The location server provides location services and the MPOI server provides map services and the POIs of certain locations. Alternatively, such location and MPOI information may be cached locally in a persistent storage device of perception and planning system  110 . 
     While autonomous vehicle  101  is moving along the route, perception and planning system  110  may also obtain real-time traffic information from a traffic information system or server (TIS). Note that servers  103 - 104  may be operated by a third party entity. Alternatively, the functionalities of servers  103 - 104  may be integrated with perception and planning system  110 . Based on the real-time traffic information, MPOI information, and location information, as well as real-time local environment data detected or sensed by sensor system  115  (e.g., obstacles, objects, nearby vehicles), perception and planning system  110  can plan an optimal route and drive vehicle  101 , for example, via control system  111 , according to the planned route to reach the specified destination safely and efficiently. 
     Server  103  may be a data analytics system to perform data analytics services for a variety of clients. In one embodiment, data analytics system  103  includes data collector  121  and machine learning engine  122 . Data collector  121  collects driving statistics  123  from a variety of vehicles, either autonomous vehicles or regular vehicles driven by human drivers. Driving statistics  123  include information indicating the driving commands (e.g., throttle, brake, steering commands) issued and responses of the vehicles (e.g., speeds, accelerations, decelerations, directions) captured by sensors of the vehicles at different points in time. Driving statistics  123  may further include information describing the driving environments at different points in time, such as, for example, routes (including starting and destination locations), MPOIs, road conditions, weather conditions, etc. 
     Based on driving statistics  123 , machine learning engine  122  generates or trains a set of rules, algorithms, and/or predictive models  124  for a variety of purposes. In one embodiment, algorithms  124  may include forward driving models, reverse driving models, look-ahead predictive feedback models, linear quadratic regulators, and augmented control models as described below with respect to  FIG. 3C . 
     Algorithms  124  can then be uploaded on ADVs to be utilized during autonomous driving in real-time. 
       FIGS. 3A through 3C  are block diagrams illustrating an example of a perception and planning system used with an autonomous vehicle, according to one embodiment. System  300  may be implemented as a part of autonomous vehicle  101  of  FIG. 1  including, but is not limited to, perception and planning system  110 , control system  111 , and sensor system  115 . Referring to  FIGS. 3A-3B , perception and planning system  110  includes, but is not limited to, localization module  301 , perception module  302 , prediction module  303 , decision module  304 , planning module  305 , control module  306 , a routing module  307 , and an open space planning module  308 . 
     Some or all of modules  301 - 308  may be implemented in software, hardware, or a combination thereof. For example, these modules may be installed in persistent storage device  352 , loaded into memory  351 , and executed by one or more processors (not shown). Note that some or all of these modules may be communicatively coupled to or integrated with some or all modules of vehicle control system  111  of  FIG. 2 . Some of modules  301 - 308  may be integrated together as an integrated module. 
     Localization module  301  determines a current location of autonomous vehicle  300  (e.g., leveraging GPS unit  212 ) and manages any data related to a trip or route of a user. Localization module  301  (also referred to as a map and route module) manages any data related to a trip or route of a user. A user may log in and specify a starting location and a destination of a trip, for example, via a user interface. Localization module  301  communicates with other components of autonomous vehicle  300 , such as map and route information  311 , to obtain the trip related data. For example, localization module  301  may obtain location and route information from a location server and a map and POI (MPOI) server. A location server provides location services and an MPOI server provides map services and the POIs of certain locations, which may be cached as part of map and route information  311 . While autonomous vehicle  300  is moving along the route, localization module  301  may also obtain real-time traffic information from a traffic information system or server. 
     Based on the sensor data provided by sensor system  115  and localization information obtained by localization module  301 , a perception of the surrounding environment is determined by perception module  302 . The perception information may represent what an ordinary driver would perceive surrounding a vehicle in which the driver is driving. The perception can include the lane configuration, traffic light signals, a relative position of another vehicle, a pedestrian, a building, crosswalk, or other traffic related signs (e.g., stop signs, yield signs), etc., for example, in a form of an object. The lane configuration includes information describing a lane or lanes, such as, for example, a shape of the lane (e.g., straight or curvature), a width of the lane, how many lanes in a road, one-way or two-way lane, merging or splitting lanes, exiting lane, etc. 
     Perception module  302  may include a computer vision system or functionalities of a computer vision system to process and analyze images captured by one or more cameras in order to identify objects and/or features in the environment of autonomous vehicle. The objects can include traffic signals, road way boundaries, other vehicles, pedestrians, and/or obstacles, etc. The computer vision system may use an object recognition algorithm, video tracking, and other computer vision techniques. In some embodiments, the computer vision system can map an environment, track objects, and estimate the speed of objects, etc. Perception module  302  can also detect objects based on other sensors data provided by other sensors such as a radar and/or LIDAR. 
     For each of the objects, prediction module  303  predicts what the object will behave under the circumstances. The prediction is performed based on the perception data perceiving the driving environment at the point in time in view of a set of map/rout information  311  and traffic rules  312 . For example, if the object is a vehicle at an opposing direction and the current driving environment includes an intersection, prediction module  303  will predict whether the vehicle will likely move straight forward or make a turn. If the perception data indicates that the intersection has no traffic light, prediction module  303  may predict that the vehicle may have to fully stop prior to enter the intersection. If the perception data indicates that the vehicle is currently at a left-turn only lane or a right-turn only lane, prediction module  303  may predict that the vehicle will more likely make a left turn or right turn respectively. 
     For each of the objects, decision module  304  makes a decision regarding how to handle the object. For example, for a particular object (e.g., another vehicle in a crossing route) as well as its metadata describing the object (e.g., a speed, direction, turning angle), decision module  304  decides how to encounter the object (e.g., overtake, yield, stop, pass). Decision module  304  may make such decisions according to a set of rules such as traffic rules or driving rules  312 , which may be stored in persistent storage device  352 . 
     Routing module  307  is configured to provide one or more routes or paths from a starting point to a destination point. For a given trip from a start location to a destination location, for example, received from a user, routing module  307  obtains route and map information  311  and determines all possible routes or paths from the starting location to reach the destination location. Routing module  307  may generate a reference line in a form of a topographic map for each of the routes it determines from the starting location to reach the destination location. A reference line refers to an ideal route or path without any interference from others such as other vehicles, obstacles, or traffic condition. That is, if there is no other vehicle, pedestrians, or obstacles on the road, an ADV should exactly or closely follows the reference line. The topographic maps are then provided to decision module  304  and/or planning module  305 . Decision module  304  and/or planning module  305  examine all of the possible routes to select and modify one of the most optimal routes in view of other data provided by other modules such as traffic conditions from localization module  301 , driving environment perceived by perception module  302 , and traffic condition predicted by prediction module  303 . The actual path or route for controlling the ADV may be close to or different from the reference line provided by routing module  307  dependent upon the specific driving environment at the point in time. 
     Based on a decision for each of the objects perceived, planning module  305  plans a path or route for the autonomous vehicle, as well as driving parameters (e.g., distance, speed, and/or turning angle), using a reference line provided by routing module  307  as a basis. That is, for a given object, decision module  304  decides what to do with the object, while planning module  305  determines how to do it. For example, for a given object, decision module  304  may decide to pass the object, while planning module  305  may determine whether to pass on the left side or right side of the object. Planning and control data is generated by planning module  305  including information describing how vehicle  300  would move in a next moving cycle (e.g., next route/path segment). For example, the planning and control data may instruct vehicle  300  to move 10 meters at a speed of 30 mile per hour (mph), then change to a right lane at the speed of 25 mph. 
     Based on the planning and control data, control module  306  controls and drives the autonomous vehicle, by sending proper commands or signals to vehicle control system  111 , according to a route or path defined by the planning and control data. Control module  306  can include logic for open-space, low-speed controls for both forward and reverse driving wherein additional control may be needed to increase accuracy for open-space, low-speed, and reverse driving scenarios, such as U-turns, 3-point turns, parking in tight-spaces such as parking in a parking lot. The additional logic is described in detail with respect to  FIG. 3C , below. The planning and control data include sufficient information to drive the vehicle from a first point to a second point of a route or path using appropriate vehicle settings or driving parameters (e.g., throttle, braking, steering commands) at different points in time along the path or route. 
     In one embodiment, the planning phase is performed in a number of planning cycles, also referred to as driving cycles, such as, for example, in every time interval of 100 milliseconds (ms). For each of the planning cycles or driving cycles, one or more control commands will be issued based on the planning and control data. That is, for every 100 ms, planning module  305  plans a next route segment or path segment, for example, including a target position and the time required for the ADV to reach the target position. Alternatively, planning module  305  may further specify the specific speed, direction, and/or steering angle, etc. In one embodiment, planning module  305  plans a route segment or path segment for the next predetermined period of time such as 5 seconds. For each planning cycle, planning module  305  plans a target position for the current cycle (e.g., next 5 seconds) based on a target position planned in a previous cycle. Control module  306  then generates one or more control commands (e.g., throttle, brake, steering control commands) based on the planning and control data of the current cycle. 
     Note that decision module  304  and planning module  305  may be integrated as an integrated module. Decision module  304 /planning module  305  may include a navigation system or functionalities of a navigation system to determine a driving path for the autonomous vehicle. For example, the navigation system may determine a series of speeds and directional headings to affect movement of the autonomous vehicle along a path that substantially avoids perceived obstacles while generally advancing the autonomous vehicle along a roadway-based path leading to an ultimate destination. The destination may be set according to user inputs via user interface system  113 . The navigation system may update the driving path dynamically while the autonomous vehicle is in operation. The navigation system can incorporate data from a GPS system and one or more maps so as to determine the driving path for the autonomous vehicle. 
     Open space planning module  308  is described below with reference to  FIG. 4 . Another aspect of the open space planning module  308  is described below with reference to  FIG. 7 . Open space planning module  308  may be implemented as a part of planning module  305 . 
     Referring now to  FIG. 3C , additional logic for controlling the ADV in special driving scenarios is described. Special driving scenarios can include performing a U-turn, a 3-point turn, parking in a parking lot, or other driving that may require low speed (e.g. less than 10 miles per hour), sharp turns at, or near, the maximum turning angle for the vehicle, and driving in both forward in reverse. Control system  306  can include a driving model switching module  320 , a look-ahead feedback module and a linear quadratic regulator (LQR) and augmented control module  340 . 
     Control module  306 , described above with reference to  FIGS. 2, 3A, and 3B , can produce outputs that are received and processed by both the model switching module  320  and the look-ahead feedback module  330 . Model switching  320  can include logic  321  to detect a gear position of the ADV. A gear position can include a forward driving gear and a reverse driving gear. In an embodiment, gear position detection logic  321  can receive an indication of one or more different forward driving gears, e.g. “1 st , 2 nd  . . . etc.,” and determine that each of these gears is a forward driving gear. Based upon the determination that a gear is a forward driving gear or a reverse driving gear, model switching module  320  can select a forward driving model  322  or a reverse driving model  323  for determining a current lateral error and heading error of the ADV. Look-ahead feedback module  330  contains logic to output a predicted lateral error and heading error based on a predictive “look-head” model for lateral error  331  and a predictive look-ahead model for heading error  332 . Both of the predictive models  331  (lateral error) and  332  (heading error) can each produce error outputs for a forward gear driving and reverse gear driving by changing a sign of each predictive model  331  or  332  output. As described herein, the output of a predicted lateral error and heading error is based upon the determined driving gear position to distinguish between “look-ahead” prediction when a forward driving gear is selected and “look-back” prediction when a reverse driving gear is selected. A forward driving model  322  and a reverse driving model  323  are described below. 
     A forward driving model  322  can be a 4 th  order dynamic model, such as the following: 
               [             e   .     1                 e   ¨     1                 e   .     2                 e   ¨     2           ]     =     
     ⁢         [         0       1       0       0           0               -   2     ⁢           ⁢     C   af       -     2   ⁢           ⁢     C   ar           mV   x                 2   ⁢           ⁢     C   af       +     2   ⁢           ⁢     C   ar         m                 -   2     ⁢           ⁢     C   af     ⁢     l   f       +     2   ⁢           ⁢     C   ar     ⁢     l   r                   ⁢     mV   x                 0       0       0       1           0               -   2     ⁢           ⁢     C   af     ⁢     l   f       +     2   ⁢           ⁢     C   ar     ⁢     l   r             I   z     ⁢     V   x                   2   ⁢           ⁢     C   af     ⁢     l   f       -     2   ⁢           ⁢     C   ar     ⁢     l   r           I   z                   -   2     ⁢           ⁢     C   af     ⁢     l   f   2       -     2   ⁢           ⁢     C   ar     ⁢     l   r   2             I   z     ⁢     V   x               ]     ⁡     [           e   1                 e   .     1               e   2                 e   .     2           ]       +       B   1     ⁢   δ     +       B   2     ⁢       ψ   .     des               
wherein:
 
     
       
         
           
             
               
                 
                   
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         (3) e 1  is the distance of the center of gravity of the autonomous driving vehicle (ADV) from the center trajectory line, and in the reverse model, this is stricken out, ė 1  and ë 1  are first and second derivatives of e 1 , 
         (4) e 2  is the orientation error of the vehicle with respect to the lane (in radians), ė 2  and ë 2  are first and second derivatives of e 2 , 
         (5) δ is the steering angle of the ADV (in radians), 
         (6) {dot over (ψ)} des  is the desired yaw rate (orientation error rate) from road radius R, 
         (7) m is the mass of the ADV (e.g. 1500 kg), 
         (8) V x  is the longitudinal velocity of the ADV, V y  is the lateral velocity of the ADV (e.g. in meters per second: m/s), 
         (9) I z  is the yaw moment of inertia (e.g. 2900 kgm 2 ), 
         (10) l f  and l r  are the distances between the center of gravity of the ADV and the front and rear wheels, respectively (e.g. 1.1 and 1.6 meters), and 
         (11) C af  and C ar  are the friction force of the front and rear wheels, respectively (e.g. C af =C ar =40000 N/rad). 
       
    
     A reverse driving model  323  can be a 3 rd  order hybrid driving model, wherein a portion of the 4 th  order dynamic model, described above, is replaced with a kinematic model. The portion of the dynamic model that is replaced can be computed and discarded, or constants can replace the computations in the dynamic model that would otherwise be discarded. 
                         
wherein the crossed-out portion of the equivalent dynamic model is either not computed, or is discarded if computed, or is replaced with appropriate constants, and wherein:
 
     
       
         
           
             
               
                 
                   
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         (3) e 1  is the distance of the center of gravity of the autonomous driving vehicle (ADV) from the center trajectory line, and in the reverse model, this is stricken out, ė 1  and ë 1  are first and second derivatives of e 1 , 
         (4) e 2  is the orientation error of the vehicle with respect to the lane (in radians), ė 2  and ë 2  are first and second derivatives of e 2 , 
         (5) δ is the steering angle of the ADV (in radians), 
         (6) {dot over (ψ)} des  is the desired yaw rate (orientation error rate) from road radius R, 
         (7) m is the mass of the ADV (e.g. 1500 kg), 
         (8) V x  is the longitudinal velocity of the ADV, V y  is the lateral velocity of the ADV (e.g. in meters per second: m/s), 
         (9) I z  is the yaw moment of inertia (e.g. 2900 kgm 2 ), measured at the center of mass of the ADV, 
         (10) l f  and l r  are the distances between the center of mass of the ADV and the front and rear wheels, respectively (e.g. 1.1 and 1.6 meters), and 
         (11) C af  and C ar  are friction forces of the front and rear wheels, respectively (e.g. C af =C ar =40000 N/rad). 
       
    
     Look-ahead predictive feedback module  323  can include the following lateral and heading error calculations. 
     When the ADV is in a forward driving gear, the look-ahead predicted lateral error  323 , pe 1  at time i+1, is given by: pe 1 =f(e 1 , e 2 , d s ), wherein e 1  is the lateral error of the ADV at current time i, ds is a predicted distance that the ADV will have traveled by a predicted future time i+1, based on the current longitudinal speed v x , and e 2  is the heading error of the ADV at time i. In an embodiment, f=e 1 +d s *e 2 . In an embodiment, the predicted lateral error pe 1  may be scaled by a tuning constant. Predicted heading error at time i+1, is given by: pe 2 =g(e 1 , e 2 , d s , v x , θ des ) wherein e 2  is the current heading error at time i, d s  is the predicted distance traveled by the ADV at time i+1, v x  is the current speed of the ADV, and θ des  is the maximum design steering angle of the ADV. 
     When the ADV is in a reverse driving gear, the look-back predicted lateral error  323 , pe 1 , at time i+1, is given by: pe 1 =f(e 1 , e 2 , −d s ), wherein e 1  is a the lateral error of the ADV at current time i, ds is a predicted distance that the ADV will have traveled by a predicted future time i+1, based on the current longitudinal speed −v x , and e 2  is the heading error of the ADV at time i. In an embodiment, the predicted lateral error pe 1  may be scaled by a tuning constant. Predicted heading error at time i+1, is given by: pe 2 =(e 1 , e 2 , −d s , −v x , θ des ) wherein e 2  is the current heading error at time i, −d s  is the predicted distance traveled by the ADV at time i+1, v x  is the current speed of the ADV, and θ des  is the maximum design steering angle of the ADV. 
     The current lateral and heading error output by model switching  320 , and the predicted lateral and heading error output by look-ahead/look-back feedback module  330 , are passed to LQR+Augmented Control module  340 . LQR+Augmented Control module  340  includes a main control: LQR  341  and an augmented control module  342 . Each of the LQR module  341  and Augmented Control module  342  outputs control effort values for controlling the ADV. The LQR module  341  control effort output and the Augmented Control module  342  control effort output are summed and output to control system  306  for controlling the ADV driving. Linear quadratic regulators (LQR) are known in the art, and are not further described herein. 
     The augmented control is derived from a Fourier Transform, in the frequency domain, of an error signal error, s, obtained from a sequence of cumulative errors of the control of the ADV taken at time increments, i, i+1, . . . n, for a positive integer n. From the viewpoint of the control theory, the augmented control is essentially a Lead-Lag controller, in which the control gains are assigned with specific emphasis in the targeted frequency range. Augmented (“aug”) control  342  is described as follows: 
                 aug   ⁡     (   s   )       =       β   ⁡     (       τ   ⁢           ⁢   s     +   1     )           ατ   ⁢           ⁢   s     +   1         ,         
wherein α, β, and σ, are constants used to tune the shape of the aug(s) controller. The output of aug(s) is in the time domain. In the low frequency of s, e.g. 0 to 1 Hz, the control gain will be large. In the high frequency of s, e.g. 100 Hz, the control gain will low. The aug(s) controller aids the LQR to produce the correct output. Total feedback control action, output to control the ADV, is LQR+aug(s).
 
       FIG. 4  is a block diagram illustrating an example of an open space planning module  308  according to one embodiment. Open space planning module  308  can generate a trajectory for an ADV in an open space, where there is no reference lines or traffic lanes to be followed. Examples of an open space include a parking lot, or a roadway where a vehicle performs a parallel parking, a U-turn, or a three-point turn. Referring to  FIG. 4 , in one embodiment, open space planning module  308  includes environment perception module  401 , target function determiner module  403 , constraints determiner module  405 , dual variable warming up module  407 , trajectory generator module  409 , and hybrid A* search module  411 . Environment perception module  401  can perceives an environment of the ADV. Target function determiner module  403  can determine a target function for an optimization model (e.g., open space optimization model  421  (as part of models  313  of  FIG. 3A )) to optimize. Constraints determiner module  405  can determine constraints for the optimization model. Constraints can include inequality, equality, and bound constraints. Dual variable warming up module  407  can apply a quadratic programming (QP) solver to a target (objective) function to solve for one or more variables (such as dual/two variables) subject to some constraints, where the target function is a quadratic function. Trajectory generator module  409  can generate a trajectory based on the solved variables. Hybrid A* search module  411  can search for an initial trajectory (zig zag, non-smooth trajectory without consideration for observed obstacles) using a search algorithm, such as an A* search algorithm, or a hybrid A* search algorithm. 
       FIGS. 5A and 5B  are block diagrams illustrating an example of a predicting a lateral error and heading error in forward driving ( FIG. 5A ) and reverse driving ( FIG. 5B ) scenarios, according to one embodiment. 
     Referring now to  FIG. 5A , an autonomous driving vehicle (ADV) is driving in a forward driving gear position. L 1  refers to a trajectory line that indicates a predicted direction that the ADV would travel given a current state of ADV control, u(i), at time i. L 2  represents at target line for the ADV to follow, given the current planned “look-ahead” trajectory line L 3 . As shown in  FIG. 5A , the ADV is not currently adhering to the look-ahead trajectory L 3 . At the current time, i, the ADV has a lateral error indicated by e 1  and a heading error indicated by e 2 : e 2  is the rotational difference between lines L 1  and L 2 . At time i+1, the ADV is predicted to be at a look-ahead station (location) d s , and to have a predicted lateral error of pe 1 . Additional control effort will be required to overcome the predicted error and get the ADV back onto the look-ahead trajectory line L 3 . Such additional effort is determined as described above, with reference to  FIG. 3C . 
     Referring now to  FIG. 5B , an autonomous driving vehicle (ADV) is driving in a reverse driving gear position. L 1  refers to a trajectory line that indicates a predicted direction that the ADV would travel given a current state of ADV control, u(i), at time i. L 2  represents at target line for the ADV to follow, given the current planned “look-back” trajectory line L 3 . As shown in  FIG. 5B , the ADV is not currently adhering to the look-back trajectory L 3 . At the current time, i, the ADV has a lateral error indicated by e 1  and a heading error indicated by e 2 : e 2  is the rotational difference between lines L 1  and L 2 . At time i+1, the ADV is predicted to be at a look-back station (location) d s , and to have a predicted lateral error of pe 1 . Additional control effort will be required to overcome the predicted error and get the ADV back onto the look-ahead trajectory line L 3 . Such additional effort is determined as described above, with reference to  FIG. 3C . 
       FIG. 6  illustrates a method  600  of controlling an autonomous driving vehicle, according to one embodiment. 
     In operation  601 , a gear positions module  321  of a model switching module  320  can determine a current driving gear position of the ADV. The current driving gear position can be a forward driving gear or a reverse driving gear. The driving gear position can be used to select driving models and error models for the current driving gear position. 
     In operation  602 , model switching module  320  selects a forward or reverse driving model, according to the current driving gear position. Look-ahead feedback module  330  can determine a look-ahead, or look-back lateral error routine  331  and a look-ahead or look-back heading error routine  332 , based upon the current driving gear position. 
     In operation  603 , the selected driving model (forward model  322  or reverse model  323 ) can determine the lateral error and heading error of the ADV. 
     In operation  604 , the selected lateral error module  331  and selected heading error module  332  of the look-ahead feedback module  330  can determine a predicted lateral error and a predicted heading (rotational) error. 
     In operation  605 , an LQR module can determine a first control effort, based upon the lateral error and heading error determined by the driving model ( 322  or  323 ) and the predicted lateral error  331  and predicted heading error  332  determined by look-ahead feedback module  330 . In an embodiment, a second augmented feedback control amount can be added to the LQR module first control effort to generate a cumulative control amount for controlling the ADV. 
     In operation  606 , the ADV can be controlled using the control effort determined in operation  605 . 
       FIG. 7  illustrates a method  700  of controlling an autonomous driving vehicle, according to one embodiment. 
     In operation  701 , a planning module can generate outputs that define a trajectory for an ADV. A model switching module  320  of a control system  306  of the ADV can determine a current driving gear position of the ADV. The current driving gear can be forward driving gear or a reverse driving gear. 
     In operation  702 , it can be determined whether the current driving gear is a reverse driving gear. If so, then method  700  continues at operation  703 , otherwise method  700  continues at operation  705 . 
     In operation  703 , the current driving gear is a reverse driving gear, and model switching module  320  can select a hybrid dynamic and kinematic model determining as a reverse driving model, and select a “look-back” model for the look-ahead feedback  330 . 
     In operation  704 , the reverse driving, hybrid dynamic and kinematic model  323 , can determine a current lateral error and current heading error of the ADV. The look-back feedback model can determine a predicted lateral error ( 331 ) and predicted heading error ( 332 ). Method  700  continues at operation  707 . 
     In operation  705 , the current driving gear is a forward driving gear, and model switching module  320  can select a 4th order dynamic model as a forward model  322 , and select a “look-ahead” model for the look-ahead feedback  330 . 
     In operation  706 , the forward driving model can determine a current lateral error and a current heading error of the ADV. The look-ahead model can determine a predicted lateral error and a predicted heading error of the ADV for the look-ahead feedback  330 . 
     In operation  307 , a linear quadratic regulator (LQR) can determine a first control effort for controlling the ADV. The output of the LQR is based upon the current and predicted lateral and heading errors determined above. In addition, an augmented control effort can be determined using a Fourier Transform, in the frequency domain, of an error signal determined from a sequence of lateral and heading errors at times i, i+1, . . . n. The augmented control effort, which is determined in the frequency domain, can be output as an augmented control effort in the time domain. The total control effort that is output to the control module  306  for controlling the ADV driving is the sum of the LQR control effort and the augmented control effort. 
     Note that some or all of the components as shown and described above may be implemented in software, hardware, or a combination thereof. For example, such components can be implemented as software installed and stored in a persistent storage device, which can be loaded and executed in a memory by a processor (not shown) to carry out the processes or operations described throughout this application. Alternatively, such components can be implemented as executable code programmed or embedded into dedicated hardware such as an integrated circuit (e.g., an application specific IC or ASIC), a digital signal processor (DSP), or a field programmable gate array (FPGA), which can be accessed via a corresponding driver and/or operating system from an application. Furthermore, such components can be implemented as specific hardware logic in a processor or processor core as part of an instruction set accessible by a software component via one or more specific instructions. 
     Some portions of the preceding detailed descriptions have been presented in terms of algorithms and symbolic representations of operations on data bits within a computer memory. These algorithmic descriptions and representations are the ways used by those skilled in the data processing arts to most effectively convey the substance of their work to others skilled in the art. An algorithm is here, and generally, conceived to be a self-consistent sequence of operations leading to a desired result. The operations are those requiring physical manipulations of physical quantities. 
     It should be borne in mind, however, that all of these and similar terms are to be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities. Unless specifically stated otherwise as apparent from the above discussion, it is appreciated that throughout the description, discussions utilizing terms such as those set forth in the claims below, refer to the action and processes of a computer system, or similar electronic computing device, that manipulates and transforms data represented as physical (electronic) quantities within the computer system&#39;s registers and memories into other data similarly represented as physical quantities within the computer system memories or registers or other such information storage, transmission or display devices. 
     Embodiments of the disclosure also relate to an apparatus for performing the operations herein. Such a computer program is stored in a non-transitory computer readable medium. A machine-readable medium includes any mechanism for storing information in a form readable by a machine (e.g., a computer). For example, a machine-readable (e.g., computer-readable) medium includes a machine (e.g., a computer) readable storage medium (e.g., read only memory (“ROM”), random access memory (“RAM”), magnetic disk storage media, optical storage media, flash memory devices). 
     The processes or methods depicted in the preceding figures may be performed by processing logic that comprises hardware (e.g. circuitry, dedicated logic, etc.), software (e.g., embodied on a non-transitory computer readable medium), or a combination of both. Although the processes or methods are described above in terms of some sequential operations, it should be appreciated that some of the operations described may be performed in a different order. Moreover, some operations may be performed in parallel rather than sequentially. 
     Embodiments of the present disclosure are not described with reference to any particular programming language. It will be appreciated that a variety of programming languages may be used to implement the teachings of embodiments of the disclosure as described herein. 
     In the foregoing specification, embodiments of the disclosure have been described with reference to specific exemplary embodiments thereof. It will be evident that various modifications may be made thereto without departing from the broader spirit and scope of the disclosure as set forth in the following claims. The specification and drawings are, accordingly, to be regarded in an illustrative sense rather than a restrictive sense.