Patent Publication Number: US-2022234575-A1

Title: Vehicle operation using maneuver generation

Description:
RELATED APPLICATION 
     This application claims the benefit of U.S. Provisional Application Ser. No. 63/142,882, filed Jan. 28, 2021, the entire contents of which are incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     This description relates generally to operation of vehicles and specifically to vehicle operation using maneuver generation. 
     BACKGROUND 
     Operation of a vehicle from an initial location to a final destination often requires a user or a vehicle&#39;s decision-making system to select a route through a road network from the initial location to a final destination. The route may involve meeting objectives, such as not exceeding a maximum driving time. A complex route can require many decisions, making traditional algorithms for autonomous driving impractical. 
     SUMMARY 
     Methods, apparatus, and systems for vehicle operation using maneuver generation are disclosed. In an embodiment, at least one processor of a vehicle generates multiple trajectories for the vehicle based on a road segment traveled by the vehicle. The at least one processor receives sensor data from at least one sensor of the vehicle. The vehicle is traveling the road segment in accordance with a first trajectory of the multiple trajectories. The at least one processor predicts a potential collision between the vehicle and an object moving on the road segment based on the sensor data and the first trajectory. The at least one processor determines a set of constraints for the vehicle to avoid the potential collision. The set of constraints is determined based on the sensor data. The at least one processor determines a maneuver for the vehicle by superimposing each constraint of the set of constraints on each other constraint of the set of constraints. The maneuver includes a second trajectory independent of the multiple trajectories. The at least one processor transmits instructions to a control circuit of the vehicle to override the first trajectory and traverse the road segment according to the second trajectory to perform the maneuver. 
     In an embodiment, the set of constraints includes environmental constraints indicating at least one of a drivable area of the road segment or lane markings of the road segment. 
     In an embodiment, the set of constraints includes hard logical constraints that the AV must obey to avoid the potential collision. The AV can violate soft logical constraints to avoid the potential collision. 
     In an embodiment, the set of constraints includes station-based constraints that are parameterized, by the at least one processor, over time using the sensor data. Spatial-based constraints are parameterized, by the at least one processor, over station and time using the sensor data. 
     In an embodiment, determining the maneuver includes generating, by the at least one processor, a union of the station-based constraints and the spatial-based constraints to provide the maneuver. 
     In an embodiment, determining the set of constraints is performed at a first frequency and determining the maneuver to generate the second trajectory is performed at a second frequency higher than the first frequency. 
     In an embodiment, performing the maneuver comprises operating the vehicle to a particular location relative to the object. 
     In an embodiment, the at least one processor determines multiple homotopies. Each homotopy of the multiple homotopies includes a different respective combination of the set of constraints. Determining the maneuver is based on at least some of the multiple homotopies. 
     In an embodiment, the at least one processor predicts a motion of the vehicle on the road segment according to a degree of precision. The at least one processor determines that the vehicle can traverse the road segment in accordance with a subset of the multiple homotopies based on the predicted motion. Determining the maneuver is further based on the subset of the multiple homotopies. 
     In an embodiment, determining that the vehicle can traverse the road segment in accordance with the subset of the multiple homotopies includes generating, by the at least one processor, a decision graph based on the subset of the multiple homotopies. The graph includes multiple nodes. Each node corresponds to a different maneuver. 
     In an embodiment, determining the maneuver to generate the second trajectory includes assigning, by the at least one processor, a respective quality metric to each homotopy of the multiple homotopies. The at least one processor selects the second trajectory based on the respective quality metric. 
     In an embodiment, the respective quality metric is determined based on at least one of a predicted time for traversing the road segment in accordance with the each homotopy, a predicted safety of a passenger of the vehicle while traversing the road segment in accordance with the each homotopy, or a predicted comfort of the passenger while traversing the road segment in accordance with the each homotopy. 
     In an embodiment, performing the maneuver includes positioning, by the control circuit, the vehicle ahead of two moving objects while traversing the road segment. 
     In an embodiment, performing the maneuver includes positioning, by the control circuit, the vehicle behind two moving objects while traversing the road segment. 
     In an embodiment, performing the maneuver includes positioning, by the control circuit, the vehicle between two moving objects while traversing the road segment. 
     In an embodiment, superimposing each constraint of the set of constraints on each other constraint of the set of constraints includes sampling, by the at least one processor, each constraint of the set of constraints with respect to time in accordance with changes in the sensor data to provide the maneuver. 
     These and other aspects, features, and implementations can be expressed as methods, apparatus, systems, components, program products, means or steps for performing a function, and in other ways. 
     These and other aspects, features, and implementations will become apparent from the following descriptions, including the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram illustrating an example of an autonomous vehicle (AV) having autonomous capability, in accordance with one or more embodiments. 
         FIG. 2  is a block diagram illustrating an example “cloud” computing environment, in accordance with one or more embodiments. 
         FIG. 3  is a block diagram illustrating a computer system, in accordance with one or more embodiments. 
         FIG. 4A  is a block diagram illustrating an example architecture for an AV, in accordance with one or more embodiments. 
         FIG. 4B  is a block diagram of a planning module, in accordance with one or more embodiments. 
         FIG. 5  is a block diagram illustrating an example of inputs and outputs that may be used by a perception module, in accordance with one or more embodiments. 
         FIG. 6  is a block diagram illustrating an example of a LiDAR system, in accordance with one or more embodiments. 
         FIG. 7  is a block diagram illustrating the LiDAR system in operation, in accordance with one or more embodiments. 
         FIG. 8  is a block diagram illustrating the operation of the LiDAR system in additional detail, in accordance with one or more embodiments. 
         FIG. 9  is a block diagram illustrating the relationships between inputs and outputs of a planning module, in accordance with one or more embodiments. 
         FIG. 10  illustrates a directed graph used in path planning, in accordance with one or more embodiments. 
         FIG. 11  is a block diagram illustrating the inputs and outputs of a control module, in accordance with one or more embodiments. 
         FIG. 12  is a block diagram illustrating the inputs, outputs, and components of a controller, in accordance with one or more embodiments. 
         FIG. 13  is a flow diagram illustrating an example process for determining a maneuver, in accordance with one or more embodiments. 
         FIG. 14  illustrates an example decision graph, in accordance with one or more embodiments. 
         FIG. 15  is a block diagram illustrating an example maneuver, in accordance with one or more embodiments. 
         FIG. 16  is a flow diagram illustrating a process for operation of a vehicle, in accordance with one or more embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     In the following description, for the purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present invention. It will be apparent, however, that the present invention may be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form in order to avoid unnecessarily obscuring the present invention. 
     In the drawings, specific arrangements or orderings of schematic elements, such as those representing devices, modules, instruction blocks and data elements, are shown for ease of description. However, it should be understood by those skilled in the art that the specific ordering or arrangement of the schematic elements in the drawings is not meant to imply that a particular order or sequence of processing, or separation of processes, is required. Further, the inclusion of a schematic element in a drawing is not meant to imply that such element is required in all embodiments or that the features represented by such element may not be included in or combined with other elements in an embodiment. 
     Further, in the drawings, where connecting elements, such as solid or dashed lines or arrows, are used to illustrate a connection, relationship, or association between or among two or more other schematic elements, the absence of any such connecting elements is not meant to imply that no connection, relationship, or association can exist. In other words, some connections, relationships, or associations between elements are not shown in the drawings so as not to obscure the disclosure. In addition, for ease of illustration, a single connecting element is used to represent multiple connections, relationships or associations between elements. For example, where a connecting element represents a communication of signals, data, or instructions, it should be understood by those skilled in the art that such element represents one or multiple signal paths (e.g., a bus), as may be needed, to affect the communication. 
     Reference will now be made in detail to embodiments, examples of which are illustrated in the accompanying drawings. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the various described embodiments. However, it will be apparent to one of ordinary skill in the art that the various described embodiments may be practiced without these specific details. In other instances, well-known methods, procedures, components, circuits, and networks have not been described in detail so as not to unnecessarily obscure aspects of the embodiments. 
     Several features are described hereafter that can each be used independently of one another or with any combination of other features. However, any individual feature may not address any of the problems discussed above or might only address one of the problems discussed above. Some of the problems discussed above might not be fully addressed by any of the features described herein. Although headings are provided, information related to a particular heading, but not found in the section having that heading, may also be found elsewhere in this description. Embodiments are described herein according to the following outline: 
     1. General Overview 
     2. System Overview 
     3. Autonomous Vehicle Architecture 
     4. Autonomous Vehicle Inputs 
     5. Autonomous Vehicle Planning 
     6. Autonomous Vehicle Control 
     7. Autonomous Vehicle Operation Using Maneuver Generation 
     General Overview 
     This document presents methods, systems, and apparatuses for operating an autonomous vehicle (AV) using maneuver generation. A planning module for the AV generates a graphical representation of the environment and the AV&#39;s sensor signal measurements (for example, speed and position). The nodes of the graphical representation denote a sample of the AV&#39;s decision space (for example, a set of maneuvers of the AV in relation to other vehicles and environmental constraints, such as the driveable area or lane markings. The edges of the graphical representation denote the different possible trajectories that the AV can follow to perform the different maneuvers. 
     The advantages and benefits of AV operation using maneuver generation include a reduction in the computational complexity of determining a trajectory for the AV. The need for a planning module to determine a trajectory in a brute force manner by generating a large number of candidate trajectories and evaluating each of the candidate trajectories is obviated. Using the embodiments disclosed herein, the planning module can reduce the search space by identifying a subset of the search space corresponding to feasible homotopies (e.g., combinations of constraints that the AV is capable of adhering to safely while traversing the route) and generating candidate trajectories only for that subset. 
     System Overview 
       FIG. 1  is a block diagram illustrating an example of an autonomous vehicle  100  having autonomous capability, in accordance with one or more embodiments. 
     As used herein, the term “autonomous capability” refers to a function, feature, or facility that enables a vehicle to be partially or fully operated without real-time human intervention, including without limitation fully autonomous vehicles, highly autonomous vehicles, and conditionally autonomous vehicles. 
     As used herein, an autonomous vehicle (AV) is a vehicle that possesses autonomous capability. 
     As used herein, “vehicle” includes means of transportation of goods or people. For example, cars, buses, trains, airplanes, drones, trucks, boats, ships, submersibles, dirigibles, etc. A driverless car is an example of a vehicle. 
     As used herein, “trajectory” refers to a path or route to operate an AV from a first spatiotemporal location to second spatiotemporal location. In an embodiment, the first spatiotemporal location is referred to as the initial or starting location and the second spatiotemporal location is referred to as the destination, final location, goal, goal position, or goal location. In some examples, a trajectory is made up of one or more segments (e.g., sections of road) and each segment is made up of one or more blocks (e.g., portions of a lane or intersection). In an embodiment, the spatiotemporal locations correspond to real world locations. For example, the spatiotemporal locations are pick up or drop-off locations to pick up or drop-off persons or goods. 
     As used herein, “sensor(s)” includes one or more hardware components that detect information about the environment surrounding the sensor. Some of the hardware components can include sensing components (e.g., image sensors, biometric sensors), transmitting and/or receiving components (e.g., laser or radio frequency wave transmitters and receivers), electronic components such as analog-to-digital converters, a data storage device (such as a RAM and/or a nonvolatile storage), software or firmware components and data processing components such as an ASIC (application-specific integrated circuit), a microprocessor and/or a microcontroller. 
     As used herein, a “scene description” is a data structure (e.g., list) or data stream that includes one or more classified or labeled objects detected by one or more sensors on the AV vehicle or provided by a source external to the AV. 
     As used herein, a “road” is a physical area that can be traversed by a vehicle, and may correspond to a named thoroughfare (e.g., city street, interstate freeway, etc.) or may correspond to an unnamed thoroughfare (e.g., a driveway in a house or office building, a section of a parking lot, a section of a vacant lot, a dirt path in a rural area, etc.). Because some vehicles (e.g., 4-wheel-drive pickup trucks, sport utility vehicles, etc.) are capable of traversing a variety of physical areas not specifically adapted for vehicle travel, a “road” may be a physical area not formally defined as a thoroughfare by any municipality or other governmental or administrative body. 
     As used herein, a “lane” is a portion of a road that can be traversed by a vehicle and may correspond to most or all of the space between lane markings, or may correspond to only some (e.g., less than 50%) of the space between lane markings. For example, a road having lane markings spaced far apart might accommodate two or more vehicles between the markings, such that one vehicle can pass the other without traversing the lane markings, and thus could be interpreted as having a lane narrower than the space between the lane markings or having two lanes between the lane markings. A lane could also be interpreted in the absence of lane markings. For example, a lane may be defined based on physical features of an environment, e.g., rocks and trees along a thoroughfare in a rural area. 
     As used herein, “homotopy” means a subset of a set of constraints on a trajectory of an AV that the AV can adhere to while traversing a particular route. 
     “One or more” includes a function being performed by one element, a function being performed by more than one element, e.g., in a distributed fashion, several functions being performed by one element, several functions being performed by several elements, or any combination of the above. 
     It will also be understood that, although the terms first, second, etc. are, in some instances, used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first contact could be termed a second contact, and, similarly, a second contact could be termed a first contact, without departing from the scope of the various described embodiments. The first contact and the second contact are both contacts, but they are not the same contact. 
     The terminology used in the description of the various described embodiments herein is for the purpose of describing particular embodiments only and is not intended to be limiting. As used in the description of the various described embodiments and the appended claims, the singular forms “a,” “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that the term “and/or” as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items. It will be further understood that the terms “includes,” “including,” “includes,” and/or “including,” when used in this description, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
     As used herein, the term “if” is, optionally, construed to mean “when” or “upon” or “in response to determining” or “in response to detecting,” depending on the context. Similarly, the phrase “if it is determined” or “if [a stated condition or event] is detected” is, optionally, construed to mean “upon determining” or “in response to determining” or “upon detecting [the stated condition or event]” or “in response to detecting [the stated condition or event],” depending on the context. 
     As used herein, an AV system refers to the AV along with the array of hardware, software, stored data, and data generated in real-time that supports the operation of the AV. In an embodiment, the AV system is incorporated within the AV. In an embodiment, the AV system is spread across several locations. For example, some of the software of the AV system is implemented on a cloud computing environment similar to cloud computing environment  300  described below with respect to  FIG. 3 . 
     In general, this document describes technologies applicable to any vehicles that have one or more autonomous capabilities including fully autonomous vehicles, highly autonomous vehicles, and conditionally autonomous vehicles, such as so-called Level 5, Level 4 and Level 3 vehicles, respectively (see SAE International&#39;s standard J3016: Taxonomy and Definitions for Terms Related to On-Road Motor Vehicle Automated Driving Systems, which is incorporated by reference in its entirety, for more details on the classification of levels of autonomy in vehicles). The technologies described in this document are also applicable to partially autonomous vehicles and driver assisted vehicles, such as so-called Level 2 and Level 1 vehicles (see SAE International&#39;s standard J3016: Taxonomy and Definitions for Terms Related to On-Road Motor Vehicle Automated Driving Systems). In an embodiment, one or more of the Level 1, 2, 3, 4 and 5 vehicle systems may automate certain vehicle operations (e.g., steering, braking, and using maps) under certain operating conditions based on processing of sensor inputs. The technologies described in this document can benefit vehicles in any levels, ranging from fully autonomous vehicles to human-operated vehicles. 
     Referring to  FIG. 1 , an AV system  120  operates the AV  100  along a trajectory  198  through an environment  190  to a destination  199  (sometimes referred to as a final location) while avoiding objects (e.g., natural obstructions  191 , vehicles  193 , pedestrians  192 , cyclists, and other obstacles) and obeying rules of the road (e.g., rules of operation or driving preferences). 
     In an embodiment, the AV system  120  includes devices  101  that are instrumented to receive and act on operational commands from the computer processors  146 . In an embodiment, computing processors  146  are similar to the processor  304  described below in reference to  FIG. 3 . Examples of devices  101  include a steering control  102 , brakes  103 , gears, accelerator pedal or other acceleration control mechanisms, windshield wipers, side-door locks, window controls, and turn-indicators. 
     In an embodiment, the AV system  120  includes sensors  121  for measuring or inferring properties of state or condition of the AV  100 , such as the AV&#39;s position, linear velocity and acceleration, angular velocity and acceleration, and heading (e.g., an orientation of the leading end of AV  100 ). Example of sensors  121  are GNSS, inertial measurement units (IMU) that measure both vehicle linear accelerations and angular rates, wheel sensors for measuring or estimating wheel slip ratios, wheel brake pressure or braking torque sensors, engine torque or wheel torque sensors, and steering angle and angular rate sensors. 
     In an embodiment, the sensors  121  also include sensors for sensing or measuring properties of the AV&#39;s environment. For example, monocular or stereo video cameras  122  in the visible light, infrared or thermal (or both) spectra, LiDAR  123 , RADAR, ultrasonic sensors, time-of-flight (TOF) depth sensors, speed sensors, temperature sensors, humidity sensors, and precipitation sensors. 
     In an embodiment, the AV system  120  includes a data storage unit  142  and memory  144  for storing machine instructions associated with computer processors  146  or data collected by sensors  121 . In an embodiment, the data storage unit  142  is similar to the ROM  308  or storage device  310  described below in relation to  FIG. 3 . In an embodiment, memory  144  is similar to the main memory  306  described below. In an embodiment, the data storage unit  142  and memory  144  store historical, real-time, and/or predictive information about the environment  190 . In an embodiment, the stored information includes maps, driving performance, traffic congestion updates or weather conditions. In an embodiment, data relating to the environment  190  is transmitted to the AV  100  via a communications channel from a remotely located database  134 . 
     In an embodiment, the AV system  120  includes communications devices  140  for communicating measured or inferred properties of other vehicles&#39; states and conditions, such as positions, linear and angular velocities, linear and angular accelerations, and linear and angular headings to the AV  100 . These devices include Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I) communication devices and devices for wireless communications over point-to-point or ad hoc networks or both. In an embodiment, the communications devices  140  communicate across the electromagnetic spectrum (including radio and optical communications) or other media (e.g., air and acoustic media). A combination of Vehicle-to-Vehicle (V2V) Vehicle-to-Infrastructure (V2I) communication (and, in an embodiment, one or more other types of communication) is sometimes referred to as Vehicle-to-Everything (V2X) communication. V2X communication typically conforms to one or more communications standards for communication with, between, and among autonomous vehicles. 
     In an embodiment, the communication devices  140  include communication interfaces. For example, wired, wireless, WiMAX, Wi-Fi, Bluetooth, satellite, cellular, optical, near field, infrared, or radio interfaces. The communication interfaces transmit data from a remotely located database  134  to AV system  120 . In an embodiment, the remotely located database  134  is embedded in a cloud computing environment  200  as described in  FIG. 2 . The communication interfaces  140  transmit data collected from sensors  121  or other data related to the operation of AV  100  to the remotely located database  134 . In an embodiment, communication interfaces  140  transmit information that relates to teleoperations to the AV  100 . In an embodiment, the AV  100  communicates with other remote (e.g., “cloud”) servers  136 . 
     In an embodiment, the remotely located database  134  also stores and transmits digital data (e.g., storing data such as road and street locations). Such data is stored on the memory  144  on the AV  100 , or transmitted to the AV  100  via a communications channel from the remotely located database  134 . 
     In an embodiment, the remotely located database  134  stores and transmits historical information about driving properties (e.g., speed and acceleration profiles) of vehicles that have previously traveled along trajectory  198  at similar times of day. In one implementation, such data may be stored on the memory  144  on the AV  100 , or transmitted to the AV  100  via a communications channel from the remotely located database  134 . 
     Computing devices  146  located on the AV  100  algorithmically generate control actions based on both real-time sensor data and prior information, allowing the AV system  120  to execute its autonomous driving capabilities. 
     In an embodiment, the AV system  120  includes computer peripherals  132  coupled to computing devices  146  for providing information and alerts to, and receiving input from, a user (e.g., an occupant or a remote user) of the AV  100 . In an embodiment, peripherals  132  are similar to the display  312 , input device  314 , and cursor controller  316  discussed below in reference to  FIG. 3 . The coupling is wireless or wired. Any two or more of the interface devices may be integrated into a single device. 
     Example Cloud Computing Environment 
       FIG. 2  is a block diagram illustrating an example “cloud” computing environment, in accordance with one or more embodiments. Cloud computing is a model of service delivery for enabling convenient, on-demand network access to a shared pool of configurable computing resources (e.g. networks, network bandwidth, servers, processing, memory, storage, applications, virtual machines, and services). In typical cloud computing systems, one or more large cloud data centers house the machines used to deliver the services provided by the cloud. Referring now to  FIG. 2 , the cloud computing environment  200  includes cloud data centers  204   a ,  204   b , and  204   c  that are interconnected through the cloud  202 . Data centers  204   a ,  204   b , and  204   c  provide cloud computing services to computer systems  206   a ,  206   b ,  206   c ,  206   d ,  206   e , and  206   f  connected to cloud  202 . 
     The cloud computing environment  200  includes one or more cloud data centers. In general, a cloud data center, for example the cloud data center  204   a  shown in  FIG. 2 , refers to the physical arrangement of servers that make up a cloud, for example the cloud  202  shown in  FIG. 2 , or a particular portion of a cloud. For example, servers are physically arranged in the cloud datacenter into rooms, groups, rows, and racks. A cloud datacenter has one or more zones, which include one or more rooms of servers. Each room has one or more rows of servers, and each row includes one or more racks. Each rack includes one or more individual server nodes. In some implementation, servers in zones, rooms, racks, and/or rows are arranged into groups based on physical infrastructure requirements of the datacenter facility, which include power, energy, thermal, heat, and/or other requirements. In an embodiment, the server nodes are similar to the computer system described in  FIG. 3 . The data center  204   a  has many computing systems distributed through many racks. 
     The cloud  202  includes cloud data centers  204   a ,  204   b , and  204   c  along with the network and networking resources (for example, networking equipment, nodes, routers, switches, and networking cables) that interconnect the cloud data centers  204   a ,  204   b , and  204   c  and help facilitate the computing systems&#39;  206   a - f  access to cloud computing services. In an embodiment, the network represents any combination of one or more local networks, wide area networks, or internetworks coupled using wired or wireless links deployed using terrestrial or satellite connections. Data exchanged over the network, is transferred using any number of network layer protocols, such as Internet Protocol (IP), Multiprotocol Label Switching (MPLS), Asynchronous Transfer Mode (ATM), Frame Relay, etc. Furthermore, in embodiments where the network represents a combination of multiple sub-networks, different network layer protocols are used at each of the underlying sub-networks. In an embodiment, the network represents one or more interconnected internetworks, such as the public Internet. 
     The computing systems  206   a - f  or cloud computing services consumers are connected to the cloud  202  through network links and network adapters. In an embodiment, the computing systems  206   a - f  are implemented as various computing devices, for example servers, desktops, laptops, tablet, smartphones, Internet of Things (IoT) devices, autonomous vehicles (including, cars, drones, shuttles, trains, buses, etc.) and consumer electronics. In an embodiment, the computing systems  206   a - f  are implemented in or as a part of other systems. 
     Computer System 
       FIG. 3  is a block diagram illustrating a computer system  300 , in accordance with one or more embodiments. In an implementation, the computer system  300  is a special purpose computing device. The special-purpose computing device is hard-wired to perform the techniques or includes digital electronic devices such as one or more application-specific integrated circuits (ASICs) or field programmable gate arrays (FPGAs) that are persistently programmed to perform the techniques or may include one or more general purpose hardware processors programmed to perform the techniques pursuant to program instructions in firmware, memory, other storage, or a combination. Such special-purpose computing devices may also combine custom hard-wired logic, ASICs, or FPGAs with custom programming to accomplish the techniques. In various embodiments, the special-purpose computing devices are desktop computer systems, portable computer systems, handheld devices, network devices or any other device that incorporates hard-wired and/or program logic to implement the techniques. 
     In an embodiment, the computer system  300  includes a bus  302  or other communication mechanism for communicating information, and a hardware processor  304  coupled with a bus  302  for processing information. The hardware processor  304  is, for example, a general-purpose microprocessor. The computer system  300  also includes a main memory  306 , such as a random-access memory (RAM) or other dynamic storage device, coupled to the bus  302  for storing information and instructions to be executed by processor  304 . In one implementation, the main memory  306  is used for storing temporary variables or other intermediate information during execution of instructions to be executed by the processor  304 . Such instructions, when stored in non-transitory storage media accessible to the processor  304 , render the computer system  300  into a special-purpose machine that is customized to perform the operations specified in the instructions. 
     In an embodiment, the computer system  300  further includes a read only memory (ROM)  308  or other static storage device coupled to the bus  302  for storing static information and instructions for the processor  304 . A storage device  310 , such as a magnetic disk, optical disk, solid-state drive, or three-dimensional cross point memory is provided and coupled to the bus  302  for storing information and instructions. 
     In an embodiment, the computer system  300  is coupled via the bus  302  to a display  312 , such as a cathode ray tube (CRT), a liquid crystal display (LCD), plasma display, light emitting diode (LED) display, or an organic light emitting diode (OLED) display for displaying information to a computer user. An input device  314 , including alphanumeric and other keys, is coupled to bus  302  for communicating information and command selections to the processor  304 . Another type of user input device is a cursor controller  316 , such as a mouse, a trackball, a touch-enabled display, or cursor direction keys for communicating direction information and command selections to the processor  304  and for controlling cursor movement on the display  312 . This input device typically has two degrees of freedom in two axes, a first axis (e.g., x-axis) and a second axis (e.g., y-axis), that allows the device to specify positions in a plane. 
     According to one embodiment, the techniques herein are performed by the computer system  300  in response to the processor  304  executing one or more sequences of one or more instructions contained in the main memory  306 . Such instructions are read into the main memory  306  from another storage medium, such as the storage device  310 . Execution of the sequences of instructions contained in the main memory  306  causes the processor  304  to perform the process steps described herein. In alternative embodiments, hard-wired circuitry is used in place of or in combination with software instructions. 
     The term “storage media” as used herein refers to any non-transitory media that store data and/or instructions that cause a machine to operate in a specific fashion. Such storage media includes non-volatile media and/or volatile media. Non-volatile media includes, for example, optical disks, magnetic disks, solid-state drives, or three-dimensional cross point memory, such as the storage device  310 . Volatile media includes dynamic memory, such as the main memory  306 . Common forms of storage media include, for example, a floppy disk, a flexible disk, hard disk, solid-state drive, magnetic tape, or any other magnetic data storage medium, a CD-ROM, any other optical data storage medium, any physical medium with patterns of holes, a RAM, a PROM, and EPROM, a FLASH-EPROM, NV-RAM, or any other memory chip or cartridge. 
     Storage media is distinct from but may be used in conjunction with transmission media. Transmission media participates in transferring information between storage media. For example, transmission media includes coaxial cables, copper wire and fiber optics, including the wires that include the bus  302 . Transmission media can also take the form of acoustic or light waves, such as those generated during radio-wave and infrared data communications. 
     In an embodiment, various forms of media are involved in carrying one or more sequences of one or more instructions to the processor  304  for execution. For example, the instructions are initially carried on a magnetic disk or solid-state drive of a remote computer. The remote computer loads the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to the computer system  300  receives the data on the telephone line and use an infrared transmitter to convert the data to an infrared signal. An infrared detector receives the data carried in the infrared signal and appropriate circuitry places the data on the bus  302 . The bus  302  carries the data to the main memory  306 , from which processor  304  retrieves and executes the instructions. The instructions received by the main memory  306  may optionally be stored on the storage device  310  either before or after execution by processor  304 . 
     The computer system  300  also includes a communication interface  318  coupled to the bus  302 . The communication interface  318  provides a two-way data communication coupling to a network link  320  that is connected to a local network  322 . For example, the communication interface  318  is an integrated service digital network (ISDN) card, cable modem, satellite modem, or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, the communication interface  318  is a local area network (LAN) card to provide a data communication connection to a compatible LAN. In some implementations, wireless links are also implemented. In any such implementation, the communication interface  318  sends and receives electrical, electromagnetic, or optical signals that carry digital data streams representing various types of information. 
     The network link  320  typically provides data communication through one or more networks to other data devices. For example, the network link  320  provides a connection through the local network  322  to a host computer  324  or to a cloud data center or equipment operated by an Internet Service Provider (ISP)  326 . The ISP  326  in turn provides data communication services through the world-wide packet data communication network now commonly referred to as the “Internet”  328 . The local network  322  and Internet  328  both use electrical, electromagnetic, or optical signals that carry digital data streams. The signals through the various networks and the signals on the network link  320  and through the communication interface  318 , which carry the digital data to and from the computer system  300 , are example forms of transmission media. In an embodiment, the network  320  contains the cloud  202  or a part of the cloud  202  described above. 
     The computer system  300  sends messages and receives data, including program code, through the network(s), the network link  320 , and the communication interface  318 . In an embodiment, the computer system  300  receives code for processing. The received code is executed by the processor  304  as it is received, and/or stored in storage device  310 , or other non-volatile storage for later execution. 
     Autonomous Vehicle Architecture 
       FIG. 4A  is a block diagram illustrating an example architecture  400  for an autonomous vehicle (e.g., the AV  100  shown in  FIG. 1 ), in accordance with one or more embodiments. The architecture  400  includes a perception module  402  (sometimes referred to as a perception circuit), a planning module  404  (sometimes referred to as a planning circuit), a control module  406  (sometimes referred to as a control circuit), a localization module  408  (sometimes referred to as a localization circuit), and a database module  410  (sometimes referred to as a database circuit). Each module plays a role in the operation of the AV  100 . Together, the modules  402 ,  404 ,  406 ,  408 , and  410  may be part of the AV system  120  shown in  FIG. 1 . In an embodiment, any of the modules  402 ,  404 ,  406 ,  408 , and  410  is a combination of computer software (e.g., executable code stored on a computer-readable medium) and computer hardware (e.g., one or more microprocessors, microcontrollers, application-specific integrated circuits [ASICs]), hardware memory devices, other types of integrated circuits, other types of computer hardware, or a combination of any or all of these things). 
     In use, the planning module  404  receives data representing a destination  412  and determines data representing a trajectory  414  (sometimes referred to as a route) that can be traveled by the AV  100  to reach (e.g., arrive at) the destination  412 . In order for the planning module  404  to determine the data representing the trajectory  414 , the planning module  404  receives data from the perception module  402 , the localization module  408 , and the database module  410 . 
     The perception module  402  identifies nearby physical objects using one or more sensors  121 , e.g., as also shown in  FIG. 1 . The objects are classified (e.g., grouped into types such as pedestrian, bicycle, automobile, traffic sign, etc.) and a scene description including the classified objects  416  is provided to the planning module  404 . 
     The planning module  404  also receives data representing the AV position  418  from the localization module  408 . The localization module  408  determines the AV position by using data from the sensors  121  and data from the database module  410  (e.g., a geographic data) to calculate a position. For example, the localization module  408  uses data from a global navigation satellite system (GNSS) unit and geographic data to calculate a longitude and latitude of the AV. In an embodiment, data used by the localization module  408  includes high-precision maps of the roadway geometric properties, maps describing road network connectivity properties, maps describing roadway physical properties (such as traffic speed, traffic volume, the number of vehicular and cyclist traffic lanes, lane width, lane traffic directions, or lane marker types and locations, or combinations of them), and maps describing the spatial locations of road features such as crosswalks, traffic signs or other travel signals of various types. 
     The control module  406  receives the data representing the trajectory  414  and the data representing the AV position  418  and operates the control functions  420   a - c  (e.g., steering, throttling, braking, ignition) of the AV in a manner that will cause the AV  100  to travel the trajectory  414  to the destination  412 . For example, if the trajectory  414  includes a left turn, the control module  406  will operate the control functions  420   a - c  in a manner such that the steering angle of the steering function will cause the AV  100  to turn left and the throttling and braking will cause the AV  100  to pause and wait for passing pedestrians or vehicles before the turn is made. 
       FIG. 4B  is a block diagram of the planning module  404 , in accordance with one or more embodiments. The planning module  404  includes route planner  451 , logical constraints  452 , homotopy extractor  453 , sample-based maneuver realizer  454 , trajectory score generator  455 , tracking controller  456  and AV  457 . 
     In an embodiment, the route planner  451 : 1) receives an initial and terminal state; 2) plans a desired sequence of roadblocks/lanes with a lane router; 3) splits the route into segments based on a lane change, such that a segment does not contain a lane change; 4) selects segments in which the AV is located based on the AV&#39;s state (from dynamic world model  458 ) which is projected on the road blocks; 5) extracts baseline paths for selected segments (which can be marked as baseline path “desired” in case a lane change is desired); and 6) trims baseline paths based on maximal/minimal length. In case there is no lane change required, the adjacent baseline path is extracted and labeled as a soft logical constraint, meaning the AV can use the lane if needed for collision avoidance. Soft logical constraints are illustrated and described in more detail with reference to  FIG. 13 . 
     In an embodiment, route planner  451  generates a graphical representation of the operating environment of the AV, the AV&#39;s physical state based on sensor data (e.g., speed, position), and possible outcomes. In an embodiment, the graphical representation is a directed graph or decision graph (described below) that includes a number of nodes where each node represents a sample of the AV&#39;s decision space for a particular driving scenario, such as, for example, a plurality of maneuvers related to other vehicles and objects and environmental constraints (e.g., drivable area, lane markings  1524 ). The lane markings  1524  are illustrated and described in more detail with reference to  FIG. 15 . The edges of the directed graph represent different trajectories available to the AV  100  for the particular driving scenario (see  FIG. 15 ). 
     In an embodiment, logical constraints  452  include “hard” constraints and “soft” constraints. Hard constraints are logical constraints that must not be violated because, if violated, the AV would collide with another object, such as a pedestrian who may be “jaywalking” across the road. Note that hard constraints do not imply “do not collide.” Rather, a hard constraint can be, for example, a combination of spatial and speed constraints that can lead to a collision. For example, a hard constraint can be expressed in words as: “if the AV proceeds at 30 mph in lane A or accelerates at 2 mph/s in lane B, it will collide with the pedestrian.” Hence, the hard constraint expressed formally is “do not proceed at 30 mph in lane A” and “do not exceed 25 mph in lane A.” 
     Soft constraints are constraints that should be followed by the AV but can be violated to, for example, complete a trip to a destination or to avoid a collision. Some examples of “soft” constraints include but are not limited to: passenger comfort constraints and a minimum threshold of lateral clearance from a pedestrian who is crossing the street (jaywalking) to provide comfort to the pedestrian and the AV passenger. In an embodiment, soft constraints are embodied in the one or more rulebook (s). Soft constraints can include spatial constraints that change over time. A spatial constraint can be a drivable area. 
     In an embodiment, homotopy extractor  453  generates a set of potential maneuvers for the AV. Instead of hypothesizing objectives and then choosing the objective that performs the best, homotopy extractor  453  hypothesizes active constraint sets, referred to as a “homotopy” (defined below), and then chooses the constraint sets that result in lower cost. From route planner  451 , homotopy extractor  453  receives a route plan which contains the baseline path, also referred to as an “anchor path.” The “anchor path” is the best estimate of the lane that the AV is located in, and a soft logical constraint (e.g., a potentially desired path) which can be used by the AV when performing a lane change. In an embodiment, the route planner  451  also contains speed squared and spatial constraints which are computed along the anchor path (e.g., computed with a bound generator). 
     Given an initial state of the AV, a terminal state of the AV, a map representation and predictions of other agents in the scene, the homotopy extractor  453  finds all “approximately” feasible maneuvers the AV can perform. Note that in this context the resulting maneuvers might not be dynamically feasible but the homotopy extractor  453  guarantees that the resulting constraint set describing the maneuver is not an empty set (considering also the AV footprint). An AV maneuver is described by the homotopy. As described above, a homotopy is a subset of a set of constraints on a trajectory of an AV that the AV can adhere to while traversing a particular route. When there are multiple homotopies, a subset of the multiple homotopies can be selected that include a subset of constraints. In some implementations, a homotopy can be a unique space where any path starting at a starting position (AV state) and ending at a terminal state can be continuously deformed. To find these maneuvers, the homotopy extractor  453  iterates over all possible decisions the AV can take with respect to other agents, e.g. pass on the left/right side, pass before or after or just stay behind. In short, an output of the homotopy extractor  453  describes the spatiotemporal location of the AV to an agent. Although this can be a computationally expensive search, due to a set of simple checks all infeasible combinations can be eliminated. The homotopy extractor  452  is described in further detail in co-pending application, Attorney Docket No. 46154-0261001, entitled “Homotopic-Based Planner for Autonomous Vehicles,” filed Dec. 7, 2021, which is incorporated by reference herein in its entirety. 
     To be able to describe constraints representing where the other agents are located, and what a collision of the AV with these agents mean, every agent is converted into a station-based and spatial-based obstacle. The station-based constraint is parameterized over time while the spatial-based constraint is parameterized over both station and time. Further detail regarding the homotopy extractor  503  is described in reference to  FIGS. 13-16 . 
     In an embodiment, the realization searches  454   a  . . .  454   n  are performed by sample-based maneuver realizer  454  to generate a set of trajectories 1 . . . N for all the extracted homotopies. The sample-based maneuver realizer  454  is described in further detail in co-pending application, Attorney Docket No. 46154-0310001, entitled “Sampling-Based Maneuver Realizer,” filed Dec. 7, 2021, which is incorporated by reference herein in its entirety. 
     In an embodiment, trajectory score generator  455  uses one or more rulebooks, one or more machine learning models  459  and/or one or more safety maneuver models  460  to score the trajectories 1 . . . N, and uses the scores to select the trajectory that is the most compliant with the rules in the one or more rulebooks. In an embodiment, a predefined cost function is used to generate the trajectory scores. 
     In embodiments that use a cost function, a total order or partial order hierarchical cost function can be used to score the trajectories. The cost function is applied to metrics (e.g., Boolean values) associated with the violation and/or satisfaction of a hierarchy of rules in one or more rulebooks based on priority or relative importance. An example hierarchy of rules based on priority is as follows (from top to bottom): collision avoidance (Boolean), blockage (Boolean), terminal state in desired lane (Boolean), lane change (Boolean) and comfort (double float). In this example, every non-zero priority rule is defined as Boolean to avoid over-optimization of high priority costs. The most important or highest priority rule is to avoid collision, followed by avoiding blockage, followed by avoiding a terminal state in a desired lane, followed by a lane change, followed by comfort rules (e.g., maximum accelerations or decelerations). These example rules are described more fully as follows: 
     1. Collision: Is set to TRUE if there exists a state along the scored trajectory where the AV vehicle&#39;s footprint collides with the footprint of any other agent/object (e.g., they are considered to collide if their polygons intersect). 
     2. Blockage: A trajectory is considered blocked if the terminal homotopy does not contain the desired goal state and the terminal velocity of the trajectory is below a specified threshold (e.g., 2 m/s). 
     3. Terminal State in Desired Lane: Is set to TRUE if the terminal state of a trajectory is found in a lane which is desired lane change, and is set to TRUE if the AV&#39;s footprint crosses a lane divider at any time during the trajectory. 
     4. Comfort: maximums for acceleration/deceleration, braking distance, lateral clearance can be considered. 
     For each trajectory, the rules are checked and metrics determined. A cost function is formulated using the metrics and then minimized using, for example, a least squares formulation or any other suitable solver. The trajectory with the lowest cost is the selected trajectory, i.e., the trajectory with the least rule violations or most compliant. In an embodiment the minimized cost functions can be used to score the trajectories, as described in further detail below. Note that the rules described above are merely examples. Those with ordinary skill will recognized that any suitable cost function and rulebook can be used for trajectory scoring, including rulebooks with more or fewer rules. 
     For machining learning embodiments, trajectory score generator  455  can implement one or more machine learning models  509  and/or safety maneuver models  510  to score trajectories. For example, a neural network can be used to predict a score of trajectory. 
     Tracking controller  456  is used to improve the robustness of the planning module  404  against unexpected spikes in computational demand. Tracking controller  456  is a fast-executing tracking controller that provides steady and smooth control inputs and allows the planning module  404  to react faster towards disturbances. In an embodiment, tracking controller  506  runs at 40 Hz. The input to tracking controller  456  is the selected trajectory provided by the trajectory score generator  455  that has been parameterized by time, such that tracking controller  506  can query an exact desired position of the AV at a given time. 
     In an embodiment, the tracking controller  456  is formulated as a type of model predictive control (MPC) problem with constraints on the control inputs and states. However, any suitable multivariable control algorithm can also be used. The MPC-type formulation uses an internal dynamic model of a process, a cost function J over a receding horizon and an optimization algorithm for minimizing the cost function J using a control input u. An example cost function for optimization is a quadratic cost function. 
     In an embodiment, the dynamic model is a kinematic vehicle model in Cartesian coordinates or any other suitable reference coordinate frame. For example, the kinematic vehicle model can be a bicycle model that allows a side slip angle to be defined geometrically to express yaw rate in terms of variables that are represented with respect to the center of gravity of the AV. In an embodiment, the cost function J follows a contouring error formulation (orthogonal deviation from the anchor path) where the objective is to minimize the lateral and longitudinal error. 
     Autonomous Vehicle Inputs 
       FIG. 5  is a block diagram illustrating an example of inputs  502   a - d  (e.g., sensors  121  shown in  FIG. 1 ) and outputs  504   a - d  (e.g., sensor data) that is used by the perception module  402  ( FIGS. 4A-4B ), in accordance with one or more embodiments. One input  502   a  is a LiDAR (Light Detection and Ranging) system (e.g., LiDAR  123  shown in  FIG. 1 ). LiDAR is a technology that uses light (e.g., bursts of light such as infrared light) to obtain data about physical objects in its line of sight. A LiDAR system produces LiDAR data as output  504   a . For example, LiDAR data is collections of 3D or 2D points (also known as a point clouds) that are used to construct a representation of the environment  190 . 
     Another input  502   b  is a RADAR system. RADAR is a technology that uses radio waves to obtain data about nearby physical objects. RADARs can obtain data about objects not within the line of sight of a LiDAR system. A RADAR system  502   b  produces RADAR data as output  504   b . For example, RADAR data are one or more radio frequency electromagnetic signals that are used to construct a representation of the environment  190 . 
     Another input  502   c  is a camera system. A camera system uses one or more cameras (e.g., digital cameras using a light sensor such as a charge-coupled device [CCD]) to obtain information about nearby physical objects. A camera system produces camera data as output  504   c . Camera data often takes the form of image data (e.g., data in an image data format such as RAW, JPEG, PNG, etc.). In some examples, the camera system has multiple independent cameras, e.g., for the purpose of stereopsis (stereo vision), which enables the camera system to perceive depth. Although the objects perceived by the camera system are described here as “nearby,” this is relative to the AV. In use, the camera system may be configured to “see” objects far, e.g., up to a kilometer or more ahead of the AV. Accordingly, the camera system may have features such as sensors and lenses that are optimized for perceiving objects that are far away. 
     Another input  502   d  is a traffic light detection (TLD) system. A TLD system uses one or more cameras to obtain information about traffic lights, street signs, and other physical objects that provide visual operation information. A TLD system produces TLD data as output  504   d . TLD data often takes the form of image data (e.g., data in an image data format such as RAW, JPEG, PNG, etc.). A TLD system differs from a system incorporating a camera in that a TLD system uses a camera with a wide field of view (e.g., using a wide-angle lens or a fish-eye lens) in order to obtain information about as many physical objects providing visual operation information as possible, so that the AV  100  has access to all relevant operation information provided by these objects. For example, the viewing angle of the TLD system may be about 120 degrees or more. 
     In an embodiment, outputs  504   a - d  are combined using a sensor fusion technique. Thus, either the individual outputs  504   a - d  are provided to other systems of the AV  100  (e.g., provided to a planning module  404  as shown in  FIGS. 4A-4B ), or the combined output can be provided to the other systems, either in the form of a single combined output or multiple combined outputs of the same type (e.g., using the same combination technique or combining the same outputs or both) or different types type (e.g., using different respective combination techniques or combining different respective outputs or both). In an embodiment, an early fusion technique is used. An early fusion technique is characterized by combining outputs before one or more data processing steps are applied to the combined output. In an embodiment, a late fusion technique is used. A late fusion technique is characterized by combining outputs after one or more data processing steps are applied to the individual outputs. 
       FIG. 6  is a block diagram illustrating an example of a LiDAR system  602  (e.g., the input  502   a  shown in  FIG. 5 ), in accordance with one or more embodiments. The LiDAR system  602  emits light  604   a - c  from a light emitter  606  (e.g., a laser transmitter). Light emitted by a LiDAR system is typically not in the visible spectrum; for example, infrared light is often used. Some of the light  604   b  emitted encounters a physical object  608  (e.g., a vehicle) and reflects back to the LiDAR system  602 . (Light emitted from a LiDAR system typically does not penetrate physical objects, e.g., physical objects in solid form.) The LiDAR system  602  also has one or more light detectors  610 , which detect the reflected light. In an embodiment, one or more data processing systems associated with the LiDAR system generates an image  612  representing the field of view  614  of the LiDAR system. The image  612  includes information that represents the boundaries  616  of a physical object  608 . In this way, the image  612  is used to determine the boundaries  616  of one or more physical objects near an AV. 
       FIG. 7  is a block diagram illustrating the LiDAR system  602  in operation, in accordance with one or more embodiments. In the scenario shown in this figure, the AV  100  receives both camera system output  504   c  in the form of an image  702  and LiDAR system output  504   a  in the form of LiDAR data points  704 . In use, the data processing systems of the AV  100  compares the image  702  to the data points  704 . In particular, a physical object  706  identified in the image  702  is also identified among the data points  704 . In this way, the AV  100  perceives the boundaries of the physical object based on the contour and density of the data points  704 . 
       FIG. 8  is a block diagram illustrating the operation of the LiDAR system  602  in additional detail, in accordance with one or more embodiments. As described above, the AV  100  detects the boundary of a physical object based on characteristics of the data points detected by the LiDAR system  602 . As shown in  FIG. 8 , a flat object, such as the ground  802 , will reflect light  804   a - d  emitted from a LiDAR system  602  in a consistent manner. Put another way, because the LiDAR system  602  emits light using consistent spacing, the ground  802  will reflect light back to the LiDAR system  602  with the same consistent spacing. As the AV  100  travels over the ground  802 , the LiDAR system  602  will continue to detect light reflected by the next valid ground point  806  if nothing is obstructing the road. However, if an object  808  obstructs the road, light  804   e - f  emitted by the LiDAR system  602  will be reflected from points  810   a - b  in a manner inconsistent with the expected consistent manner. From this information, the AV  100  can determine that the object  808  is present. 
     Path Planning 
       FIG. 9  is a block diagram  900  illustrating of the relationships between inputs and outputs of a planning module  404  (e.g., as shown in  FIGS. 4A-4B ), in accordance with one or more embodiments. In general, the output of a planning module  404  is a route  902  from a start point  904  (e.g., source location or initial location), and an end point  906  (e.g., destination or final location). The route  902  is typically defined by one or more segments. For example, a segment is a distance to be traveled over at least a portion of a street, road, highway, driveway, or other physical area appropriate for automobile travel. In some examples, e.g., if the AV  100  is an off-road capable vehicle such as a four-wheel-drive (4WD) or all-wheel-drive (AWD) car, SUV, pick-up truck, or the like, the route  902  includes “off-road” segments such as unpaved paths or open fields. 
     In addition to the route  902 , a planning module also outputs lane-level route planning data  908 . The lane-level route planning data  908  is used to traverse segments of the route  902  based on conditions of the segment at a particular time. For example, if the route  902  includes a multi-lane highway, the lane-level route planning data  908  includes trajectory planning data  910  that the AV  100  can use to choose a lane among the multiple lanes, e.g., based on whether an exit is approaching, whether one or more of the lanes have other vehicles, or other factors that vary over the course of a few minutes or less. Similarly, in some implementations, the lane-level route planning data  908  includes speed constraints  912  specific to a segment of the route  902 . For example, if the segment includes pedestrians or un-expected traffic, the speed constraints  912  may limit the AV  100  to a travel speed slower than an expected speed, e.g., a speed based on speed limit data for the segment. 
     In an embodiment, the inputs to the planning module  404  includes database data  914  (e.g., from the database module  410  shown in  FIGS. 4A-4B ), current location data  916  (e.g., the AV position  418  shown in  FIGS. 4A-4B ), destination data  918  (e.g., for the destination  412  shown in  FIGS. 4A-4B ), and object data  920  (e.g., the classified objects  416  as perceived by the perception module  402  as shown in  FIGS. 4A-4B ). In an embodiment, the database data  914  includes rules used in planning. Rules are specified using a formal language, e.g., using Boolean logic. In any given situation encountered by the AV  100 , at least some of the rules will apply to the situation. A rule applies to a given situation if the rule has conditions that are met based on information available to the AV  100 , e.g., information about the surrounding environment. Rules can have priority. For example, a rule that says, “if the road is a freeway, move to the leftmost lane” can have a lower priority than “if the exit is approaching within a mile, move to the rightmost lane.” 
       FIG. 10  illustrates a directed graph  1000  used in path planning, e.g., by the planning module  404  ( FIGS. 4A-4B ), in accordance with one or more embodiments. In general, a directed graph  1000  like the one shown in  FIG. 10  is used to determine a path between any start point  1002  and end point  1004 . In real-world terms, the distance separating the start point  1002  and end point  1004  may be relatively large (e.g., in two different metropolitan areas) or may be relatively small (e.g., two intersections abutting a city block or two lanes of a multi-lane road). 
     In an embodiment, the directed graph  1000  has nodes  1006   a - d  representing different locations between the start point  1002  and the end point  1004  that could be occupied by an AV  100 . In some examples, e.g., when the start point  1002  and end point  1004  represent different metropolitan areas, the nodes  1006   a - d  represent segments of roads. In some examples, e.g., when the start point  1002  and the end point  1004  represent different locations on the same road, the nodes  1006   a - d  represent different positions on that road. In this way, the directed graph  1000  includes information at varying levels of granularity. In an embodiment, a directed graph having high granularity is also a subgraph of another directed graph having a larger scale. For example, a directed graph in which the start point  1002  and the end point  1004  are far away (e.g., many miles apart) has most of its information at a low granularity and is based on stored data, but also includes some high granularity information for the portion of the graph that represents physical locations in the field of view of the AV  100 . 
     The nodes  1006   a - d  are distinct from objects  1008   a - b  which cannot overlap with a node. In an embodiment, when granularity is low, the objects  1008   a - b  represent regions that cannot be traversed by automobile, e.g., areas that have no streets or roads. When granularity is high, the objects  1008   a - b  represent physical objects in the field of view of the AV  100 , e.g., other automobiles, pedestrians, or other entities with which the AV  100  cannot share physical space. In an embodiment, some or all of the objects  1008   a - b  are static objects (e.g., an object that does not change position such as a street lamp or utility pole) or dynamic objects (e.g., an object that is capable of changing position such as a pedestrian or other car). 
     The nodes  1006   a - d  are connected by edges  1010   a - c . If two nodes  1006   a - b  are connected by an edge  1010   a , it is possible for an AV  100  to travel between one node  1006   a  and the other node  1006   b , e.g., without having to travel to an intermediate node before arriving at the other node  1006   b . (When we refer to an AV  100  traveling between nodes, we mean that the AV  100  travels between the two physical positions represented by the respective nodes.) The edges  1010   a - c  are often bidirectional, in the sense that an AV  100  travels from a first node to a second node, or from the second node to the first node. In an embodiment, edges  1010   a - c  are unidirectional, in the sense that an AV  100  can travel from a first node to a second node, however the AV  100  cannot travel from the second node to the first node. Edges  1010   a - c  are unidirectional when they represent, for example, one-way streets, individual lanes of a street, road, or highway, or other features that can only be traversed in one direction due to legal or physical constraints. 
     In an embodiment, the planning module  404  uses the directed graph  1000  to identify a path  1012  made up of nodes and edges between the start point  1002  and end point  1004 . 
     An edge  1010   a - c  has an associated cost  1014   a - b . The cost  1014   a - b  is a value that represents the resources that will be expended if the AV  100  chooses that edge. A typical resource is time. For example, if one edge  1010   a  represents a physical distance that is twice that as another edge  1010   b , then the associated cost  1014   a  of the first edge  1010   a  may be twice the associated cost  1014   b  of the second edge  1010   b . Other factors that affect time include expected traffic, number of intersections, speed limit, etc. Another typical resource is fuel economy. Two edges  1010   a - b  may represent the same physical distance, but one edge  1010   a  may require more fuel than another edge  1010   b , e.g., because of road conditions, expected weather, etc. 
     When the planning module  404  identifies a path  1012  between the start point  1002  and end point  1004 , the planning module  404  typically chooses a path optimized for cost, e.g., the path that has the least total cost when the individual costs of the edges are added together. 
     Autonomous Vehicle Control 
       FIG. 11  is a block diagram  1100  illustrating the inputs and outputs of a control module  406  (e.g., as shown in  FIGS. 4A-4B ), in accordance with one or more embodiments. A control module operates in accordance with a controller  1102  which includes, for example, one or more processors (e.g., one or more computer processors such as microprocessors or microcontrollers or both) similar to processor  304 , short-term and/or long-term data storage (e.g., memory random-access memory or flash memory or both) similar to main memory  306 , ROM  308 , and storage device  310 , and instructions stored in memory that carry out operations of the controller  1102  when the instructions are executed (e.g., by the one or more processors). 
     In an embodiment, the controller  1102  receives data representing a desired output  1104 . The desired output  1104  typically includes a velocity, e.g., a speed and a heading. The desired output  1104  can be based on, for example, data received from a planning module  404  (e.g., as shown in  FIGS. 4A-4B ). In accordance with the desired output  1104 , the controller  1102  produces data usable as a throttle input  1106  and a steering input  1108 . The throttle input  1106  represents the magnitude in which to engage the throttle (e.g., acceleration control) of an AV  100 , e.g., by engaging the steering pedal, or engaging another throttle control, to achieve the desired output  1104 . In some examples, the throttle input  1106  also includes data usable to engage the brake (e.g., deceleration control) of the AV  100 . The steering input  1108  represents a steering angle, e.g., the angle at which the steering control (e.g., steering wheel, steering angle actuator, or other functionality for controlling steering angle) of the AV should be positioned to achieve the desired output  1104 . 
     In an embodiment, the controller  1102  receives feedback that is used in adjusting the inputs provided to the throttle and steering. For example, if the AV  100  encounters a disturbance  1110 , such as a hill, the measured speed  1112  of the AV  100  is lowered below the desired output speed. In an embodiment, any measured output  1114  is provided to the controller  1102  so that the necessary adjustments are performed, e.g., based on the differential  1113  between the measured speed and desired output. The measured output  1114  includes measured position  1116 , measured velocity  1118 , (including speed and heading), measured acceleration  1120 , and other outputs measurable by sensors of the AV  100 . 
     In an embodiment, information about the disturbance  1110  is detected in advance, e.g., by a sensor such as a camera or LiDAR sensor, and provided to a predictive feedback module  1122 . The predictive feedback module  1122  then provides information to the controller  1102  that the controller  1102  can use to adjust accordingly. For example, if the sensors of the AV  100  detect (“see”) a hill, this information can be used by the controller  1102  to prepare to engage the throttle at the appropriate time to avoid significant deceleration. 
       FIG. 12  is a block diagram  1200  illustrating the inputs, outputs, and components of the controller  1102 , in accordance with one or more embodiments. The controller  1102  has a speed profiler  1202  which affects the operation of a throttle/brake controller  1204 . For example, the speed profiler  1202  instructs the throttle/brake controller  1204  to engage acceleration or engage deceleration using the throttle/brake  1206  depending on, e.g., feedback received by the controller  1102  and processed by the speed profiler  1202 . 
     The controller  1102  also has a lateral tracking controller  1208  which affects the operation of a steering controller  1210 . For example, the lateral tracking controller  1208  instructs the steering controller  1204  to adjust the position of the steering angle actuator  1212  depending on, e.g., feedback received by the controller  1102  and processed by the lateral tracking controller  1208 . 
     The controller  1102  receives several inputs used to determine how to control the throttle/brake  1206  and steering angle actuator  1212 . A planning module  404  provides information used by the controller  1102 , for example, to choose a heading when the AV  100  begins operation and to determine which road segment to traverse when the AV  100  reaches an intersection. A localization module  408  provides information to the controller  1102  describing the current location of the AV  100 , for example, so that the controller  1102  can determine if the AV  100  is at a location expected based on the manner in which the throttle/brake  1206  and steering angle actuator  1212  are being controlled. In an embodiment, the controller  1102  receives information from other inputs  1214 , e.g., information received from databases, computer networks, etc. 
     Autonomous Vehicle Operation Using Maneuver Generation 
       FIG. 13  is a flow diagram illustrating an example process  1300  for determining a maneuver for the AV  100 , in accordance with one or more embodiments. The AV  100  is illustrated and described in more detail with reference to  FIG. 1 . In some implementations, the process  1300  can be performed, at least in part, using the homotopy extractor  453  of the planning module  404  of the AV  100  (e.g., as described with respect to  FIGS. 4A and 4B ). 
     The AV  100  uses at least one processor  146  of the AV  100  to generate multiple, initial trajectories for the AV  100  based on a road segment (e.g., the road segment  1500  can include lanes  1512 ,  1516 ). The processor  146  is illustrated and described in more detail with reference to  FIG. 1 . The road segment  1500  and lanes  1512 ,  1516  are illustrated and described in more detail with reference to  FIG. 15 . The process for trajectory generation is illustrated and described in more detail with reference to  FIG. 10 . The AV  100  receives sensor data (e.g., LiDAR output data  504   a ) from at least one sensor  121  of the AV  100 . The sensor  121  is illustrated and described in more detail with reference to  FIG. 10 . The LiDAR output data  504   a  is illustrated and described in more detail with reference to  FIG. 5 . The AV  100 &#39;s use of sensor data is also described in more detail with reference to  FIG. 4B . The AV  100  is traveling the road segment  1500  in lane  1516  in accordance with a trajectory  198  belonging to the multiple, initial trajectories. The trajectory  198  is further illustrated and described with reference to  FIG. 1 . The AV  100  predicts a potential collision between the AV  100  and an object (e.g., object  416 ) moving on the lane  1516  based on the sensor data  504   a  and the trajectory  198 . The object  416  is illustrated and described in more detail with reference to  FIGS. 4 and 15 . 
     The AV  100  determines a set of constraints  1302  for the AV  100  to avoid the potential collision. The set of constraints is determined based on the sensor data  504   a . For example, as shown in  FIG. 13 , the homotopy extractor  453  can generate a set of constraints  1302  associated with the AV  100  traversing the road segment  1500 . In some implementations, each constraint of the set of constraints  1302  can include a particular parameter and a corresponding parameter value. For example, one constraint denotes that a particular parameter C_1 should be equal to a particular parameter value X_1. As another example, another constraint denotes that the same parameter C_1 should equal a different parameter value X_2. As another example, another constraint can denote that a different parameter C_2 equal a parameter value Y_1. 
     In an embodiment, the set of constraints includes hard logical constraints and soft logical constraints. Hard logical constraints are those that that the AV  100  must obey, for example, to avoid a potential collision or to reach the destination  199 . The destination  199  is illustrated and described in more detail with reference to  FIG. 1 . Hard logical constraints are described in more detail with reference to  FIG. 4B . A constraint can thus be required or “hard” (e.g., the AV  100  must adhere to hard constraints while traversing to the destination  199 ). For example, hard logical constraints can pertain to a predicted safety of one or more passengers of the AV  100  and/or the safety of the AV  100 . A constraint can specify that the AV  100  not make contact with certain objects (e.g., other vehicles  193 , pedestrians  192 , or obstacles), remain within the boundaries  1528 ,  1532  of a road segment  1500 , travel in a direction of traffic of a road, not accelerate or decelerate in a manner that would injury its passengers, etc. The vehicle  193  and pedestrian  192  are illustrated and described in more detail with reference to  FIG. 1 . The boundaries  1528 ,  1532  and road segment  1500  are illustrated and described in more detail with reference to  FIG. 15 . As another example, a constraint can specify that a likelihood of the AV  100  colliding with the object  416 , a vehicle  193 , a pedestrian  192 , or other object be less than a threshold value. The object  416  is illustrated and described in more detail with reference to  FIGS. 4A, 15 . In some implementations, the likelihood is calculated by the homotopy extractor  453  using one or more computer simulations or dynamic models. 
     Soft logical constraints are those that the AV  100  should obey but can violate, for example, to avoid a potential collision. Soft logical constraints are described in more detail with reference to  FIG. 4B . For example, at least some of the set of constraints  1302  can be soft logical constraints (e.g., the AV  100  should try to but does not necessarily need to adhere to soft logical constraints while traversing to the destination  199 ). Soft logical constraints can pertain to a predicted comfort of one or more passengers of the AV. For instance, a constraint can specify that the AV  100  adhere to certain acceleration limitations, braking limitations, speed limitations, turning rate limitations, etc. based on the effect these constraints have on the comfort of a passenger of the AV. 
     The set of constraints  1302  can represent any aspect that may restrict, control, or otherwise influence the operation of the AV  100  as it traverses to the destination. As an example, at least some of the set of constraints  1302  can pertain to the performance capabilities of the AV  100 . For instance, a constraint can specify that the AV  100  is to adhere to certain map constraints based on the performance capabilities of the AV, including but not limited to: acceleration limitations, braking limitations, speed limitations, turning rate limitations, inertial limitations, etc. As another example, a constraint can specify a range of motion of the AV  100  (e.g., the AV  100  can travel forward or backward, while remaining straight or turning, but cannot travel side to side). 
     In an embodiment, the set of constraints  1302  includes environmental constraints indicating at least one of a drivable area of the road segment  1500  or lane markings  1524  of the road segment  1500 . The drivable area and lane markings  1524  of the road segment  1500  are illustrated in  FIG. 15 . For example, at least some of the set of constraints  1302  can be map constraints that pertain to the map geometry of one or more roads that that AV  100  can use to traverse to the destination. For instance, a constraint can specify that the AV  100  is to be confined to certain lanes of a road and/or within certain boundaries  1528 ,  1532  of a road segment  1500  (e.g., between the left and right edges of a navigable portion of a road). As another example, a constraint can specify that presence and location of obstacles (e.g., the object  416 ) on a road, through which an AV  100  cannot pass. 
     In an embodiments, at least some of the set of constraints  1302  can pertain to legal constraints regarding an operation of the AV  100 . For instance, a constraint can specify that the AV  100  is to adhere to a particular speed limit of a road and/or a particular flow of traffic of a road (e.g., a direction of travel). As another example, a constraint can specify that the AV  100  is to adhere to traffic rules or laws in a particular jurisdiction. Although example constraints  1302  are described herein, these are merely illustrative examples. In practice, the set of constraints  1302  can include additional constraints, either instead of or in addition to those described herein. 
     In an embodiment, the AV  100  determines multiple homotopies  1304   a - 1304   n . Each homotopy of the multiple homotopies  1304   a - 1304   n  includes a different respective combination of the set of constraints  1302 . The homotopy extractor  453  generates one or more homotopies  1304   a - 1304   n  based on the set of constraints  1302 . For example, each homotopy can include a different one of the set of constraints  1302  and/or a different combination of two or more of the set of constraints  1302 . Determining a maneuver for the AV  100  is based on at least some of the multiple homotopies  1304   a - 1304   n.    
     In some implementations, each homotopy includes one or more of the soft logical constraints. Further, each homotopy can include each of the hard logical constraints. In practice, whether a particular constraint is a soft or a hard logical constraint can vary, depending on the implementation. As an example, in some implementations, constraints pertaining to the performance capabilities of the AV  100 , the map (environmental) constraints of one or more roads that that AV  100  can use to traverse to the destination  199 , the legal constraints regarding an operation of the AV  100 , and/or the safety of one or more passengers of the AV may be considered “required.” As another example, in some implementations, constraints pertaining to comfort of one or more passengers of the AV  100  and/or constraints specifying that the AV  100  perform certain operations or tasks may be considered soft logical constraints. 
     In the example shown in  FIG. 13 , a first homotopy  1304   a  (“Homotopy 1”) includes (i) the soft logical constraint that a parameter C_1 be equal to a parameter value X_1, (ii) the soft logical constraint that a parameter C_2 be equal to a parameter value Y_2, and (iii) each of the hard logical constraints. Further, a second homotopy  1304   b  (“Homotopy 2”) includes (i) the soft logical constraint that the parameter C_1 be equal to the parameter value X_1 (as in the Homotopy 1), (ii) the soft logical constraint that the parameter C_2 be equal to the parameter value Y_2 (as in the Homotopy 1), (iii) an additional soft logical constraint that a parameter C N be equal to a parameter value Z_1, and (iv) each of the hard logical constraints (as in the Homotopy 1). That is, although the Homotopy 2 shares some of the same constraints as in the Homotopy 2, it includes an additional constraint that is not in the Homotopy 1. 
     Further, a third homotopy  1304   n  (“Homotopy N”) includes (i) the soft logical constraint that the parameter C_1 be equal to the parameter value X_1 (as in the Homotopies 1 and 2), (ii) the soft logical constraint that the parameter C_2 be equal to the parameter value Y_2 (as in the Homotopies 1 and 2), (iii) the soft logical constraint that a parameter C N be equal to a parameter value Z_2, and (iv) each of the hard logical constraints (as in the Homotopies 1 and 2). That is, although the Homotopy 3 shares some of the constraints as in the Homotopies 1 and 2, it specifies a different parameter value for one of its constraints. 
     Although three example homotopies are shown in  FIG. 13 , this is merely an illustrative example. In practice, the homotopy extractor  453  can generate any number of homotopies, each having a different respective subset of the set of constraints  1302 . The homotopy extractor  453  determines whether each of the homotopies  1304   a - 1304   n  is “feasible.” As an example, for each homotopy, the homotopy extractor  453  can determine whether the AV can traverse to the destination  199  in accordance with the constraints of that homotopy, without colliding with other objects (e.g., the object  416 ) on the road segment  1500 , without negatively impacting the safety of its passengers, without violating traffic rules or laws of the jurisdictions, etc. 
     In an embodiment, the AV  100  predicts a motion of the AV  100  on the road segment  1500  according to a degree of precision. The AV  100  determines that the AV  100  can traverse the road segment  1500  in accordance with a subset of the multiple homotopies (a particular combination of constraints) based on the predicted motion. Determining the maneuver is further based on the subset of the multiple homotopies. For example, the homotopy extractor  453  can determine whether each of the homotopies  1304   a - 1304   n  is feasible by predicting the motion of the AV  100 . For each homotopy, the homotopy extractor  453  performs a simulation of the AV motion using computer simulation or a dynamic model to predict how the AV  100  will move as it traverses the road segment  1500 , while attempting to adhere to each of the constraints of that homotopy. If the homotopy extractor  453  determines that the AV  100  is unable to traverse the road segment  1500  while adhering to each of the constraints of that homotopy, the homotopy extractor  453  determines that the homotopy is “not feasible.” If the homotopy extractor  453  determines that the AV  100  is able to traverse the road segment  1500  while adhering to each of the constraints of that homotopy, the homotopy extractor  453  determines that the homotopy (and associated maneuver) is “feasible.” 
     In an embodiment, the AV  100  determines that the AV  100  can traverse the road segment  1500  in accordance with a subset of the multiple homotopies based on the predicted motion. Determining the maneuver is further based on the subset of the multiple homotopies. As an example, a homotopy can include a subset of constraints (subset of the multiple homotopies) specifying that: (i) the AV  100  perform certain operations and tasks at certain times and locations; (ii) the AV  100  adhere to all traffic rules and laws in the jurisdiction; (iii) the AV  100  perform in a manner that does not exceed its performance capabilities; and (iv) the AV  100  does not collide with any objects (e.g., the vehicle  193 ) or obstacles (e.g., the object  416 ) on the road. The homotopy extractor  453  can simulate the motion of the AV  100  in accordance with these constraints. 
     If the homotopy extractor  453  determines that the AV  100  cannot perform the specified operations and tasks unless it violates certain traffic rules or laws, the homotopy extractor  453  determines that the homotopy is “not feasible.” Similarly, if the homotopy extractor  453  determines that the AV  100  cannot perform the specified operations and tasks without colliding with another object, the homotopy extractor  453  also determines that the homotopy is “not feasible.” Similarly, if the homotopy extractor  453  determines that performing the specified operations and tasks would require exceeding the performance capabilities of the AV  100 , the homotopy extractor  453  also determines that the homotopy is “not feasible.” However, if the homotopy extractor  453  determines that the AV  100  can perform the specified operations and tasks, and without violating any of the other constraints, the homotopy extractor  453  determines that the homotopy is “feasible.” For instance, in the example shown in  FIG. 13 , the homotopy extractor  453  determines that the Homotopies 1 and N are “feasible,” and that the Homotopy 2 is “not feasible” (e.g., due to violation of one or more of the set of constraints  1302  specified by the Homotopy 2). 
     In an embodiment, the AV  100  predicts a motion of the AV  100  on the road segment  1500  according to a first degree of precision. The homotopy extractor  453  can determine whether each of the homotopies  1304   a - 1304   n  is “feasible” according to the first degree of precision. For example, the homotopy extractor  453  generates one or more trajectories (to determine a maneuver) for each of the homotopies that are determined to be “feasible,” and refrains from generating trajectories for each of the homotopies that are determined to be “not feasible.” For example, for each homotopy that is determined to be “feasible,” the homotopy extractor  453  use a computer simulation and one or more dynamic models, control laws and equations of motion of the AV  100  to generate a trajectory (e.g., trajectory  1520 ) for the AV  100  that enable it to traverse the road segment  1500  using lane  1512 , while adhering to each of the constraints of that homotopy. In some implementations, a simulation and/or a dynamic model can be implemented using one or more equations and/or control laws specifying a motion of one or more objects (e.g., vehicle  193  or object  416 ) in the environment  190 . Example techniques for generating one or more trajectories for an AV  100  are described herein (e.g., with respect to  FIGS. 4A, 4B, 9, and 10 ). The environment  190  is illustrated and described in more detail with reference to  FIG. 1 . 
     For instance, in the example shown in  FIG. 13 , the homotopy extractor  453  generates one or more trajectories  1306   a  (to determine a maneuver) corresponding to the Homotopy 1, and one or more trajectories  1306   b  corresponding to the Homotopy N (both of which were determined to be “feasible”). However, the homotopy extractor  453  refrains from generating any trajectories corresponding to the Homotopy 2 (which was determined to be “not feasible”). 
     In some implementations, the homotopy extractor  453  can generate one or more trajectories for each of the homotopies that are determined to be “feasible” according to a second degree of precision. The second degree of precision can be higher than the first degree of precision. For example, the degree of precision with which the motion of the AV  100  is predicted and/or the trajectory  1520  for the AV  100  is generated can refer to (i) the spatial resolution with which the motion of the AV  100  is predicted and/or the trajectory  1520  for the AV  100  is generated, or (ii) the temporal resolution with which the motion of the AV  100  is predicted and/or the trajectory  1520  for the AV  100  is generated. The trajectory  1520  is illustrated and described in more detail with reference to  FIG. 15 . 
     The degree of precision with which the motion of the AV  100  is predicted and/or the trajectory  1520  for the AV  100  is generated can refer to (iii) the complexity of the computer simulations or dynamic models that are used to predict the motion of the AV  100  and/or generate the trajectory  1520  for the AV  100 , or (iv) the amount of computation resources allotted to predicting the motion of the AV  100  and/or generating the trajectory  1520  for the AV  100 . In an embodiment, the degree of precision with which the motion of the AV  100  is predicted and/or the trajectory  1520  for the AV  100  is generated can refer to (v) the tolerance or error range associated with predicting the motion of the AV  100  and/or generating the trajectory  1520  for the AV  100 , and/or other such characteristics that can influence how the motion of the AV  100  can predicted and/or the trajectory  1520  for the AV  100  can be generated. 
     In an embodiment, the homotopy extractor  453  can initially generate predictions for each of the homotopies according to a first spatial and/or temporal resolution, and subsequently generate one or more trajectories (to determine a maneuver) for each of the homotopies that are determined to be “feasible” according to a higher second spatial and/or temporal resolution. The homotopy extractor  453  can initially predict, for each of the homotopies, a motion of the AV  100  according to a lower spatial resolution (e.g., in 10 feet increments), and subsequently generate one or more trajectories for each of the homotopies that are determined to be “feasible” according to a higher spatial resolution (e.g., 1 foot increments). The homotopy extractor  453  can initially predict, for each of the homotopies, a motion of the AV  100  according to a lower temporal resolution (e.g., in 10 second increments), and subsequently generate one or more trajectories for each of the homotopies that are determined to be “feasible” according to a higher spatial resolution (e.g., 1 second increments). Although example spatial and/or temporal resolutions are described above, these are merely illustrative examples. In practice, other spatial and/or temporal resolutions can be used to predict a motion of the AV  100  and/or generate one or more trajectories for an AV. 
     In an embodiment, the homotopy extractor  453  can initially generate predictions for each of the homotopies according to a first computer simulation or first dynamic model), and subsequently generate one or more trajectories for each of the homotopies that are determined to be “feasible” according to a second computer simulation or second dynamic model that is more complex than the first computer simulation or the first dynamic model (e.g., more variables and/or parameters are modeled). For instance, the first computer simulation or dynamic model can require fewer computational resources to generate a prediction (but can be less precise), whereas the first computer simulation or dynamic model may require more computation resources to generate a trajectory (but can be more precise). As another example, the first computer simulation or dynamic model can require fewer data inputs and/or less comprehensive data inputs to generate a prediction (but can be less precise), whereas the first computer simulation or dynamic model can require more data inputs and/or more comprehensive data inputs to generate a trajectory (but can be more precise). Example data inputs can include, for example, sensor data  504   a , traffic data, weather data, and/or other data that regarding the characteristics of an environment of the AV  100 . 
     In an embodiment, the AV  100  determines a maneuver by superimposing each constraint of the set of constraints  1302  on each other constraint of the set of constraints  1302 . The maneuver includes a trajectory (e.g., trajectory  1520 ) independent of the multiple, initial trajectories (e.g., trajectory  198 ) that were generated for the AV  100  based on the road segment  1500  using the process for trajectory generation illustrated and described in more detail with reference to  FIG. 10 . The homotopy extractor  453  selects one of the generated trajectories  1306   a  and  1306   b  for the maneuver (as illustrated and described with reference to  FIG. 13 ), and instructs the control circuit  406  of the AV  100  to execute the selected trajectory (e.g., trajectory  1306   a ). For instance, in the example shown in  FIG. 13 , the homotopy extractor  453  has selected the trajectory  1306   a  (“Trajectory 1”) over the trajectory  1306   b  (“Trajectory N”). In some implementations, a trajectory  1520  can be selected using other modules, either instead of or in conjunction with the homotopy extractor  453 . For example, a trajectory can be selected using the homotopy extractor  453 , the realization sample-based maneuver realizer  454 , and/or the trajectory score generator  455  (e.g., as described in reference to  FIG. 4B ). 
     In an embodiment, superimposing each constraint of the set of constraints  1302  on each other constraint of the set of constraints  1302  includes sampling, by the at least one processor  146 , each constraint of the set of constraints  1302  with respect to time in accordance with changes in the sensor data  504   a  to provide the maneuver. For example, determining the set of constraints  1302  can be performed at a first frequency and determining the maneuver to generate the trajectory  1520  can be performed at a second frequency higher than the first frequency. The different constraints can thus be sampled differently. For example, the homotopy extractor  453  can operate at 10 Hz and the realization searches can be performed twice as fast at 20 Hz. 
     In an embodiment, determining the maneuver to generate the trajectory  1520  includes assigning, by the at least one processor  146 , a respective quality metric to each homotopy of the multiple homotopies. The trajectory  1520  is selected based on the respective quality metric. For example, the trajectory  1520  can be selected by calculating a quality score or other metric for each of the trajectories generated (by the methods illustrated and described with reference to  FIG. 13 ), and selecting the trajectory  1520  based on the quality scores or metrics. 
     In an embodiment, the respective quality metric is determined based on at least one of a predicted time for traversing the road segment  1500  in accordance with each homotopy, a predicted safety of a passenger of the AV  100  while traversing the road segment  1500  in accordance with each homotopy, or a predicted comfort of the passenger while traversing the road segment  1500  in accordance with each homotopy. For each trajectory (obtained from a homotopy), a quality score or metric based on various factors, such as the predicted safety or the passengers of the AV  100 , the predicted comfort of the passengers of the AV  100 , the predicted resources that would consumed by the AV  100  (e.g., fuel, battery charge, etc.), the predicted amount of time that it would take to transverse to the destination  199 , and/or other factors can be determined. 
     The trajectory  1520  can be selected based on the quality scores or metrics (e.g., the trajectory having the highest quality score or metric). As described above, this selection process can be performed by one or more modules of the AV  100 , such as the homotopy extractor  453 , the realization sample-based maneuver realizer  454 , and/or the trajectory score generator  455 . 
     In an embodiment, the AV  100  determines a maneuver by superimposing each constraint of the set of constraints  1320  on each other constraint of the set of constraints  1320 . The maneuver includes the trajectory  1520  that is independent of the multiple trajectories (e.g., trajectory  198 ). The AV  100  transmits instructions to the control circuit  406  of the AV  100  to override the trajectory  198 . The instructions further cause the AV  100  to traverse the road segment  1500  according to the trajectory  1520  to perform the maneuver. For example, the homotopy extractor  453  determines one or more maneuvers  1308  that can override the trajectory  198  based on the homotopies  1304   a - 1304   n . A maneuver can correspond to an evasive action (e.g., a sudden turn, braking, acceleration, lane change, etc.) to avoid an unsafe or otherwise undesirable outcome (e.g., a collision with the object  416 , running off the road, etc.). In some implementations, the homotopy extractor  453  can plan the maneuver independently from the trajectory  198  and selectively override the execution of the trajectory  198  with the maneuver based on one or more data inputs. Example data inputs can include, for instance, sensor data  504   a  indicating that action may be warranted, commands from a passenger of the AV  100  indicating that an action is to be performed, commands from a user that is remotely monitoring or controlling the AV  100  indicating that an action is to be performed, automated commands from a remote computer system indicating that an action is to be performed, etc. 
       FIG. 14  illustrates an example decision graph  1400  for the AV  100 , in accordance with one or more embodiments. The AV  100  is illustrated and described in more detail with reference to  FIG. 1 . In some implementations, the homotopy extractor  453  determines whether certain homotopies are “feasible” or “not feasible” based on the decision graph  1400 . The homotopy extractor  453  is illustrated and described in more detail with reference to  FIG. 4B . As an illustrative example, the simplified decision graph  1400  is shown in  FIG. 14 . 
     In an embodiment, determining that the AV  100  can traverse the road segment  1500  in accordance with a subset of the multiple homotopies (e.g., by performing a maneuver) includes generating, by the at least one processor  146 , the decision graph  1400  based on the subset of the multiple homotopies. The road segment  1500  illustrated and described in more detail with reference to  FIG. 1 . The processor  146  is illustrated and described in more detail with reference to  FIG. 1 . The decision graph  1400  is illustrated and described in more detail with reference to  FIG. 14 . The subset of the multiple homotopies is described in more detail with reference to  FIG. 13 . The decision graph  1400  includes multiple nodes  1402 . Each node corresponds to a different maneuver. 
     In an embodiment, the decision graph  1400  includes several interconnected nodes  1402 , each corresponding to a different respective subset of the set of constraints  1302 . The nodes can be arranged hierarchically (e.g., according to different tiers of levels) and according to one or more branches, where a “child” node inherits the constraints associated with its “parent” node and additionally includes one or more additional constraints. In some implementations, the decision graph  1400  can be similar to the directed graph  1000  shown in  FIG. 10 . The homotopy extractor  453  can determine the feasibility of the AV  100  traversing to the destination  199  according to the constraints associated with each node, beginning from the node having the highest level or tier, and progressing through the nodes of successively lower and levels or tiers. The destination  199  is illustrated and described in more detail with reference to  FIG. 1 . If the homotopy extractor  453  determines that it is not feasible to adhere to the constraints associated with a particular node, the homotopy extractor  453  can refrain from assessing the feasibility of that node&#39;s child nodes. 
     For example, referring to  FIG. 14 , the homotopy extractor  453  determines that it is feasible to traverse to the destination  199  according to the constraints associated with the highest level node  1402   a . Based on this determination, the homotopy extractor  453  subsequently assesses the feasibility each of the child nodes  1402   b  and  1402   c , and determines that it is not feasible to traverse to the destination  199  according to the constraints associated with the node  1402   b , but that it is feasible to traverse to the destination  199  according to the constraints associated with the node  1402   c . Based on this determination, the homotopy extractor  453  refrains from assessing the feasibility of any of the nodes that are dependent from the node  1402   b , and continues assessing the feasibility of the nodes that are dependent from the node  1402   c . The process described above can continue until each of the nodes in the decision graph  1400  have been assessed or omitted from assessment (due to a “not feasible” parent node). 
     In some implementations, the homotopy extractor  453  can generate one or more candidate trajectories (to determine a maneuver) based on the nodes that were determined to be “feasible.” For example, referring to  FIG. 14 , the homotopy extractor  453  can generate one or more candidate trajectories for each of the nodes  1402   a ,  1402   d ,  1402   e ,  1402   f , and/or  1402   g . In some implementations, the homotopy extractor  453  can generate one or more candidate trajectories based on the nodes that were determined to be “feasible” and that also do not have any child nodes. For example, referring to  FIG. 14 , the homotopy extractor  453  can generate one or more candidate trajectories for each of the nodes  1402   e  and  1402   g . As described above, the homotopy extractor  453  can determine a feasibility for each of the nodes according to a first degree of precision, and generate candidate trajectories according to second higher degree of precision. 
       FIG. 15  is a block diagram illustrating an example maneuver for the AV  100 , in accordance with one or more embodiments. The AV  100  is illustrated and described in more detail with reference to  FIG. 1 . In an embodiment, at least some of the set of constraints  1302  specify that the AV  100  perform certain operations or tasks. The set of constraints  1302  is illustrated and described in more detail with reference to  FIG. 13 . For instance, a constraint can specify that an AV  100  perform a particular maneuver. In an embodiment, performing the maneuver includes operating the AV  100  to a particular location relative to the object  416  to avoid a potential collision. For example, a constraint can specify that the AV  100  change lanes on a road at a particular time and location. As another example, a constraint can specify that the AV  100  remain in its current location at a particular time and location. 
     In an embodiment, the set of constraints  1302  includes station-based constraints that are parameterized, by the at least one processor  146 , over time using the sensor data  504   a . The object  416  and the vehicles  193 ,  1504  are sometimes referred to as “agents.” To be able to describe constraints representing where the agents are located, and what a collision of the AV  100  with these agents represents, each agent is converted into a station-based and spatial-based obstacle. A station-based constraint is parameterized over time. Further detail regarding the homotopy extractor  503 , and its extraction and grouping of constraints is described in reference to  FIGS. 13-14 . The set of constraints  1302  also includes spatial-based constraints that are parameterized, by the at least one processor  146 , over station and time using the sensor data  504   a . The parameterization of the constraints is performed by sampling, described in more detail with reference to  FIG. 13 . 
     In an embodiment, determining the maneuver includes generating, by the at least one processor  146 , a union of the station-based constraints and the spatial-based constraints to provide the maneuver. For example, the union of the station-based constraints and the spatial-based constraints is an operation using which the station-based constraints and the spatial-based constraints are combined and related to each other. In an embodiment, each of the station-based constraints and the spatial-based constraints are stored and manipulated as matrices. The union of two such matrices is obtained by applying the operation to entries of each pair of elements to obtain the corresponding matrix union. 
     In an embodiment, performing the maneuver includes positioning, by the control circuit  406 , the AV  100  ahead of the two moving vehicles  193 ,  1504  while traversing the road segment  1500 . The control circuit  406  is illustrated and described in more detail with reference to  FIG. 4 . For example, a constraint can specify that the AV  100  overtake the vehicle  1504  at a particular time and location. In an embodiment, performing the maneuver includes positioning, by the control circuit  406 , the AV  100  behind two moving objects (e.g., the two moving vehicles  193 ,  1504 ) while traversing the road segment  1500 . For example, a constraint can specify that the AV  100  remain behind the vehicle  193  at a particular time and location. As another example, a constraint can specify that the AV  100  wait for the vehicle  193  or a pedestrian  192  to clear the path of the AV  100  before proceeding further along the trajectory  1520 . 
     In an embodiment, performing the maneuver includes positioning, by the control circuit  406 , the AV  100  between two moving objects (the two moving vehicles  193 ,  1504 ) while traversing the road segment  1500 . For example, a constraint can specify that the AV  100  proceed along the trajectory  1520  prior to the vehicle  193  or a pedestrian entering the lane  1512 . 
       FIG. 16  is a flow diagram illustrating a process for operation of a vehicle, in accordance with one or more embodiments. The AV  100  is illustrated and described in more detail with reference to  FIG. 1 . In an embodiment, the process of  FIG. 16  is performed by the homotopy extractor  453  or the sample-based maneuver realizer  454  of the AV  100 , illustrated and described in more detail with reference to  FIG. 4B . Other entities, for example, the server  136 , perform some or all of the steps of the process in other embodiments. The server  136  is illustrated and described in more detail with reference to  FIG. 1 . Likewise, embodiments may include different and/or additional steps, or perform the steps in different orders. 
     The AV  100  uses at least one processor  146  of the AV  100  to generate ( 1604 ) multiple, initial trajectories based on a road segment  1500  (including lanes  1512 ,  1516 ) traveled by the AV  100 . The processor  146  is illustrated and described in more detail with reference to  FIG. 1 . The lanes  1512 ,  1516  are illustrated and described in more detail with reference to  FIG. 15 . The process for trajectory generation is illustrated and described in more detail with reference to  FIG. 10 . 
     The AV  100  uses the processor  146  to receive ( 1608 ) sensor data  504   a  from at least one sensor  121  of the AV  100 . The sensor  121  is illustrated and described in more detail with reference to  FIG. 10 . The LiDAR output data  504   a  is illustrated and described in more detail with reference to  FIG. 5 . The AV  100 &#39;s use of sensor data is also described in more detail with reference to  FIG. 4B . The AV  100  is traveling the road segment (lane  1516 ) in accordance with a trajectory  198  of the multiple trajectories. The trajectory  198  is illustrated and described in more detail with reference to  FIG. 1 . 
     The AV  100  uses the processor  146  to predict ( 1612 ) a potential collision between the AV  100  and an object  416  moving on the road segment  1500  based on the sensor data  504   a  and the trajectory  198 . The object  416  is illustrated and described in more detail with reference to  FIGS. 4, 15 . 
     The AV  100  uses the processor  146  to determine ( 1616 ) a set of constraints  1302  for the AV  100  to avoid the potential collision. The set of constraints  1302  is illustrated and described in more detail with reference to  FIG. 13 . The set of constraints  1302  is determined based on the sensor data  504   a . In an embodiment, the set of constraints includes hard logical constraints and soft logical constraints. Hard logical constraints are those that that the AV  100  must obey, for example, to avoid a potential collision or to reach the destination  199 . The destination  199  is illustrated and described in more detail with reference to  FIG. 1 . Soft logical constraints are those that the AV  100  should obey but can violate, for example, to avoid a potential collision. Soft logical constraints are described in more detail with reference to  FIG. 4B . For example, at least some of the set of constraints  1302  can be soft logical constraints (e.g., the AV  100  should try to but does not necessarily need to adhere to soft logical constraints while traversing to the destination  199 ). 
     The AV  100  uses the processor  146  to determine ( 1620 ) a maneuver for the AV  100  by superimposing each constraint of the set of constraints  1302  on each other constraint of the set of constraints  1302 . The maneuver includes a trajectory  1520  independent of the multiple, initial trajectories. The trajectory  1520  is illustrated and described in more detail with reference to  FIG. 15 . In an embodiment, determining the maneuver includes generating, by the at least one processor  146 , a union of the station-based constraints and the spatial-based constraints to provide the maneuver. For example, the union of the station-based constraints and the spatial-based constraints is an operation using which the station-based constraints and the spatial-based constraints are combined and related to each other. 
     The AV  100  uses the processor  146  to transmit ( 1624 ) instructions to a control circuit  406  of the AV  100 . The control circuit  406  is illustrated and described in more detail with reference to  FIG. 1 . The instructions instruct the control circuit  406  to override the initial trajectory  198 . The instructions further instruct the control circuit  406  to traverse the road segment  1500  according to the trajectory  1520  to perform the maneuver. 
     In the foregoing description, embodiments of the invention have been described with reference to numerous specific details that may vary from implementation to implementation. The description and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense. The sole and exclusive indicator of the scope of the invention, and what is intended by the applicants to be the scope of the invention, is the literal and equivalent scope of the set of claims that issue from this application, in the specific form in which such claims issue, including any subsequent correction. Any definitions expressly set forth herein for terms contained in such claims shall govern the meaning of such terms as used in the claims. In addition, when we use the term “further including,” in the foregoing description or following claims, what follows this phrase can be an additional step or entity, or a sub-step/sub-entity of a previously-recited step or entity. 
     Additional Examples 
     Example implementations of the features described herein are provided below. 
     Example 1: A method includes: generating, by at least one processor of a vehicle, a plurality of trajectories for the vehicle based on a road segment traveled by the vehicle; receiving, by the at least one processor, sensor data from at least one sensor of the vehicle, the vehicle traveling the road segment in accordance with a first trajectory of the plurality of trajectories; predicting, by the at least one processor, a potential collision between the vehicle and an object moving on the road segment based on the sensor data and the first trajectory; determining, by the at least one processor, a set of constraints for the vehicle to avoid the potential collision, the set of constraints determined based on the sensor data; determining, by the at least one processor, a maneuver for the vehicle by superimposing each constraint of the set of constraints on each other constraint of the set of constraints, the maneuver including a second trajectory independent of the plurality of trajectories; and transmitting, by the at least one processor, instructions to a control circuit of the vehicle to: override the first trajectory; and traverse the road segment according to the second trajectory to perform the maneuver. 
     Example 2: The method of Example 1, where the set of constraints includes environmental constraints indicating at least one of a drivable area of the road segment or lane markings of the road segment. 
     Example 3: The method of any one of the preceding Examples, where the set of constraints includes: hard logical constraints that the AV must obey to avoid the potential collision; and soft logical constraints that the AV can violate to avoid the potential collision. 
     Example 4: The method of any one of the preceding Examples, where the set of constraints includes: station-based constraints that are parameterized, by the at least one processor, over time using the sensor data; and spatial-based constraints that are parameterized, by the at least one processor, over station and time using the sensor data. 
     Example 5: The method of any one of the preceding Examples, where determining the maneuver includes generating, by the at least one processor, a union of the station-based constraints and the spatial-based constraints to provide the maneuver. 
     Example 6: The method of any one of the preceding Examples, where determining the set of constraints is performed at a first frequency and determining the maneuver to generate the second trajectory is performed at a second frequency higher than the first frequency. 
     Example 7: The method of any one of the preceding Examples, where performing the maneuver includes operating the vehicle to a particular location relative to the object. 
     Example 8: The method of any one of the preceding Examples, the method also including determining, by the at least one processor, a plurality of homotopies, where each homotopy of the plurality of homotopies includes a different respective combination of the set of constraints, and where determining the maneuver is based on at least some of the plurality of homotopies. 
     Example 9: The method of any one of the preceding Examples, the method also including: predicting, by the at least one processor, a motion of the vehicle on the road segment according to a degree of precision; and determining, by the at least one processor, that the vehicle can traverse the road segment in accordance with a subset of the plurality of homotopies based on the predicted motion, where determining the maneuver is further based on the subset of the plurality of homotopies. 
     Example 10: The method of any one of the preceding Examples, where determining that the vehicle can traverse the road segment in accordance with the subset of the plurality of homotopies includes generating, by the at least one processor, a decision graph based on the subset of the plurality of homotopies, the decision graph including a plurality of nodes, each node corresponding to a different maneuver. 
     Example 11: The method of any one of the preceding Examples, where determining the maneuver to generate the second trajectory includes: assigning, by the at least one processor, a respective quality metric to each homotopy of the plurality of homotopies; and selecting, by the at least one processor, the second trajectory based on the respective quality metric. 
     Example 12: The method of any one of the preceding Examples, where the respective quality metric is determined based on at least one of: a predicted time for traversing the road segment in accordance with the each homotopy; a predicted safety of a passenger of the vehicle while traversing the road segment in accordance with the each homotopy; or a predicted comfort of the passenger while traversing the road segment in accordance with the each homotopy. 
     Example 13: The method of any one of the preceding Examples, where performing the maneuver includes positioning, by the control circuit, the vehicle ahead of two moving objects while traversing the road segment. 
     Example 14: The method of any one of the preceding Examples, where performing the maneuver includes positioning, by the control circuit, the vehicle behind two moving objects while traversing the road segment. 
     Example 15: The method of any one of the preceding Examples, where performing the maneuver includes positioning, by the control circuit, the vehicle between two moving objects while traversing the road segment. 
     Example 16: The method of any one of the preceding Examples, where superimposing each constraint of the set of constraints on each other constraint of the set of constraints includes sampling, by the at least one processor, each constraint of the set of constraints with respect to time in accordance with changes in the sensor data to provide the maneuver. 
     Example 17: A vehicle includes: one or more computer processors; and one or more non-transitory storage media storing instructions which, when executed by the one or more computer processors, cause the one or more computer processors to perform the method of any one of Examples 1-16. 
     Example 18: One or more non-transitory storage media storing instructions which, when executed by the one or more computer processors, cause the one or more computer processors to perform the method of any one of Examples 1-16.