Optimal planner switching method for three-point turns of autonomous vehicles
阅读说明:本技术 自动驾驶车辆的三点转弯的最优规划器切换方法 (Optimal planner switching method for three-point turns of autonomous vehicles ) 是由 马霖 朱帆 许昕 于 2018-12-26 设计创作,主要内容包括:在自动驾驶车辆(ADV)的操作中规划并执行三点转弯。确定从起点并经过终点的候选路线,起点和终点位于与相反行进方向相关的车道中。候选路线被分类为部分重叠的第一段、第二段和第三段。与候选路线相关的总成本至少部分地基于第一段和第二段来确定。确定总成本是否低于阈值成本。响应于确定总成本低于阈值成本,基于候选路线规划三点转弯。此外,至少部分地基于规划的三点转弯来生成驾驶信号以控制ADV的操作。(Three-point turns are planned and executed in the operation of an autonomous vehicle (ADV). Candidate routes are determined from a starting point and through an end point, the starting point and the end point being located in lanes associated with opposite directions of travel. The candidate route is classified into a first segment, a second segment, and a third segment that partially overlap. A total cost associated with the candidate route is determined based at least in part on the first segment and the second segment. It is determined whether the total cost is below a threshold cost. In response to determining that the total cost is below the threshold cost, a three-point turn is planned based on the candidate route. Further, a driving signal is generated to control operation of the ADV based at least in part on the planned three-point turn.)
1. A computer-implemented method of planning a three-point turn in operating an autonomous vehicle (ADV), the method comprising:
determining a candidate route from a starting point to an ending point, the starting point being within a first lane associated with a first direction of travel and the ending point being within a second lane associated with a second direction of travel, the second direction of travel being opposite the first direction of travel;
classifying the candidate route into a first segment associated with the first direction of travel, a second segment associated with a three-point turn zone, and a third segment associated with the second direction of travel;
determining a total cost associated with the candidate route based at least in part on the first segment and the second segment; and
in response to determining that the total cost is below a threshold cost, planning the three-point turn based on the candidate route to drive the ADV to make the three-point turn.
2. The method of claim 1, wherein determining the candidate route comprises performing an a-Star search on map data, wherein both the first lane and the second lane associated with the first direction of travel and the second direction of travel, respectively, are considered searchable and connectable.
3. The method of claim 1, wherein the total cost includes at least an obstacle cost and a remaining lane length cost.
4. The method of claim 3, wherein the obstacle cost is determined based at least in part on a distance between the ADV and each of one or more obstacles near the candidate route.
5. The method of claim 3, wherein the remaining lane length cost is determined based at least in part on a length of the first segment.
6. The method of claim 1, further comprising completing the planned three-point turn when a difference between a heading of the ADV and a reference heading is less than a threshold heading difference.
7. The method of claim 6, further comprising switching operation of the ADV back into a normal operating mode after completing the planned three-point turn.
8. A non-transitory machine-readable medium having instructions stored thereon, which when executed by a processor, cause the processor to perform operations for planning a three-point turn in operating an autonomous vehicle (ADV), the operations comprising:
determining a candidate route from a starting point to an ending point, the starting point being within a first lane associated with a first direction of travel and the ending point being within a second lane associated with a second direction of travel, the second direction of travel being opposite the first direction of travel;
classifying the candidate route into a first segment associated with the first direction of travel, a second segment associated with a three-point turn zone, and a third segment associated with the second direction of travel;
determining a total cost associated with the candidate route based at least in part on the first segment and the second segment; and
in response to determining that the total cost is below a threshold cost, planning the three-point turn based on the candidate route to drive the ADV to make the three-point turn.
9. The machine-readable medium of claim 8, wherein determining the candidate route comprises performing an a-Star search on map data, wherein both the first lane and the second lane associated with the first direction of travel and the second direction of travel, respectively, are considered searchable and connectable.
10. The machine-readable medium of claim 8, wherein the total cost includes at least an obstacle cost and a remaining lane length cost.
11. The machine-readable medium of claim 10, wherein the obstacle cost is determined based at least in part on a distance between the ADV and each of one or more obstacles near the candidate route.
12. The machine-readable medium of claim 10, wherein the remaining lane length cost is determined based at least in part on a length of the first segment.
13. The machine-readable medium of claim 8, the operations further comprising completing the planned three-point turn when a difference between a heading of the ADV and a reference angle is less than a threshold heading difference.
14. The machine readable medium of claim 13, the operations further comprising switching operation of the ADV back into a normal operating mode after completing the planned three-point turn.
15. A data processing system comprising:
a processor; and
a memory coupled to the processor to store instructions that, when executed by the processor, cause the processor to perform operations for planning a three-point turn in operating an autonomous vehicle (ADV), the operations comprising:
determining a candidate route from a starting point to an ending point, the starting point being within a first lane associated with a first direction of travel and the ending point being within a second lane associated with a second direction of travel, the second direction of travel being opposite the first direction of travel,
classifying the candidate route into a first segment associated with the first direction of travel, a second segment associated with a three-point turn zone, and a third segment associated with the second direction of travel,
determining a total cost associated with the candidate route based at least in part on the first segment and the second segment, an
In response to determining that the total cost is below a threshold cost, planning the three-point turn based on the candidate route to drive the ADV to make the three-point turn.
16. The data processing system of claim 15, wherein determining the candidate route comprises performing an a-Star search on map data, wherein both the first lane and the second lane associated with the first direction of travel and the second direction of travel, respectively, are considered searchable and connectable.
17. The data processing system of claim 15, wherein the total cost includes at least an obstacle cost and a remaining lane length cost.
18. The data processing system of claim 17, wherein the obstacle cost is determined based at least in part on a distance between the ADV and each of one or more obstacles near the candidate route.
19. The data processing system of claim 17, wherein the remaining lane length cost is determined based at least in part on a length of the first segment.
20. The data processing system of claim 15, the operations further comprising completing the planned three-point turn when a difference between a heading of the ADV and a reference angle is less than a threshold heading difference.
21. The data processing system of claim 20, the operations further comprising switching operation of the ADV back into a normal operating mode after completing the planned three-point turn.
Technical Field
Embodiments of the present disclosure relate generally to operating an autonomous vehicle. More specifically, embodiments of the present disclosure relate to planning three-point turns of an autonomous vehicle.
Background
Vehicles operating in an autonomous driving mode (e.g., unmanned) may relieve occupants, particularly the driver, from some driving-related duties. When operating in an autonomous driving mode, the vehicle may be navigated to various locations using onboard sensors, allowing the vehicle to travel with minimal human interaction or in some cases without any passengers.
Three-point turns (i.e., the reversal of the direction of travel of the vehicle at a location on the map not designated as a U-turn) are complex motions in autonomous vehicles. The planning and routing of three-point turns may be very different from the planning and routing of normal operation of an autonomous vehicle. Deciding whether to switch between the two planning and routing modes can be a challenging task.
Disclosure of Invention
In an aspect of the present disclosure, a computer-implemented method for planning a three-point turn in operating an autonomous vehicle (ADV) is provided. The method comprises the following steps: determining a candidate route from a starting point to an ending point, the starting point being within a first lane associated with a first direction of travel and the ending point being within a second lane associated with a second direction of travel, the second direction of travel being opposite the first direction of travel; classifying the candidate route into a first segment associated with a first direction of travel, a second segment associated with a three-point turn zone, and a third segment associated with a second direction of travel; determining a total cost associated with the candidate route based at least in part on the first segment and the second segment; and in response to determining that the total cost is below the threshold cost, planning a three-point turn based on the candidate route to drive the ADV to make the three-point turn.
In another aspect of the disclosure, a non-transitory machine-readable medium is provided having instructions stored therein to perform operations for planning a three-point turn in operating an autonomous vehicle (ADV), the operations including determining a candidate route from a starting point to an ending point, the starting point being in a first lane associated with a first direction of travel and the ending point being in a second lane associated with a second direction of travel, the second direction of travel being opposite the first direction of travel; classifying the candidate route into a first segment associated with a first direction of travel, a second segment associated with a three-point turn zone, and a third segment associated with a second direction of travel; determining a total cost associated with the candidate route based at least in part on the first segment and the second segment; and in response to determining that the total cost is below the threshold cost, planning a three-point turn based on the candidate route to drive the ADV to make the three-point turn.
In another aspect of the present disclosure, a data processing system is provided. The system includes a processor; and a memory coupled to the processor to store instructions that, when executed by the processor, cause the processor to perform operations for planning a three-point turn in operating an autonomous vehicle (ADV), the operations comprising: determining a candidate route from a starting point to an ending point, the starting point being within a first lane associated with a first direction of travel and the ending point being within a second lane associated with a second direction of travel, the second direction of travel being opposite the first direction of travel; classifying the candidate route into a first segment associated with a first direction of travel, a second segment associated with a three-point turn zone, and a third segment associated with a second direction of travel; determining a total cost associated with the candidate route based at least in part on the first segment and the second segment; and in response to determining that the total cost is below the threshold cost, planning a three-point turn based on the candidate route to drive the ADV to make the three-point turn.
Drawings
Embodiments of the present disclosure are illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings in which like reference numerals refer to similar elements.
FIG. 1 is a block diagram illustrating a networked system according to one embodiment.
FIG. 2 is a block diagram illustrating an example of an autonomous vehicle according to one embodiment.
Fig. 3A-3B are block diagrams illustrating an example of a perception and planning system for use by an autonomous vehicle, according to one embodiment.
Fig. 4 is a diagram illustrating a typical three-point turn driving scenario.
FIG. 5 is a block diagram illustrating various modules according to one embodiment.
FIG. 6 is a diagram illustrating a planned three-point turn route, according to one embodiment.
FIG. 7 is a flow diagram illustrating an exemplary method of planning a three-point turn in operating an autonomous vehicle (ADV), according to one embodiment.
FIG. 8 is a block diagram illustrating a data processing system in accordance with one embodiment.
Detailed Description
Various embodiments and aspects of the disclosure will be described with reference to details discussed below, and the accompanying drawings will illustrate the various embodiments. The following description and drawings are illustrative of the present disclosure and are not to be construed as limiting the present disclosure. Numerous specific details are described to provide a thorough understanding of various embodiments of the present disclosure. However, in certain instances, well-known or conventional details are not described in order to provide a concise discussion of embodiments of the present disclosure.
Reference in the specification to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the disclosure. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment.
According to some embodiments, a three-point turn is planned and executed in the operation of an autonomous vehicle (ADV). A candidate route is determined from a starting point and through an ending point, the starting point being in a first lane associated with a first direction of travel and the ending point being in a second lane associated with a second direction of travel, the second direction of travel being opposite the first direction of travel. The candidate routes are classified into partially overlapping first, second, and third segments, the first segment being associated with a first direction of travel, the second segment being associated with a three-point turn zone, and the third segment being associated with a second direction of travel. A total cost associated with the candidate route is determined based at least in part on the first segment and the second segment using a predetermined cost function. It is determined whether the total cost is below a threshold cost. In response to determining that the total cost is below the threshold cost, a three-point turn is planned based on the candidate route. Further, a driving signal is generated to control operation of the ADV based at least in part on the planned three-point turn.
In one embodiment, determining the candidate route comprises performing a search algorithm, such as an a-Star search, on the map data, wherein both the first lane and the second lane, which are associated with the first direction of travel and the second direction of travel, respectively, are considered searchable and connectable.
In one embodiment, the total cost includes at least an obstacle cost and a remaining lane length cost. The obstacle cost is determined based at least in part on a distance between the ADV and each of the one or more obstacles near the candidate route. The remaining lane length cost is determined based at least in part on the length of the first segment. The remaining lane length refers to the length of the lane remaining in the current lane segment or route segment. That is, the remaining lane length is the distance between the current position of the vehicle and the end of the current lane segment.
In one embodiment, the planned three-point turn is completed when a difference between the heading of the ADV and the reference heading is less than a threshold heading difference. After completing the planned three-point turn, the operation of the ADV switches back into the normal operating mode.
Fig. 1 is a block diagram illustrating an autonomous vehicle network configuration according to one embodiment of the present disclosure. Referring to fig. 1, a network configuration 100 includes an autonomous vehicle 101 that may be communicatively coupled to one or more servers 103-104 through a network 102. Although one autonomous vehicle is shown, multiple autonomous vehicles may be coupled to each other and/or to servers 103-104 through network 102. The network 102 may be any type of network, such as a wired or wireless Local Area Network (LAN), a Wide Area Network (WAN) such as the Internet, a cellular network, a satellite network, or a combination thereof. The servers 103-104 may be any type of server or cluster of servers, such as a network or cloud server, an application server, a backend server, or a combination thereof. The servers 103 to 104 may be data analysis servers, content servers, traffic information servers, map and point of interest (MPOI) servers, or location servers, etc.
Autonomous vehicles refer to vehicles that may be configured to be in an autonomous driving mode in which the vehicle navigates through the environment with little or no input from the driver. Such autonomous vehicles may include a sensor system having one or more sensors configured to detect information related to the operating environment of the vehicle. The vehicle and its associated controller use the detected information to navigate through the environment. Autonomous vehicle 101 may operate in a manual mode, in a fully autonomous mode, or in a partially autonomous mode.
In one embodiment, autonomous vehicle 101 includes, but is not limited to, a perception and
The components 110-115 may be communicatively coupled to each other via an interconnect, bus, network, or combination thereof. For example, the components 110-115 may be communicatively coupled to one another via a Controller Area Network (CAN) bus. The CAN bus is a vehicle bus standard designed to allow microcontrollers and devices to communicate with each other in applications without a host. It is a message-based protocol originally designed for multiplexed electrical wiring within automobiles, but is also used in many other environments.
Referring now to fig. 2, in one embodiment, the
The
In one embodiment, the
Returning to fig. 1, wireless communication system 112 allows communication between autonomous vehicle 101 and external systems such as devices, sensors, other vehicles, and the like. For example, the wireless communication system 112 may be in direct wireless communication with one or more devices, or in wireless communication via a communication network, such as with the servers 103-104 through the network 102. The wireless communication system 112 may use any cellular communication network or Wireless Local Area Network (WLAN), for example, using WiFi, to communicate with another component or system. The wireless communication system 112 may communicate directly with devices (e.g., passenger's mobile device, display device, speaker within the vehicle 101), for example, using infrared links, bluetooth, etc. The user interface system 113 may be part of a peripheral device implemented within the vehicle 101, including, for example, a keypad, a touch screen display device, a microphone, and speakers, among others.
Some or all of the functions of the autonomous vehicle 101 may be controlled or managed by the perception and
For example, a user who is a passenger may specify a start location and a destination of a trip, e.g., via a user interface. The perception and
The perception and
Server 103 may be a data analysis system to perform data analysis services for various customers. In one embodiment, data analysis system 103 includes a data collector 121 and a machine learning engine 122. The data collector 121 collects driving statistics 123 from various vehicles (autonomous vehicles or regular vehicles driven by human drivers). The driving statistics 123 include information indicative of driving commands issued (e.g., throttle, brake, steering commands) and responses of the vehicle captured by sensors of the vehicle at different points in time (e.g., speed, acceleration, deceleration, direction). The driving statistics 123 may also include information describing the driving environment at different points in time, such as a route (including a start location and a destination location), MPOI, road conditions, weather conditions, and so forth.
Based on the driving statistics 123, the machine learning engine 122 generates or trains a set of rules, algorithms, and/or predictive models 124 for various purposes. In one embodiment, the algorithm 124 may include a three-point turn planner algorithm and/or a cost function to calculate the cost of making a three-point turn according to embodiments of the present disclosure. The algorithm 124 may then be uploaded to the ADV for real-time use during autonomous driving.
Fig. 3A and 3B are block diagrams illustrating an example of a perception and planning system for use with an autonomous vehicle according to one embodiment. The
Some or all of the modules 301 to 308 may be implemented in software, hardware, or a combination thereof. For example, the modules may be installed in
The location module 301 determines the current location of the autonomous vehicle 300 (e.g., using the GPS unit 212) and manages any data related to the user's trip or route. The positioning module 301 (also referred to as a map and route module) manages any data related to the user's journey or route. The user may, for example, log in via a user interface and specify a starting location and destination for the trip. The positioning module 301 communicates with other components of the
Based on the sensor data provided by
The
For each object, the
For each subject, the decision module 304 makes a decision on how to treat the subject. For example, for a particular object (e.g., another vehicle in a crossing route) and metadata describing the object (e.g., speed, direction, turn angle), the decision module 304 decides how to encounter the object (e.g., cut, yield, stop, exceed). The decision module 304 may make such a decision according to a rule set, such as traffic rules or driving
The
Based on the decisions for each of the perceived objects, the
Based on the planning and control data, the
In one embodiment, the planning phase is performed in a plurality of planning cycles (also referred to as drive cycles), for example, in cycles of 100 milliseconds (ms) each time interval. For each of the planning or driving cycles, one or more control commands will be issued based on the planning and control data. That is, for every 100ms, the
It should be noted that the decision module 304 and the
According to one embodiment, the three-point turn (TPT)
As shown in fig. 4, various factors must be considered when deciding whether to make a three-point turn. When
Referring to FIG. 5, a block diagram 400 of various modules of a three-point turn module is shown, according to one embodiment. Candidate routes from the starting point and through the ending point are determined. The starting point is located within a first lane associated with a first direction of travel (e.g., a current heading direction). The end point is located within a second lane associated with a second direction of travel (e.g., a reverse direction relative to the current direction) that is opposite the first direction of travel. The start and end points may be collectively referred to as
A-Star search is a computer algorithm widely used for path finding and graph traversal, which is the process of finding a path between multiple points (called "nodes"). It is widely used because of its performance and accuracy. A is an informed search algorithm, or best-first search, meaning that it is formulated from a weighted graph: starting from a particular starting node of the graph, it aims to find the path to a given target node with the smallest cost (minimum travel distance, shortest time, etc.). It accomplishes this by: by maintaining a tree of paths originating from the starting node and extending those paths one at a time until their termination criteria are met. In each iteration of its main loop, a needs to determine which of the paths to expand. This is done based on the cost of the path and the cost estimate needed to extend the path all the way to the target. A terminates when it chooses whether the extended path is a path from the starting point to the target or no path that can be extended.
In one embodiment,
In one embodiment, the total cost includes at least an obstacle cost and a remaining lane length cost. The obstacle cost is determined based at least in part on a distance between the ADV and each of one or more obstacles near the candidate route (e.g., obstacles that are a distance from the candidate route that is less than a threshold). The remaining lane length cost is determined based at least in part on the length of the first segment. In particular, the total cost may be determined based on a cost function:
Ctotal=α∑e-λ/dis+βe-/Δs
wherein, α∑ e-λ/disIndicating the cost of the obstacle, i.e., the total obstacle cost obtained by adding the individual obstacle costs of each obstacle all within a predetermined proximity β e-/ΔsRepresents the cost of remaining lane length, parameter dis represents the distance between the vehicle and the obstacle, Delta s (Δ s) represents the remaining lane length, parameters α, λ, β and are adjustable parameters that may be empirically determined.
As shown in the cost function above, when the distance between the vehicle and the obstacle is short, the corresponding obstacle cost will be higher, indicating that it may not be safe to make a three-point turn because of the presence of an obstacle nearby. Similarly, when the remaining lane length is shorter, the cost will be higher because there may not be enough space to make a three-point turn.
In one embodiment, the cost function and related parameters described above may be determined based on a number of driving statistics collected by a data analysis system (such as server 103 of FIG. 1) from a number of vehicles traveling in a similar travel environment or scene. When the total cost is below a predetermined threshold, the
In one embodiment, the planned three-point turn is completed when the completion
Referring to FIG. 6, a diagram of a planned three-point turn route 500 is shown, according to one embodiment. The route 500 begins at a start point 510 within a first lane 520 associated with a first direction of travel and passes through an end point 512 within a second lane 522 associated with a second direction of travel opposite the first direction of travel. The first lane 520 includes subsections 1-4 and the second lane 522 includes subsections 5-7. The route 500 is classified into first, second, and third segments that partially overlap, the first segment being associated with a first direction of travel, the second segment being associated with a three-point turn zone, and the third segment being associated with a second direction of travel. Thus, here, the first section comprises subsections 1 to 4; the second segment comprises subsections 4 and 5; the third section comprises subsections 5 to 7.
Referring to FIG. 7, a flow diagram of an
It should be noted that some or all of the components as shown and described above may be implemented in software, hardware, or a combination thereof. For example, such components may be implemented as software installed and stored in a persistent storage device, which may be loaded into and executed by a processor (not shown) to perform the processes or operations described throughout this application. Alternatively, such components may be implemented as executable code programmed or embedded into dedicated hardware, such as an integrated circuit (e.g., an application specific integrated circuit or ASIC), a Digital Signal Processor (DSP) or Field Programmable Gate Array (FPGA), which is accessible via a respective driver and/or operating system from an application. Further, such components may be implemented as specific hardware logic within a processor or processor core as part of an instruction set accessible by software components through one or more specific instructions.
FIG. 8 is a block diagram illustrating an example of a data processing system that may be used with one embodiment of the present disclosure. For example,
It should also be noted that
In one embodiment, the
Processor 1501 (which may be a low-power multi-core processor socket such as an ultra-low voltage processor) may serve as a main processing unit and central hub for communicating with the various components of the system. Such a processor may be implemented as a system on a chip (SoC).
The input device 1506 may include a mouse, a touch pad, a touch-sensitive screen (which may be integrated with the display device 1504), a pointing device (such as a stylus) and/or a keyboard (e.g., a physical keyboard or a virtual keyboard displayed as part of the touch-sensitive screen). For example, the input device 1506 may include a touch screen controller coupled to a touch screen. Touch screens and touch screen controllers, for example, may detect contact and movement or discontinuities thereof using any of a variety of touch sensitive technologies, including but not limited to capacitive, resistive, infrared, and surface acoustic wave technologies, as well as other proximity sensor arrays or other elements for determining one or more points of contact with the touch screen.
To provide persistent storage for information such as data, applications, one or more operating systems, etc., a mass storage device (not shown) may also be coupled to
The computer-readable storage medium 1509 may also be used to permanently store some of the software functions described above. While the computer-readable storage medium 1509 is shown in an exemplary embodiment to be a single medium, the term "computer-readable storage medium" should be taken to include a single medium or multiple media (e.g., a centralized or distributed database, and/or associated caches and servers) that store the one or more sets of instructions. The term "computer-readable storage medium" shall also be taken to include any medium that is capable of storing or encoding a set of instructions for execution by the machine and that cause the machine to perform any one or more of the methodologies of the present disclosure. The term "computer-readable storage medium" shall accordingly be taken to include, but not be limited to, solid-state memories, and optical and magnetic media, or any other non-transitory machine-readable medium.
The processing module/unit/
It should be noted that while
Some portions of the foregoing detailed description have been presented in terms of algorithms and symbolic representations of operations on data bits within a computer memory. These algorithmic descriptions and representations are the means used by those skilled in the data processing arts to most effectively convey the substance of their work to others skilled in the art. An algorithm is here, and generally, considered to be a self-consistent sequence of operations leading to a desired result. The operations are those requiring physical manipulations of physical quantities.
It should be borne in mind, however, that all of these and similar terms are to be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities. Unless specifically stated otherwise as apparent from the above discussion, it is appreciated that throughout the description, discussions utilizing terms such as those set forth in the appended claims, refer to the action and processes of a computer system, or similar electronic computing device, that manipulates and transforms data represented as physical (electronic) quantities within the computer system's registers and memories into other data similarly represented as physical quantities within the computer system memories or registers or other such information storage, transmission or display devices.
Embodiments of the present disclosure also relate to apparatuses for performing the operations herein. Such a computer program is stored in a non-transitory computer readable medium. A machine-readable medium includes any mechanism for storing information in a form readable by a machine (e.g., a computer). For example, a machine-readable (e.g., computer-readable) medium includes a machine (e.g., computer) readable storage medium (e.g., read only memory ("ROM"), random access memory ("RAM"), magnetic disk storage media, optical storage media, flash memory devices).
The processes or methods depicted in the foregoing figures may be performed by processing logic that comprises hardware (e.g., circuitry, dedicated logic, etc.), software (e.g., embodied on a non-transitory computer readable medium), or a combination of both. Although the processes or methods are described above in terms of some sequential operations, it should be appreciated that some of the operations may be performed in a different order. Further, some operations may be performed in parallel rather than sequentially.
Embodiments of the present disclosure are not described with reference to any particular programming language. It will be appreciated that a variety of programming languages may be used to implement the teachings of embodiments of the disclosure as described herein.
In the foregoing specification, embodiments of the disclosure have been described with reference to specific exemplary embodiments thereof. It will be evident that various modifications may be made thereto without departing from the broader spirit and scope of the disclosure as set forth in the following claims. The specification and drawings are, accordingly, to be regarded in an illustrative sense rather than a restrictive sense.
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