Adaptive cruise control system and method

By installing sensors and controllers on the vehicle, sensing the longitudinal motion characteristics of the forward vehicle and applying ecological gliding control, the problem of insufficient energy efficiency when reducing the vehicle speed is solved, and energy efficiency improvement and drivers are achieved Improved comfort.

CN119489818APending Publication Date: 2025-02-21INT ENGINE INTPROP CO LLC
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Patent Information

Application Number
CN202410992412.1
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Priority Date
2023-08-18
Filing Date
2024-07-23
Publication Date
2025-02-21

AI Technical Summary

Technical Problem

Traditional cruise control systems do not consider energy efficiency when reducing vehicle speeds, resulting in sudden loss of kinetic energy, reducing driver comfort, increasing component wear and fuel consumption.

Method used

By installing sensors and controllers on the vehicle, the longitudinal motion characteristics of the vehicle ahead are sensed, and the energy-saving control strategy is determined based on the head spacing, and ecological gliding control is applied to gradually reduce the vehicle speed and reduce energy consumption.

Benefits of technology

It has achieved a significant improvement in the energy efficiency and other key performance indicators of the vehicle while reducing the distance between the vehicle ahead, improving driver comfort and reducing fuel consumption.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention relates to an adaptive cruise control system and method. A vehicle longitudinal movement control device for controlling longitudinal movement of a vehicle. A vehicle longitudinal motion control apparatus includes at least one sensor configured to sense longitudinal motion of another vehicle in front of the vehicle, and a controller having at least one control module in communication with the at least one sensor. The at least one control module is configured to determine longitudinal motion characteristics of the two vehicles, and a headway between the first vehicle and the second vehicle. The at least one control module is further configured to apply a coasting maneuver to the vehicle based on the determined distance-at-head to reduce the distance between the vehicles and improve the energy efficiency of the vehicle.
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Description

Technical Field

[0001] The present disclosure relates to a vehicle longitudinal motion control system. In particular, the present disclosure relates to a system and method for autonomously or semi-autonomously controlling the longitudinal motion of a vehicle. STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with government support under DE-EE0007767 awarded by the U.S. Department of Energy. The government therefore has certain rights in this invention. Background Art

[0003] Adaptive cruise control (ACC) is a cruise control advanced driver assistance system for road vehicles that automatically adjusts the vehicle speed to maintain a safe distance from the vehicle in front. Control is based on sensor information from onboard sensors. Such systems can use radar or laser sensors and / or cameras. The ACC system automatically slows down the vehicle when it senses that another vehicle in front of the vehicle is traveling at a slower rate. Thereafter, when traffic permits, the ACC system accelerates the vehicle to restore the set rate. ACC technology affects the safety and convenience of the driver, and it increases road capacity by maintaining optimal intervals between vehicles and reducing driver errors. Typically, the ACC system includes a plurality of sensors for monitoring surrounding vehicles. For example, the ACC system may include a radar or optical sensor mounted on the vehicle.

[0004] Predictive cruise control (PCC) modifies vehicle speed based on calculated predictions of other vehicles, roads, various geographic features, and / or weather data. Such systems can make earlier and gentler adjustments to the speed of vehicles with PCC systems, thereby improving safety and passenger comfort.

[0005] Conventional cruise control systems do not consider energy efficiency. Such systems generally focus on maintaining a constant time gap between the host vehicle and the vehicle ahead. Additionally, such systems reduce the speed of the vehicle by applying brakes, which constitutes a sudden loss of kinetic energy. This causes reduced driver comfort, component wear, and increased fuel consumption due to the sudden loss of kinetic energy.

[0006]

[0006] Accordingly, there is an unmet need for arrangements and methods for economically reducing vehicle speed in order to reduce kinetic energy losses and improve energy efficiency and / or motion efficiency. Summary of the invention

[0007] According to one embodiment of a vehicle longitudinal motion control device for controlling the longitudinal motion of a first vehicle, the vehicle longitudinal motion control device has at least one sensor and a controller. At least one sensor is configured to sense the longitudinal motion of a second vehicle in front of the first vehicle. The controller has at least one control module that communicates with at least one sensor. At least one control module is configured to determine the longitudinal motion characteristics of the first vehicle, determine the longitudinal motion characteristics of the second vehicle, and determine the headway between the first vehicle and the second vehicle based on the longitudinal motion characteristics of the first vehicle, the longitudinal motion characteristics of the second vehicle, and at least one vehicle characteristic of the first vehicle. At least one control module is further configured to apply energy-saving maneuvers to the first vehicle based on the determined headway to reduce the distance between the first vehicle and the second vehicle and improve the energy efficiency and / or other key performance indicators (KPIs) of the first vehicle.

[0008] According to another embodiment of the vehicle longitudinal motion control device, the vehicle has a longitudinal motion control device for controlling the longitudinal motion of the vehicle. The vehicle and its longitudinal motion control device include at least one sensor, and a controller, the at least one sensor being configured to sense the longitudinal motion of the vehicle ahead. The controller has at least one control module communicating with the at least one sensor. The at least one control module is configured to determine the longitudinal motion characteristics of the vehicle, determine the longitudinal motion characteristics of the vehicle ahead, and determine the headway between the vehicle and the vehicle ahead based on the longitudinal motion characteristics of the vehicle, the longitudinal motion characteristics of the vehicle ahead, and at least one vehicle characteristic of the vehicle. At least one control module is further configured to apply energy-saving maneuvers to the vehicle based on the determined headway to reduce the distance between the vehicle and the vehicle ahead and improve the energy efficiency of the vehicle.

[0009] According to yet another embodiment of a vehicle longitudinal motion control device, a method for controlling the longitudinal motion of a first vehicle includes several steps. The method includes the steps of providing a vehicle longitudinal motion control device having at least one sensor and a controller, the at least one sensor being configured to sense the longitudinal motion of a second vehicle in front of the first vehicle. The controller has at least one control module in communication with the at least one sensor. The method also includes the steps of configuring at least one control module to determine the longitudinal motion characteristics of the first vehicle. The method includes the further steps of configuring at least one control module to determine the longitudinal motion characteristics of the second vehicle. The method includes the further steps of configuring at least one control module to determine the headway distance between the first vehicle and the second vehicle based on the longitudinal motion characteristics of the first vehicle, the longitudinal motion characteristics of the second vehicle, and at least one vehicle characteristic of the first vehicle. The method includes the further steps of configuring at least one control module to apply an energy-saving maneuver to the first vehicle based on the determined headway distance to reduce the distance between the first vehicle and the second vehicle and improve the energy efficiency of the first vehicle. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 is a graphical representation of an embodiment of a vehicle longitudinal motion control device for a vehicle of the present disclosure as described herein;

[0011] Figure 2 is another graphical representation of a vehicle longitudinal motion control device as described herein;

[0012] Figure 3 is a graph illustrating distance, speed, and acceleration of a vehicle when the apparatus economically regulates longitudinal motion of the vehicle in an energy-saving maneuver as described herein; and

[0013] Figure 4 is a flow chart of an embodiment of a method of economically decelerating a vehicle using the apparatus of the present disclosure as described herein. DETAILED DESCRIPTION

[0014] The embodiments described herein relate to arrangements of a vehicle longitudinal motion control device for efficiently and economically applying energy-saving maneuvers (such as gliding maneuvers) to vehicles and their control logic. The device and method can be applied to various types of passenger vehicles, commercial vehicles, and recreational vehicles, such as highway or semi-trailer trucks, straight trucks, buses, fire trucks, RVs, etc. It is contemplated that the device and method can be applied to vehicles with a transmission system including a diesel, gasoline, or gas fuel engine, and can be applied to vehicles with electric or hybrid electric transmission systems, as non-limiting examples. It is further contemplated that the device and method can be applied to vehicles with manual transmissions, automatic transmissions, automated manual transmissions, continuously variable transmissions, hybrid electric transmissions, and hydraulic transmissions, as non-limiting examples.

[0015] The present longitudinal motion control device and method reduce the energy consumption of a vehicle by applying energy-saving maneuvers (such as coasting maneuvers) to the vehicle via an eco-coasting control module when the vehicle is operated autonomously or semi-autonomously. The eco-coasting control module can be an independent control module, or incorporated into an existing control module (such as an ACC module). The eco-coasting control module has an algorithm that continuously calculates the headway distance between the vehicle and the vehicle in front, an object, or a change in the road (such as a stop light or a turn). The eco-coasting control module reduces fuel or other energy supply and / or cuts off power as desired to allow the vehicle to coast. As a result, the vehicle gradually reduces its rate and does not require subsequent acceleration to recover from a sudden braking maneuver. This results in improved driver comfort and a significant reduction in fuel or energy consumption.

[0016] Now go to Figure 1-Figure 2 , shows a vehicle 10 implementing an embodiment of the present economical vehicle longitudinal motion control device 12. The vehicle longitudinal motion control device 12 includes at least one sensor 14, 16 and a controller 18 for automatically controlling the longitudinal motion of the vehicle 10 based on a leading vehicle 20, another object, vehicle data, the load of the vehicle 10, map data, geographic data, and / or weather data. When approaching a leading vehicle 20 traveling at a slower speed, the controller 18 will implement an eco-gliding maneuver that gradually reduces the speed of the vehicle 10, thereby avoiding the use of sudden brakes, and improving driver comfort, and significantly improving energy efficiency and / or other KPIs. Compared with the conventional cruise control system's braking maneuver, the eco-gliding maneuver can reduce energy consumption by more than 50%.

[0017] As used herein, an eco-gliding maneuver may refer to an energy-saving maneuver in which the vehicle 10 is gliding in a forward direction. An energy-saving maneuver may be a gliding maneuver that involves reducing the fuel or energy supplied to the engine, or cutting off power to one or more components of the drivetrain. During an energy-saving maneuver, the vehicle 10 may reduce, maintain, or increase its speed. For example, if the vehicle 10 is traveling uphill or on a relatively flat road, the vehicle 10 may reduce its speed while gliding. Additionally, for example, if the vehicle 10 is traveling downhill, the vehicle 10 may increase its speed while gliding.

[0018] The vehicle 10 may include onboard sensors, offboard sensors, or other devices in communication with the controller 18 for sensing or otherwise identifying vehicle payload, vehicle longitudinal motion, vehicle GPS location data, tire pressure, fuel supply to the engine or energy supply to the motor, engine, motor and / or drive shaft torque, other vehicle data or characteristics, predicted or expected traffic motion, road or map data, geographic data, and / or weather data. The vehicle 10 may include a distance sensor 14 and / or a vehicle-to-vehicle (V2Va) communication device 16 for communicating with a V2V device 22 of another vehicle 20. The distance sensor 14 may be a direct or indirect radar sensor, a LIDAR sensor, other electromagnetic wavelength measurement and / or an optical sensor. At least one sensor 14, 16 communicates with the controller 18. The vehicle 10 may include only one sensor or two or more sensors. As non-limiting examples, the vehicle longitudinal motion characteristic may include vehicle longitudinal displacement, vehicle longitudinal velocity, vehicle longitudinal acceleration, and / or vehicle longitudinal jerk. In this sense, jerk is defined as the first time derivative of acceleration, the second time derivative of velocity, and the third time derivative of position.

[0019] The controller 18 may also communicate with one or more remote databases 24 via a network 26. The database(s) 24 may include map data, geographic data, traffic data, and / or weather data. The controller 18 may also communicate with a user interface. The driver may enter a glide command in the user interface to initiate a glide procedure.

[0020] The controller 18 includes one or more modules. For example, the controller 18 may include an ACC module 28 having an adaptive cruise control (ACC) algorithm, a PCC module 30 having a predictive cruise control (PCC) algorithm, and an eco-coasting control module 32 having an eco-coasting algorithm. The modules 28, 30, 32 may be integrated with each other, or may not be integrated with each other. For example, the ACC module 28 may include an eco-coasting algorithm therein.

[0021] The ACC module 28 detects the vehicle 20 ahead. The ACC algorithm commands the ACC target to accelerate or decelerate (e.g., 1 m / s 2 The ACC target acceleration or deceleration is calculated to maintain a safe and reasonable desired time gap (e.g., a three-second time gap).

[0022] The PCC module 30 determines future road parameters, such as whether there is an uphill or downhill section ahead. The PCC algorithm commands a PCC target acceleration or deceleration, which may be different from the ACC target acceleration or deceleration.

[0023] The eco-coasting control module 32 detects and calculates the headway between the vehicle 10 and the vehicle 20 ahead. The eco-coasting algorithm calculates the expected headway, coasting acceleration or deceleration, and / or coasting time for the vehicle 20 ahead, an object, or a road event (such as downhill travel, a turn, a stop, etc.). For example, if it is determined that the vehicle 20 ahead is decelerating, the eco-coasting algorithm will calculate the headway to the vehicle 20 ahead in order to perform an energy-saving maneuver (such as a coasting maneuver). The eco-coasting control module 32 may allow the vehicle 10 to coast until a preset distance and / or travel time is reached from the vehicle 20 ahead. The controller 18 will seamlessly switch between the modules 28, 30, and 32 to control the longitudinal motion of the vehicle.

[0024] The headway distance can be calculated continuously by the eco-coasting module 32. eco (h 生态 ), or in other words, the taxiing head distance threshold, can be calculated using the following algorithm: h eco (v0,v f , v1,a,c)=V -1 (v f )+s f (v0,v f , a, c)-v1t f (v0,v f , a, c) Among them, V -1is the inverse of the range policy function from the ACC algorithm, which sets the desired distance or range to the leading vehicle 20, v0 is the initial velocity of the vehicle 10 at the first time, v1 is the velocity of the vehicle 10 at the second time, and v f is the sensed or calculated speed of the leading vehicle 20, s f is the position of the rear of the preceding vehicle 20, t f is the glide time calculated by the eco-glide module as a function of acceleration, vehicle characteristics, drag, headwind, and geography, a is a function of the weight of the vehicle 10 and is given by , and c is a function of the air resistance of the first vehicle and is given by The elevation of the road φ may be sensed and / or determined as an average of the elevations of the front of the vehicle 10 .

[0025] Accordingly, when the altitude is constant, the taxiing speed of the vehicle 10 is can be simplified to the following equation:

[0026] Now go to Figure 3 , shows a graph illustrating an eco-gliding maneuver of the vehicle longitudinal motion control device 12. The graph illustrates the differences between a conventional braking maneuver and an eco-gliding maneuver in relation to distance, speed and acceleration. With respect to the distance or headway h, the calculated headway is shown as a dotted line, the upper line starting slightly below 200 meters represents the eco-approach design of the vehicle longitudinal motion control device 12, and the lower line represents the conventional braking approach. It can be seen that under the eco-approach, the vehicle 10 approaches the leading vehicle 20 more gradually. With respect to speed, the double solid and dotted lines represent the leading vehicle 20, the line that gradually slopes downward represents the eco-approach, and the line that suddenly drops in speed around 18 seconds represents the conventional braking approach. With respect to acceleration, the upper line with a small but persistent drop in acceleration represents the eco-approach, and the line with a sharp parabolic drop in acceleration represents the conventional braking approach. Thus, under the eco-method, the vehicle longitudinal motion control device 12 calculates the required headway, initiates the coasting of the vehicle 10, and accordingly allows the vehicle 10 to gradually approach the leading vehicle 20 until the desired headway distance (e.g., time gap and / or distance) is reached to the leading vehicle 20. Avoiding the abrupt braking procedure of the conventional method, and thereby avoiding subsequent acceleration, significantly reduces energy usage.

[0027] Now go to Figure 4, a flow chart 40 of a method of controlling the longitudinal motion of a vehicle 10 using a vehicle longitudinal motion control device 12 is shown. At step 42, the controller 18 determines the velocity of the preceding vehicle 18. At step 44, the controller 18 also determines the velocity of the vehicle 10. At step 46, the controller 18 also determines the elevation or other geographic data of the road. The controller 18 may additionally determine any other desired vehicle characteristics, headwinds, map data, weather data, etc. At step 48, the controller 18 uses the eco-coasting control module 32 to calculate the headway or headway distance required to perform an energy-saving maneuver (such as a coasting maneuver). At step 50, the controller 18 will query the eco-coasting control module 32 whether the calculated headway distance is greater than the current distance between the vehicles 10, 20. If the calculated headway distance is less than the current distance between the vehicles 10, 20, then at step 52, the controller 18 will continue to utilize the current control module, which may be the ACC module 28 or the PCC module 30. If the calculated headway distance is greater than the current distance between the vehicles 10 , 20 , then at step 54 , the controller 18 will initiate an energy saving maneuver (such as a coasting maneuver).

[0028] Although the illustrative arrangement and control logic for implementing the economical vehicle longitudinal motion control device have been described with respect to at least one embodiment, as previously demonstrated, these arrangements and methods can be further modified within the spirit and scope of the present disclosure. Therefore, the present application is intended to cover any changes, uses or adaptations of the arrangements and methods using their general principles. Further, the present application is intended to cover deviations from the present disclosure within known or customary practices in the relevant field of the present disclosure, and it falls within the limitations of the appended claims.

Claims

1. A vehicle longitudinal motion control device for controlling the longitudinal motion of a first vehicle, comprising: at least one sensor configured to sense longitudinal movement of a second vehicle in front of the first vehicle; as well as a controller having at least one control module in communication with the at least one sensor, the at least one control module being configured to: determining longitudinal motion characteristics of the first vehicle; determining a longitudinal motion characteristic of the second vehicle; determining a headway distance between the first vehicle and the second vehicle based on a longitudinal motion characteristic of the first vehicle, a longitudinal motion characteristic of the second vehicle, and at least one vehicle characteristic of the first vehicle; as well as An energy-saving maneuver is applied to the first vehicle based on the determined headway distance to reduce the distance between the first vehicle and the second vehicle and to improve energy efficiency of the first vehicle.

2. The vehicle longitudinal motion control device according to claim 1, characterized in that: The longitudinal motion characteristic of the first vehicle is at least one of: longitudinal displacement, longitudinal velocity, longitudinal acceleration, and longitudinal jerk; and The longitudinal motion characteristic of the second vehicle is at least one of: longitudinal displacement, longitudinal velocity, longitudinal acceleration, and longitudinal jerk.

3. The vehicle longitudinal motion control device according to claim 2, characterized in that: At least one of the following: The energy-saving maneuver further comprises a gliding maneuver; and The headway distance is further based on the elevation of the road.

4. The vehicle longitudinal motion control device according to claim 3, characterized in that: The at least one control module includes an eco-coasting control module having an eco-coasting algorithm for determining the headway distance.

5. The vehicle longitudinal motion control device according to claim 4, characterized in that: The eco-coasting control module determines whether the headway distance is greater than a current distance between the first vehicle and the second vehicle, and further, if the headway distance is greater than the current distance, the eco-coasting control module is configured to apply the energy-saving maneuver to the first vehicle.

6. The vehicle longitudinal motion control device according to claim 5, characterized in that: The at least one control module further includes at least one of an adaptive cruise control (ACC) module and a predictive cruise control (PCC) module, and further, if the headway distance is less than the current distance between the first vehicle and the second vehicle, the controller is configured to apply one of the ACC module and the PCC module.

7. The vehicle longitudinal motion control device according to claim 1, characterized in that: The at least one control module determines the headway distance by the following function: h eco (v0,v f ,v1,a,c)=V -1 (in f )+s f (v0,v f ,a,c)-v1t f (v0,v f ,a,c) Among them, V -1 is the inverse of the range strategy function, v0 is the initial velocity of the first vehicle at the first time, v1 is the subsequent velocity of the first vehicle at the second time, v f is the speed of the second vehicle, s f is the position of the second transport, t f is the coasting time, a is a function of the weight of the first vehicle, and c is a function of the air resistance of the first vehicle.

8. A vehicle having a longitudinal motion control device, the motion control device being used to control the longitudinal motion of the vehicle, the vehicle comprising: at least one sensor configured to sense longitudinal motion of a leading vehicle; as well as a controller having at least one control module in communication with the at least one sensor, the at least one control module being configured to: determining longitudinal motion characteristics of the vehicle; determining longitudinal motion characteristics of the leading vehicle; determining a headway distance between the vehicle and the leading vehicle based on a longitudinal motion characteristic of the vehicle, a longitudinal motion characteristic of the leading vehicle, and at least one vehicle characteristic of the vehicle; as well as An energy-saving maneuver is applied to the vehicle based on the determined headway to reduce the distance between the vehicle and the leading vehicle and improve energy efficiency of the vehicle.

9. The vehicle according to claim 8, characterized in that: The longitudinal motion characteristic of the vehicle is at least one of: longitudinal displacement, longitudinal velocity, longitudinal acceleration, and longitudinal jerk; and The longitudinal motion characteristic of the leading vehicle is at least one of the following: longitudinal displacement, longitudinal velocity, longitudinal acceleration and longitudinal jerk.

10. The vehicle according to claim 9, characterized in that: At least one of the following: The energy-saving maneuver further comprises a gliding maneuver; and The headway distance is further based on the elevation of the road.

11. The vehicle according to claim 10, characterized in that: The at least one control module includes an eco-coasting control module having an eco-coasting algorithm for determining the headway distance.

12. The vehicle according to claim 11, characterized in that: The eco-coasting control module determines whether the headway distance is greater than a current distance between the vehicle and the leading vehicle, and further, if the headway distance is greater than the current distance, the eco-coasting control module is configured to apply the energy-saving maneuver to the vehicle.

13. The vehicle according to claim 12, characterized in that: The at least one control module further includes at least one of an adaptive cruise control (ACC) module and a predictive cruise control (PCC) module, and further, if the headway distance is less than the current distance, the controller is configured to apply one of the ACC module and the PCC module.

14. The vehicle according to claim 8, characterized in that: The at least one control module determines the headway distance by the following function: h eco (v0,v f ,v1,a,c)=V -1 (in f )+s f (v0,v f ,a,c)-v1t f (v0,v f ,a,c) Among them, V -1 is the inverse of the range strategy function, v0 is the initial velocity of the vehicle at the first time, v1 is the subsequent velocity of the vehicle at the second time, v f is the speed of the vehicle ahead, s f is the position of the vehicle ahead, t f is the coasting time, a is a function of the weight of the vehicle, and c is a function of the air resistance of the vehicle.

15. A method of controlling longitudinal movement of a first vehicle, the method comprising the steps of: Providing a vehicle longitudinal motion control device, the vehicle longitudinal motion control device having at least one sensor configured to sense longitudinal motion of a second vehicle in front of the first vehicle, and a controller having at least one control module in communication with the at least one sensor; configuring the at least one control module to determine a longitudinal motion characteristic of the first vehicle; configuring the at least one control module to determine a longitudinal motion characteristic of the second vehicle; configuring the at least one control module to determine a headway distance between the first vehicle and the second vehicle based on the longitudinal motion characteristic of the first vehicle, the longitudinal motion characteristic of the second vehicle, and at least one vehicle characteristic of the first vehicle; as well as The at least one control module is configured to apply an energy-saving maneuver to the first vehicle based on the determined headway to reduce a distance between the first vehicle and the second vehicle and improve energy efficiency of the first vehicle.

16. The method according to claim 15, characterized in that: The longitudinal motion characteristic of the first vehicle is at least one of: longitudinal displacement, longitudinal velocity, longitudinal acceleration, and longitudinal jerk; and The longitudinal motion characteristic of the second vehicle is at least one of: longitudinal displacement, longitudinal velocity, longitudinal acceleration, and longitudinal jerk.

17. The method according to claim 16, characterized in that: The energy-saving maneuver further comprises a gliding maneuver; and The at least one control module includes an eco-coasting control module having an eco-coasting algorithm for determining the headway distance.

18. The method according to claim 17, further comprising the steps of: configuring the eco-coasting control module to determine whether the headway distance is greater than a current distance between the first vehicle and the second vehicle; as well as The eco-glide control module is configured to apply the energy-saving maneuver to the first vehicle if the headway distance is greater than the current distance.

19. The method according to claim 18, characterized in that: The at least one control module further includes at least one of an adaptive cruise control (ACC) module and a predictive cruise control (PCC) module, and further, if the headway distance is less than the current distance between the first vehicle and the second vehicle, the controller is configured to apply one of the ACC module and the PCC module.

20. The method according to claim 19, characterized in that: The at least one control module determines the headway distance by the following function: h eco (v0,v f ,v1,a,c)=V -1 (in f )+s f (v0,v f ,a,c)-v1t f (v0,v f ,a,c) Among them, V -1 is the inverse of the range strategy function, v0 is the initial velocity of the first vehicle at the first time, v1 is the subsequent velocity of the first vehicle at the second time, v f is the speed of the second vehicle, s f is the position of the second transport, t f is the coasting time, a is a function of the weight of the first vehicle, and c is a function of the air resistance of the first vehicle.