A segmented real-time lane-changing trajectory planning method for vehicles

Abstract

This invention discloses a segmented real-time lane-changing trajectory planning method for vehicles, used to plan the trajectory of vehicle A changing lanes from lane I to lane II via lane line L. The method includes: calculating the state range of vehicle A at its transition position on lane line L based on the states of vehicle A and its preceding vehicle B1 in lane I; then, based on the state ranges of vehicle A at the lane-changing start point and transition position, modeling multiple indicators of the first lane-changing process as an optimal control problem, and optimizing the trajectory calculation for the first lane-changing process; when the vehicle reaches the transition position, calculating the state range of vehicle A at its endpoint in lane II based on the states of the preceding vehicle B2 and the following vehicle B3 at the target position in lane II; and finally, generating multiple trajectories using a fifth-order polynomial, considering multiple indicators to select the optimal trajectory as the trajectory for the second lane-changing process. This invention segmentally plans lane-changing trajectories, enabling electric vehicles to complete energy-saving, comfortable, and safe lane changes in dynamic traffic scenarios.

Description

Technical Field

[0001] This invention belongs to the field of trajectory planning technology, specifically relating to a vehicle segmented real-time lane-changing trajectory planning method that combines optimal control and fifth-order polynomials. Background Technology

[0002] The cost reduction and iteration of power batteries, along with the large-scale application of intelligent technologies such as generative AI, will accelerate the global popularization of new energy vehicles. Incorporating energy consumption optimization into their intelligentization process is of significant practical importance. However, current lane-changing planning models for intelligent vehicles do not consider the impact of energy consumption and lack a lane-changing trajectory planning model that can balance energy saving, safety, comfort, and real-time performance in dynamic traffic scenarios. Summary of the Invention

[0003] This invention provides a segmented real-time lane-changing trajectory planning method for vehicles. With energy saving as the optimization goal and comfort as the constraint, the method plans the lane-changing trajectory in segments, enabling electric vehicles to complete energy-saving, comfortable, and safe lane changes in dynamic traffic scenarios.

[0004] To achieve the above technical objectives, the present invention adopts the following technical solution:

[0005] A segmented real-time lane-changing trajectory planning method for vehicles is used to plan the trajectory of vehicle A changing lanes from lane I to lane II via lane line L, including:

[0006] The first lane-changing trajectory of vehicle A from lane I to lane line L is planned as follows: Based on the states of vehicle A and its obstacle vehicle B1 in lane I, the state range of vehicle A at the turning position on lane line L is calculated; then, based on the state of vehicle A at the starting point of the lane change and the state range of the turning position, multiple indicators of the first lane-changing process are modeled as an optimal control problem, and the trajectory of the first lane-changing process is optimized and calculated; the state of the vehicle includes its lateral and longitudinal position and speed.

[0007] When the vehicle reaches the turning point, the second lane-changing trajectory of vehicle A from lane line L to lane II is planned: based on the state of the obstacle vehicle B2 in front and the obstacle vehicle B3 behind at the target position in lane II, the range of the endpoint state of vehicle A in lane II is calculated; then, multiple trajectories are generated using a fifth-order polynomial, and the optimal trajectory is selected from multiple indicators as the trajectory for the second lane-changing process.

[0008] Furthermore, when modeling the optimal control problem to optimize the calculation of the first trajectory segment, and / or when using a fifth-order polynomial to select the second lane-changing trajectory segment, the vehicle's energy consumption index is considered; the energy consumption index is calculated using the VT-CPEM energy consumption model.

[0009] Furthermore, the state range of vehicle A's transition position on lane line L is calculated as follows:

[0010] First, determine the conditions under which a lateral collision will not occur between vehicle A and vehicle B1:

[0011] d1+x B1 >x A1 (1)

[0012] In the formula, d1 is the distance between vehicle A and vehicle B1 at the start of the lane change, and x B1 Let x be the minimum lateral displacement of vehicle B1 during the first lane-changing process of vehicle A. A1 Let be the maximum lateral displacement of vehicle A during the first lane-changing process, and we have:

[0013]

[0014] In the formula, t c Let a be the actual time of the first lane-changing process for vehicle A. A v x0 These are the lateral acceleration and initial lateral velocity of vehicle A during the entire lane-changing process, a. B1 v B1 It is divided into the acceleration and speed of vehicle B1 during the first lane change process of vehicle A; wherein, vehicle B1 does not change lanes in the transverse lane I;

[0015] Then, by solving inequality (1), we can obtain the maximum lane-changing time t1 of vehicle A in the first lane-changing process;

[0016] Substituting the maximum lane-changing time t1 into equation (2) yields the state range of the vehicle's transition position on lane line L, including the lateral position range, longitudinal position range, lateral speed range, and longitudinal speed range:

[0017] s yc =D 车 v xc ∈[v x0 ,v x0 +a A t1], v yc ∈[0,v ymax ]

[0018] Among them, D 车 v is the width of all vehicles. ymax This represents the maximum longitudinal speed at which a vehicle changes lanes.

[0019] Furthermore, the calculation of distance d1 takes into account the algorithm solution time of the first lane-changing trajectory planning, and the calculation formula is:

[0020] d1 = d0 - (v x0 -v B1 )×tcom (4)

[0021] In the formula, d0 is the distance between vehicle A and vehicle B1 at the start of lane-changing trajectory planning, and t com The algorithm's solution time is for the first lane-changing trajectory planning.

[0022] Furthermore, the multiple indicators of the first lane-changing process are modeled as an optimal control problem, with the cost function being:

[0023]

[0024] In the formula, J represents the cost function. Let a be the longitudinal acceleration of vehicle A at time t. ymax Let v(t) be the maximum longitudinal acceleration of vehicle A, and v(t) and a(t) be the velocity and acceleration of vehicle A at time t, respectively. Let E(v(t), a(t)) be the energy consumption cost of vehicle A. max This represents the maximum energy consumption, where β1, β2, and β3 represent weighted coefficients for comfort, efficiency, and energy economy, respectively, and β1 + β2 + β3 = 1; where,

[0025]

[0026] In the formula, v x (t),a x v(t) represents the lateral velocity and lateral acceleration of vehicle A at time t, respectively. y (t),a y (t) represents the longitudinal velocity and longitudinal acceleration of vehicle A at time t, respectively, and E Recoverable (v(t), a(t)) represents the energy consumed by vehicle A at time t, E Consume (v(t),a(t)) represents the braking energy recovered by vehicle A at time t;

[0027] By solving the above cost function, the actual time t of the first lane-changing process can be obtained. c And the acceleration a(t) at each moment, and then the velocity v(t) and displacement s(t) at each moment are obtained by integration.

[0028] Furthermore, the constraints of the optimal control problem include:

[0029]

[0030] Furthermore, using the same cost function and constraints as the first segment of the optimal control problem for the lane-changing trajectory, the optimal trajectory is selected from the generated trajectories.

[0031] Furthermore, the endpoint state range of vehicle A in lane II is calculated as follows:

[0032] First, determine the conditions under which a lateral collision will not occur between vehicle A and vehicle B2:

[0033] d2+x B2 >x A2 (8)

[0034] In the formula, d2 is the distance between vehicle A and vehicle B2 at the start of the second lane change, and x B2 Let x be the minimum lateral displacement of vehicle B2 during the second lane-changing process of vehicle A. A2 Let be the maximum lateral displacement of vehicle A during the second lane-changing process, and we have:

[0035]

[0036] In the formula, t e Let a be the actual time of vehicle A's second lane-changing process. A v xc Let a be the lateral acceleration of vehicle A during the entire lane-changing process and the lateral velocity at the end of the first lane-changing segment, respectively. B2 v B2 It is divided into the acceleration and speed of vehicle B2 during the second lane change process of vehicle A; wherein, vehicle B2 does not change lanes in the transverse lane II;

[0037] Then, the conditions under which a lateral collision will not occur between vehicle A and vehicle B3 are also determined:

[0038] d3+x A3 >x B3 (11)

[0039] In the formula, d3 is the distance between vehicle A and vehicle B3 at the start of the second lane change, and x B3 Let x be the maximum lateral displacement of vehicle B3 during the second lane-changing process of vehicle A. A3 Let be the minimum lateral displacement of vehicle A during the second lane-changing process, and we have:

[0040]

[0041] In the formula, a B3 v B3 It is divided into the acceleration and speed of vehicle B3 during the second lane change process of vehicle A; among which, vehicle B3 does not change lanes in the transverse lane II;

[0042] Then, solve inequality (8) to obtain the maximum lane-changing time t2 of vehicle A in the second lane-changing process, and solve inequality (11) to obtain the minimum lane-changing time t3 of vehicle A in the second lane-changing process, thus obtaining the range of lane-changing time t of vehicle A in the second lane-changing process.e ∈[t3,t2];

[0043] Finally, substituting the maximum lane-changing time t2 of the second lane-changing process into equation (9) and the minimum lane-changing time t3 of the second lane-changing process into equation (12), we obtain the state range of the vehicle at the end position of lane-changing in lane II, including the lateral position range, longitudinal position range, lateral speed range, and longitudinal speed range:

[0044]

[0045] v xe ∈[v xc +a A t3,v xc +a A t2],v ye =0

[0046] Among them, D 车道 a is the width of the lane. A Let be the lateral acceleration of vehicle A during the entire lane-changing process.

[0047] Furthermore, the method for generating multiple trajectories using a fifth-order polynomial is as follows:

[0048] The lane-changing time range t for vehicle A in the second lane-changing process. e ∈[t3,t2], uniformly discretized into N time intervals t e1 ,t e2 ,…,t eN ; Horizontal position range Uniformly discretized into M lateral positions s xe1 ,s xe2 ,…,s xeM ;

[0049] Expressing the position of vehicle A as a function of time t in both the lateral and longitudinal directions, we obtain the following expression:

[0050]

[0051] In the formula, m and n represent the numbers of discrete time points and discrete horizontal positions, respectively, and m = 1, 2, ..., M; n = 1, 2, ..., N; s x (t), s y (t) represents the lateral and longitudinal positions of vehicle A at time t, respectively; a 0m×n a 1m×n a 2m×n a 3m×n a 4m×n a 5m×n The coefficients of the fifth-degree polynomial representing the horizontal position with respect to time t, b 0m×n b1m×n b 2m×n b 3m×n b 4m×n b 5m×n The coefficients of the fifth-degree polynomial representing the longitudinal position with respect to time t;

[0052] Based on the kinematic constraints between displacement, velocity, and acceleration, the functional expressions for the velocity and acceleration of vehicle A in the lateral and longitudinal directions with respect to time t are obtained as follows:

[0053]

[0054] In the formula, v x (t), v y (t) represent the lateral and longitudinal velocities of vehicle A at time t, respectively; a x (t), a y (t) represent the lateral acceleration and longitudinal acceleration of vehicle A at time t, respectively;

[0055] The state X of vehicle A at the start of the second lane-changing process. c =[s xc D 车 ,v xc ,v yc ,a xc ,a yc ] and the state X at the endpoint e =[s xe D 车道 ,v xe ,v ye ,a xe ,a ye ], and v ye =0,a xe =0,a ye =0, substituting into equation (14) yields:

[0056]

[0057] Wherein, the time t = 0 is set as the starting point of the second lane-changing process;

[0058] Solving equations (17) and (18) yields the coefficient a in equation (14). 0m×n a 1m×n a 2m×n a 3m×n a 4m×n a 5m×n and coefficient b 0m×n b 1m×n b 2m×n b 3m×n b 4m×n b 5m×nThus, we obtain the functional expressions for the position, velocity, and acceleration of vehicle A during the second lane-changing process;

[0059] Finally, based on the different values ​​of the discrete time points and discrete lateral position numbers m and n, multiple trajectories are obtained.

[0060] Beneficial effects

[0061] The proposed method for segmented lane-changing trajectory planning combines optimal control and fifth-order polynomials. Taking into account the time-varying characteristics of surrounding obstacles, the entire lane-changing trajectory is divided into two segments. By detecting changes in obstacle vehicles during the lane-changing process at the starting point and midpoint, the lane-changing trajectory is adjusted in real time to ensure safety.

[0062] At the start of a lane change, a safe turning point is calculated using information such as the speed and position of the vehicle and obstacles ahead in the current lane. The energy optimization problem from the lane change start point to the turning point is modeled as an optimal control problem, resulting in the first trajectory segment from the start point to the turning point. When the vehicle reaches the turning point, the range of the destination position is calculated using information such as the speed and position of obstacles in front of and behind the target lane. Multiple trajectories are generated using a fifth-order polynomial, and the optimal second lane change trajectory is determined based on comfort and economy.

[0063] This invention establishes a comprehensive evaluation system that considers comfort, safety, energy consumption, and efficiency. Considering that the solution results under the optimal control program have better performance but slightly worse real-time performance, it is placed in the first planning stage. Considering that the fifth-order polynomial has fast calculation speed and good real-time performance, but the planning result performance is average, since the vehicle is already at the midpoint in the second planning stage, and for safety reasons, higher real-time performance is required at this time, it is placed in the second planning stage. Attached Figure Description

[0064] Figure 1 This is a schematic diagram of the first lane change in an embodiment of this application;

[0065] Figure 2 This is a distribution map of longitudinal acceleration and maximum lateral velocity in the highD dataset;

[0066] Figure 3 This is a schematic diagram of the second lane change in an embodiment of this application;

[0067] Figure 4 It is a fifth-order polynomial trajectory family obtained from the embodiments of this application;

[0068] Figure 5 These are trajectory comparison diagrams for different scenarios in embodiments of this application, where (a), (b), and (c) correspond to scenario one, scenario two, and scenario three, respectively.

[0069] Figure 6This is a comparison chart of energy consumption in different scenarios according to the embodiments of this application, where (a), (b), and (c) correspond to scenario one, scenario two, and scenario three, respectively. Detailed Implementation

[0070] The embodiments of the present invention will be described in detail below. These embodiments are based on the technical solutions of the present invention and provide detailed implementation methods and specific operation processes to further explain the technical solutions of the present invention.

[0071] This embodiment provides a segmented real-time lane-changing trajectory planning method for vehicles, used to plan the trajectory of vehicle A from lane I to lane II via lane line L. The method includes: planning the first segment of the lane-changing trajectory of vehicle A from lane I to lane line L; and planning the second segment of the lane-changing trajectory of vehicle A from lane line L to lane II when the vehicle reaches the turning point.

[0072] I. Planning the first lane change trajectory.

[0073] For the first lane change process of vehicle A from lane I to lane line L, as follows: Figure 1 As shown. Assume all vehicles are traveling along the center line of the lane. At the initial moment of lane changing, the lateral speed of vehicle A is v. x0 The longitudinal speed is 0, and the speed of the obstacle vehicle B1 in front of lane I before changing lanes is v. B1 The initial longitudinal distance between the two vehicles is d0, and the center of mass of the vehicle at the starting point of the lane change is (0,0,v). x0 The center of gravity of vehicle A at the midpoint of the lane change (on the lane line between lane I and lane II) is (s). xc ,s yc ,v xc ,v yc Since the lateral angle between the car body and the road is very small during lane changing, the yaw angle of the car at the midpoint is ignored; that is, the vehicle body is parallel to the lane line at the midpoint. Considering that there is no lateral interference with the vehicle in front at the midpoint of the lane change, s... yc The width is set to 1.8m, slightly larger than the width of the obstacle vehicle (in this paper, all vehicle parameters are set to 1.8m wide and 4m long), while also ensuring no longitudinal interference with vehicles in the target lane. To generate a safe feasible region laterally, it is assumed that vehicle A always accelerates at the maximum allowable acceleration (2m / s²). 2 With uniform acceleration, for the obstacle vehicle B1 ahead, assume it decelerates uniformly, such as... Figure 2 As shown, among the 4880 sets of driving data extracted from the highD dataset, it was found that the driver's maximum lateral acceleration is generally around -2 m / s². 2 up to 2m / s 2 Therefore, the deceleration of the obstacle vehicle B1 can be set to -2m / s².2 In this invention, the vehicle's state vector sequentially includes lateral displacement, longitudinal displacement, lateral velocity, and longitudinal velocity, or may also include lateral acceleration and longitudinal acceleration.

[0074] Step 1.1: Based on the states of vehicle A and its obstacle vehicle B1 in lane I, calculate the range of vehicle A's turning position on lane line L. In step 1, the vehicle's state includes its lateral and longitudinal position and speed.

[0075] First, determine the conditions under which a lateral collision will not occur between vehicle A and vehicle B1:

[0076] d1+x B1 >x A1 (1)

[0077] In the formula, d1 is the distance between vehicle A and vehicle B1 at the start of the lane change, and x B1 Let x be the minimum lateral displacement of vehicle B1 during the first lane-changing process of vehicle A. A1 Let be the maximum lateral displacement of vehicle A during the first lane-changing process, and we have:

[0078]

[0079] d1 = d0 - (v x0 -v B1 )×t com (4)

[0080] In the formula, t c Let a be the actual time of the first lane-changing process for vehicle A. A v x0 These are the lateral acceleration and initial lateral velocity of vehicle A during the entire lane-changing process, a. B1 v B1 The acceleration and velocity of vehicle B1 during the first lane-changing phase of vehicle A's journey are divided into two parts. Vehicle B1 does not change lanes in the transverse lane I, therefore it has no longitudinal displacement, velocity, or acceleration. d0 is the distance between vehicle A and vehicle B1 at the start of the lane-changing trajectory planning, and t... com The algorithm's solution time is for the first lane-changing trajectory planning.

[0081] Then, by solving inequality (1), we can obtain the maximum lane-changing time t1 allowed for vehicle A in the first lane-changing process.

[0082] Substituting the maximum lane-changing time t1 into equation (2), we obtain the range of the vehicle's state (sxc, syc, vxc, vyc) at the midpoint of the lane line L, including the lateral position range, longitudinal position range, lateral speed range, and longitudinal speed range:

[0083] s yc =D 车 v xc ∈[v x0 ,v x0 +a A t1], v yc ∈[0,v ymax ]

[0084] Among them, D 车 The width of all vehicles is denoted as D in this embodiment. 车 =1.8; v ymax Let v be the maximum longitudinal speed of a vehicle changing lanes. Data from the highD dataset shows that drivers typically do not exceed 2 m / s in lateral speed when changing lanes. Therefore, in this embodiment, v is set as... ymax = 2m / s.

[0085] Step 1.2: Based on the state range of vehicle A at the starting point of the lane change and the intermediate position, model multiple indicators of the first lane change process as an optimal control problem.

[0086] In this invention, the lateral displacement s at any time t during the lane-changing process is... x (t), longitudinal displacement s y (t), lateral velocity v x (t), longitudinal velocity v y Together with t, the state vector of the vehicle is represented as: X(t)=[s x (t),s y (t),v x (t),v y (t)] T .

[0087] The initial state of vehicle A changing lanes is X0 = [s x0 ,s y0 ,v x0 ,v y0 ] T =[0,0,v x0 ,0] T The lane change / transfer status is X. c =[s xc ,s yc ,v xc ,v yc ] T =[[0, x A1 ],D 车 ,[v x0 v x0 +a A t c ],[0,v ymax ]]T (sx0, sy0) are the position coordinates at the start of the lane change, (v x0 ,v y0 (s) represents the lateral and longitudinal velocities at the start of a lane change. xc ,s yc (v) represents the coordinates of the lane change / transfer point. xc ,v yc ) represents the lateral and longitudinal velocities at the intermediate position.

[0088] The kinematic constraints for the vehicle are: The control vectors are lateral acceleration and longitudinal acceleration, expressed as:

[0089] The first lane-changing process models comfort, efficiency, and energy economy as an optimal control problem, with the cost function being:

[0090]

[0091] In the formula, J represents the cost function. Let a be the longitudinal acceleration of vehicle A at time t. ymax Let v(t) be the maximum longitudinal acceleration of vehicle A, and v(t) and a(t) be the velocity and acceleration of vehicle A at time t, respectively. Let E(v(t), a(t)) be the energy consumption cost of vehicle A. max β1, β2, and β3 represent the maximum energy consumption, and β1, β2, and β3 represent the weighting coefficients for comfort, efficiency, and energy economy, respectively, with β1 + β2 + β3 = 1. In this embodiment, a ymax For 2, t max Take 3s, E max It can be obtained from the maximum lane change time and the lane change end speed.

[0092] When modeling the optimal control problem to optimize the calculation of the first segment of the trajectory, this embodiment of the invention considers the vehicle's energy consumption index. Compared with traditional fuel vehicles, electric vehicles recover braking energy during braking, and their energy consumption model is more complex than that of fuel vehicles. In this embodiment, the energy consumption index is calculated using the VT-CPEM energy consumption model, which takes data such as road slope, vehicle acceleration, and speed as input, and outputs the energy consumption of the electric vehicle during a specific driving cycle.

[0093] In the VT-CPEM energy consumption model, considering the air resistance, driving resistance, road gradient, and inertial force of the electric vehicle, the power at the wheel can be expressed as:

[0094]

[0095] In the formula, v(t) is the vehicle speed, a(t) is the vehicle acceleration (negative when decelerating), g is the gravitational acceleration, α is the road slope, and C...r =1.75, c1=0.0328, c2=4.575 are rolling resistance parameters, which vary with different road surfaces, m is the vehicle mass, t is the travel time, and P Air =1.25536 is the air mass density, A f For the vehicle's frontal area, C D =0.28 is the air drag coefficient.

[0096] When acceleration a(t) > 0, the car consumes energy while moving, and the energy consumed is E. Consume When acceleration a(t) < 0, the car recovers energy during its movement, and the recovered energy is E. Recoverable The braking energy recovery efficiency is η rb The calculation formulas are as follows:

[0097]

[0098] Therefore, the energy consumption cost function can be established as follows:

[0099]

[0100] In the formula, v x (t),a x v(t) represents the lateral velocity and lateral acceleration of vehicle A at time t, respectively. y (t),a y (t) represents the longitudinal velocity and longitudinal acceleration of vehicle A at time t, respectively, and E Recoverable (v(t), a(t)) represents the energy consumed by vehicle A at time t, E Consume (v(t),a(t)) represents the braking energy recovered by vehicle A at time t;

[0101] In addition, considering the impact of lane changing operations on the comfort of vehicle passengers, the comfort during lane changing is mainly related to the lateral acceleration during lane changing. The comfort threshold of the maximum lateral acceleration that passengers prone to motion sickness can accept is 0.203g. Factors such as the maximum steering angle of the vehicle are considered, and the following constraints are added as shown in equation (7):

[0102]

[0103] Step 1.3: Optimize the calculation of the trajectory for the first lane-changing process. The model then obtains the optimal lane-changing trajectory.

[0104] The above cost function can be solved using the commercial software GPOPS2 to obtain the actual time t of the first lane-changing process. c And the acceleration a(t) at each moment. Then, by integration, we can obtain the velocity v(t) and displacement s(t) at each moment.

[0105] II. Planning of the first lane change trajectory.

[0106] When the vehicle reaches the turning point, the second phase of planning begins. Since the computation time for the fifth-order polynomial programming is only about 2ms, the time effect can be ignored. Assume that there are two obstacle vehicles, B2 and B3, in front and behind in target lane II at this time. The lane-changing process is as follows... Figure 3 As shown.

[0107] Step 2.1: Based on the states of the obstacle vehicles B2 ahead and B3 behind at the target position in lane II, calculate the end state range of vehicle A in lane II.

[0108] First, determine the conditions under which a lateral collision will not occur between vehicle A and vehicle B2:

[0109] d2+x B2 >x A2 (8)

[0110] In the formula, d2 is the distance between vehicle A and vehicle B2 at the start of the second lane change, and x B2 Let x be the minimum lateral displacement of vehicle B2 during the second lane-changing process of vehicle A. A2 This represents the maximum lateral displacement of vehicle A during the second lane change process.

[0111] Referring to the modeling method used in the first planning stage, and also to avoid a collision with vehicle B2 ahead, we can assume that the vehicle accelerates during the second lane change, accelerating uniformly at maximum acceleration, while vehicle B2 in the target lane decelerates at maximum deceleration of -2 m / s² in the transverse lane without changing lanes. The calculated x... A2 and x B2 :

[0112]

[0113] In the formula, t e Let a be the actual time of vehicle A's second lane-changing process. A v xc Let a be the lateral acceleration of vehicle A during the entire lane-changing process and the lateral velocity at the end of the first lane-changing segment, respectively. B2 v B2 It is divided into the acceleration and velocity of vehicle B2 during the second lane change process of vehicle A.

[0114] Then, the conditions under which a lateral collision will not occur between vehicle A and vehicle B3 are also determined:

[0115] d3+x A3 >x B3 (11)

[0116] In the formula, d3 is the distance between vehicle A and vehicle B3 at the start of the second lane change, and x B3 Let x be the maximum lateral displacement of vehicle B3 during the second lane-changing process of vehicle A. A3 Let be the minimum lateral displacement of vehicle A during the second lane-changing process.

[0117] To avoid a rear-end collision, we can assume that the following vehicle B3 accelerates during the lane change, while our own vehicle decelerates uniformly during the lane change. Then:

[0118]

[0119] In the formula, a B3 v B3 It is divided into the acceleration and speed of vehicle B3 during the second lane change process of vehicle A; among which, vehicle B3 does not change lanes in the transverse lane II.

[0120] Then, solve inequality (8) to obtain the maximum lane-changing time t2 of vehicle A in the second lane-changing process, and solve inequality (11) to obtain the minimum lane-changing time t3 of vehicle A in the second lane-changing process, thus obtaining the range of lane-changing time t of vehicle A in the second lane-changing process. e ∈[t3,t2].

[0121] Finally, substituting the maximum lane-changing time t2 of the second lane-changing process into equation (9) and the minimum lane-changing time t3 of the second lane-changing process into equation (12), we obtain the state range of the vehicle at the end position of lane-changing in lane II, including the lateral position range, longitudinal position range, lateral speed range, and longitudinal speed range:

[0122]

[0123] v xe ∈[v xc +a A t3,v xc +a A t2],v ye =0

[0124] Among them, D 车道 a is the width of the lane. A Let be the lateral acceleration of vehicle A during the entire lane-changing process.

[0125] Step 2.2: Generate multiple trajectories using a fifth-order polynomial.

[0126] First, the lane-changing time range t of vehicle A in the second lane-changing process. e ∈[t3,t2], uniformly discretized into N time intervals t e1 ,t e2 ,…,teN ; Horizontal position range Uniformly discretized into M lateral positions s xe1 ,s xe2 ,…,s xeM .

[0127] Then, representing the position of vehicle A as a function of time t in both the lateral and longitudinal directions, we obtain the following expression:

[0128]

[0129] In the formula, m and n represent the numbers of discrete time points and discrete horizontal positions, respectively, and m = 1, 2, ..., M; n = 1, 2, ..., N; s x (t), s y (t) represents the lateral and longitudinal positions of vehicle A at time t, respectively; a 0m×n a 1m×n a 2m×n a 3m×n a 4m×n a 5m×n The coefficients of the fifth-degree polynomial representing the horizontal position with respect to time t, b 0m×n b 1m×n b 2m×n b 3m×n b 4m×n b 5m×n The coefficients of the fifth-degree polynomial representing the longitudinal position with respect to time t;

[0130] Furthermore, based on the kinematic constraints between displacement, velocity, and acceleration, the functional expressions for the velocity and acceleration of vehicle A in the lateral and longitudinal directions with respect to time t are obtained as follows:

[0131]

[0132] In the formula, v x (t), v y (t) represent the lateral and longitudinal velocities of vehicle A at time t, respectively; a x (t), a y (t) represent the lateral acceleration and longitudinal acceleration of vehicle A at time t, respectively;

[0133] Then, the state X of vehicle A at the starting point of the second lane-changing process is... c =[s xc D 车 ,v xc ,v yc ,a xc ,a yc ] and the state X at the endpoint e =[s xe D车道 ,v xe ,v ye ,a xe ,a ye ], and v ye =0,a xe =0,a ye =0, substituting into equation (14) yields:

[0134]

[0135]

[0136] Let the time at the start of the second lane-changing process be t = 0; solve equations (17) and (18) to obtain the coefficient a in equation (14). 0m×n a 1m×n a 2m×n a 3m×n a 4m×n a 5m×n and coefficient b 0m×n b 1m×n b 2m×n b 3m×n b 4m×n b 5m×n This allows us to obtain functional expressions for the position, velocity, and acceleration of vehicle A during the second lane-changing process.

[0137] Finally, based on the different values ​​of the discrete time points and discrete lateral position numbers m and n, multiple trajectories are obtained.

[0138] Step 2.3: Consider multiple indicators and select the optimal trajectory as the trajectory for the second lane-changing process.

[0139] In this embodiment, the same cost function and constraints as the optimal control problem of the first lane-changing trajectory are used. Specifically, the weighting coefficients β1, β2, and β3, which represent comfort, efficiency, and energy economy, can be adjusted as needed. The optimal trajectory, i.e., the trajectory with the smallest cost function J, is selected from the generated trajectories.

[0140] In the segmented trajectory planning process, the requirements for the two trajectories are different. For the first trajectory segment, from the starting point to the turning point, even with the impact of computation time, since the vehicle is still traveling along the lane centerline at the beginning, considering the error in computation time, the vehicle only continues to travel a very short distance along the lane. This error can be eliminated through prediction, so the real-time requirement is not very stringent; the main considerations are economy and comfort. For the second trajectory segment, since the vehicle is already on two adjacent lanes, if the planning algorithm takes too long to compute, it may cause interference with vehicles in the target lane, resulting in poor safety and making it difficult for the vehicle to travel along the planned path. Therefore, the planning of the second trajectory segment needs to prioritize real-time performance, and the algorithm used must have the advantage of fast computation speed. To determine the trajectory planning methods used for the first and second trajectories, the trajectory of the optimal control planning is compared with the fifth-order polynomial trajectory. Three sets of complete driver lane-changing data at different lane-changing speeds were extracted from the highD dataset, as shown in Table 1, representing high speed, medium speed, and low speed during the driving process. Using these as templates, the starting and ending states of lane changes were set. In the fifth-order polynomial trajectory planning, the lane-changing time was discretized in steps of 0.1s to generate multiple trajectory clusters. Trajectories with excessive acceleration that do not meet comfort requirements were removed from these trajectory clusters. Then, the trajectory with the lowest energy consumption was selected from the remaining trajectory clusters. In this embodiment, the Nissan Leaf was used as an example, with the vehicle weight set to 1521kg, Af = 2.3316, the road slope set to 5°, and the simulation device CPU set to i5-11260H with 16GB of RAM.

[0141] Table 1. Lane Change Data

[0142]

[0143]

[0144] Simulation results are as follows Figure 5 , Figure 6 As shown, from Figure 5 The trajectory comparison chart reveals that the optimal control trajectory is smoother than both the actual driver's trajectory in the highD dataset and the trajectory of a fifth-order polynomial programming algorithm, while also exhibiting smaller lateral and longitudinal accelerations, resulting in better comfort. Figure 6 The energy consumption comparison chart shows that the energy consumption of the optimal control program trajectory is lower than that of the actual driver trajectory and the fifth-order polynomial trajectory. The solution results for different scenarios are shown in Table 2.

[0145] Table 2. Solution results for barrier-free scenarios

[0146]

[0147] Simulation results under three operating conditions show that the trajectory planned by optimal control requires less lane-changing time, shorter longitudinal displacement, lower energy consumption, and better comfort compared to the trajectory planned by quintic polynomial programming. However, the computation time of quintic polynomial programming is significantly shorter, only about 7ms, exhibiting excellent real-time performance. Although the computation time of optimal control planning is around 50ms, the displacement caused by computation time errors during high-speed lane changes is only about 1m, which can be eliminated through calculation. Therefore, the proposed scheme of using optimal control to plan the first segment of the trajectory and quintic polynomial programming for the second segment is feasible.

[0148] The above embodiments are preferred embodiments of this application. Those skilled in the art can make various changes or improvements based on them. Without departing from the overall concept of this application, these changes or improvements should fall within the scope of protection claimed in this application.

Claims

1. A segmented real-time lane-changing trajectory planning method for vehicles, characterized in that, This is used to plan the trajectory of vehicle A as it changes lanes from lane I to lane II via lane line L, including: The first lane-changing trajectory of vehicle A from lane I to lane line L is planned as follows: Based on the states of vehicle A and its obstacle vehicle B1 in lane I, the state range of vehicle A at the turning position on lane line L is calculated; then, based on the state of vehicle A at the starting point of the lane change and the state range of the turning position, multiple indicators of the first lane-changing process are modeled as an optimal control problem, and the trajectory of the first lane-changing process is optimized and calculated; the state of the vehicle includes its lateral and longitudinal position and speed. Specifically, the state range of vehicle A's turning position on lane line L is calculated as follows: First, determine the conditions under which a lateral collision will not occur between vehicle A and vehicle B1: d1+x B1 >x A1 (1) In the formula, d1 is the distance between vehicle A and vehicle B1 at the start of the lane change, and x B1 Let x be the minimum lateral displacement of vehicle B1 during the first lane-changing process of vehicle A. A1 Let be the maximum lateral displacement of vehicle A during the first lane-changing process, and we have: In the formula, t c Let a be the actual time of the first lane-changing process for vehicle A. A v x0 These are the lateral acceleration and initial lateral velocity of vehicle A during the entire lane-changing process, a. B1 v B1 It is divided into the acceleration and speed of vehicle B1 during the first lane change process of vehicle A; wherein, vehicle B1 does not change lanes in the transverse lane I; Then, by solving inequality (1), we can obtain the maximum lane-changing time t1 of vehicle A in the first lane-changing process; Substituting the maximum lane-changing time t1 into equation (2) yields the state range of the vehicle's transition position on lane line L, including the lateral position range, longitudinal position range, lateral speed range, and longitudinal speed range: s yc =D 车 ,v xc ∈[v x0 ,v x0 +a A t1],v yc ∈[0,v ymax ] Among them, D 车 v is the width of all vehicles. ymax The maximum longitudinal speed at which a vehicle changes lanes; When the vehicle reaches the turning point, the second lane-changing trajectory of vehicle A from lane line L to lane II is planned: based on the state of the obstacle vehicle B2 in front and the obstacle vehicle B3 behind at the target position in lane II, the range of the endpoint state of vehicle A in lane II is calculated; then, multiple trajectories are generated using a fifth-order polynomial, and the optimal trajectory is selected from multiple indicators as the trajectory for the second lane-changing process. Specifically, the calculation of the endpoint state range of vehicle A in lane II is as follows: First, determine the conditions under which a lateral collision will not occur between vehicle A and vehicle B2: d2+x B2 >x A2 (8) In the formula, d2 is the distance between vehicle A and vehicle B2 at the start of the second lane change, and x B2 Let x be the minimum lateral displacement of vehicle B2 during the second lane-changing process of vehicle A. A2 Let be the maximum lateral displacement of vehicle A during the second lane-changing process, and we have: In the formula, t e Let a be the actual time of vehicle A's second lane-changing process. A v xc Let a be the lateral acceleration of vehicle A during the entire lane-changing process and the lateral velocity at the end of the first lane-changing segment, respectively. B2 v B2 It is divided into the acceleration and speed of vehicle B2 during the second lane change process of vehicle A; wherein, vehicle B2 does not change lanes in the transverse lane II; Then, the conditions under which a lateral collision will not occur between vehicle A and vehicle B3 are also determined: d3+x A3 >x B3 (11) In the formula, d3 is the distance between vehicle A and vehicle B3 at the start of the second lane change, and x B3 Let x be the maximum lateral displacement of vehicle B3 during the second lane-changing process of vehicle A. A3 Let be the minimum lateral displacement of vehicle A during the second lane-changing process, and we have: In the formula, a B3 v B3 It is divided into the acceleration and speed of vehicle B3 during the second lane change process of vehicle A; among which, vehicle B3 does not change lanes in the transverse lane II; Then, solve inequality (8) to obtain the maximum lane-changing time t2 of vehicle A in the second lane-changing process, and solve inequality (11) to obtain the minimum lane-changing time t3 of vehicle A in the second lane-changing process, thus obtaining the range of lane-changing time t of vehicle A in the second lane-changing process. e ∈[t3,t2]; Finally, substituting the maximum lane-changing time t2 of the second lane-changing process into equation (9) and the minimum lane-changing time t3 of the second lane-changing process into equation (12), we obtain the state range of the vehicle at the end position of lane-changing in lane II, including the lateral position range, longitudinal position range, lateral speed range, and longitudinal speed range: in xe ∈[in xc +a A t3,v xc +a A t2],in ye =0 Among them, D 车道 a is the width of the lane. A Let be the lateral acceleration of vehicle A during the entire lane-changing process.

2. The vehicle segmented real-time lane-changing trajectory planning method according to claim 1, characterized in that, When modeling the optimal control problem to optimize the calculation of the first trajectory segment, and / or when using a fifth-order polynomial to select the second lane-changing trajectory segment, the vehicle's energy consumption index is considered; the energy consumption index is calculated using the VT-CPEM energy consumption model.

3. The vehicle segmented real-time lane-changing trajectory planning method according to claim 1, characterized in that, The calculation of distance d1 takes into account the algorithm solution time of the first lane change trajectory planning, and the calculation formula is: d1=d0-(in x0 -v B1 )×t com (4) In the formula, d0 is the distance between vehicle A and vehicle B1 at the start of lane-changing trajectory planning, and t com The algorithm's solution time is for the first lane-changing trajectory planning.

4. The vehicle segmented real-time lane-changing trajectory planning method according to claim 1, characterized in that, The multiple indicators of the first lane-changing process are modeled as an optimal control problem, with the cost function being: In the formula, J represents the cost function. Let a be the longitudinal acceleration of vehicle A at time t. ymax Let v(t) be the maximum longitudinal acceleration of vehicle A, and v(t) and a(t) be the velocity and acceleration of vehicle A at time t, respectively. Let E(v(t), a(t)) be the energy consumption cost of vehicle A. max This represents the maximum energy consumption, where β1, β2, and β3 represent weighted coefficients for comfort, efficiency, and energy economy, respectively, and β1 + β2 + β3 = 1; where, In the formula, v x (t),a x v(t) represents the lateral velocity and lateral acceleration of vehicle A at time t, respectively. y (t),a y (t) represents the longitudinal velocity and longitudinal acceleration of vehicle A at time t, respectively, and E Recoverable (v(t), a(t)) represents the energy consumed by vehicle A at time t, E Consume (v(t),a(t)) represents the braking energy recovered by vehicle A at time t; By solving the above cost function, the actual time t of the first lane-changing process can be obtained. c And the acceleration a(t) at each moment, and then the velocity v(t) and displacement s(t) at each moment are obtained by integration.

5. The vehicle segmented real-time lane-changing trajectory planning method according to claim 4, characterized in that, The constraints of the optimal control problem include:

6. The vehicle segmented real-time lane-changing trajectory planning method according to claim 5, characterized in that, Using the same cost function and constraints as the first segment of the optimal control problem for the lane-changing trajectory, the optimal trajectory is selected from the generated trajectories.

7. The vehicle segmented real-time lane-changing trajectory planning method according to claim 1, characterized in that, The method for generating multiple trajectories using a fifth-order polynomial is as follows: The lane-changing time range t for vehicle A in the second lane-changing process. e ∈[t3,t2], uniformly discretized into N time intervals t e1 ,t e2 ,…,t eN ; Horizontal position range Uniformly discretized into M lateral positions s xe1 ,s xe2 ,…,s xeM ; Expressing the position of vehicle A as a function of time t in both the lateral and longitudinal directions, we obtain the following expression: In the formula, m and n represent the discrete time point and discrete horizontal position number, respectively, and m = 1, 2, ..., M; n = 1, 2, ..., N; s x (t), s y (t) represents the lateral and longitudinal positions of vehicle A at time t, respectively; a 0m×n a 1m×n a 2m×n a 3m×n a 4m×n a 5m×n The coefficients of the fifth-degree polynomial representing the horizontal position with respect to time t, b 0m×n b 1m×n b 2m×n b 3m×n b 4m×n b 5m×n The coefficients of the fifth-degree polynomial representing the longitudinal position with respect to time t; Based on the kinematic constraints between displacement, velocity, and acceleration, the functional expressions for the velocity and acceleration of vehicle A in the lateral and longitudinal directions with respect to time t are obtained as follows: In the formula, v x (t), v y (t) represent the lateral and longitudinal velocities of vehicle A at time t, respectively; a x (t), a y (t) represent the lateral acceleration and longitudinal acceleration of vehicle A at time t, respectively; The state X of vehicle A at the start of the second lane-changing process. c =[s xc D 车 ,v xc ,v yc ,a xc ,a yc ] and the state X at the endpoint e =[s xe D 车道 ,v xe ,v ye ,a xe ,a ye ], and v ye =0,a xe =0,a ye =0, substituting into equation (14) yields: Wherein, the time t = 0 is set as the starting point of the second lane-changing process; Solving equations (17) and (18) yields the coefficient a in equation (14). 0m×n a 1m×n a 2m×n a 3m×n a 4m×n a 5m×n and coefficient b 0m×n b 1m×n b 2m×n b 3m×n b 4m×n b 5m×n Thus, we obtain the functional expressions for the position, velocity, and acceleration of vehicle A during the second lane-changing process; Finally, based on the different values ​​of the discrete time points and discrete lateral position numbers m and n, multiple trajectories are obtained.

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