A platoon longitudinal control method considering complex delay

Abstract

The application provides a platoon longitudinal control method considering complex delay, aiming at guaranteeing the following property and stability of the platoon under the conditions of communication delay and actuator delay. The method comprises establishing a vehicle state space equation and establishing a vehicle upper layer control system under two delay conditions based on a model predictive control method. The application provides more accurate state information for the vehicle by predicting and compensating the state information of the preceding vehicle under the condition of communication delay. The MPC algorithm is improved correspondingly to reduce the influence of the actuator delay. The application can guarantee that the upper layer control system can output more accurate expected acceleration under the condition of meeting multiple constraints, and improve the following property and stability of the platoon.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of vehicle platoon control, and particularly relates to a vehicle platoon longitudinal control method considering complex delay. BACKGROUND

[0002] In recent years, with the rapid development of intelligent traffic system (ITS), various intelligent vehicle driving technologies have also been developed and widely researched. Vehicle longitudinal platoon driving has become a hot spot in the field of intelligent transportation because it can improve traffic capacity, reduce traffic energy consumption, and reduce traffic accidents. Model predictive control (MPC) is an effective control technology that can explicitly handle various constraints of the system, and thus has become a commonly used control method in the engineering field. The application of MPC in vehicle platoon driving has made significant progress in stability, feasibility, and process control of vehicle platoon driving.

[0003] At present, many studies have applied MPC to vehicle platoon driving control, and a large number of studies have considered the impact of delay on the platoon. However, vehicle platoon driving involves multiple delay links including communication delay, actuator delay, etc. Most studies only consider the impact of single delay such as communication delay or actuator delay on the platoon. However, in actual vehicle platoon driving, actuator delay caused by physical limitations of vehicles and communication delay between vehicles exist at the same time, which will have a more serious impact on the following performance and stability of vehicle platoon driving. SUMMARY

[0004] In view of the deficiencies in the prior art, the present application provides a vehicle platoon longitudinal control method considering complex delay, which is used to cope with the problems of communication delay and control delay existing in the control process.

[0005] The present application achieves the above technical purpose through the following technical means.

[0006] A vehicle platoon longitudinal control method: a longitudinal vehicle following control system is established based on MPC, wherein vehicle control is implemented by solving acceleration increment Δu; MPC predicts the system state in the prediction horizon N p and calculates the system output based on the discretized model and the initial state:

[0007] X(k) = Φx(k) + ΨΔU(k) + Fu(k-1) + Gw(k)

[0008] Y(k) = C'X(k)

[0009] Wherein:

[0010]

[0011]

[0012] wherein X(k) is a control state information sequence in a prediction time domain N p , x(k) = [e s , e v , a i ] is a control state quantity of the vehicle, e s represents a tracking error of the vehicle with respect to an expected vehicle distance, e v represents a tracking error of the vehicle with respect to a speed of a preceding vehicle, a i represents an acceleration of the vehicle; w = a i-1 represents that the acceleration of the preceding vehicle is taken as a system measurement disturbance; u is a control input of the system, i.e., an expected acceleration; N c is a control time domain, N p is a prediction time domain, N p >N c ; A, B1, B2, C are respectively a state coefficient matrix, an input coefficient matrix, a disturbance quantity coefficient matrix, and an output coefficient matrix, and I is an identity matrix; T is a system sampling time interval.

[0013] Further, the objective function of the control system is:

[0014]

[0015] wherein:

[0016]

[0017] D(k) = C'Φx(k) + C'Fu(k-1) + C'Gw(k)

[0018] wherein Q is an error weight coefficient matrix, and R is a control quantity increment coefficient matrix.

[0019] Further, ΔU(k) is solved by minimizing the objective function J k , so as to obtain an acceleration change Δu at each time in a future control time domain N c .

[0020] Further, a control state information sequence X(k) of the vehicle is converted based on ΔU(k), and a motion state information sequence S p (k) of the vehicle in a future time domain N i is calculated based on X(k):

[0021]

[0022] wherein p i is a position of the vehicle, and vi V is the speed of the ego vehicle i a is the longitudinal acceleration of the ego vehicle; S i (k) is transmitted to the rear vehicle.

[0023] Further, the conversion relationship between X(k) and S i (k) is:

[0024]

[0025] where h is the headway time of the ego vehicle, L is the length of the ego vehicle, and d0 is the minimum safety distance of the ego vehicle.

[0026] Further, the expected acceleration is compensated for actuator delay:

[0027] u(k|k) = u(k-1|k) + Δu(k|k) + Δu(k+1|k) + … + Δu(k+ξ|k)

[0028] where the actuator delay σ and the sampling time T satisfy:

[0029] σ = ξT

[0030] where ξ is rounded down.

[0031] Further, the motion state information transmitted by the ego vehicle to the rear vehicle is compensated for communication delay θ = nT, where n is rounded down:

[0032]

[0033] where s i (k|k) is the actual motion state information of the ego vehicle used by the rear vehicle after compensation.

[0034] Further, the coefficient matrices A, B1, B2, and C are respectively:

[0035]

[0036] where h is the headway time of the ego vehicle, and τ is the engine time constant of the ego vehicle.

[0037] Further, the coefficient matrices Q and R are respectively:

[0038]

[0039] Further, the control time domain and the prediction time domain are respectively N p = 10 and N c = 5.

[0040] The beneficial effects of the present application are:

[0041] The present application provides a vehicle platoon longitudinal control method considering complex delays, wherein a prediction sequence obtained by model prediction is used to update the front vehicle state information, and a compensation link is introduced to further ensure information accuracy, and the original MPC algorithm is partially improved to improve the influence of actuator delay. The method improves the control effect of longitudinal vehicle platoon while considering two kinds of delays. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 Flowchart of the vehicle platoon longitudinal control method considering complex delays of the present application;

[0043] Figure 2 Control effect obtained by using the control method of the present application without any delay;

[0044] Figure 3 Control effect when no compensation measures are taken under 100ms communication delay;

[0045] Figure 4 Control effect after compensation measures are taken for 100ms communication delay;

[0046] Figure 5 Control effect when no compensation measures are taken under 200ms actuator delay;

[0047] Figure 6 Control effect after compensation measures are taken for 200ms actuator delay;

[0048] Figure 7 Control effect under the combined action of 100ms communication delay and 200ms actuator delay;

[0049] Figure 8 Control effect after communication delay compensation and actuator delay compensation are taken at the same time. DETAILED DESCRIPTION

[0050] Embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numbers represent the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by reference to the accompanying drawings are exemplary and are intended to explain the present application, and cannot be understood as limiting the present application.

[0051] For the intelligent vehicle platoon with communication delay and actuator delay, the platoon following control method based on MPC is proposed, which considers the influence of actuator delay and communication delay. Firstly, the future motion state information of the vehicle is calculated according to the state information predicted by MPC, and compensation is added to reduce the error of the predicted information. After the state information is sent to the following vehicle, the following vehicle selects the state information of the front vehicle at the corresponding time according to the communication delay time to calculate the initial value, and then inputs the MPC solver for solving. For the actuator delay, the vehicle selects the acceleration increment value at the corresponding actuator delay time in the calculated control sequence according to the size of the actuator delay, and then adds the acceleration increment from the non-delay time to the delay time to the acceleration at the last time to obtain the final expected acceleration value.

[0052] In combination Figure 1 As shown in the drawings, specifically includes the following content:

[0053] I. Vehicle state space equation

[0054] (1) The vehicle longitudinal dynamics model can be described by the following three-order nonlinear equation:

[0055]

[0056] In the formula, p is the longitudinal position of the vehicle, v is the longitudinal speed of the vehicle, a is the longitudinal acceleration of the vehicle, C d is the air resistance coefficient, m is the mass of the vehicle, τ is the engine time constant of the vehicle, d m is the mechanical resistance coefficient of the vehicle, and η is the control input of the engine.

[0057] For η, there is:

[0058] η=ma des +C d v 2 +d m +2τC d va

[0059] In the formula, a des is the expected acceleration of the vehicle.

[0060] After linearizing the above formula by using linear feedback theory, the relationship between the actual acceleration and the expected acceleration of the vehicle is represented as:

[0061]

[0062] (2) According to the vehicle kinematics model, the vehicle state space equation is established:

[0063]

[0064] y=Cx(t)

[0065] where u=a des is the control input of the system, i.e. the desired acceleration; w is the measured disturbance of the system, in this system it represents the acceleration of the preceding vehicle, i.e. w=a i-1 ; x(t)=[e s ,e v ,a i ] is the control state of the vehicle (the ith vehicle), where e s represents the tracking error of the ith vehicle with respect to the desired inter-vehicle distance, e v represents the speed tracking error of the ith vehicle with respect to the preceding vehicle, and a i represents the acceleration of the ith vehicle.

[0066] Note that in this embodiment, the characters without the subscript "i" are all assumed to represent the vehicle (the ith vehicle). For example, x(t) is the control state of the vehicle (the ith vehicle), and x i-1 (t) is the control state of the (i-1)th vehicle.

[0067] The specific calculation formulas of e s , e v , and a i are as follows:

[0068] e s = p i-1 -p i -L-hv i -d0

[0069] e v =v i-1 -v i

[0070]

[0071] where h is the fixed headway, L is the vehicle length, and d0 is the minimum safe distance of the vehicle, which is generally 2-6 m.

[0072] A, B1, B2, and C are respectively the state coefficient matrix, the input coefficient matrix, the disturbance coefficient matrix, and the output coefficient matrix. Their specific expressions are as follows:

[0073]

[0074] (3) The above vehicle state space equation is discretized by Laplace approximation to obtain a discretized state equation:

[0075]

[0076] y=Cx(k)

[0077] where:

[0078]

[0079] where T is the system sampling time interval, I is the identity matrix of the same dimension as A and B.

[0080] In summary, the vehicle state space equation can be written as:

[0081]

[0082] II. Longitudinal vehicle following control system based on model predictive control (MPC) algorithm

[0083] (1) In order to ensure the comfort of the ride, i.e. the acceleration does not change abruptly; the control amount increment Δu is used to represent the change of acceleration, and the system realizes vehicle control by solving the acceleration increment Δu. The relationship between Δu and u is expressed as:

[0084] u(k+j|k) = u(k+j-1) + Δu(k+j|k)

[0085] MPC predicts the system state in the prediction horizon N p and calculates the system output according to the discretized model and the initial state:

[0086] X(k) = Φx(k) + ΨΔU(k) + Fu(k-1) + Gw(k)

[0087] Y(k) = C'X(k)

[0088] where X(k) is the sequence of control state information in the prediction horizon N p

[0089]

[0090] Suppose that the acceleration of the preceding vehicle does not change in the prediction horizon N p , i.e. w(k) = w(k+1) = … = w(k+N p 0 = a i-1 ; and let Then we have

[0091]

[0092]

[0093] where N c is the control horizon, N p is the prediction horizon, N p > N c ; in this embodiment, N p = 10, N c ​​= 5.

[0094] (2) Establish the system objective function:

[0095]

[0096] where y ref is the reference trajectory, Q is the error weight coefficient matrix, and R is the control amount increment coefficient matrix. The symbol represents a quadratic function. The first term of the above objective function indicates control of the vehicle following ability, and the second term indicates control of the acceleration increment.

[0097] Further arrangement of the above objective function can obtain the general formula:

[0098]

[0099] where:

[0100]

[0101] (3) Set D(k) = C'Φx(k) + C'Fu(k-1) + C'Gw(k), and the objective function can be further written as the following standard quadratic programming function:

[0102]

[0103] where:

[0104]

[0105] In the formula, M(k) is a constant value under known conditions, which does not affect the optimization solution of the objective function; and the objective function can be written as the following standard quadratic function:

[0106]

[0107] III. Platoon control

[0108] 1. Vehicle control

[0109] For the vehicle (the ith vehicle), the MPC solves ΔU(k) by minimizing the objective function J k

[0110]

[0111] Thus, the acceleration change Δu at each time in the future control time domain N c is obtained:

[0112]

[0113] Thus, the future control time domain N​c Control of acceleration at each time instant:

[0114] u(k+j|k) = u(k+j-1) + Δu(k+j|k)

[0115] 2. Vehicle motion state information transmission

[0116] The control of the rear vehicle (the (i+1)th vehicle) requires the motion state of the front vehicle (the ith vehicle) as a control basis. Therefore, the vehicle (the ith vehicle) also needs to transmit its own motion state information to the rear vehicle (the (i+1)th vehicle).

[0117] After solving the ΔU(k) of the vehicle (the ith vehicle), based on the formula:

[0118] X(k) = Φx(k) + ΨΔU(k) + Fu(k-1) + Gw(k)

[0119] Convert the control state information sequence X(k) of the vehicle, and calculate the motion state information sequence S(k) of the vehicle in the future N p time domain: i

[0120]

[0121] The above control state quantity x(t) = [e s , e v , a i ] has a conversion relationship expression with the motion state information s i :

[0122]

[0123] Finally, the motion state information sequence S i (k) of the vehicle (the ith vehicle) is transmitted to the rear vehicle (the (i+1)th vehicle) to help the rear vehicle repeat the above process to complete vehicle control.

[0124] Four, delay compensation

[0125] 1. Actuator delay

[0126] After optimizing the optimal ΔU(k) of the vehicle (the ith vehicle), the lower control mechanism of the vehicle (the acceleration and deceleration control mechanism of each vehicle itself) needs to execute the corresponding acceleration and deceleration control instructions. However, due to the existence of actuator delay, there is a time delay error between the time when the control instruction is actually executed and the originally scheduled time. Therefore, corresponding actuator delay compensation measures need to be taken.

[0127] Let the relationship between the actuator delay and the sampling time be:

[0128] σ = ξT ​

[0129] where ξ is the floor function. According to the principle of model predictive control, MPC generates a control sequence and anticipates that the MPC cost function will gradually approach the target value when the control sequence is applied to the vehicle in turn. If the first value of the control sequence is taken as the actual control amount when there is an actuator delay, it will not be in line with the actual situation. In order to achieve the desired control effect after the actuator delay, the control amount (i.e. the acceleration increment value sequence) generated during the delay period needs to be applied to the vehicle after the delay in turn; that is, relative to the original acceleration control amount u(k|k) = u(k-1|k) + Au(k|k), the following compensation operation of the expected acceleration is performed:

[0130] u(k|k) = u(k-1|k) + Au(k|k) + Au(k+1|k) +... + Au(k+ξ|k)

[0131] Finally, u(k|k) after the above compensation is output as a control amount to the lower-level control mechanism of the vehicle to achieve the acceleration / deceleration of each vehicle in the vehicle platoon.

[0132] 2. Communication delay

[0133] In the process of transmitting vehicle motion state information from the front vehicle to the rear vehicle, there is a communication delay, so for the rear vehicle (the i+1th vehicle), the motion state information of the front vehicle (the ith vehicle) obtained has a time delay error from the actual situation. Therefore, in view of the information error caused by the communication delay, the vehicle state information is predicted using the MPC prediction sequence, and the prediction error is compensated. In order to compensate for the error between the predicted vehicle control state information and the actual information, the following compensation link is introduced:

[0134] At time k, assume that the predicted value for the next time is x(k+1|k); then for time k+1, the control state amount of the vehicle predicted by MPC is x'(k+1+j|k+1), j≥n, after experiencing a communication delay θ = nT.

[0135] Therefore, the prediction error value is defined as:

[0136] Δx(k+1|k) = x(k+1) - x(k+1|k)

[0137] Therefore, theoretically, x'(k+1+j|k+1), 0≤j≤N p needs to be compensated in reverse:

[0138] x(k+1+j|k+1) = x'(k+1+j|k+1) + Δx(k+1|k)

[0139] The specific compensation method in the application is: the rear vehicle (the i+1th vehicle) according to the known communication delay time θ = nT (n is rounded down), the motion state information sequence S i (k) of the front vehicle (the ith vehicle) at the k+n moment is selected in the k moment in the equation (k) to replace the original motion state information s i (k) of the front vehicle at the k moment. i (k|k) is obtained:

[0140]

[0141] In the formula, s i ′(k|k) is the motion state information of the front vehicle (the ith vehicle) actually used by the rear vehicle (the i+1th vehicle) after compensation via the application.

[0142] Finally, the rear vehicle (the i+1th vehicle) calculates the control state quantity x i (k) according to the compensated motion state information s i+1 ′(k|k) of the front vehicle and in combination with the motion state information s i+1 (k|k) of the rear vehicle itself:

[0143] e s,i+1 (k) = p i (k+n|k) - p i+1 (k) - L - hv i+1 (k) - d0

[0144] e v,i+1 (k) = v i (k+n|k) - v i+1 (k)

[0145] a i+1 (k) = a i+1 (k)

[0146] Five, simulation test

[0147] In the embodiment, the algorithm is verified under the communication delay of 100ms and the actuator delay of 200ms. The simulink model is built in MATLAB, the initial positions of 1 vehicle, 2 vehicles, 3 vehicles and 4 vehicles are respectively set to 40m, 30m, 20m and 10m, the initial speeds are all 0, the working condition is set to uniform acceleration motion with an acceleration of 1.5m / s 2 in 0-20s, uniform motion in 21-30s, uniform deceleration motion with an acceleration of -3m / s 2 in 31-40s, and finally uniform motion. The prediction time domain N p =10 and the control time domain N c =5 are set.

[0148] like Figure 2 As shown, under conditions of no communication delay and actuator delay, and considering both speed and distance errors, MPC provides good control performance. When the preceding vehicle accelerates or decelerates, it can control the speed error and spacing error within -3m / s to 1.5m / s and -0.75m to 1.5m, respectively. Furthermore, the speed tracking error and spacing error of vehicles along the convoy direction both show a decreasing trend, indicating that the errors do not propagate backward along the convoy, ensuring the convoy's chordal stability. Simultaneously, when the preceding vehicle moves at a constant speed, the speed and spacing errors of the following vehicles converge within a short time, further verifying the algorithm's effectiveness.

[0149] Figure 3 , Figure 4 The diagram shows the effect when there is a 100ms communication delay in the convoy and the effect after the algorithm improvement. It can be seen that when there is a 100ms communication delay, the maximum speed error exceeds -3m / s, and the maximum position tracking error exceeds 3m. After adding the optimization algorithm (including communication delay compensation), the speed error and spacing error are close to the ideal control effect. The speed error and spacing error are controlled between -3m / s and 1.5m / s and -0.75m and 1.5m, respectively, while ensuring string stability and error convergence.

[0150] Figure 5 , Figure 6 The image shows the effect of a 200ms actuator delay inside the vehicle and the effect after algorithm improvement. It can be seen that the actuator delay causes significant oscillations in speed and spacing errors, increasing both errors. Furthermore, the amplitude of the error oscillations gradually increases as the convoy moves backward, with the maximum amplitude of both speed error and spacing tracking error exceeding 1m / s. 2 The 1m error affected the stability of the convoy; simultaneously, the speed and spacing errors failed to converge to zero within a finite time. After incorporating an optimization algorithm (including actuator delay compensation), the error oscillation curve was significantly improved. Although local error fluctuations still existed, the fluctuation amplitude was controlled within 0.3m / s. 2 Both errors converge to 0 within a finite time, and the result is 0.3m. This demonstrates the effectiveness of the algorithm.

[0151] Figure 7 , Figure 8 The diagrams shown are the effects of a 100ms communication delay and a 200ms actuator delay, as well as the effect after the algorithm improvement. Figure 7 As can be seen, the increased error peak caused by communication delay and the oscillation effect caused by actuator delay are both reflected in the control effect. Figure 8After the control algorithm is applied to the application, the speed error value and the interval error value are close to the ideal effect, and the error oscillation improvement effect is consistent with the single delay verification effect. It is proved that the application can also improve the control effect of the vehicle fleet under the double delay condition, which proves the effectiveness of the algorithm.

[0152] In the description of the application, it should be understood that the terms "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the application and simplifying the description, and do not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the application.

[0153] The application is not limited to the above-mentioned embodiments, and any obvious improvements, replacements or modifications made by those skilled in the art without departing from the essential content of the application shall fall within the protection scope of the application.

Claims

1. A platoon longitudinal control method considering complex delays, characterized in that: A longitudinal vehicle following control system is established based on MPC, where vehicle control is implemented by solving an acceleration increment MPC predicts system states within a prediction horizon and calculates system outputs according to a discretized model and initial states ​ ； Wherein: ， ， ， ， ， ； wherein is the prediction horizon is the control state information sequence in the prediction horizon is the control state quantity of the host vehicle is the tracking error of the inter-vehicle distance between the host vehicle and the desired vehicle is the tracking error of the speed of the host vehicle relative to the preceding vehicle is the acceleration of the host vehicle is the preceding vehicle acceleration as a system measurement disturbance is the control input of the system, i.e. the desired acceleration is the control horizon is the prediction horizon ; , , , are respectively the state coefficient matrix, the input coefficient matrix, the disturbance quantity coefficient matrix, the output coefficient matrix is the unit matrix is the system sampling time interval Based on the above acceleration increment, the actuator delay compensation is performed, and the expected acceleration is calculated: ； where the actuator delay between the sampling time and: ； In the formulae rounded down; based on converts the control state information sequence of the host vehicle , based on calculates the motion state information sequence of the host vehicle in the future time domain ; Communication delay for motion state information , Downward rounding, communication delay compensation for motion state information transmitted from the preceding vehicle to the following vehicle ； wherein is the actual adopted motion state information of the preceding vehicle after compensation for the following vehicle, is the position of the host vehicle, is the speed of the host vehicle, is the longitudinal acceleration of the host vehicle.

2. The vehicle platoon longitudinal control method of claim 1, wherein: The objective function of the control system is: ； Wherein: ， ， ； In the formula, is an error weight coefficient matrix, is a control amount increment coefficient matrix.

3. The vehicle platoon longitudinal control method of claim 2, wherein: by minimizing an objective function solving , to obtain the acceleration change at each time in the future control time domain .​ 4. The vehicle platoon longitudinal control method of claim 3, wherein: Based on converts the control state information sequence of the host vehicle , based on calculates the motion state information sequence of the host vehicle in the future time domain : ； In the formula, is the position of the host vehicle, is the speed of the host vehicle, is the longitudinal acceleration of the host vehicle; the motion state information sequence of the host vehicle is transmitted to the rear vehicle.

5. The vehicle platoon longitudinal control method of claim 4, wherein: and The conversion relationship between them is as follows: ； wherein is the fixed headway time; is the vehicle length; is the minimum safety distance of the vehicle.

6. The vehicle platoon longitudinal control method of claim 1, wherein: The coefficient matrix , , , respectively: ； wherein is the fixed headway time, is the engine time constant of the vehicle.

7. The vehicle platoon longitudinal control method of claim 2, wherein: The coefficient matrix and are respectively: 。 8. The vehicle platoon longitudinal control method of claim 1, wherein: The control horizon and the prediction horizon are respectively , .

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