A road multi-vehicle longitudinal platoon safe following method based on model prediction control

Abstract

A method for safe platooning of multiple vehicles on roads based on model predictive control includes: establishing a discrete kinematic model of multiple vehicles considering vehicle spacing constraints and sideslip disturbances; designing a longitudinal model predictive controller based on the model, introducing a one-sided hinge function and time-varying weights to construct an asymmetric vehicle spacing penalty term in the cost function, and adding vehicle spacing and velocity / acceleration boundary constraints in rolling optimization to obtain longitudinal control quantities; designing a nonlinear extended state observer to estimate sideslip disturbances online; designing an integral sliding mode controller based on lateral tracking error, and combining a nonlinear fal(·) function to suppress chattering and output steering control quantities; this invention solves the problems of insufficient safety margin, decreased coordination accuracy, and lateral control chattering that easily occur in multi-vehicle platooning under strict vehicle spacing constraints and sideslip disturbances on curved roads, improves safe platooning capability under vehicle spacing constraints, enhances steering accuracy and trajectory tracking robustness on curved roads, and improves the smoothness of control commands.

Description

Technical Field

[0001] This invention relates to the field of autonomous driving control technology, specifically a method for safe platooning and following of multiple vehicles in longitudinal formation on roads based on model predictive control. Background Technology

[0002] With the development of vehicle-road cooperation and autonomous driving technologies, longitudinal platooning / convoy driving of multiple autonomous vehicles on urban roads has become an important means to improve road traffic efficiency, enhance traffic safety, and reduce energy consumption. Longitudinal platooning refers to multiple autonomous vehicles traveling along the same lane or the same reference trajectory, maintaining a predetermined distance (or headway) between vehicles while ensuring safety. Longitudinal control coordinates the platoon's speed, while lateral control tracks the road curvature and the reference trajectory.

[0003] In urban road environments, longitudinal formation control typically faces two types of key constraints / disturbances simultaneously:

[0004] 1) Vehicle spacing safety constraints: To avoid rear-end collisions, following vehicles must maintain a minimum safe distance / safe time distance from the vehicle in front. When the safety margin is small, the feasible domain of control input is significantly reduced, which can easily lead to problems such as control saturation, response lag and decreased queue coordination accuracy.

[0005] 2) Sideslip disturbance and lateral stability issues: On wet and slippery roads, curved sections, or during lane changes or turns, vehicles may experience sideslip disturbances (increased sideslip angle, decreased tire lateral stiffness, etc.), which can lead to yaw error and deterioration of lateral tracking accuracy, further affecting the coordination and safety of the longitudinal convoy.

[0006] To address the above problems, common solutions in the prior art include:

[0007] 1) Longitudinal formation control based on model predictive control: By establishing a longitudinal dynamics / kinematic model of the vehicle, constraints such as vehicle spacing, speed, and acceleration are introduced, and the control variables are solved under the rolling optimization framework to achieve vehicle spacing adjustment and speed tracking; it can also be extended to distributed MPC to reduce the pressure of centralized computing and communication.

[0008] 2) Lateral robust tracking based on sliding mode control: The robustness of sliding mode control to uncertain disturbances is used to improve lateral tracking capability; in order to reduce chattering, some schemes introduce nonlinear functions or neural network approximations.

[0009] 3) Disturbance estimation and compensation based on extended state observer: External disturbances or unmodeled dynamics are estimated by extending the state observer, and the estimated values ​​are used for control compensation to improve control performance under disturbances such as crosswinds and sideslip.

[0010] Considering the actual needs of multi-vehicle longitudinal platooning on urban roads, existing technologies have the following shortcomings:

[0011] 1) The handling of vehicle spacing constraints presents a safety and performance conflict due to the "symmetric penalty / uniform weight" approach;

[0012] Many longitudinal controls based on model predictive control employ symmetrical quadratic penalties for vehicle spacing errors in their cost functions, or use fixed weights to handle safety distance errors. When vehicle spacing approaches the safety lower bound, they cannot differentiate between penalties for "too small distance (high risk)" and "too large distance (low risk)," which can easily lead to the following problems: when the safety margin decreases and traffic disturbances increase, the controller is not "sensitive" enough to suppress the dangerous side (too small distance); conservative adjustments are made to avoid touching constraints, resulting in decreased responsiveness, reduced coordination accuracy, and even deterioration of tandem stability.

[0013] 2) Under sideslip disturbances, lateral control is prone to decreased steering accuracy and chattering issues;

[0014] When sideslip disturbances reduce tire lateral stiffness, steering response weakens, and traditional lateral control is prone to accumulating yaw error, leading to decreased trajectory tracking accuracy. Meanwhile, although sliding mode methods are robust, they are prone to chattering under real vehicle and discrete control conditions. Chattering can further cause uneven steering commands, affecting comfort and stability.

[0015] 3) The disturbance estimation and compensation mechanism is imperfect, making it difficult to simultaneously ensure both accuracy and real-time performance;

[0016] Some extended state observer schemes suffer from estimation lag when sideslip disturbances change rapidly or are insufficiently adaptable to nonlinear disturbances; other schemes increase observer bandwidth to improve estimation accuracy, which may amplify noise and induce control chattering. Due to the lack of co-design with the lateral robust controller, the "estimation-compensation-execution" link is not stable enough, which in turn affects the steering accuracy and platoon coordination of platooned vehicles in scenarios such as curves.

[0017] In addition, most of the existing solutions mentioned above are designed separately from the longitudinal or lateral perspectives, or lack a collaborative processing mechanism for the coexistence of "strict vehicle spacing constraints + sideslip disturbances" in coupled scenarios, resulting in performance bottlenecks under complex urban road conditions. Summary of the Invention

[0018] To address the aforementioned technical problems, this invention proposes a method for safe platooning and following of multiple vehicles in a road based on model predictive control, comprising:

[0019] A method for safe platooning of multiple vehicles on roads based on model predictive control includes the following steps:

[0020] S1. Considering the safety constraints of vehicle spacing and the influence of sideslip disturbance, establish a kinematic model of multiple automated vehicles, and provide the control input, state variables and constraint set;

[0021] S2. Construct a longitudinal model predictive controller, introduce vehicle spacing constraints, speed and acceleration boundary constraints in the prediction time domain, and solve the longitudinal control quantity through rolling optimization to achieve safe multi-vehicle following and longitudinal coordination.

[0022] S3. To address the issue of decreased lateral tracking accuracy caused by sideslip disturbances, a nonlinear extended state observer is designed to estimate sideslip disturbances online, providing disturbance compensation information for lateral control.

[0023] S4. An integral sliding mode controller is designed based on lateral tracking error, and disturbance estimation is combined for compensation to output steering control quantity, so as to realize robust lateral trajectory tracking of sideslip disturbance and improve steering accuracy on curved road sections.

[0024] S5. Establish the calibration relationship between the vehicle's longitudinal and lateral actuators, map the longitudinal control quantity to the throttle opening command or brake opening command, map the steering control quantity to the front wheel angle or steering wheel angle command, and send the mapped chassis control command to the vehicle chassis for execution, so as to achieve consistency between the controller output and the actual vehicle actuator.

[0025] Furthermore, step S1 is detailed as follows:

[0026] S1.1, Establish the first autonomous vehicles at the sampling time Discrete longitudinal kinematic model:

[0027]

[0028] in, Indicates the vehicle number of the following vehicle; This refers to the mileage traveled. Longitudinal velocity; For longitudinal control input, it represents the desired acceleration or desired deceleration; The sampling period;

[0029] S1.2 To ensure the safety and comfort of longitudinal formation, the first A self-driving car meets the following constraints:

[0030] 1) Driver and state box constraints

[0031] Considering the physical limitations and safe operation of autonomous vehicles, the control input constraints and linear velocity constraints are set as follows:

[0032]

[0033] in, and Indicates the acceleration limit. and Indicates the limit of linear velocity;

[0034] 2) Vehicle spacing constraints

[0035] To avoid collision, the first autonomous vehicles and the first The autonomous vehicles maintain a safe distance, and the vehicle distance constraint is set as follows:

[0036]

[0037] Among them, safety distance , It is a positive constant representing the minimum distance between adjacent autonomous vehicles. It is the safety margin coefficient;

[0038] Set up virtual pioneers to provide reference trajectories, the first The autonomous vehicle receives data from the first autonomous vehicle via its onboard communication unit. Motion information of an autonomous vehicle;

[0039] Virtual pioneers at a constant speed Driving, under steady-state conditions The control objective is to ensure that all following autonomous vehicles track the virtual leader under the aforementioned constraints, maintaining a small desired vehicle-to-vehicle distance:

[0040]

[0041] The reference speed is assigned to subsequent autonomous vehicles to organize longitudinal movement;

[0042] For the A self-driving car, reference speed Set as:

[0043]

[0044] in, Indicates the first The speed of the self-driving car Indicates the maximum allowed formation speed;

[0045] S1.3, proceed with the first... Kinematic analysis of an autonomous vehicle and These represent the resultant lateral forces at the front and rear tires, respectively. It is the front wheel steering angle. and These are the distances from the vehicle's center of gravity to the centers of the front and rear wheels, respectively.

[0046] The first in the horizontal layer The kinematic model of an autonomous vehicle is represented as follows:

[0047]

[0048] in, and These represent longitudinal velocity and lateral velocity, respectively. It is a lateral displacement. It's the yaw angle. It's angular velocity. and These are mass and moment of inertia; and for:

[0049]

[0050]

[0051] in, and These represent the lateral stiffness of the front and rear wheels, respectively. and These are the slip angles of the front and rear tires, respectively. and These represent the lateral slip forces of the front and rear tires, respectively.

[0052] Based on the assumption of a small slip angle with known longitudinal velocity, the results show that:

[0053]

[0054] make , , , and ;

[0055] The kinematic model was rewritten as follows:

[0056]

[0057] in,

[0058]

[0059] Since the tire-road friction coefficient is finite and the steering angle is physically limited, there exists a normal coefficient. and , making and .

[0060] Furthermore, step S2 is detailed as follows:

[0061] S2.1, The state error between adjacent autonomous vehicles is set as follows:

[0062]

[0063] set up For state error, there exists a linear feedback control law. and terminal set ,in It is a positive definite constant, such that In closed-loop system The value below is positive and unchanging, among which... Indicates the controller gain. It is a positive definite matrix. and It is the state gain matrix; for all Control input Satisfy input constraints; terminal constraints This holds true under optimization problems.

[0064] S2.2 To ensure the safety and comfort of longitudinal formation, a stage cost function is designed in the prediction time domain to penalize spacing errors. Speed ​​tracking error Input smoothness; using the super-spacing penalty as a soft constraint, stage cost function Represented as:

[0065]

[0066] in, , , and It is the penalty weighting coefficient. , This represents a modified linear unitary hinge function to address situations exceeding the comfort margin. Apply a soft penalty to excessively large spacing; asymmetric weights The following is given:

[0067]

[0068] in, It is the penalty weighting coefficient;

[0069] Terminal cost is defined as:

[0070]

[0071] in, and It is the terminal weight;

[0072] Based on dynamic model, constraint set and objective function , No. The cooperative longitudinal control of two autonomous vehicles can be represented by the following constrained finite-time optimization problem:

[0073]

[0074] Depends on

[0075]

[0076] in, The control input sequence is generated through this optimization problem. ;

[0077] Assuming at the initial time The optimization problem is feasible and the terminal error satisfies ,consider and terminal set Let the input constraint box and the velocity constraint box be respectively and If the terminal reference speed remains within the known range For Terminal set It is permissible under the following conditions:

[0078]

[0079] in, It is the velocity error component;

[0080] Considering the above longitudinal control system and optimization problem, if the first... The optimization problem for an autonomous vehicle is feasible at the initial moment, and the terminal state satisfies... Therefore, the above optimization problem is recursively feasible for all vehicles in every subsequent time step.

[0081] Furthermore, step S3 is as follows:

[0082] S3.1, Assume extended lateral state Extended sideslip disturbance , and The extended state system model is set as follows:

[0083]

[0084] in, ,and It is a continuous and bounded function;

[0085] S3.2. Based on the extended state system model, the nonlinear extended state observer is constructed as follows:

[0086]

[0087] in, , , , and For positive integers, The estimation error is the velocity state, and thus the estimation error system can be obtained as follows:

[0088]

[0089] in, This represents the error in perturbation estimation.

[0090] Considering a lateral tracking system and a nonlinear extended state observer, if there exist two positive constant parameters... and , making , and If it is a positive number, then and Bounded means that the estimation error system is stable.

[0091] Furthermore, step S4 is detailed as follows:

[0092] S4.1, Position error is defined as:

[0093]

[0094] in, and These represent the lateral position error and the heading angle error, respectively. and These represent the reference lateral position and the reference heading angle, respectively.

[0095] S4.2, The integral sliding surface is defined as:

[0096]

[0097] in, , , and For positive integers, ;

[0098] Sliding surface The derivative is:

[0099]

[0100] The following power-law arrival rule is given:

[0101]

[0102] in, , and It is a positive number;

[0103] S4.3. Combining the nonlinear extended state observer, the integral sliding mode control law is obtained:

[0104]

[0105] Consider a lateral tracking control system with an integral sliding mode controller. If a constant exists... and Then the position error and It converges to a sufficiently small neighborhood.

[0106] Furthermore, step S5 is detailed as follows:

[0107] S5.1 Apply step or ramp inputs to the throttle opening and brake opening respectively; synchronously collect vehicle speed. Longitudinal acceleration Throttle opening With brake opening ,in This forms a longitudinal calibration dataset. Steering wheel angle at speeds between 0 km / h and 30 km / h Apply multiple sets of inputs and simultaneously collect the front wheel steering angle. This forms a steering calibration dataset. The collected data is time-aligned, outlier removed, and filtered. Steady-state or quasi-steady-state segments are extracted to reduce the impact of noise and transient disturbances on the calibration results.

[0108] S5.2, Divide longitudinal acceleration relationships into two categories: driving and braking: when Establish driving relationships when Establish braking relationship in time;

[0109] Quadratic multinomial regression models were constructed for each vehicle speed range. Indicates the first The initial velocity threshold of the segment;

[0110] The driving relationship expression is:

[0111]

[0112] in, , and These are weighting coefficients;

[0113] The braking relationship expression is:

[0114]

[0115] in, , and These are weighting coefficients;

[0116] The least squares method is used to determine the model coefficients for each interval, and the objective function is constructed as follows:

[0117]

[0118]

[0119] in, Indicates that the vehicle speed is within a range The set of sample indexes;

[0120] The obtained coefficient set Stored in the vehicle-mounted industrial control computer for online instruction calculation;

[0121] S5.3, Based on steering calibration dataset Establish a linear relationship between the steering wheel angle and the front wheel angle:

[0122]

[0123] in, and It is the gain coefficient;

[0124] The steering ratio coefficient and zero-partial term are solved using the least squares method. and will Stored in the vehicle's industrial control computer for online steering command calculation;

[0125] S5.4 During control operation, the longitudinal model predicts the desired acceleration output of the controller. The onboard industrial control computer adjusts the speed based on the current vehicle speed. Determine the corresponding speed range and select the appropriate longitudinal relationship expression:

[0126] when At that time, reverse the throttle opening. ;

[0127] when At that time, the reverse braking opening ;

[0128] in, and It is obtained by solving the expression of the quadratic polynomial;

[0129] The integral sliding mode controller outputs the desired front wheel steering angle. The onboard industrial control computer inversely decodes the steering wheel angle command based on the steering relationship expression:

[0130]

[0131] Saturation constraints and rate of change constraints are applied to the throttle opening, brake opening, and steering wheel angle, respectively, to generate the final chassis control commands. The onboard industrial control computer sends throttle opening, brake opening and steering wheel angle commands to the vehicle chassis actuators via the onboard bus, and reads the vehicle speed, acceleration and steering angle information fed back by the chassis in the next sampling cycle for closed-loop update.

[0132] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0133] 1. To address the contradiction of "insensitivity to the danger side / overly conservative" under strict vehicle spacing constraints, this invention combines a one-sided hinge function with time-varying weights in the cost function of model predictive control to construct an asymmetric vehicle spacing penalty term: when the vehicle spacing approaches or touches the safety lower bound, the high-risk side of "too small distance" is rapidly penalized and adaptively weighted, thereby more effectively suppressing dangerous approach and reducing the risk of rear-end collisions when traffic disturbances increase; while when the vehicle spacing is within the safety margin range, the penalty weight is relatively gentle, allowing the controller to avoid unnecessary conservatism and balance responsiveness, cooperative accuracy, and queue stability.

[0134] 2. To address the issue of chattering and uneven steering commands caused by sliding mode in discrete implementations and actual vehicles, this invention introduces nonlinearity into the lateral control layer. The function performs nonlinear modulation on the error and sliding mode terms, which effectively reduces the chatter caused by high-frequency switching while maintaining the robustness of the sliding mode, making the steering control more continuous and smooth, thereby improving the comfort and lateral stability of the vehicle during urban driving and reducing the indirect disturbance caused by chatter to longitudinal formation coordination.

[0135] 3. To address the issues of decreased steering accuracy under sideslip disturbances such as curves and wet surfaces, and the tendency of traditional estimation compensation to lag or amplify noise, this invention employs a nonlinear extended state observer to estimate sideslip disturbances online and uses the estimation results for lateral control compensation. This enables the vehicle to maintain high disturbance tracking and suppression capabilities even when sideslip disturbances change rapidly, thereby improving the steering accuracy and trajectory tracking consistency of vehicles on curved sections in longitudinal formation scenarios, and further ensuring the safety and stability of vehicle spacing control. Attached Figure Description

[0136] Figure 1 This is a schematic diagram of the multi-vehicle longitudinal formation safe following method of the present invention.

[0137] Figure 2 This is a kinematic analysis diagram of the autonomous vehicle of the present invention.

[0138] Figure 3 The diagram shows the trajectory tracking control effect of three autonomous vehicles designed for an embodiment of the present invention.

[0139] Figure 4 The diagram shows the effect of the nonlinear extended state observer for three autonomous vehicles designed in an embodiment of the present invention.

[0140] Figure 5 This diagram illustrates the effect of maintaining distance between three autonomous vehicles as designed in an embodiment of the present invention.

[0141] Figure 6 This is an overall flowchart of the multi-vehicle longitudinal formation safe following method of the present invention. Detailed Implementation

[0142] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0143] This invention provides a model predictive control-based method for safe longitudinal platooning of multiple vehicles on urban roads. It proposes a longitudinal platooning control strategy for multiple autonomous vehicles under strict distance constraints and sideslip interference. A hierarchical control structure is designed to maintain accurate longitudinal coordination and ensure robust lateral trajectory tracking against sideslip interference.

[0144] This invention designs a model predictive controller to maintain the desired spacing and achieve coordinated longitudinal motion among multiple autonomous vehicles; for lateral motion, this invention designs a nonlinear extended state observer to estimate sideslip disturbances and an integral sliding mode controller to compensate for sideslip disturbances and slip interference, and ensures accurate trajectory tracking for each autonomous vehicle.

[0145] like Figure 6 As shown, a method for safe platooning of multiple vehicles on roads based on model predictive control includes the following steps:

[0146] S1. Considering the safety constraints of vehicle spacing and the influence of sideslip disturbance, establish a kinematic model of multiple automated vehicles, and provide the control input, state variables and constraint set;

[0147] S2. Construct a longitudinal model predictive controller, introduce vehicle spacing constraints, speed and acceleration boundary constraints in the prediction time domain, and solve the longitudinal control quantity through rolling optimization to achieve safe multi-vehicle following and longitudinal coordination.

[0148] S3. To address the issue of decreased lateral tracking accuracy caused by sideslip disturbances, a nonlinear extended state observer is designed to estimate sideslip disturbances online, providing disturbance compensation information for lateral control.

[0149] S4. An integral sliding mode controller is designed based on lateral tracking error, and disturbance estimation is combined for compensation to output steering control quantity, so as to realize robust lateral trajectory tracking of sideslip disturbance and improve steering accuracy on curved road sections.

[0150] S5. Establish the calibration relationship between the vehicle's longitudinal and lateral actuators, map the longitudinal control quantity to the throttle opening command or brake opening command, map the steering control quantity to the front wheel angle or steering wheel angle command, and send the mapped chassis control command to the vehicle chassis for execution, so as to achieve consistency between the controller output and the actual vehicle actuator.

[0151] Reference Figure 1 As shown below, each step will be explained in detail.

[0152] In step S1, considering the safety constraints of vehicle spacing and the influence of sideslip disturbances, a discrete kinematic model of multiple automated vehicles is established, and the control inputs, state variables, and constraint sets are given as follows:

[0153] S1.1, Establish the first autonomous vehicles at the sampling time Discrete longitudinal kinematic model:

[0154]

[0155] in, Indicates the vehicle number of the following vehicle; This refers to the mileage traveled. Longitudinal velocity; For longitudinal control input (desired acceleration or desired deceleration); The sampling period.

[0156] S1.2 To ensure the safety and comfort of longitudinal formation, the first A self-driving car meets the following constraints:

[0157] 1) Driver and state box constraints

[0158] Considering the physical limitations and safe operation of autonomous vehicles, the control input constraints and linear velocity constraints are set as follows:

[0159]

[0160] in, and Indicates the acceleration limit. and Indicates the limit of linear velocity.

[0161] 2) Vehicle spacing constraints

[0162] To avoid collision, the first The autonomous vehicle must be in contact with the first The autonomous vehicles maintain a safe distance, and the vehicle distance constraint is set as follows:

[0163]

[0164] Among them, safety distance , It is a positive constant representing the minimum distance between adjacent autonomous vehicles. It is the safety margin coefficient.

[0165] Set up virtual pioneers to provide reference trajectories, the first The autonomous vehicle receives data from the first autonomous vehicle via its onboard communication unit. Motion information of an autonomous vehicle.

[0166] Virtual pioneers at a constant speed Driving, i.e., under steady-state conditions The control objective is to ensure that all following autonomous vehicles track the virtual leader under the above constraints, maintaining a small desired vehicle-to-vehicle distance, i.e.:

[0167]

[0168] The reference speed is assigned to subsequent autonomous vehicles to organize longitudinal movement.

[0169] For the A self-driving car, reference speed Set as:

[0170]

[0171] in, Indicates the first The speed of the self-driving car This indicates the maximum allowed formation speed.

[0172] Therefore, on city roads, following an autonomous vehicle will not be faster than the vehicle in front, nor will it exceed the speed limit for longitudinal formation.

[0173] S1.3, proceed with the first... Kinematic analysis of an autonomous vehicle, such as Figure 2 As shown, Represents global coordinates. Indicates center of gravity The local vehicle coordinates are the origin. and These represent the combined longitudinal forces at the front and rear tires, respectively. and These represent the resultant lateral forces at the front and rear tires, respectively. It is the front wheel steering angle. and These are the distances from the vehicle's center of gravity to the centers of the front and rear wheels, respectively.

[0174] The first in the horizontal layer The kinematic model of an autonomous vehicle is represented as follows:

[0175]

[0176] in, and These represent longitudinal velocity and lateral velocity, respectively. It is a lateral displacement. It's the yaw angle. It's angular velocity. and These are mass and moment of inertia, respectively. and for:

[0177]

[0178]

[0179] in, and These represent the lateral stiffness of the front and rear wheels, respectively. and These are the slip angles of the front and rear tires, respectively. and These represent the lateral slip forces of the front and rear tires, respectively.

[0180] Based on the assumption of a small slip angle with known longitudinal velocity, the results show that:

[0181]

[0182] make , , , and Then, the kinematic model was rewritten as:

[0183]

[0184] in,

[0185]

[0186] Since the tire-road friction coefficient is finite and the steering angle is physically limited, there exists a normal coefficient. and , making and .

[0187] In step S2, a longitudinal model predictive controller is constructed. Vehicle spacing constraints and speed / acceleration boundary constraints are introduced in the prediction time domain. The longitudinal control variables are solved through rolling optimization to achieve safe multi-vehicle following and longitudinal coordination, as detailed below:

[0188] S2.1, The state error between adjacent autonomous vehicles is set as follows:

[0189]

[0190] set up For state error, there exists a linear feedback control law. and terminal set ,in It is an appropriate positive definite constant such that In closed-loop system The value below is positive and unchanging, among which... Indicates the controller gain. It is a suitable positive definite matrix. and It is the state gain matrix. Furthermore, for all... Control input Input constraints are satisfied. Finally, terminal constraints. This holds true under the premise of optimization problems.

[0191] S2.2 To ensure the safety and comfort of longitudinal formation, a stage cost function is designed in the prediction time domain to penalize spacing errors. Speed ​​tracking error Input smoothness; using the super-spacing penalty as a soft constraint, stage cost function Represented as:

[0192]

[0193] in, , , and It is the penalty weighting coefficient. , This represents a modified linear unitary hinge function to address situations exceeding the comfort margin. Apply a soft penalty to excessively large spacing; asymmetric weights The following is given:

[0194]

[0195] in, It is the penalty weighting coefficient.

[0196] In addition, the terminal cost is defined as:

[0197]

[0198] in, and It is the terminal weight.

[0199] Based on dynamic model, constraint set and objective function , No. The cooperative longitudinal control of two autonomous vehicles can be represented by the following constrained finite-time optimization problem:

[0200]

[0201] Depends on

[0202]

[0203] in, This optimization problem generates the control input sequence. .

[0204] Assuming at the initial time The optimization problem is feasible and the terminal error satisfies ;consider and terminal set Let the input constraint box and the velocity constraint box be respectively and If the terminal reference speed remains within the known range For Terminal set It is permissible under the following conditions:

[0205]

[0206] in, It is the velocity error component.

[0207] Considering the above longitudinal control system and optimization problem, if the first... The optimization problem for an autonomous vehicle is feasible at the initial moment, and the terminal state satisfies... Therefore, the above optimization problem is recursively feasible for all vehicles in every subsequent time step.

[0208] Proof: Assume the optimization problem is time-independent. The first Self-driving cars are feasible, making It satisfies the terminal error The corresponding optimal solution, proof time There is also a feasible solution at this location;

[0209] First input optimal sequence Application in time ,Right now ; Through the longitudinal control system, at any time The actual state is given as:

[0210]

[0211]

[0212] exist At time 1, the following candidate input sequences are constructed using standard shifting and additional strategies:

[0213]

[0214] in, , It is the terminal controller gain.

[0215] set up It is controlled by input The resulting state sequence; because this longitudinal control system is time-invariant, therefore for We can obtain:

[0216]

[0217]

[0218] for , Optimal shift Consistent, its satisfaction at time Vehicle spacing constraints, speed constraints, and input constraints at time [time value missing]. Candidate sequence Satisfaction, in every moment The previous predicted trajectory at time is moved. The feasible predictable trajectory at the location is obtained, and the spacing constraint is also satisfied.

[0219] Considering the terminal step size At any moment The terminal error at that point is set as follows:

[0220]

[0221] In control law Under its influence, the terminal set It is positive and unchanging; therefore, when At any given moment Terminal constraints It still holds true.

[0222] At the same time, for any Control Law It can satisfy both speed and input constraints. Therefore, in the terminal step... The additional end control input at that location and its corresponding state It also satisfies the speed constraint and input constraint.

[0223] In summary, at any time Candidate states can be constructed—input sequences This ensures that the constraints are satisfied. In other words, as long as the optimization problem is at time... If feasible, then at time It is still feasible, thus optimizing the problem for all Both are feasible recursively.

[0224] Consider a longitudinal control system and a model predictive controller. If a class-... function and , so that for any All conditions are met:

[0225]

[0226]

[0227] Then the longitudinal tracking error system is asymptotically stable, that is, when hour, .

[0228] Proof: Take the Lyapunov function To optimize for the minimum cost, i.e.:

[0229]

[0230] From the inequality Therefore, It is a positive definite and radially unbounded function; the candidate control sequence Substituting into the cost function, we get:

[0231]

[0232] in,

[0233]

[0234]

[0235] Therefore, the Lyapunov function It can be written as:

[0236]

[0237] Therefore, we can conclude that:

[0238]

[0239] Existing class - function , so that for any have

[0240]

[0241] Considering ,and We can obtain:

[0242]

[0243] in,

[0244]

[0245] Furthermore, we can obtain:

[0246]

[0247] And because ,and For a moment The actual control input applied, therefore, has

[0248]

[0249] Therefore, Monotonically non-increasing, and when The error decreases strictly over time. Therefore, the longitudinal tracking error system is asymptotically stable.

[0250] In step S3, to address the issue of decreased lateral tracking accuracy caused by sideslip disturbances, a nonlinear extended state observer is designed to estimate the sideslip disturbances online, providing disturbance compensation information for lateral control, as detailed below:

[0251] S3.1, Assume extended lateral state Extended sideslip disturbance , and The extended state system model is set as follows:

[0252]

[0253] in, ,and It is a continuous and bounded function.

[0254] S3.2. Based on the extended state system model, the nonlinear extended state observer is constructed as follows:

[0255]

[0256] in, , , , and For positive integers, The estimation error is the velocity state, and thus the estimation error system can be obtained as follows:

[0257]

[0258] in, This represents the disturbance estimation error.

[0259] Considering a lateral tracking system and a nonlinear extended state observer, if two suitable constant parameters exist... and , making ,but and Bounded means that the estimation error system is stable.

[0260] Proof: Choose the Lyapunov function:

[0261]

[0262] in, , and It is a positive number;

[0263] when At that time, Differentiating, we get:

[0264]

[0265] in,

[0266]

[0267] and , Therefore, it can be concluded that , ,therefore It is a negative definite function. On a parabola Located in the plane Within the area below, you can obtain However, in parabolic surfaces With plane In the intersecting upper region, No longer guaranteed to be negative definite; for intersecting boundaries ,have ;

[0268] Using Young's inequality, we can obtain:

[0269]

[0270] in, ;Pick , ,get:

[0271]

[0272] Therefore, there are two positive numbers. , so that:

[0273]

[0274] because It is bounded, therefore it can be known that it is within the upper region. and Each is bounded; furthermore, when When it is sufficiently large, there is By choosing the appropriate ensure ;at this time Keep within the linear sector, i.e. Therefore, this will not be discussed further. The situation is as follows. From the error equation... It can be seen that, To be launched In particular, when When it is bounded, It also has boundaries.

[0275] Combining the conclusions of the lower region with the boundaries of the upper region, we can obtain that for any estimation error and Both are bounded. Using the same method, by selecting an appropriate positive gain... and This can also prove and It is bounded. Therefore, the estimation error system is stable.

[0276] In step S4, an integral sliding mode controller is designed based on the lateral tracking error, and compensation is performed by combining disturbance estimation to output the steering control quantity, thereby achieving robust lateral trajectory tracking against sideslip disturbances and improving steering accuracy on curved sections, as detailed below:

[0277] S4.1, Position error is defined as:

[0278]

[0279] in, and These represent the lateral position error and the heading angle error, respectively. and These represent the reference lateral position and the reference heading angle, respectively.

[0280] S4.2, The integral sliding surface is defined as:

[0281]

[0282] in, , , For appropriate positive numbers, .

[0283] Sliding surface The derivative is:

[0284]

[0285] The following power-law arrival rule is given:

[0286]

[0287] in, , and It is a suitable positive number.

[0288] S4.3. Combining the nonlinear extended state observer, the integral sliding mode control law can be obtained:

[0289]

[0290] Consider a lateral tracking control system with an integral sliding mode controller. If a suitable constant exists... and Then the position error and It converges to a sufficiently small neighborhood.

[0291] Proof: Choose the following Lyapunov function:

[0292]

[0293] The derivative is:

[0294]

[0295] Due to estimation error It is bounded, therefore it has positive constants. , making ,and .when Sometimes,

[0296]

[0297] Therefore, when hour, It is negative definite, which means asymptotic convergence to the boundary .when At that time, it can be further obtained

[0298]

[0299] or

[0300]

[0301] When the condition is met Sometimes, Established.

[0302] Therefore, we can conclude that: , Under the condition of integral sliding surface It asymptotically converges to a sufficiently small value. Therefore, the lateral position error Eventually, it converges to a sufficiently small range.

[0303] In step S5, the calibration relationship between the vehicle's longitudinal and lateral actuators is established. The longitudinal control quantity is mapped to the throttle opening command or the brake opening command, and the steering control quantity is mapped to the front wheel angle or the steering wheel angle command. The mapped chassis control commands are then sent to the vehicle chassis for execution to achieve consistency between the controller output and the actual vehicle actuators, as detailed below:

[0304] S5.1 Apply step or ramp inputs to the throttle opening and brake opening respectively; synchronously collect vehicle speed. Longitudinal acceleration Throttle opening With brake opening This forms a longitudinal calibration dataset. Steering wheel angle at speeds between 0 km / h and 30 km / h Apply multiple sets of inputs and simultaneously collect the front wheel steering angle. This forms a steering calibration dataset. The collected data is time-aligned, outlier removed, and filtered. Steady-state or quasi-steady-state segments are extracted to reduce the impact of noise and transient disturbances on the calibration results.

[0305] S5.2, Divide longitudinal acceleration relationships into two categories: driving and braking: when Establish driving relationships when Establish braking relationship in time;

[0306] Quadratic multinomial regression models were constructed for each vehicle speed range. Indicates the first The initial velocity threshold of the segment;

[0307] The driving relationship expression is:

[0308]

[0309] in, , and It is an appropriate weighting coefficient;

[0310] The braking relationship expression is:

[0311]

[0312] in, , and These are appropriate weighting coefficients.

[0313] The least squares method is used to determine the model coefficients for each interval, and the objective function is constructed as follows:

[0314]

[0315]

[0316] in, Indicates that the vehicle speed is within a range The sample index set.

[0317] The obtained coefficient set It is stored in the vehicle-mounted industrial control computer for online instruction calculation.

[0318] S5.3, Based on steering calibration dataset Establish a linear relationship between the steering wheel angle and the front wheel angle:

[0319]

[0320] in, and It is the gain coefficient.

[0321] The steering ratio coefficient and zero-partial term are solved using the least squares method. and will Stored in the vehicle's industrial control computer for online steering command calculation;

[0322] S5.4 During control operation, the longitudinal model predicts the desired acceleration output of the controller. The onboard industrial control computer adjusts the speed based on the current vehicle speed. Determine the corresponding speed range and select the appropriate longitudinal relationship expression:

[0323] when At that time, reverse the throttle opening. ;

[0324] when At that time, the reverse braking opening ;

[0325] in, and It is obtained by solving the expression of the quadratic polynomial;

[0326] The integral sliding mode controller outputs the desired front wheel steering angle. The onboard industrial control computer inversely decodes the steering wheel angle command based on the steering relationship expression:

[0327]

[0328] Saturation constraints and rate of change constraints are applied to the throttle opening, brake opening, and steering wheel angle, respectively, to generate the final chassis control commands. The onboard industrial control computer sends the throttle opening, brake opening, and steering wheel angle commands to the vehicle chassis actuators via the onboard bus, and reads the vehicle speed, acceleration, and steering angle information fed back by the chassis in the next sampling cycle for closed-loop updates.

[0329] Example:

[0330] To verify the effectiveness of the multi-vehicle longitudinal platooning safety following method of the present invention, specific embodiments are provided for illustration:

[0331] Pick That is, a convoy of 3 vehicles, with the following parameter settings for the autonomous vehicles:

[0332] Vehicle quality Distance from center of mass to front axle Distance from center of mass to rear axle Front wheel lateral stiffness Rear wheel lateral stiffness Moment of inertia about the vertical axis Front wheel slip angle Rear wheel slip angle The sampling period is selected as The prediction time domain is set to The minimum following distance is .

[0333] In addition, the main parameter values ​​for the model predictive controller, integral sliding mode controller, and nonlinear extended state observer are as follows:

[0334] ; ; ; ; ;as well as .

[0335] Therefore, the trajectory tracking control effect of the three designed autonomous vehicles can be obtained as follows: Figure 3 As shown, the nonlinear extended state observer effect for the three vehicles is as follows: Figure 4 As shown, the vehicle spacing maintenance effect is as follows: Figure 5 As shown above, the results demonstrate that the present invention can improve the lateral tracking accuracy on curved road sections under road conditions where sideslip disturbances exist, and achieve multi-vehicle longitudinal safe following and cooperative stability under strict vehicle spacing constraints.

[0336] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for safe platooning and following of multiple vehicles on roads based on model predictive control, characterized in that, Includes the following steps: S1. Considering the safety constraints of vehicle spacing and the influence of sideslip disturbance, establish a kinematic model of multiple automated vehicles, and provide the control input, state variables and constraint set; S2. Construct a longitudinal model predictive controller, introduce vehicle spacing constraints, speed and acceleration boundary constraints in the prediction time domain, and solve the longitudinal control quantity through rolling optimization to achieve safe multi-vehicle following and longitudinal coordination. S3. To address the issue of decreased lateral tracking accuracy caused by sideslip disturbances, a nonlinear extended state observer is designed to estimate sideslip disturbances online, providing disturbance compensation information for lateral control. S4. An integral sliding mode controller is designed based on lateral tracking error, and disturbance estimation is combined for compensation to output steering control quantity, so as to realize robust lateral trajectory tracking of sideslip disturbance and improve steering accuracy on curved road sections. S5. Establish the calibration relationship between the vehicle's longitudinal and lateral actuators, map the longitudinal control quantity to the throttle opening command or brake opening command, map the steering control quantity to the front wheel angle or steering wheel angle command, and send the mapped chassis control command to the vehicle chassis for execution, so as to achieve consistency between the controller output and the actual vehicle actuator.

2. The method for safe platooning of multiple vehicles on a road based on model predictive control according to claim 1, characterized in that, Step S1 is as follows: S1.1, Establish the first autonomous vehicles at the sampling time Discrete longitudinal kinematic model: in, Indicates the vehicle number of the following vehicle; This refers to the mileage traveled. Longitudinal velocity; For longitudinal control input, it represents the desired acceleration or desired deceleration; The sampling period; S1.2 To ensure the safety and comfort of longitudinal formation, the first A self-driving car meets the following constraints: 1) Driver and state box constraints Considering the physical limitations and safe operation of autonomous vehicles, the control input constraints and linear velocity constraints are set as follows: in, and Indicates the acceleration limit. and Indicates the limit of linear velocity; 2) Vehicle spacing constraints To avoid collision, the first autonomous vehicles and the first The autonomous vehicles maintain a safe distance, and the vehicle distance constraint is set as follows: Among them, safety distance , It is a positive constant representing the minimum distance between adjacent autonomous vehicles. It is the safety margin coefficient; Set up virtual pioneers to provide reference trajectories, the first The autonomous vehicle receives data from the first autonomous vehicle via its onboard communication unit. Motion information of an autonomous vehicle; Virtual pioneers at a constant speed Driving, under steady-state conditions The control objective is to ensure that all following autonomous vehicles track the virtual leader under the aforementioned constraints, maintaining a small desired vehicle-to-vehicle distance: The reference speed is assigned to subsequent autonomous vehicles to organize longitudinal movement; For the A self-driving car, reference speed Set as: in, Indicates the first The speed of the self-driving car Indicates the maximum allowed formation speed; S1.3, proceed with the first... Kinematic analysis of an autonomous vehicle and These represent the resultant lateral forces at the front and rear tires, respectively. It is the front wheel steering angle. and These are the distances from the vehicle's center of gravity to the centers of the front and rear wheels, respectively. The first in the horizontal layer The kinematic model of an autonomous vehicle is represented as follows: in, and These represent longitudinal velocity and lateral velocity, respectively. It is a lateral displacement. It's the yaw angle. It's angular velocity. and These are mass and moment of inertia; and for: in, and These represent the lateral stiffness of the front and rear wheels, respectively. and These are the slip angles of the front and rear tires, respectively. and These represent the lateral slip forces of the front and rear tires, respectively. Based on the assumption of a small slip angle with known longitudinal velocity, the results show that: make , , , and ; The kinematic model was rewritten as follows: in, Since the tire-road friction coefficient is finite and the steering angle is physically limited, there exists a normal coefficient. and , making and .

3. The method for safe platooning of multiple vehicles on a road based on model predictive control according to claim 2, characterized in that, Step S2 is as follows: S2.1, The state error between adjacent autonomous vehicles is set as follows: set up For state error, there exists a linear feedback control law. and terminal set ,in It is a positive definite constant, such that In closed-loop system The value below is positive and unchanging, among which... Indicates the controller gain. It is a positive definite matrix. and It is the state gain matrix; for all Control input Satisfy input constraints; terminal constraints This holds true under optimization problems. S2.2 To ensure the safety and comfort of longitudinal formation, a stage cost function is designed in the prediction time domain to penalize spacing errors. Speed ​​tracking error Input smoothness; using the super-spacing penalty as a soft constraint, stage cost function Represented as: in, , , and It is the penalty weighting coefficient. , This represents a modified linear unitary hinge function to address situations exceeding the comfort margin. Apply a soft penalty to excessively large spacing; asymmetric weights The following is given: in, It is the penalty weighting coefficient; Terminal cost is defined as: in, and It is the terminal weight; Based on dynamic model, constraint set and objective function , No. The cooperative longitudinal control of two autonomous vehicles can be represented by the following constrained finite-time optimization problem: Depends on in, The control input sequence is generated through this optimization problem. ; Assuming at the initial time The optimization problem is feasible and the terminal error satisfies ,consider and terminal set Let the input constraint box and the velocity constraint box be respectively and If the terminal reference speed remains within the known range For Terminal set It is permissible under the following conditions: in, It is the velocity error component; Considering the above longitudinal control system and optimization problem, if the first... The optimization problem for an autonomous vehicle is feasible at the initial moment, and the terminal state satisfies... Therefore, the above optimization problem is recursively feasible for all vehicles in every subsequent time step.

4. A method for safe platooning of multiple vehicles on a road based on model predictive control, as described in claim 3, is characterized in that... Step S3 is as follows: S3.1, Assume extended lateral state Extended sideslip disturbance , and The extended state system model is set as follows: in, ,and It is a continuous and bounded function; S3.

2. Based on the extended state system model, the nonlinear extended state observer is constructed as follows: in, , , , and For positive integers, The estimation error is the velocity state, and thus the estimation error system can be obtained as follows: in, This represents the error in perturbation estimation. Considering a lateral tracking system and a nonlinear extended state observer, if there exist two positive constant parameters... and , making , and If it is a positive number, then and Bounded means that the estimation error system is stable.

5. A method for safe platooning of multiple vehicles on a road based on model predictive control, as described in claim 4, is characterized in that... Step S4 is as follows: S4.1, Position error is defined as: in, and These represent the lateral position error and the heading angle error, respectively. and These represent the reference lateral position and the reference heading angle, respectively. S4.2, The integral sliding surface is defined as: in, , , and For positive integers, ; Sliding surface The derivative is: The following power-law arrival rule is given: in, , and It is a positive number; S4.

3. Combining the nonlinear extended state observer, the integral sliding mode control law is obtained: Consider a lateral tracking control system with an integral sliding mode controller. If a constant exists... and Then the position error and It converges to a sufficiently small neighborhood.

6. A method for safe platooning of multiple vehicles on a road based on model predictive control, as described in claim 5, is characterized in that... Step S5 is as follows: S5.1 Apply step or ramp inputs to the throttle opening and brake opening respectively; synchronously collect vehicle speed. Longitudinal acceleration Throttle opening With brake opening ,in This forms a longitudinal calibration dataset. Steering wheel angle at speeds between 0 km / h and 30 km / h Apply multiple sets of inputs and simultaneously collect the front wheel steering angle. This forms a steering calibration dataset. The collected data is time-aligned, outlier removed, and filtered. Steady-state or quasi-steady-state segments are extracted to reduce the impact of noise and transient disturbances on the calibration results. S5.2, Divide longitudinal acceleration relationships into two categories: driving and braking: when Establish driving relationships when Establish braking relationship in time; Quadratic multinomial regression models were constructed for each vehicle speed range. Indicates the first The initial velocity threshold of the segment; The driving relationship expression is: in, , and These are weighting coefficients; The braking relationship expression is: in, , and These are weighting coefficients; The least squares method is used to determine the model coefficients for each interval, and the objective function is constructed as follows: in, Indicates that the vehicle speed is within a range The set of sample indexes; The obtained coefficient set Stored in the vehicle-mounted industrial control computer for online instruction calculation; S5.3, Based on steering calibration dataset Establish a linear relationship between the steering wheel angle and the front wheel angle: in, and It is the gain coefficient; The steering ratio coefficient and zero-partial term are solved using the least squares method. and will Stored in the vehicle's industrial control computer for online steering command calculation; S5.4 During control operation, the longitudinal model predicts the desired acceleration output of the controller. The onboard industrial control computer adjusts the speed based on the current vehicle speed. Determine the corresponding speed range and select the appropriate longitudinal relationship expression: when At that time, reverse the throttle opening. ; when At that time, the reverse braking opening ; in, and It is obtained by solving the expression of the quadratic polynomial; The integral sliding mode controller outputs the desired front wheel steering angle. The onboard industrial control computer inversely decodes the steering wheel angle command based on the steering relationship expression: Saturation constraints and rate of change constraints are applied to the throttle opening, brake opening, and steering wheel angle, respectively, to generate the final chassis control commands. The onboard industrial control computer sends throttle opening, brake opening and steering wheel angle commands to the vehicle chassis actuators via the onboard bus, and reads the vehicle speed, acceleration and steering angle information fed back by the chassis in the next sampling cycle for closed-loop update.

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