Two-dimensional planar vehicle platoon control method based on fixed time pre-scheduled performance control

Abstract

This invention provides a two-dimensional planar vehicle formation control method based on fixed-time predetermined performance control, relating to the field of vehicle formation technology. First, the actual distance and azimuth angle between the following vehicle and the target vehicle are calculated, along with the distance tracking error and heading angle tracking error of the following vehicle. Then, a fixed-time predetermined performance function, independent of the initial tracking error value, is constructed to nonlinearly transform the intermediate tracking error into an equivalent tracking error, thereby constructing a composite sliding surface. Further, a second-order composite sliding surface is designed, and an adaptive law is established. Combined with a fixed-time approaching law and a third-order nonlinear dynamic model of the vehicle, the final control input of the following vehicle is calculated, achieving coordinated control of the following vehicle. This method does not depend on the initial value of the tracking error and can effectively constrain the tracking error under any initial state, ensuring that all tracking errors converge to the steady-state region within a fixed time.

Description

Technical Field

[0001] This invention relates to the field of vehicle platooning technology, and in particular to a two-dimensional planar vehicle platooning control method based on fixed-time predetermined performance control. Background Technology

[0002] Vehicle platooning technology, as a core component of intelligent transportation systems, enables multiple vehicles to travel in a compact and stable formation through wireless communication and cooperative control. This effectively improves road traffic efficiency, reduces fuel consumption, and enhances driving safety. Traditional research on vehicle platooning control has largely focused on one-dimensional straight-line scenarios, with the primary control objective being to maintain a fixed distance between vehicles. However, in real-world traffic environments, vehicles need to perform complex maneuvers in a two-dimensional plane, such as merging into multiple lanes, cooperative lane changes, and cornering. These scenarios place higher demands on platooning control: it requires not only controlling the longitudinal distance between vehicles but also precisely coordinating their lateral position and heading angle, while ensuring driving safety and passenger comfort throughout the entire dynamic process.

[0003] In two-dimensional planar formation control, ensuring the transient and steady-state performance of the system is crucial. Predefined performance control (PPC) is a control strategy that pre-defines the convergence process of the tracking error. By designing a time-varying performance function, the error is constrained within a preset boundary, thereby ensuring overshoot, convergence speed, and steady-state accuracy. However, most existing PPC methods are sensitive to the initial value of the tracking error; that is, the initial boundary of the performance function must include the initial value of the error, otherwise the control law will fail. This limits its application in real-world scenarios dealing with sudden situations or uncertain initial states. Furthermore, most methods can only guarantee that the error converges in infinite time (asymptotic stability) or in finite time, dependent on the initial value. They cannot achieve fixed-time stability where the upper bound of the convergence time can be pre-defined and is independent of the initial state, thus limiting the predictability and reliability of the system response.

[0004] On the other hand, sliding mode control (SMC) is widely used in vehicle control due to its strong robustness to parameter uncertainties and external disturbances. However, traditional sliding mode control suffers from chattering, and its finite-time convergence and settling time depend on the initial state. Although fixed-time sliding mode control overcomes this drawback, combining it with the PPC method to ensure fixed-time convergence while strictly satisfying the error constraints defined by the performance function, and further addressing singularity, reducing chattering, and achieving train stability (i.e., preventing error propagation amplification along the vehicle convoy), remains a challenging problem.

[0005] Therefore, there is an urgent need for an intelligent vehicle platooning control method that is applicable to complex two-dimensional plane scenarios, is completely independent of initial conditions, can pre-set convergence time and dynamic performance, and has strong robustness. Summary of the Invention

[0006] The technical problem to be solved by this invention is to address the shortcomings of the prior art by providing a two-dimensional planar vehicle formation control method based on fixed-time predetermined performance control. This method eliminates the dependence on the initial value of the tracking error and can effectively constrain the error under any initial state. It ensures that all tracking errors converge to an arbitrarily small steady-state interval within a fixed time period set by the user and independent of the initial state. During the convergence process, it actively limits the overshoot of the tracking error to ensure a smooth and fast transient response. In the presence of model uncertainties and external disturbances, it guarantees the stability of the closed-loop system and ensures that the spacing error is not amplified when it propagates along the vehicle platoon.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a two-dimensional planar vehicle platooning control method based on fixed-time predetermined performance control, applied to a vehicle platoon consisting of one lead vehicle and N following vehicles, comprising the following steps:

[0008] Step S1: Obtain the actual position and heading information of each following vehicle in the two-dimensional plane, as well as the motion state information of the leading or trailing vehicle corresponding to each following vehicle, and then calculate the actual distance and actual azimuth between the following vehicle and the target leading vehicle.

[0009] Step S2: Based on the actual distance and azimuth angle between the following vehicle and the target vehicle, as well as the pre-stored expected distance and expected azimuth angle, calculate the tracking error of the following vehicle. The tracking error includes distance tracking error and heading angle tracking error.

[0010] Step S3: Based on the initial tracking error of the following vehicle and the preset convergence time, steady-state error range, and overshoot constraint parameters, construct a fixed-time predetermined performance function that is independent of the initial tracking error value. The performance function is used to provide time-varying constraint boundaries for the transient and steady-state performance of the tracking error.

[0011] Step S4: Based on the fixed-time predetermined performance function, perform a nonlinear transformation on the intermediate tracking error to map the tracking error from the constrained original space to the unconstrained new space, and obtain the transformed equivalent tracking error;

[0012] Step S5: Based on the equivalent tracking error and its derivative, and combined with the fixed-time convergence parameter, construct a composite sliding surface;

[0013] Step S6: Based on the composite sliding surface and its derivative, a second-order composite sliding surface is further designed, and an adaptive law is established to estimate the upper bound of the disturbance in real time. Combined with the fixed-time approaching law and the third-order nonlinear dynamic model of the vehicle, the final control input of the following vehicle is calculated.

[0014] Step S7: Send the longitudinal drive control quantity and lateral steering control quantity of the following vehicle to the actuator of the following vehicle to achieve coordinated control of the following vehicle, so that it tracks the motion state of the leading vehicle in a dynamic process with a preset overshoot amount within a preset fixed time.

[0015] Furthermore, the actual position and heading information of the following vehicle in the two-dimensional plane includes the x-coordinate of the i-th following vehicle in the global coordinate system. y-axis and heading angle ,in, , The total number of vehicles following in the formation; the motion status information of the leading vehicle or the vehicle in front, including the x-coordinate of the leading vehicle or the vehicle in the global coordinate system. y-axis ,speed and heading angle The subscript i-1 indicates the number of the car preceding the i-th following car. When i equals 1, the car preceding the i-th following car is the lead car.

[0016] Furthermore, the specific method for calculating the tracking error of the following vehicle is as follows:

[0017] Based on the actual position information of the following vehicle and the position information of the target vehicle in front, calculate the actual distance between the i-th following vehicle and the vehicle in front. relative azimuth Then, the distance tracking error is calculated based on the preset expected distance and expected relative angle. and heading angle tracking error As shown in the formula below:

[0018] ;

[0019] ;

[0020] in, For time, To preset the desired distance, This is the preset desired relative angle.

[0021] Furthermore, the specific method for constructing the fixed-time predetermined performance function independent of the initial tracking error value is as follows:

[0022] First, we introduce a time-related offset function. Its expression is:

[0023] ;

[0024] in, This is a preset offset time constant;

[0025] Using the offset function The original tracking error of the following vehicle After processing, a new intermediate tracking error is obtained. Where j=1 represents the distance tracking error and j=2 represents the heading angle tracking error; then, a method is designed to constrain the intermediate tracking error. The time-varying performance boundary function, the performance boundary function including the upper boundary function. With lower boundary function The specific forms of the two boundary functions are determined by the preset convergence time of the tracking error. Initial boundary values ​​of the core decay function Steady-state boundary values and boundary shape parameters The original tracking error is jointly determined and ensured for any initial time. Intermediate tracking error Always at the initial boundary and between;

[0026] The upper boundary function The design formula is:

[0027] ;

[0028] The lower boundary function The design formula is:

[0029] ;

[0030] in, For symbolic functions, It is a preset positive integer, and ; The core decay function is expressed as follows:

[0031] ;

[0032] Based on the fundamental requirements of predetermined performance control, the intermediate tracking error at the initial moment... The following conditions must be met:

[0033] ;

[0034] in, The upper boundary functions are respectively and lower boundary function The value at the initial moment, These are the second set of performance boundary functions. and The value at the initial moment, and The second upper boundary function and the second lower boundary function are respectively shown in the following formulas:

[0035] ;

[0036] in, This is the offset function used to control the overshoot shape.

[0037] Furthermore, the composite sliding surface constructed in step S5 is shown in the following formula:

[0038] ;

[0039] in, It is a composite sliding surface. For equivalent tracking error, for First derivative, For power sign functions, , All are sliding mode gains. The parameters are the power-law parameters for fixed-time convergence.

[0040] Furthermore, step S6 is based on a composite sliding surface. and its derivative The design of the second-order composite sliding surface As shown in the formula below:

[0041] ;

[0042] in, and The value is a preset positive constant, representing the gain coefficient of the second-order sliding surface. and This is a predefined composite function containing linear terms and smooth exponential terms;

[0043] The established adaptive law is as follows:

[0044] ;

[0045] ;

[0046] in, and These are the estimated values ​​of the longitudinal and lateral lumped disturbances of the i-th following vehicle, respectively. A nonlinear feedback mechanism is used to ensure that the estimation error enters the steady-state range within a fixed time. They are respectively and The derivative; , All are gain functions obtained from predetermined performance conversion. Let i be the state-related variables of the i-th following vehicle; The preset proportional gain constant satisfies ; These are the state values ​​of the second-order composite sliding surface in the longitudinal and transverse directions, respectively, serving as the driving terms of the adaptive law; These are all preset adaptive law positive gain parameters used to adjust the convergence rate of the perturbation estimation; All are power-law parameters of fixed-time convergence correlation, satisfying and This ensures that the disturbance estimation error converges to the steady-state region within a fixed time independent of the initial state;

[0047] Fixed-time approach law Substituting the third-order nonlinear dynamics model of the vehicle, the final control input of the following vehicle is calculated, where, This is a preset positive gain constant for the approach law, used to adjust the rate at which the system state approaches the sliding surface; Let the power parameter of the fixed-time reaching law satisfy... .

[0048] Furthermore, the final control inputs of the following vehicle include longitudinal drive control quantities for adjusting the distance and speed, and lateral steering control quantities for adjusting the heading angle and lateral offset.

[0049] The beneficial effects of adopting the above technical solution are as follows: The two-dimensional planar vehicle formation control method based on fixed-time predetermined performance control provided by the present invention (1) has no initial error dependence. By introducing an initial offset mechanism and an innovative performance function structure, the problem of prior knowledge dependence on the initial value of the tracking error is solved, so that the predetermined performance control can be applied to any initial state, improving the practicality and robustness of the system. (2) The convergence time is predictable and adjustable. Through the dual design of fixed-time performance function and fixed-time sliding mode controller, the convergence of the system state within the fixed time set by the user is realized. The operator can directly set the convergence time parameter according to the task requirements (such as the merging time requirement), which improves the predictability and controllability of the system. (3) Superior dynamic and steady-state performance. The designed performance function can finely shape the convergence trajectory of the error, effectively limit overshoot, realize a smooth and fast transition process, and ensure that the steady-state error is less than any preset small positive number, taking into account driving safety, comfort and control accuracy. (4) Strong scene adaptability, adaptable to multi-lane merging and lane changing scenarios in two-dimensional plane, ensuring queue chord stability (i.e., the error of the following vehicle is not greater than the error of the preceding vehicle). (5) High robustness, the error conversion mechanism realizes the equivalent transmission of constrained error and unconstrained error, and can still ensure the error constraint effect even if there is vehicle dynamic disturbance. Attached Figure Description

[0050] Figure 1 A flowchart of a two-dimensional planar vehicle formation control method based on fixed-time predetermined performance control provided in an embodiment of the present invention;

[0051] Figure 2 This is a schematic diagram illustrating the configuration of a two-dimensional planar vehicle queue according to an embodiment of the present invention;

[0052] Figure 3 The vehicle change diagrams are obtained from the simulation results of the multi-lane merging scenario provided in the embodiments of the present invention, wherein (a) is a diagram of the vehicle position trajectory change under the multi-lane merging scenario, and (b) is a diagram of the vehicle heading angle change.

[0053] Figure 4 The diagram shows the dynamic change curves of the predetermined performance function provided in the embodiments of the present invention, wherein (a) is the dynamic change curve of the conventional predetermined performance function, and (b) is the dynamic change curve of the fixed-time predetermined performance function of the method of the present invention.

[0054] Figure 5 The following diagrams are provided for tracking error curves of four following vehicles in a multi-lane merging scenario according to an embodiment of the present invention. (a) is a distance tracking error constraint curve in the multi-lane merging scenario, and (b) is a heading angle tracking error constraint curve in the multi-lane merging scenario.

[0055] Figure 6 This invention provides trajectory diagrams of vehicles in a platoon at different times during a lane-changing scenario, wherein (a) is the overall trajectory diagram of the vehicles in the lane-changing scenario. (a) is the initial position map of the lane change scenario (t=20 s~38 s), and (c) is the mid-term position map of the lane change scenario. (d) is the completed location map in the lane-changing scenario. ).

[0056] Figure 7 The following diagrams are provided for tracking error curves of four following vehicles under different initial conditions in the embodiments of the present invention. (a) is the distance tracking error curve under different initial conditions, and (b) is the heading angle tracking error curve.

[0057] Figure 8 The following is a comparison chart of the tracking error between the method of the present invention and the existing PPC method provided for the embodiments of the present invention. (a) is a distance tracking error curve of four following vehicles, and (b) is a comparison chart of the distance tracking error control effect of four following vehicles. Detailed Implementation

[0058] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0059] In this embodiment, the two-dimensional planar vehicle platooning control method based on fixed-time predetermined performance control is applied to a vehicle platoon consisting of one lead vehicle and N following vehicles, such as... Figure 1 As shown, it includes the following steps:

[0060] Step S1: Obtain the actual position and heading information of the following vehicle in the two-dimensional plane through the sensing module of each following vehicle, and receive the motion status information from the corresponding leading vehicle or the lead vehicle through the communication module, and then calculate the actual distance and actual azimuth between the following vehicle and the target leading vehicle.

[0061] The actual position and heading information of the following vehicle in the two-dimensional plane includes the x-coordinate of the i-th following vehicle in the global coordinate system. y-axis and heading angle ,in, , The total number of vehicles following in the formation; the motion status information of the leading vehicle or the vehicle in front, including the x-coordinate of the leading vehicle or the vehicle in the global coordinate system. y-axis ,speed and heading angle The subscript i-1 indicates the number of the car preceding the i-th following car. When i equals 1, the car preceding the i-th following car is the lead car.

[0062] Step S2: Based on the actual distance and actual azimuth angle between the following vehicle and the target vehicle obtained in Step S1, as well as the pre-stored expected distance and expected azimuth angle, calculate the tracking error of the following vehicle. The tracking error includes distance tracking error and heading angle tracking error.

[0063] In this embodiment, the specific method for calculating the tracking error of the following vehicle is as follows:

[0064] Based on the actual position information of the following vehicle and the position information of the target vehicle in front, calculate the actual distance between the i-th following vehicle and the vehicle in front. relative azimuth Wherein, the actual distance between the i-th following vehicle and the vehicle in front at time t. The calculation formula is:

[0065] ;

[0066] relative azimuth The calculation formula is:

[0067] ;

[0068] Then, the distance tracking error is calculated based on the preset expected distance and expected relative angle. and heading angle tracking error Among them, distance tracking error The actual distance Distance from preset expectations The difference, that is:

[0069] ;

[0070] Heading angle tracking error To follow the vehicle's heading angle Relative azimuth relative angle to the preset expectation The combination is:

[0071] ;

[0072] The distance tracking error and heading angle tracking error Together with their corresponding first and second derivatives, they constitute the state of the vehicle formation closed-loop system.

[0073] Step S3: Based on the initial tracking error of the following vehicle and the preset convergence time, steady-state error range, and overshoot constraint parameters, construct a fixed-time predetermined performance function that is independent of the initial tracking error value. The performance function is used to provide time-varying constraint boundaries for the transient and steady-state performance of the tracking error.

[0074] Construct a fixed-time predetermined performance function that is independent of the initial tracking error value, including:

[0075] First, we introduce a time-related offset function. Its expression is:

[0076] ;

[0077] in, This is a preset offset time constant;

[0078] Using the offset function The original tracking error of the following vehicle After processing, a new intermediate tracking error is obtained. Where j=1 represents the distance tracking error and j=2 represents the heading angle tracking error; then, a method is designed to constrain the intermediate tracking error. The time-varying performance boundary function, the performance boundary function including the upper boundary function. With lower boundary function The specific forms of the two boundary functions are determined by the preset convergence time of the tracking error. Initial boundary values ​​of the core decay function Steady-state boundary values and boundary shape parameters The original tracking error is jointly determined and ensured for any initial time. Intermediate tracking error Always at the initial boundary and between.

[0079] The upper boundary function The design formula is:

[0080] ;

[0081] The lower boundary function The design formula is:

[0082] ;

[0083] in, For symbolic functions, It is a preset positive integer, and ; The core decay function is expressed as follows:

[0084] ;

[0085] To ensure that the initial conditions of the predefined performance control (PPC) are met and to effectively suppress overshoot of the tracking error, a second set of performance boundary functions needs to be designed. and According to the basic requirements of Predicted Performance Control (PPC), the intermediate tracking error at the initial moment... Must meet:

[0086] ;

[0087] Due to the intermediate tracking error at the initial moment The above conditions can be automatically met through the following design:

[0088] ;

[0089] in, The upper boundary functions are respectively and lower boundary function The value at the initial moment, These are the second set of performance boundary functions. and The value at the initial moment, The offset function used to control the overshoot shape is expressed as follows:

[0090] ;

[0091] in, These are preset parameters, and .

[0092] Step S4: Based on the fixed-time predetermined performance function constructed in step S3, perform a nonlinear transformation on the intermediate tracking error to map the tracking error from the constrained original space to the unconstrained new space, and obtain the transformed equivalent tracking error.

[0093] The intermediate tracking error at any time obtained in step S3 Perform a nonlinear transformation to obtain the equivalent tracking error. Its specific calculation formula is based on the original tracking error. The initial value is determined as follows:

[0094] ;

[0095] in, It is the natural logarithm function.

[0096] Step S5: Based on the equivalent tracking error and its derivative obtained in step S4, and combined with the fixed-time convergence parameter, construct a composite sliding surface;

[0097] The composite sliding surface constructed in this step is based on the equivalent tracking error of the single-lane following vehicle and its derivatives, and integrates fixed-time convergence power parameters to form a single-channel dynamic surface. Its design focuses on adapting to the fixed-time predetermined performance constraints in step S3. By combining smooth power terms and linear terms, it achieves the coordination between the dynamics of the tracking error and the constraint boundary, avoiding singularity and chattering while ensuring fixed-time convergence characteristics.

[0098] Based on equivalent tracking error and its first derivative Construct a composite sliding surface as shown in the following formula:

[0099] ;

[0100] in, It is a composite sliding surface. Let k be a power function, where x is a variable and k is the power. , All are sliding mode gains. The parameters are the power-law parameters for fixed-time convergence.

[0101] Step S6: Based on the composite sliding surface and its derivative constructed in step S5, a second-order composite sliding surface is further designed, and an adaptive law is established to estimate the upper bound of the disturbance in real time. Combined with the fixed-time approaching law and the third-order nonlinear dynamic model of the vehicle, the final control input of the following vehicle is calculated.

[0102] Based on the composite sliding surface constructed in step S5 and its derivative Further design of second-order composite sliding surface As shown in the formula below:

[0103] ;

[0104] in, and The value is a preset positive constant, representing the gain coefficient of the second-order sliding surface. and It is a pre-defined composite function containing linear terms and smooth power terms, used to ensure that the vehicle formation closed-loop system state (i.e., distance tracking error and heading tracking error state) established based on steps S1 to S3 has fixed-time convergence characteristics in the neighborhood of the sliding surface.

[0105] To address parameter uncertainties in vehicle dynamics and external environmental disturbances (such as wind resistance and slope), an adaptive law is established to estimate the upper bound of disturbances in real time. The established adaptive law is as follows:

[0106] ;

[0107] ;

[0108] in, and These are the estimated values ​​of the longitudinal and lateral lumped disturbances of the i-th following vehicle, respectively. A nonlinear feedback mechanism is used to ensure that the estimation error enters the steady-state range within a fixed time. They are respectively and The derivative of , that is, the adaptive law; , All are gain functions obtained from predetermined performance conversion. Let i be the state-related variables of the i-th following vehicle; The preset proportional gain constant satisfies This is used to ensure chord stability when spacing errors propagate along the vehicle platoon; These are the state values ​​of the second-order composite sliding surface in the longitudinal and transverse directions, respectively, serving as the driving terms of the adaptive law; These are all preset adaptive law positive gain parameters used to adjust the convergence rate of the perturbation estimation; All are power-law parameters of fixed-time convergence correlation, satisfying and This ensures that the disturbance estimation error converges to the steady-state region within a fixed time independent of the initial state;

[0109] Fixed-time approach law Substituting the third-order nonlinear dynamics model of the vehicle, the final control input of the following vehicle is calculated;

[0110] The final control inputs for following vehicles include longitudinal drive control variables used to adjust distance and speed. And the lateral steering control quantity used to adjust the heading angle and lateral offset As shown in the formula below:

[0111] ;

[0112] ;

[0113] in Let the mass of the i-th following vehicle be... Let be the time constant of the drive system of the i-th following vehicle. This is a preset positive gain constant for the approach law, used to adjust the rate at which the system state approaches the sliding surface; Let the power parameter of the fixed-time reaching law satisfy... This is used to ensure that the sliding surface can converge to zero within a preset fixed time, regardless of the initial state of the system. , These are compensation sets that include known nonlinear terms, performance function derivative terms, and sliding mode switching terms of the vehicle formation closed-loop system.

[0114] Step S7: Send the longitudinal drive control quantity and lateral steering control quantity of the following vehicle calculated in step S6 to the actuator of the following vehicle to achieve coordinated control of the following vehicle, so that it tracks the motion state of the leading vehicle in a dynamic process with a preset overshoot amount within a preset fixed time.

[0115] In this embodiment, the convoy includes one lead vehicle and four follower vehicles, such as... Figure 2 As shown, each following vehicle includes a perception module, a communication module, a processing module, and an execution module;

[0116] The perception module is used to obtain the vehicle's actual position coordinates, heading angle, and speed information in a two-dimensional plane.

[0117] The communication module is used to receive motion status information from the leading vehicle or the lead vehicle in the formation;

[0118] The processing module is used to run a two-dimensional planar vehicle formation control method based on fixed-time predetermined performance control. It calculates the longitudinal drive control quantity and the lateral steering control quantity based on the information input from the sensing module and the communication module.

[0119] The execution module is used to receive and execute the longitudinal drive control quantity and the lateral steering control quantity issued by the processing module to drive the vehicle to move.

[0120] The processing module includes an error calculation unit, a performance management unit, a transformation unit, and a control law calculation unit.

[0121] The error calculation unit is used to calculate the actual distance between the following vehicle and the vehicle in front, the actual azimuth angle, the distance tracking error, and the heading angle tracking error.

[0122] The performance management unit is used to store the data acquired and received by the sensing module and the communication module, and to calculate the fixed-time predetermined performance function and its boundaries.

[0123] The transformation unit is used to perform a nonlinear transformation on the tracking error.

[0124] The control quantity calculation unit is used to construct the composite sliding surface and calculate the final control quantity in conjunction with the adaptive law.

[0125] In this embodiment, by means of... Figure 3 The simulation results of the multi-lane merging scenario shown yielded relevant data curves, including the position trajectory curve and heading angle change curve of the controlled object. Combining the two core error variables—distance tracking error and heading angle tracking error—the method designed in this invention... Figure 4 The fixed-time-prescribed performance functions (FxTPFs) and the constraint-to-unconstraint error transformation mechanism shown are used to obtain the error constraint curve, as follows. Figure 5 As shown; vehicle trajectories at different times in a lane-changing scenario are as follows: Figure 6 As shown in the figure, lane changes by the convoy tend to be stable under different conditions at different times. Through dynamic error adjustment, adapting to the distance and heading angle coupling constraints of the two-dimensional planar convoy, the steady-state convergence curve of distance tracking error and the small overshoot curve of heading angle tracking error are obtained, as shown in the figure. Figure 7 As shown; this embodiment also compares the distance tracking error and heading angle tracking error obtained by the method of the present invention with the errors provided by the prior art (traditional PPC method) through overshoot (m / rad), convergence time (s), and steady-state accuracy (m / rad), as follows. Figure 8 As shown, the method of the present invention can achieve control effects such as no initial error dependence, fast convergence speed, small overshoot and fixed-time convergence, while ensuring the stability of the queue string.

[0126] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the present invention.

Claims

1. A two-dimensional planar vehicle platooning control method based on fixed-time predetermined performance control, applied to a vehicle platoon consisting of one lead vehicle and N following vehicles, characterized in that: Includes the following steps: Step S1: Obtain the actual position and heading information of each following vehicle in the two-dimensional plane, as well as the motion state information of the leading or trailing vehicle corresponding to each following vehicle, and then calculate the actual distance and actual azimuth between the following vehicle and the target leading vehicle. Step S2: Based on the actual distance and azimuth angle between the following vehicle and the target vehicle, as well as the pre-stored expected distance and expected azimuth angle, calculate the tracking error of the following vehicle. The tracking error includes distance tracking error and heading angle tracking error. Step S3: Based on the initial tracking error of the following vehicle and the preset convergence time, steady-state error range, and overshoot constraint parameters, construct a fixed-time predetermined performance function that is independent of the initial tracking error value. The performance function is used to provide time-varying constraint boundaries for the transient and steady-state performance of the tracking error. Step S4: Based on the fixed-time predetermined performance function, perform a nonlinear transformation on the intermediate tracking error to map the tracking error from the constrained original space to the unconstrained new space, and obtain the transformed equivalent tracking error; Step S5: Based on the equivalent tracking error and its derivative, and combined with the fixed-time convergence parameter, construct a composite sliding surface; Step S6: Based on the composite sliding surface and its derivative, a second-order composite sliding surface is further designed, and an adaptive law is established to estimate the upper bound of the disturbance in real time. Combined with the fixed-time approach law and the third-order nonlinear dynamic model of the vehicle, the final control input of the following vehicle is calculated to achieve coordinated control of the following vehicle.

2. The two-dimensional planar vehicle formation control method based on fixed-time predetermined performance control according to claim 1, characterized in that: The actual position and heading information of the following vehicle in the two-dimensional plane includes the x-coordinate of the i-th following vehicle in the global coordinate system. y-axis and heading angle ,in, , The total number of vehicles following in the formation; the motion status information of the leading vehicle or the vehicle in front, including the x-coordinate of the leading vehicle or the vehicle in the global coordinate system. y-axis ,speed and heading angle The subscript i-1 indicates the number of the car preceding the i-th following car. When i equals 1, the car preceding the i-th following car is the lead car.

3. The two-dimensional planar vehicle formation control method based on fixed-time predetermined performance control according to claim 2, characterized in that: The specific method for calculating the tracking error of the following vehicle is as follows: Based on the actual position information of the following vehicle and the position information of the target vehicle in front, calculate the actual distance between the i-th following vehicle and the vehicle in front. relative azimuth Then, the distance tracking error is calculated based on the preset expected distance and expected relative angle. and heading angle tracking error As shown in the formula below: ； ； in, For time, To preset the desired distance, This is the preset desired relative angle.

4. The two-dimensional planar vehicle formation control method based on fixed-time predetermined performance control according to claim 3, characterized in that: The specific method for constructing a fixed-time predetermined performance function that is independent of the initial tracking error value is as follows: First, we introduce a time-related offset function. Its expression is: ； in, This is a preset offset time constant; Using the offset function The original tracking error of the following vehicle After processing, a new intermediate tracking error is obtained. Where j=1 represents the distance tracking error and j=2 represents the heading angle tracking error; then, a method is designed to constrain the intermediate tracking error. The time-varying performance boundary function, the performance boundary function including the upper boundary function. With lower boundary function The specific forms of the two boundary functions are determined by the preset convergence time of the tracking error. Initial boundary values ​​of the core decay function Steady-state boundary values and boundary shape parameters The original tracking error is jointly determined and ensured for any initial time. Intermediate tracking error Always at the initial boundary and between; The upper boundary function The design formula is: ； The lower boundary function The design formula is: ； in, For symbolic functions, It is a preset positive integer, and ; The core decay function is expressed as follows: ； Based on the fundamental requirements of predetermined performance control, the intermediate tracking error at the initial moment... The following must be met: ； in, The upper boundary functions are respectively and lower boundary function The value at the initial moment, These are the second set of performance boundary functions. and The value at the initial moment, and The second upper boundary function and the second lower boundary function are respectively shown in the following formulas: ； in, This is the offset function used to control the overshoot shape.

5. The two-dimensional planar vehicle formation control method based on fixed-time predetermined performance control according to claim 4, characterized in that: The composite sliding surface constructed in step S5 is shown in the following formula: ； in, It is a composite sliding surface. For equivalent tracking error, for First derivative, For power sign functions, , All are sliding mode gains. The parameters are the power-law parameters for fixed-time convergence.

6. The two-dimensional planar vehicle formation control method based on fixed-time predetermined performance control according to claim 5, characterized in that: Step S6 is based on a composite sliding surface. and its derivative The design of the second-order composite sliding surface As shown in the formula below: ； in, and The value is a preset positive constant, representing the gain coefficient of the second-order sliding surface. and This is a predefined composite function containing linear terms and smooth exponential terms; The established adaptive law is as follows: ； ； in, and These are the estimated values ​​of the longitudinal and lateral lumped disturbances of the i-th following vehicle, respectively. A nonlinear feedback mechanism is used to ensure that the estimation error enters the steady-state range within a fixed time. They are respectively and The derivative; , All are gain functions obtained from predetermined performance conversion. Let i be the state-related variables of the i-th following vehicle; The preset proportional gain constant satisfies ; These are the state values ​​of the second-order composite sliding surface in the longitudinal and transverse directions, respectively, serving as the driving terms of the adaptive law; These are all preset adaptive law positive gain parameters used to adjust the convergence rate of the perturbation estimation; All are power-law parameters of fixed-time convergence correlation, satisfying and This ensures that the disturbance estimation error converges to the steady-state region within a fixed time independent of the initial state; Fixed-time approach law Substituting the third-order nonlinear dynamics model of the vehicle, the final control input of the following vehicle is calculated, where, This is a preset positive gain constant for the approach law, used to adjust the rate at which the system state approaches the sliding surface; Let the power parameter of the fixed-time reaching law satisfy... .

7. The two-dimensional planar vehicle formation control method based on fixed-time predetermined performance control according to claim 6, characterized in that: The final control inputs of the following vehicle include longitudinal drive control quantities for adjusting the distance and speed, and lateral steering control quantities for adjusting the heading angle and lateral offset.

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