An automatic driving vehicle predictive control method of disturbance reachable set adaptive contraction

Abstract

The application discloses an automatic driving vehicle prediction control method based on disturbance reachable set adaptive contraction, belongs to the field of automatic driving, and aims at solving the problems that the disturbance set is fixed, the constraint contraction is too conservative and it is difficult to accurately depict time-varying uncertainty in actual driving in traditional tubular model predictive control. The method comprises the following steps: collecting vehicle operation condition characteristic parameters, constructing a training data set and offline training a disturbance prediction model, multi-step prediction is carried out on system disturbance to generate a time-varying disturbance set sequence; on this basis, error reachable set propagation and time-varying constraint contraction are combined to obtain a time-varying constraint contraction sequence in a prediction time domain, and tubular model predictive control optimization solving is carried out under the constraint condition, so that the control conservatism is reduced under the premise of guaranteeing system robustness, and the path tracking performance of the vehicle is improved.

Description

Technical Field

[0001] This invention belongs to the field of autonomous driving, specifically a predictive control method for autonomous vehicles with adaptive shrinkage of the reachability domain due to disturbance. Background Technology

[0002] When autonomous vehicles perform path tracking under complex road conditions, the system state is susceptible to model uncertainties and external disturbances, leading to decreased control accuracy or even constraint violations. How to reasonably adjust control constraints to balance tracking accuracy and system stability while ensuring robustness has become a pressing problem. To address this, researchers have applied Tube-MPC to vehicle control, effectively guaranteeing robust stability under bounded disturbances by constructing a robust positive invariant set and tightening constraints. However, traditional Tube-MPC designs are typically based on worst-case assumptions, assuming that the disturbance reaches a preset maximum amplitude throughout the prediction time domain, and calculating the robust invariant set offline accordingly. This results in a constant and excessively large constraint tightening, overly compressed usable control space, and high system conservatism. To address these issues, existing research has attempted to improve the conservatism of Tube-MPC from different perspectives.

[0003] In terms of disturbance prediction and data-driven modeling, patent CN119239657A predicts the changing trend of tire side stiffness by inversely solving the vehicle motion model. It treats the deviation between the predicted and actual values ​​as a bounded disturbance and calculates a robust invariant set offline based on this disturbance range to compress the nominal system constraints. However, the robust invariant set used in this method is a fixed set calculated offline, and its constraint compression amount does not change with the prediction step, making it difficult to dynamically adjust the constraint boundary according to disturbance changes. This invention, on the other hand, constructs a time-varying disturbance set that changes with the prediction step and propagates it to obtain an error reachable set sequence, achieving dynamic adjustment of the constraint boundary and enabling the compression amount to adaptively change with the prediction step. Patent CN115857494A uses an extended dynamic mode decomposition algorithm to establish a linear model of a hybrid vehicle queue, introduces model mismatch error into the model, and uses Tube-MPC to design a robust controller, ensuring that the actual trajectory is constrained within a conduit around the nominal trajectory. Although this method improves model accuracy through data-driven approaches, its pipe dimensions remain fixed and it does not utilize the prediction information of model mismatch error to dynamically adjust the pipe, resulting in the pipe maintaining a large amount of compression even when the model mismatch is small. Patent CN121515974A unifies multiple types of uncertainties into equivalent disturbances and obtains the disturbance invariant set. Based on this invariant set, it expands the vehicle profile for robust collision detection and uses Tube-MPC to achieve tracking control. This method uses the invariant set of disturbances only for contour expansion, rather than dynamically compressing the constraint boundary of the nominal system. Moreover, this invariant set is a fixed set calculated offline, which cannot adjust the expansion amount in real time according to the vehicle's operating state or disturbance changes. This results in maintaining a large expansion even when the uncertainty is small, and the obstacle avoidance path is too conservative. Patent CN116872948A collects truck driving state signals in real time through sensors and constructs a variable cross-section Tube to reduce the impact of variable load on trajectory tracking performance. However, its pipe cross-section adjustment mainly depends on the current state feedback and lacks the ability to predict future disturbance changes. This results in the pipe adjustment being lagging and unable to respond to rapidly changing load disturbances in advance.

[0004] In terms of disturbance uncertainty modeling, patent CN119356103A parameterizes model mismatch as a bounded disturbance, uses the Linear Matrix Inequality (LMI) method to solve the robust state feedback matrix, and approximates the minimum robust invariant set of the nominal model based on Tube-MPC theory to reconstruct state and control constraints. This method uses a fixed minimum robust invariant set obtained offline through LMI, meaning the reconstructed constraints do not change with the prediction step. Furthermore, LMI computation is computationally burdensome and difficult to update online to address time-varying model mismatch characteristics. Patent CN121515974A constructs a vehicle servo model under multi-source disturbances and designs a dynamic switching control strategy, using estimated control gain and an automatic switching mechanism to adjust control parameters in real time. This method relies on preset switching rules and thresholds, and the switching timing is limited by the accuracy of the current state estimation. It lacks the ability to predict future disturbance evolution, resulting in switching lag and decreased control performance when disturbances change rapidly.

[0005] In summary, if we can combine the vehicle's operating state with the disturbance prediction sequence to construct a time-varying disturbance set sequence that changes with the prediction step, and then use the error reachable set propagation to achieve dynamic contraction of the constraint boundary, enabling the constraint processing process to adaptively adjust with changes in vehicle operating conditions, it will help reduce control conservatism while ensuring system robustness, thereby improving the path tracking performance of autonomous vehicles under complex operating conditions. Summary of the Invention

[0006] To address the aforementioned issues, this invention proposes a predictive control method for autonomous vehicles with adaptive shrinking of the disturbance reachability domain. This method collects characteristic parameters of vehicle operating conditions, constructs a training dataset, and trains a disturbance prediction model offline. It then performs multi-step prediction of system disturbances, generating a time-varying disturbance set sequence. Based on this, it combines error reachability set propagation with time-varying constraint contraction to obtain a time-varying constraint contraction sequence in the prediction time domain. Under these constraints, it performs tubular model predictive control optimization, thereby reducing control conservatism while ensuring system robustness and improving the vehicle's path-tracking performance.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] This invention discloses a predictive control method for autonomous vehicles with adaptive shrinkage of the reachable domain due to disturbances. The method comprises a closed-loop control system consisting of five modules: an offline training module for a disturbance prediction model, a time-varying tubular model construction module, a reference path module, a tubular model predictive controller, and a vehicle module. Specifically, it includes the following steps:

[0009] Step 1: Offline training module for the perturbation prediction model:

[0010] Obtain operating condition characteristic parameters from the vehicle module. including longitudinal velocity Road surface adhesion coefficient Road surface curvature Front wheel vertical load and rear wheel vertical load Construct a sequence of operating condition characteristics by arranging them in chronological order. ,in This represents the total number of sampling points.

[0011] At the same time, based on vehicle status Compared with nominal condition Define system state error:

[0012] (1)

[0013] in In nominal condition, An index for historical sampling times;

[0014] Based on the closed-loop error system:

[0015] (2)

[0016] Calculate the disturbance label:

[0017] (3)

[0018] in, This is the closed-loop error state transition matrix.

[0019] Constructing perturbation label sequences The working condition feature sequence and the disturbance label sequence are normalized, and the input-output pair is extracted using the sliding window technique. The extracted time-series features and labels are converted into tensor data to form the training dataset.

[0020] Step 2, Time-varying tubular construction module:

[0021] The time-varying tubular construction module is used to construct a time-varying constrained compressed sequence based on the perturbation prediction sequence in the prediction time domain. It includes: a perturbation prediction module, a perturbation set construction module, an error reachable set propagation module, and a time-varying constrained compression module. The specific steps are as follows:

[0022] Step 2.1, Disturbance Prediction Module:

[0023] Load the disturbance prediction model to collect historical data in real time. Step condition characteristic parameters are used as input:

[0024]

[0025] in, The length of the historical time window. These are the characteristic parameters of the operating conditions.

[0026] Define prediction step index Then the model output predicts the time domain. In-step perturbation prediction sequence:

[0027]

[0028] in, To predict the length of the time domain, Indicates at time For future moments The predicted system disturbance value.

[0029] Step 2.2, Perturbation Set Construction Module:

[0030] Based on the perturbation prediction sequence obtained in step 2.1 Calculate the upper bound vector of the disturbance amplitude at each time step:

[0031] (4)

[0032] Subsequently, a time-varying perturbation set is constructed based on the upper bound vector of the perturbation amplitude:

[0033] (5)

[0034] This yields the prediction time domain. Time-varying perturbation set sequence within a step .

[0035] Step 2.3, Error Reachable Set Propagation Module:

[0036] At the current sampling time System state error as the initial set ,in As shown in equation (1). Based on the closed-loop error system equation (2) and the time-varying perturbation set sequence. The propagation yields a sequence of errors that can be reached in the prediction time domain, as shown in the formula:

[0037] (6)

[0038] in, Minkowski and, This is the closed-loop error state transition matrix. The time-varying perturbation set sequence constructed in step 3.2 The first in Step; propagation yields an error-achievable set sequence. .

[0039] Step 2.4, Time-varying constraint compression module:

[0040] The state constraints of the actual system are The control input constraints are Based on error reachable set sequences The actual system state is decomposed into the sum of the nominal state and the error: for each prediction step ,have

[0041] (7)

[0042] Wherein the error , For sequence The Each element.

[0043] To ensure that the actual system satisfies the state constraints and control input constraints By using Minkowski difference operations, the time-varying constrained compressed sequence that varies with the prediction step in the Tube-MPC prediction time domain is obtained:

[0044] (8)

[0045] in, Indicates Minkowski's difference, The state feedback gain matrix; for The first time predicted Time-varying compacted state constraint set for The first time predicted The time-varying, compact control input constraint set is obtained by integrating all single-step constraint sets in the prediction time domain in chronological order. Time-varying constrained compressed state sequence and time-varying constrained compressed control input sequence at time t:

[0046] (9)

[0047] Together, they constitute the time-varying constrained compaction sequence.

[0048] Step 3, Reference Path Module:

[0049] The reference path module provides a reference state sequence in the prediction time domain. ,in , ;in, For reference centroid sideslip angle, For reference yaw rate, For reference heading deviation, The reference state sequence serves as the tracking target input for the tubular model predictive controller, with reference to the lateral deviation.

[0050] Step 4, Tubular Model Predictive Controller:

[0051] The tubular model predictive controller is used to decompose the actual system into a nominal system and an error system. It performs rolling optimization on the nominal system based on a time-varying constrained compaction sequence and achieves tracking of the nominal state by the actual state through state feedback compensation. Specific steps include:

[0052] Step 4.1, Prediction Model Construction:

[0053] Construct a lateral dynamics model for the vehicle, using a two-degree-of-freedom vehicle model, with the following expression:

[0054] (10)

[0055] in, For vehicle quality, For the longitudinal speed of the vehicle, For the vehicle's lateral speed, The yaw rate is angular velocity. For the front wheel steering angle, and These are the lateral stiffness of the front and rear axle tires, respectively. and These are the distances from the vehicle's center of gravity to the front and rear axles, respectively. Let be the yaw moment of inertia of the vehicle about its center of mass. It is lateral acceleration. It is the yaw acceleration.

[0056] Establish a tracking error model:

[0057] (11)

[0058] in, For heading deviation, For lateral deviation, For road curvature, The rate of change of heading deviation. This represents the rate of change of lateral deviation.

[0059] The vehicle dynamics model equation (10) and the tracking error model equation (11) are rearranged into a continuous-time state-space equation:

[0060] (12)

[0061] Wherein, the system state vector Control input For the front wheel steering angle, Input the road curvature.

[0062] Discretize the above model using the zero-order preservation method to obtain a discrete-time state-space model:

[0063] (13)

[0064] in, , , These are the discrete state matrix, the input matrix, and the curvature input matrix, respectively.

[0065] Step 4.2, Decomposition of Nominal System and Error System:

[0066] Considering modeling errors and external disturbances, the actual system is represented as follows:

[0067] (14)

[0068] in This is the actual state. For actual control input, Input the road curvature. This is a bounded perturbation.

[0069] The nominal system is defined as:

[0070] (15)

[0071] in In nominal condition, For nominal control input, Input the road curvature.

[0072] State feedback control law is adopted:

[0073] (16)

[0074] in for The actual control input of the vehicle at any given time. for The optimal nominal control input for the current step at any given time. The state feedback gain matrix, for The system state error at time t.

[0075] Step 4.3, Optimize problem formulation:

[0076] Let the prediction time domain be The nominal control input sequence to be optimized is defined as follows:

[0077]

[0078] The corresponding nominal state sequence is:

[0079]

[0080] The initial nominal state .

[0081] Based on the nominal system formula (15), a reference state sequence is introduced. Construct the objective function for the tubular model predictive controller:

[0082] (17)

[0083] in, , and These are the state weight matrix, the control input weight matrix, and the terminal weight matrix, respectively.

[0084] Based on the objective function (17) and combined with the time-varying constrained compressed sequence, the optimization problem of tubular model predictive control is constructed:

[0085] (18)

[0086] in This represents the difference in control input between two adjacent prediction times. To maximize the rate of change of control input, It is a terminal robust invariant set.

[0087] Solving the optimization problem yields the optimal nominal control sequence. And based on the state feedback control law (16), the actual control input is calculated, and the actual control input is... Send to the vehicle module for execution.

[0088] Step 5, Vehicle Module:

[0089] The vehicle module receives the control input from the tubular model predictive controller. And execute, while outputting the current time. Vehicle status and operating condition characteristic parameters The signals are fed back to the tubular model predictive controller and the time-varying tubular construction module, respectively, forming a closed-loop control.

[0090] The beneficial effects of this invention are as follows: By constructing a disturbance prediction model based on vehicle operating condition characteristic parameters, multi-step prediction of system disturbances in the prediction time domain is performed, constructing a time-varying disturbance set sequence; based on this, by combining error reachability set propagation and time-varying constraint contraction, a time-varying constraint contraction sequence in the prediction time domain is obtained, and the tubular model predictive control is optimized under this constraint condition. Compared with the traditional method of using fixed disturbance boundaries and fixed constraint contraction, this invention can more accurately reflect the characteristics of disturbance changes over time, effectively reducing control conservatism while ensuring system robustness. Attached Figure Description

[0091] Figure 1 This is a schematic diagram of the overall structure of the predictive control method for autonomous vehicles with adaptive shrinkage of the reachable domain under disturbance, as proposed in this invention.

[0092] Figure 2 This is a schematic diagram of the time-varying tubular building block.

[0093] Figure 3 This is a yaw rate response curve under sinusoidal maneuvering conditions in an embodiment of the present invention.

[0094] Figure 4 This is a graph showing the center of mass sideslip angle response under sinusoidal maneuvering conditions in an embodiment of the present invention.

[0095] Figure 5 This is a diagram showing the front wheel steering angle response curve under sinusoidal driving conditions in an embodiment of the present invention. Detailed Implementation

[0096] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0097] like Figure 1 As shown, this invention proposes a predictive control method for autonomous vehicles with adaptive shrinking of the perturbation reachability domain. By performing multi-step prediction of system perturbations and constructing a time-varying perturbation set sequence, combined with error reachability set propagation and time-varying constraint contraction, dynamic adaptive adjustment of tubular constraints is achieved. This reduces control conservatism while ensuring system robustness, improving the vehicle's path tracking performance in complex road environments. The method comprises five modules: an offline training module for the perturbation prediction model, a time-varying tubular constraint construction module, a reference path module, a tubular model predictive controller, and a vehicle module. The time-varying tubular constraint construction module loads the perturbation prediction model and generates a perturbation prediction sequence in the prediction time domain based on the operating condition characteristic parameters obtained in real time from the vehicle module. And construct a time-varying perturbation set sequence. The error reachable set sequence in the prediction time domain is obtained through error reachable set propagation. Furthermore, based on the error reachable set sequence, the actual constraints are time-varyingly compressed to obtain a time-varying constraint-compressed state sequence that varies with the prediction step. With time-varying constrained compaction control input sequence The reference path module generates the reference state in the prediction time domain. ,in For reference centroid sideslip angle, For reference yaw rate, For reference heading deviation, To reference the lateral deviation, a reference state sequence is obtained by arranging the states according to the predicted time domain. The target input is used as the tracking target input for the tubular model predictive controller optimization problem; the tubular model predictive controller solves for the optimal nominal control sequence through rolling optimization based on the time-varying constrained compressed sequence, vehicle state, and desired path. The actual front wheel steering angle is calculated by combining the state feedback control law. The vehicle module executes the front wheel steering angle. To update vehicle status and output vehicle status in real time. and operating condition characteristic parameters .

[0098] Step 1: Offline training module for the perturbation prediction model:

[0099] This module is used to collect vehicle operating condition characteristic parameters and calculate disturbance labels, build a training dataset, and train a disturbance prediction model. Specifically, it includes the following steps:

[0100] Step 1.1: Acquisition of operating condition characteristic parameters:

[0101] During actual vehicle operation or simulation testing, on-board sensors and environmental perception systems are used to collect real-time information on vehicle operating status and road environment, and extract operating condition characteristic parameters to characterize vehicle operation. including vehicle longitudinal speed Road surface adhesion coefficient Road surface curvature Front wheel vertical load and rear wheel vertical load Construct a sequence of operating condition characteristics by arranging them in chronological order. ,in This represents the total number of sampling points.

[0102] Step 1.2, Disturbance Tag Calculation:

[0103] Vehicle at time The state is The nominal condition is Define systematic error:

[0104]

[0105] Based on the closed-loop error system:

[0106]

[0107] Calculate the disturbance label:

[0108]

[0109] in, This is the closed-loop error state transition matrix.

[0110] Iterate through all sampling times to construct a perturbation label sequence. .

[0111] Step 1.3, Dataset Construction and Preprocessing:

[0112] Operating condition time series With perturbed sample sequence Pairing is performed to form the original training dataset. Then, normalization preprocessing is performed, applying a min-max normalization method to each component of the original training dataset to scale its numerical range to... To eliminate the influence of different characteristic dimensions, the normalization formula is:

[0113] (19)

[0114] The next step is to extract the history time window by setting its length. and prediction time domain length A sliding window technique is used to extract input-output pairs from the normalized sequence. For each time step... Input as history Step-by-step working condition characteristic sequence The corresponding tag is future. Step perturbation label sequence .

[0115] Finally, tensor transformation is performed to convert all input-output pairs into a three-dimensional tensor data format (batch dimension, time step dimension, feature dimension), which serves as the standard input for subsequent network training.

[0116] Step 1.4: Training the perturbation prediction network:

[0117] The perturbation prediction model constructed by this method strictly consists of: an input layer, an LSTM layer, a Dropout layer, and a fully connected output layer. The input layer receives... Tensor data; two consecutive LSTM layers are used to extract deep temporal features from the work condition sequence, with 128 hidden units; Dropout layers are used to randomly deactivate neurons during training to suppress model overfitting; the output dimension of the fully connected layer is set to... The mean squared error (MSE) is used as the loss function:

[0118] (20)

[0119] The AdamW optimizer was used for parameter updates, with an initial learning rate of 0.001 and a weight decay coefficient of 0.0001. During training, the model with the smallest loss function value on the validation set was selected and retained as the perturbation prediction model, and saved for real-time use in the online phase.

[0120] Step 2, Time-varying tubular construction module:

[0121] like Figure 2 As shown, the time-varying tubular construction module is used to construct a time-varying constraint contraction sequence based on the perturbation prediction sequence in the prediction time domain, providing the tubular model predictive controller with constraint boundaries that change with the prediction step. Specifically, it includes: a perturbation prediction module, a perturbation set construction module, an error reachable set propagation module, and a time-varying constraint contraction module. The specific steps are as follows:

[0122] Step 2.1, Disturbance Prediction Module:

[0123] Load the perturbation prediction model trained in step 1.4, and use the historical data collected in real time. Step-by-step working condition characteristic time series as input ,in These are the characteristic parameters of the operating condition. Input disturbance prediction model, model output prediction time domain Internal perturbation prediction sequence ,in Indicates at time For future moments The predicted value of system disturbance, .

[0124] Step 2.2, Perturbation Set Construction Module:

[0125] Based on the disturbance prediction sequence For each prediction step Construct the corresponding time-varying perturbation sets. Considering the finite error of the prediction model and that the actual perturbation may appear in both the positive and negative directions of the predicted value, a symmetrical hyperrectangular boundary centered at the origin is adopted to simplify the calculation and ensure robustness. First, calculate the upper bound vector of the perturbation amplitude at each time step:

[0126]

[0127] Subsequently, a time-varying perturbation set is constructed based on the upper bound vector of the perturbation amplitude:

[0128]

[0129] The vector inequality indicates that each component satisfies:

[0130] (twenty one)

[0131] in The upper bound vector of the disturbance amplitude The One portion, perturbation vector The Each component; thus, the prediction time domain is obtained. Time-varying perturbation set sequence .

[0132] Step 2.3, Error Reachable Set Propagation Module:

[0133] At the current moment System state error as the initial set ,in This represents the deviation between the actual state and the nominal state, and Closed-loop system matrix Time-varying perturbation set Based on the closed-loop error system equation (2) and the time-varying perturbation set sequence, the error reachable set for each step in the prediction time domain is calculated according to the recursive relationship of equation (22):

[0134] (twenty two)

[0135] in, This is the closed-loop error state transition matrix. At any moment Predicted future The error of the step can reach a set. Minkowski and, The time-varying perturbation set sequence constructed in step 2.2 The Middle A set of time-varying perturbations for each step.

[0136] because Follow The changes and errors can reach a set that also exhibits time-varying characteristics during propagation. Calculations can be performed sequentially to obtain:

[0137] (twenty three)

[0138] This results in a sequence of error reachable sets within the prediction time domain. .

[0139] Step 2.4, Time-varying constraint compression module:

[0140] Let the state constraints and control input constraints of the actual system be as follows:

[0141] (twenty four)

[0142] in, and These are the lower and upper limits of the vehicle's state constraints, i.e., the physical limits of each state quantity of the vehicle. and These are the lower and upper limits of the control input, respectively, representing the physical limits of the front wheel steering angle. This is to ensure that the actual system satisfies the state constraints under disturbances. and control input constraints Based on error reachable set sequence The nominal system's state and control inputs are subjected to time-varying constraint compression. The actual state is decomposed into:

[0143]

[0144] in Hyperrectangular Outer Approximation Based on Error Reachability Set By using the Minkowski difference operation, for each prediction step Define the set of time-varying, compacted state constraints:

[0145] (25)

[0146] in for The semi-axis vector.

[0147] For control input constraints, calculate:

[0148] (26)

[0149] Indicating in prediction Within a step, since the error can reach a set The existence of this constraint determines the maximum possible amplitude of the feedback control input, which is the amount by which the control input constraint needs to be further tightened. Therefore, the set of time-varying tightened control input constraints is:

[0150] (27)

[0151] in The state feedback gain matrix; The Minkowski difference set is defined as follows:

[0152] (28)

[0153] That is, all that make translation Still included in vector The set is constructed. This operation shrinks the original constraint set inward by the size of an error reachable set, thus ensuring that the actual state is within the constraint range. All single-step constraint sets in the prediction time domain are integrated in chronological order to obtain... Time-varying constrained compressed state sequence and time-varying constrained compressed control input sequence at time t:

[0154]

[0155] and Together, they constitute the time-varying constraint compression sequence, which is used as a constraint condition by the subsequent tubular model predictive controller during the rolling optimization process. for The first time predicted Time-varying compacted state constraint set for The first time predicted Step-time variable compression control input constraint set.

[0156] Step 3, Reference Path Module:

[0157] Based on road information, a smooth desired path is generated using a fifth-order polynomial fitting method. The longitudinal position of the vehicle is used as the independent variable. Then the lateral displacement is the dependent variable. for:

[0158] (29)

[0159] in The fitting coefficients are uniquely determined by the positions of the starting and ending points, the heading, and the curvature boundary conditions. The desired path is discretized to obtain reference points at each time point in the prediction time domain.

[0160] For each moment in the prediction time domain ( The corresponding reference state component is extracted from the reference trajectory. The reference state is defined as follows:

[0161]

[0162] in, For reference centroid sideslip angle, For reference yaw rate, For reference heading deviation, As a reference for lateral deviation, the reference state sequence is obtained by arranging each time step. It will be used as the tracking target input in the tubular model predictive controller optimization problem.

[0163] Step 4: Design the tubular model prediction controller module:

[0164] The tubular model predictive controller is used to decompose the actual system into a nominal system and an error system. It performs rolling optimization on the nominal system based on a time-varying constrained compressed sequence and achieves tracking of the nominal trajectory by the actual state through state feedback compensation. Specific steps include:

[0165] Step 4.1, Prediction Model Establishment:

[0166] A lateral dynamics model of the vehicle is constructed using a two-degree-of-freedom vehicle model, and its expression is as follows:

[0167]

[0168] in, For vehicle quality, For the longitudinal speed of the vehicle, For the vehicle's lateral speed, The yaw rate is angular velocity. For the front wheel steering angle, and These are the lateral stiffness of the front and rear axle tires, respectively. and These are the distances from the vehicle's center of gravity to the front and rear axles, respectively. Let be the yaw moment of inertia of the vehicle about its center of mass. It is lateral acceleration. It is the yaw acceleration.

[0169] Establish a tracking error model:

[0170]

[0171] in, For heading deviation, For lateral deviation, For road curvature, The rate of change of heading deviation. This represents the rate of change of heading deviation.

[0172] The vehicle dynamics model equation (10) and the tracking error model equation (11) are rearranged into a continuous-time state-space equation:

[0173]

[0174] Among them, system status Control input For the front wheel steering angle, The input is the road curvature; the system matrices are as follows:

[0175]

[0176] Discretization is performed using the zero-order hold method, with a sampling period of Thus, the discrete-time state-space model is obtained:

[0177]

[0178] in, , , These are the discrete state matrix, the input matrix, and the curvature input matrix, respectively.

[0179] Step 4.2, Decomposition of Nominal System and Error System:

[0180] Considering modeling errors and external disturbances, the actual system is represented as:

[0181]

[0182] in This is the actual state. For actual control input, This is a bounded perturbation.

[0183] The nominal system is defined as:

[0184]

[0185] in In nominal condition, This is the nominal control input.

[0186] State feedback control law is adopted:

[0187]

[0188] in for The actual control input of the vehicle at any given time. for The optimal nominal control input for the current step at any given time. The state feedback gain matrix, for The system state error at time t.

[0189] Step 4.3, Optimize problem formulation:

[0190] Let the prediction time domain be The nominal control input sequence to be optimized is defined as follows:

[0191]

[0192] The nominal state sequence is:

[0193]

[0194] The initial nominal state is the vehicle state. .

[0195] Based on the nominal system (15), a reference state sequence provided by the reference path module is introduced. Construct the objective function for the tubular model predictive controller:

[0196]

[0197] in , , These are the state weight matrix, the control input weight matrix, and the terminal weight matrix, respectively.

[0198] Based on the objective function and the aforementioned time-varying constrained compressed sequence, the optimization problem of the tubular model predictive controller is constructed as follows:

[0199]

[0200] in for The future that can be predicted at any time The 4-dimensional nominal state vector of the step; This refers to the compressed state constraints corresponding to the 4D time-varying constraints of the prediction step; for The future that can be predicted at any time The nominal control input of the step, The control input constraints are compressed from the 4D time-varying constraints corresponding to the prediction step; This represents the difference in control input between two adjacent prediction times. To maximize the rate of change of control input, The first time-varying constrained compressed sequence (9) in the invention content step, It is a terminal robust invariant set.

[0201] In this embodiment, the controller parameters are set as follows: prediction time domain Sampling period State weight matrix The weight of the centroid side slip angle Yaw velocity weight Heading deviation weight Lateral error weights Control weights Terminal weight matrix Control Incremental Constraints Actual state constraints In the middle, the centroid side slip angle yaw rate heading deviation lateral error Actual control input constraint: front wheel steering angle .

[0202] To ensure system stability and constraint satisfaction after the end of the prediction time domain, this invention adopts a piecewise perturbation boundary design strategy: in the prediction time domain... Within, a time-varying perturbation set sequence is generated using the perturbation prediction module. Time-varying constraint compression is performed to reduce control conservatism; at the end of the prediction time domain, due to the lack of future prediction information, the system switches to a method based on the maximum perturbation set. Robust control mode. Among them, The maximum possible disturbance amplitude, which is pre-calibrated, can be determined offline based on vehicle dynamics limits or through real vehicle test / high-fidelity simulation data, and is used as a known prior parameter.

[0203] Therefore, a robust invariant set for the terminal is constructed. , satisfying: for any In auxiliary control law Under the influence of the system, the system state For all It remains within the compressed constraint set, i.e.

[0204] (30)

[0205] in For the actual state constraint set, To correspond to the maximum disturbance The robust positive invariant set. This condition guarantees that even if the disturbance reaches its maximum possible value after the prediction time domain ends, the system state will remain within the constraint boundaries. The terminal constraint is:

[0206] (31)

[0207] This design ensures that the system automatically switches to robust control mode after the predictive information is exhausted, and it is recursively feasible: if If a feasible solution always exists, then candidate solutions (previous solutions) can be constructed. (Using the original sequence for the first step, and an auxiliary control law for the last step), it can be proven that... A feasible solution still exists at any given time, thus ensuring that constraints are satisfied throughout the entire time domain and that the system remains stable.

[0208] Solving the optimization problem yields the optimal nominal control sequence. And based on the state feedback control law (16) in the invention, calculate the actual control input, and then... The data is sent to the vehicle module for execution, enabling path tracking control. At the next sampling time, the system state is updated, and the process repeats until the next time step.

[0209] Step 5, Vehicle Module:

[0210] To verify the effectiveness and engineering feasibility of the control method proposed in this invention, the high-fidelity vehicle dynamics simulation software CarSim 2019.0 was used as the vehicle model platform. A whole vehicle dynamics system was constructed based on typical operating conditions. Through joint simulation using CarSim and Simulink, the comprehensive effect evaluation of path tracking control and time-varying constraint compression strategy was achieved, laying the foundation for subsequent real-vehicle experiments. In this method, a C-type passenger car built into CarSim was used as the object, and its main parameter settings are as follows: vehicle mass... Distance from center of gravity to front axle Distance from center of mass to rear axle yaw moment of inertia .

[0211] The vehicle module receives the actual control input from the tubular model predictive controller. This is then used as a front wheel steering angle command to apply to the vehicle system, updating the vehicle's motion state. At each discrete sampling time, the vehicle module outputs the current... Vehicle status at any time ,in The sideslip angle is the angle of the center of mass. The yaw rate is angular velocity. For heading deviation, This is for lateral deviation; simultaneously, the vehicle module outputs the current... Operating condition characteristic parameters at time ,in For longitudinal velocity, The road surface adhesion coefficient, For road curvature, , These are the vertical loads on the front and rear axles, respectively.

[0212] Vehicle state vector Feedback is sent to the tubular model predictive controller to initialize the initial nominal state of the optimization problem. and error calculation Operating condition characteristic parameter vector Feedback is sent to the time-varying tubular construction module for building history. Step working condition characteristic parameters And generate the prediction time domain In-step perturbation prediction sequence The aforementioned feedback mechanism forms a complete closed-loop control structure, enabling real-time path tracking control of autonomous vehicles.

[0213] Taking sinusoidal motion as an example, the longitudinal speed is set. The road surface adhesion coefficient was set to 0.3 to simulate extreme handling scenarios under low adhesion conditions. Tracking control was performed using both the traditional Tube-MPC control method (TMPC) and a designed predictive control method for autonomous vehicles with adaptive shrinking perturbation reachability domain (STMPC). Simulation results are as follows: Figure 3 , Figure 4 and Figure 5 As shown in the figure, the performance of the two controllers will be analyzed below with reference to the figure.

[0214] Depend on Figure 3 As can be seen from the yaw rate curve, the reference trajectory represents the desired yaw rate. TMPC, due to its use of a fixed robust invariant set, employs an overly conservative control strategy, resulting in a slow response and slight oscillations in the tracking curve, failing to adequately suppress the effects of disturbances. STMPC, through adaptive contraction of the disturbance reachable domain, appropriately reduces conservatism and improves response speed during the initial and dynamic change phases; it enhances robustness when dealing with larger disturbances, suppressing overshoot and avoiding oscillations. Its tracking curve more closely approximates the reference trajectory, demonstrating good dynamic tracking accuracy and robust adaptability.

[0215] The sideslip angle is a key indicator for evaluating vehicle stability. Figure 4 It is evident that while TMPC can reduce the fluctuation of the center of gravity sideslip angle and enhance stability, it sacrifices vehicle maneuverability, resulting in insufficient steering response and a still relatively high peak value. STMPC, through an adaptive contraction mechanism, allows the sideslip angle to increase moderately to improve steering response while ensuring that it does not exceed the safety boundary, thus achieving an effective balance between stability and maneuverability.

[0216] Depend on Figure 5 As can be seen from the front wheel steering angle curve, the TMPC significantly reduces the input amplitude of the steering angle. While this avoids over-excitation of the actuator, it fails to respond to the desired motion in a timely manner. The STMPC steering angle curve is closer to the reference curve, with a reasonable rate of change. It can respond quickly to the desired motion while maintaining smooth control, significantly improving the stability and ride comfort of the vehicle.

[0217] In summary, this invention constructs a disturbance prediction model based on vehicle operating condition characteristic parameters to perform multi-step prediction of system disturbances and constructs a time-varying disturbance set. Based on this, through error reachability set propagation and time-varying constraint contraction, a time-varying constraint contraction sequence in the prediction time domain is obtained, and a tubular model predictive controller is introduced. Compared to traditional tubular model predictive controllers that use fixed disturbance boundaries, this invention can more accurately characterize the time-varying characteristics of system uncertainties, reduce the conservatism of constraint contraction while ensuring robustness, expand the feasible range of the system, and thus improve path tracking performance.

Claims

1. A predictive control method for autonomous vehicles with adaptive shrinkage of the reachable domain due to disturbance, characterized in that, include: The system comprises an offline training module for the disturbance prediction model, a time-varying tubular model construction module, a reference path module, a tubular model prediction controller, and a vehicle module. The offline training module trains the disturbance prediction model offline to obtain the model. The time-varying tubular model construction module loads the disturbance prediction model and generates a disturbance prediction sequence in the prediction time domain based on the operating condition feature parameters obtained in real time from the vehicle module. And construct a time-varying perturbation set sequence. The error reachable set sequence in the prediction time domain is obtained through error reachable set propagation. Furthermore, based on the error reachable set sequence, the actual constraints are time-varyingly compressed to obtain a time-varying constraint-compressed state sequence that varies with the prediction step. With time-varying constrained compaction control input sequence The reference path module generates the reference state in the prediction time domain. ,in For reference centroid sideslip angle, For reference yaw rate, For reference heading deviation, The lateral deviation is used as the tracking target input for the tubular model predictive controller optimization problem. The tubular model predictive controller uses a rolling optimization method to solve for the optimal nominal control sequence based on a time-varying constrained compressed sequence, vehicle state, and reference state sequence. The actual front wheel steering angle is calculated by combining the state feedback control law. The vehicle module executes the front wheel steering angle. To update vehicle status and output vehicle status in real time. and operating condition characteristic parameters ; The time-varying tubular construction module is used to construct a time-varying constrained compressed sequence based on the perturbation prediction sequence in the prediction time domain. It includes: a perturbation prediction module, a perturbation set construction module, an error reachable set propagation module, and a time-varying constrained compressed module. The specific steps are as follows: Step 1.1, Disturbance Prediction Module: Load the disturbance prediction model to collect historical data in real time. Step condition characteristic parameters are used as input: in, The length of the historical time window. These are the characteristic parameters of the operating conditions; Define prediction step index Then the model output predicts the time domain. In-step perturbation prediction sequence: in, To predict the length of the time domain, Indicates at time For future moments The predicted value of the system disturbance; Step 1.2, Perturbation Set Construction Module: Based on the perturbation prediction sequence obtained in step 1.1 Calculate the upper bound vector of the disturbance amplitude at each time step: Subsequently, a time-varying perturbation set is constructed based on the upper bound vector of the perturbation amplitude: The vector inequality represents that each component satisfies... ,here The upper bound vector of the disturbance amplitude The One portion, perturbation vector The Each component; thus, the prediction time domain is obtained. Time-varying perturbation set sequence within a step ; Step 1.3, Error Reachable Set Propagation Module: At the current moment System state error as the initial set ,in The deviation between the actual state and the nominal state is based on the closed-loop error system. The time-varying perturbation set sequence is propagated to obtain the error reachable set sequence in the prediction time domain, as shown in the formula: in, Minkowski and, This is the closed-loop error state transition matrix. The time-varying perturbation set sequence constructed in step 1.2 The first in Step; the error set sequence obtained by propagation is ; Step 1.4, Time-varying constraint compression module: The state constraints of the actual system are The control input constraints are Based on error reachable set sequences The actual system state is decomposed into the sum of the nominal state and the error: for each prediction step ,have: Wherein the error , For sequence The One element; To ensure that the actual system satisfies the state constraints and control input constraints By using Minkowski difference operations, the time-varying compressed state constraint set and the time-varying compressed control input constraint set, which vary with the prediction step in the Tube-MPC prediction time domain, are obtained: in, Indicates Minkowski's difference, The state feedback gain matrix; for The first time predicted Time-varying compacted state constraint set for The first time predicted The time-varying, compact control input constraint set is obtained by integrating all single-step constraint sets in the prediction time domain in chronological order. Time-varying constrained compressed state sequence and time-varying constrained compressed control input sequence and Together, they constitute the time-varying constrained compaction sequence.

2. The predictive control method for autonomous vehicles with adaptive shrinkage of the reachability domain according to claim 1, characterized in that, The offline training module of the disturbance prediction model collects data. The system calculates vehicle operating condition characteristic parameters and disturbance labels at various times, constructs a training dataset, and trains an offline disturbance prediction model based on the training dataset. Specifically, it includes a dataset construction module and a model training module; the specific steps are as follows: Step 2.1, Dataset Construction Module: Obtain operating condition characteristic parameters from the vehicle module. including vehicle longitudinal speed Road surface adhesion coefficient Road surface curvature Front wheel vertical load and rear wheel vertical load Construct a sequence of operating condition features arranged in chronological order. ,in This represents the total number of sampling points; At the same time, based on vehicle status Compared with nominal condition Define system state error: in In nominal condition, An index for historical sampling times; Based on the closed-loop error system: Calculate the disturbance label: in, This is the closed-loop error state transition matrix; Constructing perturbation label sequences Normalize the working condition feature sequence and the disturbance label sequence, use the sliding window technique to extract input-output pairs, and convert the extracted time-series features and labels into tensor data to form the training dataset. Step 2.2, Model Training Module: A perturbation prediction network combining a long short-term memory network and a fully connected layer is constructed. The working condition feature sequence in the training dataset is used as input, and the corresponding perturbation label sequence is used as supervision label. The error between the network prediction output and the label is minimized to update the network parameters. During the training process, the network model with the smallest loss function value is selected and retained as the perturbation prediction model and saved.

3. The predictive control method for autonomous vehicles with adaptive shrinkage of the reachability domain according to claim 1, characterized in that, The tubular model predictive controller is used to decompose the actual system into a nominal system and an error system, perform rolling optimization of the nominal system based on a time-varying constraint compression sequence, and achieve the tracking of the nominal state by the actual state through state feedback compensation. The tubular model predictive controller includes predictive model construction, nominal system and error system decomposition and optimization problem construction, and specific steps include: Step 3.1, Prediction Model Construction: A lateral dynamics model of the vehicle is constructed using a two-degree-of-freedom vehicle model, and its expression is as follows: in, For vehicle quality, For the longitudinal speed of the vehicle, For the vehicle's lateral speed, The yaw rate is angular velocity. For the front wheel steering angle, and These are the lateral stiffness of the front and rear axle tires, respectively. and These are the distances from the vehicle's center of gravity to the front and rear axles, respectively. Let be the yaw moment of inertia of the vehicle about its center of mass. It is lateral acceleration. It is the yaw acceleration; Establish a tracking error model: in, For heading deviation, For lateral deviation, For road curvature, The rate of change of heading deviation. This represents the rate of change of the lateral deviation. The vehicle dynamics model and the tracking error model are then reorganized into a continuous-time state-space equation: Among them, system status Control input For the front wheel steering angle, Input the road curvature; Discretization is performed using the zero-order hold method, and the sampling period is... The discrete-time state-space equation is obtained as follows: in, , , These are the discrete state matrix, the input matrix, and the curvature input matrix, respectively. Step 3.2, Decomposition of Nominal System and Error System: Considering modeling errors and external disturbances, the actual system is represented as: in This is the actual state. For actual control input, For bounded perturbations; The nominal system is defined as: in In nominal condition, For nominal control input; State feedback control law is adopted: in, for The actual control input of the vehicle at any given time. for The optimal nominal control input for the current step at any given time. The state feedback gain matrix, for The system state error at time t; Step 3.3, Optimize problem construction: Let the prediction time domain be The nominal control input sequence to be optimized is defined as follows: The corresponding nominal state sequence is The initial nominal state ; The reference path module provides a reference state sequence in the prediction time domain. ,in , ; Based on the nominal system established in step 3.2, the reference state sequence provided by the reference path module is introduced. Construct the objective function for the tubular model predictive controller: in, , , These are the state weight matrix, the control input weight matrix, and the terminal weight matrix, respectively. Based on the objective function and combined with the time-varying constrained compressed sequence, the optimization problem of the tubular model predictive controller is constructed as follows: in This represents the difference in control input between two adjacent prediction times. To maximize the rate of change of control input, For terminal robust invariant set; Solving the optimization problem yields the optimal nominal control sequence. And calculate the actual control input based on the state feedback control law. , will input actual control The data is sent to the vehicle module to achieve vehicle motion control.

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