A longitudinal-lateral trajectory tracking control method for an electrically driven vehicle train

Abstract

The application relates to the technical field of intelligent driving vehicle motion control, and discloses a longitudinal and lateral trajectory tracking control method for an electrically driven automobile train. The method establishes an eight-dimensional discrete linear time-varying state space model which is updated online with a running state as a prediction control basis, introduces a hinged angle as a target control variable into lateral LTV-MPC to realize collaborative optimization of trajectory tracking and posture stability, and decomposes longitudinal control into outer ring position-speed sliding mode control and inner ring super-twisting high-order sliding mode acceleration control through a cascade sliding mode control structure, so that the method has the advantages of lateral and longitudinal collaborative decoupling, high calculation real-time performance, strong anti-interference robustness and consideration of trailer posture stability.

Description

Technical Field

[0001] This invention relates to the field of motion control technology for intelligent driving vehicles, specifically to a longitudinal and lateral trajectory tracking control method for electric-driven automobile trains. Background Technology

[0002] With the rapid development of intelligent driving technology, trajectory planning and control, as a core functional module of autonomous driving, directly affects the driving safety and comfort of vehicles. For a special type of vehicle, the car train, consisting of a tractor and trailer connected by an articulated joint, is characterized by its long body, high center of gravity, and numerous axles. This results in its dynamic model exhibiting strong nonlinearity, strong coupling, and significant articulated sway characteristics. In actual driving, the vehicle's lateral movement (path tracking) and longitudinal movement (speed regulation) interact and are tightly coupled, posing a significant challenge to the design of the trajectory tracking controller.

[0003] Currently, Model Predictive Control (MPC) is widely used in vehicle trajectory tracking control due to its ability to handle multi-constraint, multi-variable optimization problems and predict future states. However, when traditional nonlinear MPC is directly applied to vehicle-train systems, the high system state dimension and highly nonlinear dynamics require the controller to solve complex nonlinear optimization problems online in each sampling period, resulting in an extremely heavy computational burden that cannot meet the real-time requirements of millisecond-level response times for actual vehicle controllers. Although existing technologies have attempted to simplify the model using linearization methods, they often neglect the critical influence of the articulation angle state variables on the trailer's attitude stability, leading to instability phenomena such as folding and tail-wagging under extreme or complex conditions.

[0004] Meanwhile, in terms of longitudinal speed control, the mass of the vehicle train varies greatly (significant difference between empty and fully loaded), and it is susceptible to external disturbances such as slope and wind resistance during operation. Traditional PID control or feedforward control strategies are insufficiently robust to such model uncertainties and time-varying disturbances, making it difficult to guarantee speed tracking accuracy under all operating conditions. Although sliding mode control (SMC) is considered an effective robust control strategy due to its insensitivity to parameter perturbations and external disturbances, how to effectively combine it with the unique drive / braking execution characteristics of vehicle trains, and coordinate it with lateral control to resolve the contradiction between lateral and longitudinal coupling, remains a pressing technical challenge.

[0005] In summary, the existing technologies have the following shortcomings: First, traditional nonlinear MPC has a huge computational load and poor real-time performance when applied to automobile trains, and the existing linearization schemes fail to properly handle the trailer attitude stability problem; Second, longitudinal control lacks sufficient robustness to cope with strong disturbances and parameter changes; Third, there is a lack of a systematic control architecture that can organically unify lateral precise tracking and longitudinal strong robust control, and effectively decouple the lateral and longitudinal synergistic effects. Summary of the Invention

[0006] (a) Technical problems to be solved To address the shortcomings of existing technologies, this invention provides a longitudinal and lateral trajectory tracking control method for electric-driven vehicle trains. It has the advantages of longitudinal and lateral cooperative decoupling, high real-time computation, strong anti-interference robustness, and consideration of trailer attitude stability. It solves the problems of existing nonlinear MPC in vehicle train systems, which are too computationally intensive and difficult to solve in real time; neglecting the articulation angle state during linearization, which makes the trailer prone to instability under complex working conditions; poor robustness of longitudinal speed control in the face of model uncertainty and external disturbances; and difficulty in co-optimization of strong longitudinal and lateral coupling.

[0007] (II) Technical Solution To achieve the above objectives, the present invention provides the following technical solution: a method for longitudinal and lateral trajectory tracking control of an electric-driven vehicle train, comprising the following steps: S1. Model Establishment: Establish the state-space equations of the truck train dynamics, solve the dynamic equations of the tractor and trailer simultaneously using the algebraic method, eliminate the articulation force, and combine the attitude and heading geometric relationship of the tractor and trailer to define the state vector containing the state variables of the tractor and trailer. After linearization by the Jacobian matrix, a continuous-time state-space model is constructed. Further discretization is performed using the explicit Euler method to obtain the discrete linear time-varying state-space model of the semi-trailer truck train. S2. Set the state and reference quantities of the lateral LTV-MPC controller: Based on the discrete linear time-varying state space model established in step S1, the planning module provides reference trajectory information, including the reference lateral position and the reference tractor heading angle. The actual state quantities at the current moment are obtained by vehicle state sampling to determine the state and reference quantities of the LTV-MPC controller. S3. Update the linear time-varying prediction model and construct the incremental prediction equation: In each sampling period, using the state variables fed back in real time by the vehicle dynamics model, and based on the discrete linear time-varying model parameters updated in step S1... , Furthermore, a control increment parameterization method is introduced to convert the control input into an incremental form and construct an augmented state vector containing the control quantity of the previous time step, and finally derive the prediction model in incremental form. S4. Construct a quadratic programming optimization problem for horizontal LTV-MPC: Based on the linear prediction expression obtained in step S3, design a quadratic performance index that includes output error weighting, control increment weighting, and relaxation factor, and transform the trajectory tracking problem into a constrained standard convex quadratic programming problem. At the same time, apply control increment magnitude constraints, relaxation factor boundary constraints, steering magnitude constraints, and prediction output boundary constraints. S5. Perform rolling time-domain optimization and output lateral control quantity: Based on the standard convex quadratic programming problem constructed in step S4, a numerical solver is used to solve the problem online within a fixed sampling period to obtain the optimal control increment sequence. A rolling time-domain strategy is adopted to apply only the first component of the control increment sequence to the system and superimpose it with the control quantity at the previous moment to obtain the front wheel steering angle control command at the current moment, which is then output to the controlled vehicle dynamics model. S6. Design of the outer loop controller for longitudinal cascade sliding mode control: Based on the cascade control structure, the longitudinal velocity and position control are used as the outer loop. The desired longitudinal displacement and desired vehicle speed given by the planning module are used as reference inputs, and the actual position and actual vehicle speed output by the vehicle dynamics model are used as feedback quantities. The position-velocity integrated sliding surface is constructed, and the outer loop sliding mode control law containing linear feedback terms and switching terms is designed. The acceleration compensation quantity is output to correct the planned acceleration, and the amplitude and rate of change constraints are applied and then transmitted to the inner loop. S7. Design of the inner loop controller for longitudinal cascade sliding mode control: The corrected target acceleration output from the outer loop is used as the set value, and the actual longitudinal acceleration of the vehicle is used as the feedback quantity. A first-order low-pass filter is used to suppress noise in the actual acceleration measurement value. The acceleration error and its sliding mode variable are constructed. The inner loop control law is designed using the super-twisting high-order sliding mode algorithm. The final acceleration command is output, and actuator capability and longitudinal comfort constraints are applied at the same time. S8. Constructing a lateral and longitudinal coordinated control closed loop: The lateral LTV-MPC controller and the longitudinal cascade sliding mode controller are integrated in a coordinated manner. The lateral controller outputs the front wheel steering angle command based on the real-time vehicle status in each sampling cycle, and the longitudinal controller outputs the drive / braking command synchronously. The two work together to act on the dynamic model of the controlled vehicle to form a lateral and longitudinal coordinated control closed loop.

[0008] Preferably, the model building process in S1 is as follows: S1.1 Establish the vehicle dynamics state-space equations: Let 1 and 2 represent the relevant parameters of the tractor and trailer, respectively, and define the total mass of the tractor as... The total mass of the trailer is The distance from the center of gravity of the tractor to the front axle is The distance from the center of gravity of the tractor to the rear axle is The distance from the trailer's center of gravity to the front axle is The distance from the trailer's center of gravity to the axle is The yaw rate of the tractor is The trailer's yaw rate is The sideslip angle of the tractor's center of gravity is The trailer's center of gravity sideslip angle is The moment of inertia of the tractor about the Z-axis is The moment of inertia of the trailer about the Z-axis is The steering angle of the tractor's front wheels is The distance from the center of gravity of the tractor to the traction pin is The lateral stiffness of the front axle of the tractor is The lateral stiffness of the rear axle of the tractor is The equivalent axle lateral stiffness of the trailer is The hinge angle is The longitudinal speed of the tractor is The longitudinal speed of the trailer is The lateral velocity of the tractor's center of gravity is , Lateral velocity of the trailer's center of gravity, and the rate of change of the tractor's center of gravity's lateral velocity. The rate of change of the lateral velocity of the trailer's center of gravity is The heading angle of the tractor is The trailer heading angle is The directional angular velocity of the tractor is The trailer's angular velocity is The x-coordinate of the tractor's center of gravity is X, and the y-coordinate is Y; the rate of change of the x-coordinate of the tractor's center of gravity is... The rate of change of the tractor's center of gravity ordinate is ; By solving the dynamic equations of the tractor and trailer simultaneously using algebraic methods, eliminating the articulation force, and simplifying, we obtain the following differential equation: lateral velocity change rate of the tractor's center of gravity satisfy:

[0009] in, = , = , = , = , = , = , = , = ; yaw rate of change of tractor satisfy:

[0010] Trailer yaw rate of change satisfy:

[0011] Analysis of the tractor-trailer attitude and heading geometry yields the following results:

[0012] The position of the tractor's center of gravity is updated during driving as follows:

[0013] S1.2 Constructing the continuous-time state-space equation: Based on the relationship in step S1.1, define the state vector containing the tractor and trailer as follows:

[0014] Rewriting the above dynamic equations in matrix form and solving for the Jacobian matrix yields the following matrix:

[0015] Where the control input u is the front wheel steering angle of the tractor. ; System Matrix , Specifically, it can be elaborated as follows:

[0016]

[0017] ,

[0018] ,

[0019] , , ,

[0020] ,

[0021] ,

[0022] , , , , ,

[0023]

[0024] At this point, the continuous-time state-space model of the semi-trailer train under the small-angle assumption has been completed; S1.3 Discretization: The continuous-time state-space equations in step S1.2 are then discretized using the explicit Euler method.

[0025] Where I is the identity matrix and T is the sampling period. , These represent the discretized system matrix and the input matrix, respectively.

[0026] Preferably, in step S2, the state variables and reference variables of the horizontal LTV-MPC controller are set, and the controller state vector is taken from the state vector defined in step S1.2:

[0027] Among them, matrix , Include The item, and the location update line also contains , Item, therefore , It will change online according to the vehicle's operating status; Simultaneously, attitude stability constraints for the train system are introduced, with the tractor's heading angle, lateral position, and articulation angle selected as target control variables, defined as:

[0028] Among them, the output matrix The value of is determined by the state vector. By directly selecting the corresponding component, we can obtain:

[0029] Control input quantity For the steering angle of the front wheels of the tractor The reference values ​​for the trajectory tracking section are provided by the planning module, and for the hinge angle reference... Zero hinge angle is used as the stability target, that is:

[0030] in, To predict the step size, during the model predictive control rolling optimization process, Y is used to ensure geometrical trajectory tracking accuracy, while θ is used to limit the hinge angle and oscillation.

[0031] Preferably, the update process of the linear time-varying prediction model and the construction of the incremental prediction equation in S3 is as follows: S3.1 Real-time update of the linear time-varying model: In each sampling period, the actual state quantity x(k) and longitudinal velocity output by the vehicle dynamics model are used. Update system matrix (k) and input matrix (k); S3.2. Establish an incremental prediction model using the control increment parameterization method: Apply a rate of change constraint and use control increment parameterization, defined as follows:

[0032] Where u is the control input vector. To control the increment; Further, we introduce an augmented state that includes the control quantity from the previous time step: This yields the incremental prediction model:

[0033] in, , For the reason , The block matrix formed This is an affine deviation compensation term; In programming implementation, affine deviation compensation term Obtained by one-step nonlinear update One-step prediction with linear models The difference is worth; S3.3 Constructing the reference output sequence and linear prediction expression in the prediction time domain: The reference output is constructed in the prediction domain as follows: in, and The hinge angle reference is obtained from the reference trajectory of the planning module. Zero hinge angle is used as the stability target; Let the prediction step size be... Control step size is The predicted domain output and the reference output are stacked as follows:

[0034] And stack the control increment sequences as follows: The standard linear prediction expression is obtained from the augmented model: in, , , For the reason , , The prediction matrix is ​​constructed recursively. The vector is a stack of deviation terms.

[0035] Preferably, in S4, a quadratic programming optimization problem for constructing horizontal LTV-MPC is: S4.1 Constructing Quadratic Performance Indicators: Based on the comprehensive requirements of tracking error and control smoothness, construct quadratic performance indicators: in, Used for weighing , , The Importance of the Three Types of Output Errors Used to suppress excessive steering increments For relaxation factor, Its weight; Define the vector of optimization variables within the predictive control domain as: in, For the steering angle of the tractor's front wheels, satisfy the rolling update relationship: Using the above quadratic performance index, and rearranging it equivalently into a standard quadratic programming problem: Among them, matrix with vector From the prediction model and weight matrix , The current system state and the reference trajectory are used to determine this. S4.2 Applying complete constraints to form the optimal feasible region: To match the physical limitations of the actuators and ensure vehicle attitude safety, both input and output constraints are applied. The final feasible region is written as: First, upper and lower bound constraints are imposed on the control increment: Then apply boundary constraints to the relaxation factor: The above constraints are uniformly written in the form of upper and lower bounds for the optimization variables: in, For dimension is A vector of all 1s This is the upper bound parameter for the relaxation factor; Secondly, to limit the steering amplitude and suppress the risk of vehicle folding during operation, boundary constraints are applied to the control amplitude and the predicted output. The control amplitude constraint is as follows: Simultaneously, an output boundary is applied within the prediction time domain: in, , These represent the hard / soft boundaries of the predicted output.

[0036] Preferably, the rolling time-domain optimization solution and output of the lateral control quantity in S5 is as follows: within each sampling period, based on the current measured state quantity... Control quantity at the previous moment Construct augmented states The numerical solver is then used to solve the standard quadratic programming problem described above, and the optimal optimization variables are obtained. Extract the first component of the optimal control increment sequence from it. ; The optimal control increment is superimposed with the control value from the previous moment to obtain the current steering angle of the tractor's front wheels:

[0037] Will = The output is sent to the vehicle dynamics model and acts on the steering actuator of the front wheels of the tractor. In the next sampling period, the vehicle state quantity will be measured again. Update the parameters of the linear time-varying model (k+1) (k+1) and the affine deviation compensation term d(k+1).

[0038] Preferably, the design flow of the longitudinal cascade sliding mode control outer loop controller in S6 is as follows: S6.1 Define the outer loop error variable: The control objective of the outer loop is to minimize the actual displacement of the vehicle given the longitudinal displacement and vehicle speed reference trajectory. speed Achieve asymptotic tracking, longitudinal position error Speed ​​error and its integral Defined as:

[0039] Where x and v are the actual longitudinal displacement and actual longitudinal velocity, respectively. , These represent the reference displacement and reference velocity given by the planning module, respectively. S6.2 Constructing the outer ring sliding surface: To simultaneously consider both steady-state position accuracy and dynamic velocity performance, the following first-order sliding surface is selected:

[0040] in, , For sliding surface parameters, by It is obtained that during the sliding motion phase At that time, the error approximately satisfies:

[0041] Its eigenvalues ​​are located in the left half-plane, ensuring , It converges to zero at the desired decay rate; S6.3 Design of the outer-loop sliding mode control law: Combining the sliding mode approach condition, a control law consisting of linear terms and switching terms is constructed. The outer-loop output is the longitudinal acceleration compensation quantity.

[0042] in, For linear feedback gain, To switch gain, The boundary layer thickness. Saturation function. Defined as: In the boundary layer Continuous control is achieved within the neighborhood to reduce chattering caused by high-frequency switching; S6.4 Apply outer ring constraints and generate inner ring target acceleration benchmark: Considering vehicle longitudinal dynamics and ride comfort constraints, apply compensation acceleration... The amplitude and rate of change are limited, and their amplitude and rate of change satisfy:

[0043] in , Given by the vehicle calibration, the corrected compensation acceleration is finally superimposed with the planned acceleration to obtain the target acceleration benchmark for the inner loop: in, , , These represent the reference acceleration and sliding mode compensation acceleration provided by the planning module, respectively. Inner Ring Road The actual acceleration of the vehicle is rapidly adjusted to a set value, so that the whole vehicle appears to be an ideal acceleration actuator from the perspective of the outer ring.

[0044] Preferably, the design flow of the longitudinal cascade sliding mode control inner loop controller in S7 is as follows: S7.1 Acceleration signal filtering: The actual longitudinal acceleration output by the vehicle dynamics model is denoted as... To suppress measurement noise, a first-order low-pass filter is first used to filter it, resulting in: in, The filtered acceleration. It is a time constant; S7.2, Define the acceleration error and inner loop sliding mode variables as follows: S7.3 The inner loop adopts a super-twisting high-order sliding mode algorithm and introduces auxiliary states. ,definition:

[0045]

[0046]

[0047]

[0048] in, , For inner loop sliding mode gain, The thickness of the inner ring boundary layer. Consistent with the aforementioned definition; S7.4 Apply inner loop constraints and output acceleration command: Also considering actuator capability and longitudinal comfort constraints, the final acceleration command is... Apply amplitude and rate of change limits: in, , Acceleration command selected based on the allowable range of the powertrain and braking system. The accelerator-brake pedal calibration relationship is mapped to traction torque command and braking pressure command, which are then applied to the vehicle dynamics model.

[0049] Preferably, the process of constructing a horizontal and vertical collaborative control closed loop in S8 is as follows: S8.1, Cooperative integration of horizontal and vertical controllers: Horizontal and vertical control are executed in parallel within each sampling period. The horizontal control quantity and the vertical control quantity are calculated independently and act together on the controlled object. S8.2 Formation of lateral and longitudinal coordinated closed-loop control: The TruckSim high-fidelity vehicle dynamics model is used as the controlled object, receiving the front wheel steering angle command u(k) = (k) and drive / brake commands, outputting real-time vehicle state quantities, and tuning key controller parameters through the TruckSim and MATLAB / Simulink co-simulation platform.

[0050] Preferably, in step S8.1, lateral control and longitudinal control are performed in parallel: the lateral channel executes steps S3 to S5 based on the current state of the vehicle. As input, the front wheel steering angle u(k) of the tractor is obtained by solving LTV-MPC. (k); The longitudinal channel executes steps S6 to S7 to obtain planning information. , , And actual feedback X, , As input, acceleration commands are obtained through cascade sliding mode control. This is then mapped to throttle / brake commands via the drive / brake integrated calibration table.

[0051] Compared with the prior art, the present invention provides a longitudinal and lateral trajectory tracking control method for electric-driven vehicle trains, which has the following advantages: 1. This invention establishes an eight-dimensional discrete linear time-varying state-space model that is updated online with the vehicle's operating state by simultaneously solving the dynamic equations of the tractor and trailer using an algebraic method and eliminating the articulation force. It combines Jacobian matrix linearization under the small-angle assumption with explicit Euler discretization. This ensures that the linear model effectively approximates the original nonlinear dynamic system near the operating point in each sampling period. This reduces the dimensionality of the multi-rigid-body coupled dynamic model of the vehicle train while maintaining model accuracy. Ultimately, this lays the model foundation for the real-time deployment and engineering application of model predictive control on the combined vehicle platform.

[0052] 2. This invention introduces the hinge angle as the target control variable into the output matrix of the lateral LTV-MPC, and uses zero hinge angle as the stability reference target. In the quadratic programming performance index, three-dimensional output error weighting terms of the tractor's heading angle, lateral position and hinge angle are set simultaneously. The hinge angle prediction output boundary constraint is applied in the constraint conditions, so that the lateral controller can simultaneously take into account the path tracking accuracy and train attitude stability under a unified optimization framework. In the process of vehicle train trajectory tracking, the hinge angle sway and folding risk are directly suppressed, and the path geometric tracking accuracy and train attitude stability are synergistically optimized. This overcomes the shortcomings of existing methods where the desired trajectory of the trailer is difficult to give directly and the relative rotation of the tractor and trailer lacks active constraints.

[0053] 3. This invention decomposes longitudinal control into an outer-loop position-velocity integrated sliding mode control and an inner-loop super-twisting high-order sliding mode acceleration tracking control through a cascade sliding mode control architecture. The outer-loop output, after amplitude and rate of change limiting, serves as the target acceleration reference for the inner loop. The inner loop employs a high-order sliding mode algorithm to continuously adjust the acceleration error with high bandwidth. This enables the longitudinal controller to achieve asymptotic tracking of position, velocity, and acceleration variables under uncertainties in the longitudinal dynamics model of the electric vehicle train and external disturbances such as slope / wind resistance, without the need for precise acquisition of tire-ground longitudinal force parameters and road slope information. It also significantly reduces sliding mode chattering, ultimately effectively improving the comfort of longitudinal driving and the service life of the drive / brake actuators. Attached Figure Description

[0054] Figure 1 This is the control logic diagram of the vehicle dynamics model of the present invention; Figure 2 This is a diagram illustrating the architecture of the vehicle-train lateral model prediction trajectory tracking control strategy of the present invention. Figure 3 This is a diagram of the longitudinal speed-acceleration cascade control structure of the vehicle according to the present invention; Figure 4 This is a logic diagram of the longitudinal cascade trajectory tracking control strategy for automobile trains according to the present invention; Figure 5 This is a diagram of a car train for the present invention. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] Please see Figures 1-5A method for longitudinal and lateral trajectory tracking control of an electric vehicle train includes the following steps: S1. Model Establishment: Establish the dynamic state-space equations of the vehicle-train, unifying the relevant parameters of the tractor and trailer with 1 and 2 respectively. Solve the dynamic equations of the tractor and trailer simultaneously using the algebraic method, eliminate the articulation force, and combine the attitude and heading geometric relationship of the tractor and trailer to define the state vector containing the state variables of the tractor and trailer. After linearization by the Jacobian matrix, a continuous-time state-space model is constructed. Further discretization is performed using the explicit Euler method to obtain a discrete linear time-varying state-space model of the vehicle-train suitable for predictive control. It is also clarified that the model parameters are updated online with the vehicle's operating status in each sampling period. S2. Set the state and reference variables of the lateral LTV-MPC controller: Based on the discrete linear time-varying state space model established in step S1, the planning module provides reference trajectory information, including the reference lateral position and the reference tractor heading angle. The actual state variables at the current moment are obtained by vehicle state sampling, and the state and reference variables of the LTV-MPC controller are determined to provide input for subsequent prediction model updates and optimization solutions. S3. Update the linear time-varying prediction model and construct the incremental prediction equation: In each sampling period, use the state variables fed back in real time by the vehicle dynamics model to calculate and update the parameters of the discrete linear time-varying model according to step S1.3. , Furthermore, a control increment parameterization method is introduced to convert the control input into an incremental form and construct an augmented state vector containing the control quantity of the previous time step. Finally, an incremental form prediction model is derived, providing a linear prediction expression for the construction of subsequent quadratic programming problems. S4. Constructing a quadratic programming optimization problem for the horizontal LTV-MPC: Based on the linear prediction expression obtained in step S3, considering the trajectory tracking error, control input smoothness, and articulation angle attitude stability, a quadratic performance index including output error weighting, control increment weighting, and relaxation factor is designed. The trajectory tracking problem is uniformly transformed into a constrained standard convex quadratic programming problem. At the same time, control increment magnitude constraints, relaxation factor boundary constraints, steering magnitude constraints, and prediction output boundary constraints are applied to form a complete optimization feasible region. S5. Perform rolling time-domain optimization and output lateral control quantity: Based on the standard convex quadratic programming problem constructed in step S4, a numerical solver is used to solve the problem online within a fixed sampling period to obtain the optimal control increment sequence. A rolling time-domain strategy is adopted to apply only the first component of the control increment sequence to the system. This component is then superimposed with the control quantity at the previous moment to obtain the front wheel steering angle control command at the current moment. This command is then output to the dynamic model of the controlled vehicle to achieve closed-loop control for lateral trajectory tracking. S6. Design of the outer loop controller for longitudinal cascade sliding mode control: Based on the cascade control structure, longitudinal velocity and position control are used as the outer loop. The desired longitudinal displacement and desired vehicle speed given by the planning module are used as reference inputs, and the actual position and actual vehicle speed output by the vehicle dynamics model are used as feedback quantities. A position-velocity integrated sliding surface is constructed, and an outer loop sliding mode control law containing linear feedback terms and switching terms is designed. The acceleration compensation quantity is output to correct the planned acceleration, and the amplitude and rate of change constraints are applied and then transmitted to the inner loop. S7. Design of the inner loop controller for longitudinal cascade sliding mode control: The corrected target acceleration output from the outer loop is used as the setpoint, and the actual longitudinal acceleration of the vehicle is used as the feedback. A first-order low-pass filter is used to suppress noise in the actual acceleration measurement value. The acceleration error and its sliding mode variable are constructed. The inner loop control law is designed using a super-twisting high-order sliding mode algorithm. The final acceleration command is output. At the same time, actuator capability and longitudinal comfort constraints are applied to achieve high bandwidth and robust tracking adjustment of acceleration. S8. Constructing a lateral and longitudinal coordinated control closed loop: The lateral LTV-MPC controller and the longitudinal cascade sliding mode controller are integrated in a coordinated manner. The lateral controller outputs the front wheel steering angle command based on the real-time vehicle status in each sampling cycle, and the longitudinal controller outputs the drive / braking command synchronously. The two work together to act on the dynamic model of the controlled vehicle to form a lateral and longitudinal coordinated control closed loop. The controller performance is verified and the parameters are tuned through a joint simulation platform, and finally, the accurate tracking of the planned trajectory and the stable control of the vehicle attitude are achieved.

[0057] Specifically, the model building process in S1: S1.1 Establish the vehicle dynamics state-space equations: Let 1 and 2 represent the relevant parameters of the tractor and trailer, respectively: Table 1 Meaning of Vehicle Parameter Symbols ; By solving the dynamic equations of the tractor and trailer simultaneously using algebraic methods, eliminating the articulation force, and simplifying, we obtain the following differential equation: lateral velocity change rate of the tractor's center of gravity satisfy:

[0058] in, = , = , = , = , = , = , = , = ; yaw rate of change of tractor satisfy:

[0059] Trailer yaw rate of change satisfy:

[0060] Analysis of the tractor-trailer attitude and heading geometry yields the following results:

[0061] The position of the tractor's center of gravity is updated during driving as follows:

[0062] By combining the dynamic equations of the tractor and trailer using an algebraic method and eliminating the articulation force, the complex multi-rigid-body coupled system is reduced to a unified state-space description. This effectively avoids the dimensionality expansion and solution difficulties caused by using the articulation force as a state variable, thereby reducing model complexity and improving computational efficiency in subsequent controller design. By introducing a small-angle assumption to linearize the nonlinear trigonometric functions, the system matrix has an affine structure while ensuring model accuracy under low- and medium-speed driving conditions. This ultimately facilitates the analytical solution of the Jacobian matrix and the online updating of the linear time-varying model. S1.2 Constructing the continuous-time state-space equation: Based on the relationship in step S1.1, define the state vector containing the tractor and trailer as follows:

[0063] Rewriting the above dynamic equations in matrix form and solving for the Jacobian matrix yields the following matrix:

[0064] Where the control input u is the front wheel steering angle of the tractor. ; System Matrix , Specifically, it can be elaborated as follows:

[0065]

[0066] ,

[0067] ,

[0068] , , , , , , , , , ,

[0069]

[0070] At this point, the continuous-time state-space model of the train under the small-angle assumption has been completed; By defining an eight-dimensional state vector containing the lateral velocity, heading angle, yaw rate of the tractor, heading angle, yaw rate of the trailer, articulation angle, and the lateral and longitudinal coordinates of the tractor's center of mass, the complex dynamic differential equations of the train are unified into a linear time-varying (LTV) state-space standard form. This facilitates the full utilization of controllability and observability analysis and controller design tools in linear system theory. By linearizing the Jacobian matrix, explicit expansion terms of the system matrix A and the input matrix B are obtained, clarifying the quantitative contribution of each dynamic parameter to the system state evolution, which is beneficial for subsequent discretization processing and accurate updating of the prediction model. S1.3 Discretization: To facilitate predictive control in the discrete sampling system, the continuous-time state-space equations in step S1.2 are discretized using the explicit Euler method.

[0071] Where I is the identity matrix and T is the sampling period. , These represent the discretized system matrix and the input matrix, respectively.

[0072] By discretizing the continuous-time state-space model using the explicit Euler method, the controller can directly perform rolling time-domain optimization on the digital processor with a fixed sampling period, which is beneficial for engineering deployment and real-time control implementation. The discretized model parameters are refreshed online with the vehicle's operating status in each sampling period, enabling the linear model to effectively approximate the original nonlinear system near the operating point. This helps to improve the model's prediction accuracy and the controller's robustness while ensuring that the computational burden is acceptable.

[0073] Specifically, in S2, the state and reference variables of the horizontal LTV-MPC controller are set as follows: the controller state vector is taken from the state vector defined in step S1.2.

[0074] It should be noted that: matrix , Includes The item, and the location update line also contains , Item, therefore , The system will change online according to the vehicle's operating status. The model is a discrete linear time-varying (LTV) system, and the state variables output by TruckSim are used for calculation in each sampling period to refresh the discrete model parameters in real time. Meanwhile, to avoid issues under low-speed conditions... The numerical problems it caused, in To ensure computational stability, a minimum value is added. Furthermore, while ensuring path geometric tracking accuracy, attitude stability constraints for the train system are introduced. This takes into account the trailer's heading. The desired trajectory is difficult to give directly in most cases, while the hinge angle The relative attitude and folding risk between the tractor and trailer can be directly characterized. The tractor's heading angle, lateral position, and articulation angle are selected as target control variables and defined as follows:

[0075] The output matrix The value of is determined by the state vector. By directly selecting the corresponding component, we can obtain:

[0076] Control input quantity For the steering angle of the front wheels of the tractor The reference values ​​for the trajectory tracking section are provided by the planning module, and for the hinge angle reference... Zero hinge angle is used as the stability target, that is:

[0077] This indirectly controls the trailer's heading angle, directly suppresses the relative deflection between the tractor and trailer, improves the attitude stability of the train-type combined vehicle during operation, and further enhances the rolling optimization process of model predictive control. Used to ensure geometrical trajectory tracking accuracy, This term is used to limit the hinge angle and oscillation, achieving unified optimization of trajectory tracking and attitude stabilization; in, To predict the step size, during the model predictive control rolling optimization process, Y is used to ensure the accuracy of trajectory tracking in a geometric sense, while θ is used to limit the hinge angle and oscillation, so as to achieve unified optimization of trajectory tracking and attitude stabilization.

[0078] By selecting the tractor's heading angle, lateral position, and articulation angle as target control variables, path geometry tracking and train attitude stability are integrated into the same control framework. φ1 and Y are used to ensure the tractor's accurate tracking of the reference trajectory, while θ is used to directly suppress articulation angle sway and folding risks, which is beneficial for achieving comprehensive optimization between trajectory tracking accuracy and the driving safety of combined vehicles. By using zero articulation angle as the stability target, the trailer attitude is indirectly constrained when the desired trailer heading trajectory is difficult to give directly. This simplifies the setting of reference variables and improves the lateral stability of combined train vehicles during high-speed lane changes and curves.

[0079] Specifically, the update process of the linear time-varying prediction model in S3 and the construction of the incremental prediction equation: S3.1 Real-time update of the linear time-varying model: In each sampling period, the actual state quantity x(k) and longitudinal velocity output by the vehicle dynamics model are used. Update system matrix (k) and input matrix (k); The system matrix is ​​refreshed in real time using the actual state variables and longitudinal velocity output by TruckSim in each sampling period. (k) and input matrix (k) enables the discrete LTV model to maintain a high-fidelity approximation of the real system in the region of strong nonlinear vehicle dynamics, which is beneficial to extend the effective time domain of the prediction model and reduce the tracking error caused by model mismatch. S3.2. Establishing an incremental prediction model using the control increment parameterization method: To suppress abrupt changes in the steering input and facilitate the application of rate of change constraints, control increment parameterization is adopted, defined as follows:

[0080] Where u is the control input vector. To control the increment; Further, we introduce an augmented state that includes the control quantity from the previous time step: This yields the incremental prediction model:

[0081] in, , For the reason , The block matrix formed This is an affine bias compensation term, used to reduce the impact of linearization and discretization errors on prediction consistency; In programming implementation, affine deviation compensation term Obtained by one-step nonlinear update One-step prediction with linear models The difference is obtained and approximated within the prediction domain to improve prediction accuracy and numerical stability without significantly increasing the computational burden. By introducing control increments And construct an augmented state that includes the control quantity from the previous time step. The absolute value of the control input in the original system is transformed into an incremental form. Combined with the affine deviation compensation term d(k), the linearization error is corrected online. This helps to improve the prediction consistency without increasing the computational burden of the prediction step size. At the same time, it provides a direct mathematical expression for the application of the steering rate constraint. S3.3 Constructing the reference output sequence and linear prediction expression in the prediction time domain: The reference output is constructed in the prediction domain as follows: in, and The hinge angle reference is obtained from the reference trajectory of the planning module. Zero hinge angle is used as the stability target; Let the prediction step size be... Control step size is The predicted domain output and the reference output are stacked as follows:

[0082] And stack the control increment sequences as follows: The standard linear prediction expression is obtained from the augmented model: in, , , For the reason , , The prediction matrix is ​​constructed recursively. The vector is a stack of deviation terms.

[0083] By constructing the reference output within the prediction domain as containing , , By adopting the form of a zero-hinged-angle target, the trajectory tracking and attitude control problem in the finite time domain is transformed into a standard linear prediction expression, which is beneficial for the structured construction and efficient solution of the subsequent quadratic programming problem.

[0084] Specifically, the quadratic programming optimization problem for constructing a horizontal LTV-MPC in S4: S4.1 Constructing Quadratic Performance Indicators: Based on the comprehensive requirements of tracking error and control smoothness, construct quadratic performance indicators: in, Used for weighing , , The Importance of the Three Types of Output Errors Used to suppress excessive steering increments For relaxation factor, Its weight; In the prediction time domain, based on the discretized LTV state-space model, the future output of the system can be represented as a linear function of the control increment sequence. Substituting this prediction relationship into the above quadratic performance index and organizing the output error and control increment term at each step in the prediction time domain, the trajectory tracking problem can be uniformly transformed into a constrained quadratic programming problem. Define the vector of optimization variables within the predictive control domain as: in, For the steering angle of the tractor's front wheels, satisfy the rolling update relationship: Using the above quadratic performance index, and rearranging it equivalently into a standard quadratic programming problem: Among them, matrix with vector From the prediction model and weight matrix , The current system state and the reference trajectory are used together to determine the overall trade-off between the tracking error of the predicted output and the smoothness of the control input; By introducing a hinge angle weighting term and a relaxation factor, the performance indicators simultaneously quantify the requirements for trajectory tracking accuracy, hinge angle stability, and constraint feasible region softening. This facilitates the explicit inclusion of train safety attitude control under extreme conditions into the optimization objective. By equivalently transforming the original trajectory tracking problem into a standard convex quadratic programming form, efficient numerical solvers can be fully utilized to achieve millisecond-level online optimization, which helps meet the dual requirements of real-time performance and numerical stability for actual vehicle control. S4.2 Applying complete constraints to form the optimal feasible region: To match the physical limitations of the actuators and ensure vehicle attitude safety, both input and output constraints are applied. The final feasible region is written as: First, upper and lower bound constraints are imposed on the control increment: To prevent unbounded growth of slack variables and ensure that they only act as a buffer when necessary, boundary constraints are imposed on the slack factors: The above constraints are uniformly written in the form of upper and lower bounds for the optimization variables: in, For dimension is A vector of all 1s This is the upper bound parameter for the relaxation factor, used to limit the maximum extent of constraint relaxation and ensure that the optimization problem is bounded; Secondly, to limit the steering amplitude and suppress the risk of vehicle folding during operation, boundary constraints are applied to the control amplitude and the predicted output. The control amplitude constraint is as follows: Simultaneously, an output boundary is applied within the prediction time domain: in, , These represent the hard / soft boundaries of the predicted output; In summary, based on the discrete LTV prediction model, trajectory tracking control is uniformly transformed into a convex quadratic programming problem with input and output constraints, and a rolling time-domain strategy is used for online solution, achieving closed-loop control by applying only the first steering increment. Figure 1 This paper presents a closed-loop control architecture for lateral trajectory tracking of a vehicle-train based on LTV-MPC, demonstrating the control flow of reference input, model update, QP solution, steering output, and vehicle state feedback. This architecture adapts to the nonlinear characteristics of the vehicle-train by updating the linearized model cycle by cycle, introduces safety hard constraints such as articulation angle in the QP solution, and adopts an incremental control strategy to suppress sudden steering changes, thus ensuring trajectory tracking accuracy and driving stability.

[0085] By simultaneously applying control increment amplitude constraints, steering amplitude constraints, prediction output boundary constraints, and relaxation factor boundary constraints, the actuator physical limit, vehicle safe driving envelope, and attitude anti-folding limit are uniformly expressed as a set of linear inequalities of optimization variables. This helps ensure that the solved control commands are always within the allowable range of the electric drive steering actuator. By explicitly introducing the articulation angle output constraint, the risk of folding is directly suppressed during the vehicle-train trajectory tracking process, which helps improve the driving safety of the combined vehicle in dangerous conditions such as emergency obstacle avoidance and low-adhesion road surfaces.

[0086] Specifically, the rolling time-domain optimization solution and output of the lateral control quantity in S5 is as follows: within each sampling period, based on the current measured state quantity... Control quantity at the previous moment Construct augmented states The numerical solver is then used to solve the standard quadratic programming problem described above, and the optimal optimization variables are obtained. Extract the first component of the optimal control increment sequence from it. ; The optimal control increment is superimposed with the control quantity from the previous moment to obtain the current steering angle of the tractor's front wheels:

[0087] Will = The output is sent to the vehicle dynamics model and acts on the steering actuator of the front wheels of the tractor. In the next sampling period, the vehicle state quantity will be measured again. Update the parameters of the linear time-varying model (k+1) (k+1) and affine bias compensation term d(k+1), repeat steps S2.1→S4.2 to form a rolling time-domain closed-loop control strategy of sampling→updating→predicting→optimizing→applying.

[0088] By applying only the first component of the optimal control increment sequence to the system and discarding subsequent components, the optimal solution is recalculated using the newly measured state in each sampling period. This helps to compensate for the uncertainty caused by model mismatch and external disturbances, forming a rolling time-domain closed-loop control strategy of "sampling → updating → predicting → optimizing → applying". This significantly improves the robustness of the trajectory tracking system to sudden changes in road curvature and crosswind interference.

[0089] Design the outer loop controller for longitudinal cascade sliding mode control: Design the longitudinal velocity-acceleration cascade control structure (e.g.) Figure 2As shown), longitudinal tracking employs cascaded PID control. The outer loop uses vehicle speed or displacement as the controlled variable to provide the desired acceleration or driving force. The inner loop then converts this desired variable into actuator commands such as throttle and brake to complete closed-loop regulation. Based on this, longitudinal speed and position control are used as the outer loop. The desired longitudinal displacement and desired vehicle speed given by the planning module are used as reference inputs, and the actual position and actual vehicle speed output by the vehicle dynamics model are used as feedback variables. A position-velocity integrated sliding mode surface is constructed, and an outer-loop sliding mode control law containing linear feedback and switching terms is designed. The output acceleration compensation is used to correct the planned acceleration. Simultaneously, amplitude and rate of change constraints are applied and passed to the inner loop. This introduces sliding mode control (SMC) within the speed-acceleration cascade framework. The logic diagram of the longitudinal cascade trajectory tracking control strategy for the vehicle train is designed (e.g., ...). Figure 3 (As shown).

[0090] Specifically, the design flow of the outer loop controller for the longitudinal cascade sliding mode control in S6 is as follows: S6.1 Define the outer loop error variable: The control objective of the outer loop is to minimize the actual displacement of the vehicle given the longitudinal displacement and vehicle speed reference trajectory. speed Achieve asymptotic tracking, longitudinal position error Speed ​​error and its integral Defined as:

[0091] By incorporating the integrals of position error and velocity error into the error definition, a comprehensive error description containing displacement, vehicle speed, and their integral information is constructed, which helps to eliminate steady-state position deviation and ensure zero steady-state error performance in longitudinal tracking. Where x and v are the actual longitudinal displacement and actual longitudinal velocity, respectively. , These represent the reference displacement and reference velocity given by the planning module, respectively. S6.2 Constructing the outer ring sliding surface: To simultaneously consider both steady-state position accuracy and dynamic velocity performance, the following first-order sliding surface is selected:

[0092] in, , For sliding surface parameters, by It is obtained that during the sliding motion phase At that time, the error approximately satisfies:

[0093] Its eigenvalues ​​are located in the left half-plane, ensuring , It converges to zero at the desired decay rate; By designing a position-velocity integrated first-order sliding surface and configuring the sliding surface coefficients , By placing the eigenvalues ​​in the left half-plane, the position and velocity errors are ensured to converge to zero synchronously at the desired decay rate during the sliding mode motion phase. This is beneficial for achieving coordinated and unified displacement tracking and vehicle speed regulation at the controller design level. S6.3 Design of the outer-loop sliding mode control law: Combining the sliding mode approach condition, a control law consisting of linear terms and switching terms is constructed. The outer-loop output is the longitudinal acceleration compensation quantity.

[0094] in, For linear feedback gain, To switch gain, The boundary layer thickness. Saturation function. Defined as: In the boundary layer Continuous control is achieved within the neighborhood to reduce chattering caused by high-frequency switching; By constructing an outer-loop control law consisting of linear feedback terms and switching terms and introducing a boundary layer saturation function to replace the ideal sign function, the high-frequency switching is smoothed while ensuring that the sliding mode approach condition is met. This is beneficial to significantly suppress longitudinal acceleration chattering caused by switching control, and improve the ride comfort of the electric drive system and the service life of the actuator. S6.4 Apply outer ring constraints and generate inner ring target acceleration benchmark: Considering vehicle longitudinal dynamics and ride comfort constraints, apply compensation acceleration... The amplitude and rate of change are limited, and their amplitude and rate of change satisfy:

[0095] in, , Given by the vehicle calibration, the corrected compensation acceleration is finally superimposed with the planned acceleration to obtain the target acceleration benchmark for the inner loop: in, , , These represent the reference acceleration and sliding mode compensation acceleration provided by the planning module, respectively. Inner Ring Road The actual acceleration of the vehicle is rapidly adjusted to a set value, so that the whole vehicle appears to be an ideal acceleration actuator from the perspective of the outer ring.

[0096] By limiting the amplitude and rate of change of the acceleration compensation, it is ensured that the target acceleration output by the outer loop is always within the physically feasible domain of the vehicle's longitudinal dynamics. The corrected compensation acceleration is then superimposed with the planned acceleration and transmitted to the inner loop, which facilitates a smooth connection between the outer loop position-speed control and the inner loop acceleration tracking, forming a clear cascade control architecture.

[0097] S7. Design of the inner loop controller for longitudinal cascade sliding mode control: The corrected target acceleration output from the outer loop is used as the setpoint, and the actual longitudinal acceleration of the vehicle is used as the feedback. A first-order low-pass filter is used to suppress noise in the actual acceleration measurement value. The acceleration error and its sliding mode variable are constructed. The inner loop control law is designed using a super-twisting high-order sliding mode algorithm. The final acceleration command is output. At the same time, actuator capability and longitudinal comfort constraints are applied to achieve high bandwidth and robust tracking adjustment of acceleration. Specifically, the design flow of the inner loop controller for longitudinal cascade sliding mode control in S7 is as follows: S7.1 Acceleration signal filtering: The actual longitudinal acceleration output by the vehicle dynamics model is denoted as... To suppress measurement noise, a first-order low-pass filter is first used to filter it, resulting in: in, The filtered acceleration. It is a time constant; The noise suppression of the actual longitudinal acceleration measurement value of the vehicle is achieved by using a first-order low-pass filter, which effectively filters out the influence of high-frequency measurement noise on the differential signal. This helps to avoid noise amplification that leads to deterioration of the inner loop control quality and frequent actuator operation. S7.2, Define the acceleration error and inner loop sliding mode variables as follows: Using acceleration error directly as the sliding mode variable avoids the differential operation of the outer loop output acceleration signal, ultimately reducing sensitivity to measurement noise and simplifying the inner loop controller structure. S7.3 The inner loop adopts a super-twisting high-order sliding mode algorithm and introduces auxiliary states. ,definition:

[0098]

[0099]

[0100]

[0101] in, , For inner loop sliding mode gain, The thickness of the inner ring boundary layer. Consistent with the aforementioned definition, existing higher-order sliding mode theories have shown that, under conditions of model uncertainty and bounded external disturbances, appropriately selecting... , Can guarantee Its derivative converges to zero in a finite time, exhibiting less chattering and better noise robustness compared to first-order sliding mode; By introducing an auxiliary state v and employing a super-twisting high-order sliding mode algorithm to design the inner-loop control law, while retaining the strong robustness of sliding mode control against model uncertainties and external disturbances, the control quantity is made continuous, thus significantly reducing the chattering phenomenon inherent in first-order sliding mode. This is beneficial for achieving high-bandwidth, low-chattering tracking and regulation of acceleration in electric drive systems. Existing high-order sliding mode theory guarantees that the acceleration error and its derivative converge to zero within a finite time, which is beneficial for improving the dynamic response speed and steady-state accuracy of the inner loop. S7.4 Apply inner loop constraints and output acceleration command: Also considering actuator capability and longitudinal comfort constraints, the final acceleration command is... Apply amplitude and rate of change limits: in, , Acceleration command selected based on the allowable range of the powertrain and braking system. The throttle-brake pedal calibration relationship is mapped to traction torque command and braking pressure command, which are applied to the vehicle dynamics model, thereby creating a closed-loop longitudinal cascade sliding mode control loop for the electric drive vehicle train.

[0102] By imposing amplitude and rate of change limits on the final acceleration command, the control command is ensured to fall within the physical capabilities of the powertrain and braking system, while also meeting longitudinal comfort constraints. The throttle-brake integrated calibration table is then used to map the commands to traction torque and braking pressure, which facilitates the smooth switching and precise execution of drive and braking in electric vehicle trains.

[0103] Specifically, the process of constructing a horizontal and vertical collaborative control closed loop in S8 is as follows: S8.1, Cooperative integration of lateral and longitudinal controllers: Horizontal and longitudinal control are executed in parallel within each sampling period. (1) Lateral passage: Execute steps S3 to S5, based on the current state of the vehicle. As input, the front wheel steering angle u(k) of the tractor is obtained by solving LTV-MPC. (k); (2) Vertical channel: Perform steps S6 to S7 to plan information. , , And actual feedback X, , As input, acceleration commands are obtained through cascade sliding mode control. And mapped to throttle / brake commands via the drive / brake integrated calibration table; The lateral control quantity and the longitudinal control quantity are calculated independently, but together they act on the controlled object. By executing lateral LTV-MPC optimization and longitudinal cascade sliding mode control in parallel within each sampling period, the front wheel steering angle command and drive / braking command are calculated independently and applied to the controlled vehicle simultaneously. This is beneficial to fully leverage the advantages of MPC in multi-constraint and multi-objective optimization and the strengths of sliding mode control in robust acceleration tracking, thereby achieving a reasonable division of labor and efficient collaboration between lateral and longitudinal control tasks. S8.2 Formation of lateral and longitudinal coordinated closed-loop control: The TruckSim high-fidelity vehicle dynamics model is used as the controlled object, receiving the front wheel steering angle command u(k) = (k) and drive / brake commands, outputting real-time vehicle status quantities; Its closed-loop control process is as follows: (1) The planning module provides a reference trajectory to the lateral controller. , Provide reference speed to the longitudinal controller Reference position Reference acceleration ; (2) The TruckSim vehicle dynamics model feeds back state variables to the lateral controller Feedback X to the longitudinal controller , ; (3) The lateral controller performs LTV-MPC optimization based on the current state and reference trajectory, and outputs the front wheel steering angle. ; (4) Based on the current state and reference values, the longitudinal controller performs outer loop sliding mode and inner loop super-twisting sliding mode control, outputs acceleration commands and maps them to drive / brake commands; (5) The front wheel steering angle and drive / brake commands work together on the TruckSim model to update the vehicle status; (6) Enter the next sampling cycle and repeat the above steps to achieve rolling time-domain closed-loop control; By using a joint simulation closed-loop architecture of TruckSim high-fidelity vehicle dynamics model and MATLAB / Simulink controller, the entire process of reference trajectory input, vehicle state feedback, parallel controller solution and execution command output is fully automated under unified timing scheduling. This is beneficial for fully verifying the control performance under lateral and longitudinal coupling conditions in an offline simulation environment and provides a reliable performance benchmark for real vehicle deployment. S8.3 Joint simulation verification and parameter tuning: The key parameters of the controller were tuned using the TruckSim and MATLAB / Simulink co-simulation platform. (1) Lateral LTV-MPC parameters: prediction step size Control step size Weight matrix Q, weight coefficients R, relaxation factor weights ρ, constraint boundary , , ; (2) Longitudinal outer ring SMC parameters: sliding surface coefficient Linear gain Switching gain Boundary layer Amplitude limit , ; (3) Longitudinal inner loop super-twisting parameters: gain , Boundary layer Filtering time constant Amplitude limit , ; Through simulation verification under typical working conditions (straight acceleration, cornering tracking, double lane change, braking deceleration, etc.), the trajectory tracking accuracy, hinge angle suppression effect, longitudinal speed following performance, and robustness under lateral and longitudinal coupling interference are evaluated until the control performance meets the design requirements.

[0104] Through a systematic parameter tuning process and typical operating condition coverage testing, the controller's trajectory tracking accuracy, articulation angle suppression effect, longitudinal speed following performance, and anti-interference capability of lateral and longitudinal coupling are comprehensively evaluated in various scenarios such as straight acceleration, cornering tracking, double lane change, and braking deceleration. This facilitates the optimization and matching of control parameters under a unified evaluation framework, ensuring that the method of this invention has good comprehensive control quality under complex driving conditions.

[0105] In summary: By establishing a discrete linear time-varying state-space model of the vehicle train, the challenge of dynamic coupling modeling for multi-axle articulated vehicles is solved; through incremental rolling time-domain optimization of the lateral LTV-MPC controller and the application of hard constraints on the articulation angle, the risk of train folding is effectively suppressed while ensuring trajectory tracking accuracy; through a longitudinal cascaded dual-loop sliding mode control architecture, a reasonable decomposition and highly robust tracking of the three-level control tasks of position, velocity, and acceleration are achieved; through parallel collaborative integration of the lateral and longitudinal controllers and closed-loop verification by TruckSim-MATLAB / Simulink co-simulation, it is fully demonstrated that the trajectory tracking accuracy, attitude stability, and lateral and longitudinal coupling robustness of the method proposed in this invention meet the design requirements under typical driving conditions, verifying the effectiveness and engineering application value of the longitudinal and lateral trajectory tracking control method proposed in this invention for electric vehicle trains.

[0106] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for longitudinal and lateral trajectory tracking control of an electric-driven vehicle train, characterized in that, Includes the following steps: S1. Model Establishment: Establish the dynamic state-space equations of the vehicle train, solve the dynamic equations of the tractor and trailer simultaneously using the algebraic method, eliminate the articulation force, and define the state vector containing the state variables of the tractor and trailer by combining the attitude and heading geometric relationship of the tractor and trailer. After linearization by the Jacobian matrix, a continuous-time state-space model is constructed. Further discretization is performed by the explicit Euler method to obtain the discrete linear time-varying state-space model of the vehicle train. S2. Set the state and reference quantities of the lateral LTV-MPC controller: Based on the discrete linear time-varying state space model established in step S1, the planning module provides reference trajectory information, including the reference lateral position and the reference tractor heading angle. The actual state quantities at the current moment are obtained by vehicle state sampling to determine the state and reference quantities of the LTV-MPC controller. S3. Update the linear time-varying prediction model and construct the incremental prediction equation: In each sampling period, using the state variables fed back in real time by the vehicle dynamics model, and based on the discrete linear time-varying model parameters updated in step S1... , Furthermore, a control increment parameterization method is introduced to convert the control input into an incremental form and construct an augmented state vector containing the control quantity of the previous time step, and finally derive the prediction model in incremental form. S4. Construct a quadratic programming optimization problem for horizontal LTV-MPC: Based on the linear prediction expression obtained in step S3, design a quadratic performance index that includes output error weighting, control increment weighting, and relaxation factor, and transform the trajectory tracking problem into a constrained standard convex quadratic programming problem. At the same time, apply control increment magnitude constraints, relaxation factor boundary constraints, steering magnitude constraints, and prediction output boundary constraints. S5. Perform rolling time-domain optimization and output lateral control quantity: Based on the standard convex quadratic programming problem constructed in step S4, a numerical solver is used to solve the problem online within a fixed sampling period to obtain the optimal control increment sequence. A rolling time-domain strategy is adopted to apply only the first component of the control increment sequence to the system and superimpose it with the control quantity at the previous moment to obtain the front wheel steering angle control command at the current moment, which is then output to the controlled vehicle dynamics model. S6. Design of the outer loop controller for longitudinal cascade sliding mode control: Based on the cascade control structure, the longitudinal velocity and position control are used as the outer loop. The desired longitudinal displacement and desired vehicle speed given by the planning module are used as reference inputs, and the actual position and actual vehicle speed output by the vehicle dynamics model are used as feedback quantities. The position-velocity integrated sliding surface is constructed, and the outer loop sliding mode control law containing linear feedback terms and switching terms is designed. The acceleration compensation quantity is output to correct the planned acceleration, and the amplitude and rate of change constraints are applied and then transmitted to the inner loop. S7. Design of the inner loop controller for longitudinal cascade sliding mode control: The corrected target acceleration output from the outer loop is used as the set value, and the actual longitudinal acceleration of the vehicle is used as the feedback quantity. A first-order low-pass filter is used to suppress noise in the actual acceleration measurement value. The acceleration error and its sliding mode variable are constructed. The inner loop control law is designed using the super-twisting high-order sliding mode algorithm. The final acceleration command is output, and actuator capability and longitudinal comfort constraints are applied at the same time. S8. Constructing a lateral and longitudinal coordinated control closed loop: The lateral LTV-MPC controller and the longitudinal cascade sliding mode controller are integrated in a coordinated manner. The lateral controller outputs the front wheel steering angle command based on the real-time vehicle status in each sampling cycle, and the longitudinal controller outputs the drive / braking command synchronously. The two work together to act on the dynamic model of the controlled vehicle to form a lateral and longitudinal coordinated control closed loop.

2. The longitudinal and lateral trajectory tracking control method for an electric-driven vehicle train according to claim 1, characterized in that, The model building process in S1: S1.1 Establish the vehicle dynamics state-space equations: Let 1 and 2 represent the relevant parameters of the tractor and trailer, respectively, and define the total mass of the tractor as... The total mass of the trailer is The distance from the center of gravity of the tractor to the front axle is The distance from the center of gravity of the tractor to the rear axle is The distance from the trailer's center of gravity to the front axle is The distance from the trailer's center of gravity to the axle is The yaw rate of the tractor is The trailer's yaw rate is The sideslip angle of the tractor's center of gravity is The trailer's center of gravity sideslip angle is The moment of inertia of the tractor about the Z-axis is The moment of inertia of the trailer about the Z-axis is The steering angle of the tractor's front wheels is ; The distance from the center of gravity of the tractor unit to the traction pin is The lateral stiffness of the front axle of the tractor is The lateral stiffness of the rear axle of the tractor is The equivalent axle lateral stiffness of the trailer is The hinge angle is The longitudinal speed of the tractor is The longitudinal speed of the trailer is The lateral velocity of the tractor's center of gravity is , Lateral velocity of the trailer's center of gravity, and the rate of change of the tractor's center of gravity's lateral velocity. The rate of change of the lateral velocity of the trailer's center of gravity is The heading angle of the tractor is The trailer heading angle is The directional angular velocity of the tractor is The trailer's angular velocity is The x-coordinate of the tractor's center of gravity is X, and the y-coordinate is Y; the rate of change of the x-coordinate of the tractor's center of gravity is... The rate of change of the tractor's center of gravity ordinate is ; By solving the dynamic equations of the tractor and trailer simultaneously using algebraic methods, eliminating the articulation force, and simplifying, we obtain the following differential equation: lateral velocity change rate of the tractor's center of gravity satisfy: ； in, = , = , = , = , = , = , = , = ; yaw rate of change of tractor satisfy: ； Trailer yaw rate of change satisfy: ； Analysis of the tractor-trailer attitude and heading geometry yields the following results: ； The position of the tractor's center of gravity is updated during driving as follows: ； S1.2 Constructing the continuous-time state-space equation: Based on the relationship in step S1.1, define the state vector containing the tractor and trailer as follows: ； Rewriting the above dynamic equations in matrix form and solving for the Jacobian matrix yields the following matrix: ； Where the control input u is the front wheel steering angle of the tractor. ; System Matrix , Specifically, it can be elaborated as follows: ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， At this point, the continuous-time state-space model of the train under the small-angle assumption has been completed; S1.3 Discretization: The continuous-time state-space equations in step S1.2 are then discretized using the explicit Euler method. ； Where I is the identity matrix and T is the sampling period. , These represent the discretized system matrix and the input matrix, respectively.

3. The longitudinal and lateral trajectory tracking control method for an electric-driven vehicle train according to claim 1, characterized in that, In step S2, the state and reference variables of the horizontal LTV-MPC controller are set, and the controller state vector is taken from the state vector defined in step S1.2: ， Among them, matrix , Include The item, and the location update line also contains , Item, therefore , It will change online according to the vehicle's operating status; Simultaneously, attitude stability constraints for the train system are introduced, with the tractor's heading angle, lateral position, and articulation angle selected as target control variables, defined as: ； Among them, the output matrix The value of is determined by the state vector. By directly selecting the corresponding component, we can obtain: ； Control input quantity For the steering angle of the front wheels of the tractor The reference values ​​for the trajectory tracking section are provided by the planning module, and for the hinge angle reference... Zero hinge angle is used as the stability target, that is: ； in, To predict the step size, during the model predictive control rolling optimization process, Y is used to ensure geometrical trajectory tracking accuracy, while θ is used to limit the hinge angle and oscillation.

4. The longitudinal and lateral trajectory tracking control method for an electric-driven vehicle train according to claim 1, characterized in that, The update process of the linear time-varying prediction model in S3 and the construction of the incremental prediction equation: S3.1 Real-time update of the linear time-varying model: In each sampling period, the actual state quantity x(k) and longitudinal velocity output by the vehicle dynamics model are used. Update system matrix (k) and input matrix (k); S3.

2. Establish an incremental prediction model using the control increment parameterization method: Apply a rate of change constraint and use control increment parameterization, defined as follows: ； Where u is the control input vector. To control the increment; Further, we introduce an augmented state that includes the control quantity from the previous time step: ； This yields the incremental prediction model: ； in, , For the reason , The block matrix formed This is an affine deviation compensation term; In programming implementation, affine deviation compensation term Obtained by one-step nonlinear update One-step prediction with linear models The difference is worth; S3.3 Constructing the reference output sequence and linear prediction expression in the prediction time domain: The reference output is constructed in the prediction domain as follows: ； in, and The hinge angle reference is obtained from the reference trajectory of the planning module. Zero hinge angle is used as the stability target; Let the prediction step size be... Control step size is The predicted domain output and the reference output are stacked as follows: ， ， And stack the control increment sequences as follows: ， The standard linear prediction expression is obtained from the augmented model: ， in, , , For the reason , , The prediction matrix is ​​constructed recursively. The vector is a stack of deviation terms.

5. The longitudinal and lateral trajectory tracking control method for an electric-driven vehicle train according to claim 1, characterized in that, The S4 section describes a quadratic programming optimization problem involving horizontal LTV-MPC: S4.1 Constructing Quadratic Performance Indicators: Based on the comprehensive requirements of tracking error and control smoothness, construct quadratic performance indicators: ； in, Used for weighing , , The Importance of the Three Types of Output Errors Used to suppress excessive steering increments For relaxation factor, Its weight; Define the vector of optimization variables within the predictive control domain as: ； in, For the steering angle of the tractor's front wheels, satisfy the rolling update relationship: ； Using the above quadratic performance index, and rearranging it equivalently into a standard quadratic programming problem: ； Among them, matrix with vector From the prediction model and weight matrix , The current system state and the reference trajectory are used to determine this. S4.2 Applying complete constraints to form the optimal feasible region: To match the physical limitations of the actuators and ensure vehicle attitude safety, both input and output constraints are applied. The final feasible region is written as: ； First, upper and lower bound constraints are imposed on the control increment: ； Then apply boundary constraints to the relaxation factor: ； The above constraints are uniformly written in the form of upper and lower bounds for the optimization variables: ； in, For dimension is A vector of all 1s This is the upper bound parameter for the relaxation factor; Secondly, to limit the steering amplitude and suppress the risk of vehicle folding during operation, boundary constraints are applied to the control amplitude and the predicted output. The control amplitude constraint is as follows: ； Simultaneously, an output boundary is applied within the prediction time domain: ； in, , f represents the hard / soft boundary of the predicted output.

6. The longitudinal and lateral trajectory tracking control method for an electric-driven vehicle train according to claim 1, characterized in that, The rolling time-domain optimization solution and output of the lateral control quantity in S5 is as follows: In each sampling period, based on the current measured state quantity... Control quantity at the previous moment Construct augmented states The numerical solver is then used to solve the standard quadratic programming problem described above, and the optimal optimization variables are obtained. Extract the first component of the optimal control increment sequence from it. ; The optimal control increment is superimposed with the control value from the previous moment to obtain the current steering angle of the tractor's front wheels: ； Will = The output is sent to the vehicle dynamics model and acts on the steering actuator of the front wheels of the tractor. In the next sampling period, the vehicle state quantity will be measured again. Update the parameters of the linear time-varying model (k+1) (k+1) and the affine deviation compensation term d(k+1).

7. The longitudinal and lateral trajectory tracking control method for an electric-driven vehicle train according to claim 1, characterized in that, Design flow of the longitudinal cascade sliding mode control outer loop controller in S6: S6.1 Define the outer loop error variable: The control objective of the outer loop is to minimize the actual displacement of the vehicle given the longitudinal displacement and vehicle speed reference trajectory. speed Achieve asymptotic tracking, longitudinal position error Speed ​​error and its integral Defined as: ； Where x and v are the actual longitudinal displacement and actual longitudinal velocity, respectively. , These represent the reference displacement and reference velocity given by the planning module, respectively. S6.2 Constructing the outer ring sliding surface: To simultaneously consider both steady-state position accuracy and dynamic velocity performance, the following first-order sliding surface is selected: ； in, , For sliding surface parameters, by It is obtained that during the sliding motion phase At that time, the error approximately satisfies: ； Its eigenvalues ​​are located in the left half-plane, ensuring , It converges to zero at the desired decay rate; S6.3 Design of the outer-loop sliding mode control law: Combining the sliding mode approach condition, a control law consisting of linear terms and switching terms is constructed. The outer-loop output is the longitudinal acceleration compensation quantity. ； in, For linear feedback gain, To switch gain, The boundary layer thickness. Saturation function. Defined as: ； In the boundary layer Continuous control is achieved within the neighborhood to reduce chattering caused by high-frequency switching; S6.4 Apply outer ring constraints and generate inner ring target acceleration benchmark: Considering vehicle longitudinal dynamics and ride comfort constraints, apply compensation acceleration... The amplitude and rate of change are limited, and their amplitude and rate of change satisfy: ； in , Given by the vehicle calibration, the corrected compensation acceleration is finally superimposed with the planned acceleration to obtain the target acceleration benchmark for the inner loop: ； in, 、 、 These represent the reference acceleration and sliding mode compensation acceleration provided by the planning module, respectively. Inner Ring Road The actual acceleration of the vehicle is rapidly adjusted to a set value, so that the whole vehicle appears to be an ideal acceleration actuator from the perspective of the outer ring.

8. The longitudinal and lateral trajectory tracking control method for an electric-driven vehicle train according to claim 1, characterized in that, Design flow of the longitudinal cascade sliding mode control inner loop controller in S7: S7.1 Acceleration signal filtering: The actual longitudinal acceleration output by the vehicle dynamics model is denoted as... To suppress measurement noise, a first-order low-pass filter is first used to filter it, resulting in: ； in, The filtered acceleration. It is a time constant; S7.2, Define the acceleration error and inner loop sliding mode variables as follows: ； S7.3 The inner loop adopts a super-twisting high-order sliding mode algorithm and introduces auxiliary states. ,definition: ， ， ， ， in, , For inner loop sliding mode gain, The thickness of the inner ring boundary layer. Consistent with the aforementioned definition; S7.4 Apply inner loop constraints and output acceleration command: Also considering actuator capability and longitudinal comfort constraints, the final acceleration command is... Apply amplitude and rate of change limits: ； in, , Acceleration command selected based on the allowable range of the powertrain and braking system. The accelerator-brake pedal calibration relationship is mapped to traction torque command and braking pressure command, which are then applied to the vehicle dynamics model.

9. The longitudinal and lateral trajectory tracking control method for an electric-driven vehicle train according to claim 1, characterized in that, The process of constructing a horizontal and vertical collaborative control closed loop in S8 is as follows: S8.1, Cooperative integration of horizontal and vertical controllers: Horizontal and vertical control are executed in parallel within each sampling period. The horizontal control quantity and the vertical control quantity are calculated independently and act together on the controlled object. S8.2 Formation of lateral and longitudinal coordinated closed-loop control: The TruckSim high-fidelity vehicle dynamics model is used as the controlled object, receiving the front wheel steering angle command u(k) = (k) and drive / brake commands, outputting real-time vehicle state quantities, and tuning key controller parameters through the TruckSim and MATLAB / Simulink co-simulation platform.

10. A longitudinal and lateral trajectory tracking control method for an electric-driven vehicle train according to claim 9, characterized in that, In S8.1, lateral control and longitudinal control are executed in parallel: the lateral channel executes steps S3 to S5, based on the current state of the vehicle. As input, the front wheel steering angle u(k) of the tractor is obtained by solving LTV-MPC. (k); The longitudinal channel executes steps S6 to S7 to obtain planning information. , , And actual feedback X, , As input, acceleration commands are obtained through cascade sliding mode control. This is then mapped to throttle / brake commands via the drive / brake integrated calibration table.

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