A co-conicentric collaborative control method for a multi-axle steer-by-wire system of a heavy-duty vehicle

Abstract

The application discloses a kind of heavy vehicle multi-axis steer-by-wire system common instantaneous center collaborative control methods, comprising: establishing heavy vehicle multi-axis steer-by-wire system dynamics model;The motion of multi-axis steer-by-wire system is decomposed into translation mode and rotation mode;Stable domain of common instantaneous center is constructed, and common instantaneous center stability margin is obtained quantitatively;Determine the master-slave game relationship between translation mode and rotation mode;Solve the optimal control input of translation mode and rotation mode;Each steering axle target rotation angle is generated by polar coordinate common instantaneous center rotation angle mapping relationship, and the common instantaneous center collaborative control of heavy vehicle multi-axis steer-by-wire system is realized.The application constructs the steering coordination model of multi-axis steer-by-wire system based on polar coordinate common instantaneous center, and converts the high-dimensional optimization problem of multi-axis rotation angle into low-dimensional control problem of translation mode and rotation mode, so as to reduce the difficulty of multi-axis steering coordination optimization, improve control real-time performance.

Description

Technical Field

[0001] This invention belongs to the field of multi-axle steering cooperative control technology for heavy-duty vehicles, and specifically relates to a method for co-centering control of the instantaneous center of gravity of a multi-axle steering system for heavy-duty vehicles. Background Technology

[0002] Heavy-duty vehicles are widely used in scenarios such as transporting large equipment, engineering operations, special transportation, and maneuvering in complex terrains. Due to their large overall weight, numerous axles, long wheelbase, and high center of gravity, they place high demands on steering maneuverability, trajectory tracking accuracy, and driving stability during low-speed turning, path tracking, obstacle avoidance, lane changing, and driving on complex curvature roads. Traditional multi-axle vehicle steering systems typically rely on mechanical linkages or fixed transmission relationships to achieve inter-axle angular coordination. The angular relationships between each steering axle are relatively fixed, making it difficult to actively adjust according to vehicle operating conditions, road curvature, and stability requirements.

[0003] With the development of drive-by-wire chassis and distributed control technology, multi-axis steerable systems enable different steering axes to independently receive target angle commands, providing higher steering freedom for heavy-duty vehicles. However, this also makes the multi-axis steering coordination control problem more complex. If the angle of each steering axis is directly used as a control variable for optimization, the control dimension will increase significantly with the number of steering axes, leading to complex optimization solutions, reduced real-time control performance, and potentially unreasonable inter-axle angle allocation.

[0004] Therefore, how to reduce the multi-axis steering angle control dimension, establish a unified variable that can characterize the multi-axis steering cooperation, and adaptively adjust the steering cooperation relationship according to the vehicle stability state is a technical problem that urgently needs to be solved in the control of multi-axis steering systems for heavy-duty vehicles. Summary of the Invention

[0005] In view of the shortcomings of the prior art, the purpose of this invention is to provide a common instantaneous center of gravity cooperative control method for multi-axis steering systems of heavy-duty vehicles, so as to solve the technical problems of high control dimension, complex coordination relationship of rotation angle of each axle, difficulty in using stability information for steering mode decision-making, and difficulty in balancing trajectory tracking performance and vehicle stability in the cooperative control process of existing multi-axis steering systems of heavy-duty vehicles.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] The present invention discloses a method for coordinated control of the instantaneous center of gravity of a multi-axis steering system for heavy-duty vehicles, comprising the following steps:

[0008] 1) Establish a dynamic model of the multi-axis steering system for heavy-duty vehicles;

[0009] 2) Based on the dynamic model of the multi-axis steering system of heavy-duty vehicles established in step 1), construct a steering coordination model of the multi-axis steering system based on the polar coordinate concentric center, and decompose the motion of the multi-axis steering system into translation mode and rotation mode;

[0010] 3) Based on the steering coordination model of the multi-axis axial steering system with polar coordinate concentric center constructed in step 2), combined with vehicle side slip constraints and rollover constraints, the concentric center stability domain is constructed, and the concentric center stability margin is quantified.

[0011] 4) Based on the common instantaneous center stability margin obtained in step 3), construct a neural network mode switching strategy and determine the master-slave game relationship between translation mode and rotation mode;

[0012] 5) Construct a bimodal Stackelberg game predictive controller and solve for the optimal control inputs for the translation and rotation modes;

[0013] 6) Based on the optimal control inputs of the translation mode and rotation mode obtained in step 5), the target steering angles of each steering axis are generated through the polar coordinate common instantaneous center of rotation angle mapping relationship, thereby realizing the common instantaneous center of rotation coordinated control of the multi-axis steering system of heavy-duty vehicles.

[0014] Further, step 1) specifically includes:

[0015] 11) Determine the modeling object for the multi-axle steering system of heavy-duty vehicles;

[0016] 12) Establish the lateral-yaw dynamics relationship of the multi-axle steering system of heavy-duty vehicles;

[0017] 13) Establish the first The relationship between tire slip angle and equivalent lateral force for each steering axle;

[0018] 14) Establish the global kinematic relationships of the vehicle;

[0019] 15) Establish a dynamic model of the multi-axle steering system for heavy-duty vehicles.

[0020] Further, step 2) specifically includes:

[0021] 21) Based on the dynamic model of the multi-axle steering system of heavy-duty vehicles established in step 1), polar coordinate concentric center variables are introduced to describe the cooperative steering state of the multi-axle steering system.

[0022] 22) Establish the mapping relationship between the rotation angle of each steering axis and the state of the concentric center based on the polar coordinate concentric center variables;

[0023] 23) Define the polar coordinate concentric center state variable corresponding to the actual motion of the vehicle;

[0024] 24) Based on the polar coordinate concentric center state variables corresponding to the actual motion of the vehicle, rewrite the lateral-yaw dynamic relationship in step 1) into a polar coordinate concentric center dynamic form;

[0025] 25) Based on the definition of tire slip angle and the mapping relationship between the steering axle angles and the concentric center state, establish the first... The relationship between the tire slip angle of each steering axle and the polar coordinate concentricity variable;

[0026] 26) Construct a steering coordination model for a multi-axis steering system based on the common instantaneous center of polar coordinates;

[0027] 27) The motion of the multi-axis steering system is decomposed into translational and rotational modes. The motion part characterized by the lateral translational state variables of the actual vehicle motion and their corresponding control variables is defined as the translational mode, which is used to describe and adjust the lateral translational response of the multi-axis steering system. The motion part characterized by the yaw curvature state variables of the actual vehicle motion and their corresponding control variables is defined as the rotational mode, which is used to describe and adjust the yaw rotational response of the multi-axis steering system.

[0028] Furthermore, step 3) specifically includes:

[0029] 31) Based on the steering coordination model of the multi-axis steering system based on polar coordinate common instantaneous center constructed in step 2), determine the steady-state common instantaneous center state corresponding to the dual-modal common instantaneous center control input;

[0030] 32) Based on the vehicle lateral slip safety requirements, construct steady-state lateral translation variable constraints and obtain the set of steady-state lateral translation variable constraints;

[0031] 33) Based on the vehicle rollover safety requirements, construct steady-state yaw curvature variable constraints and obtain the set of steady-state yaw curvature variable constraints;

[0032] 34) Based on the steady-state lateral translation variable constraint set obtained in step 32) and the steady-state yaw curvature variable constraint set obtained in step 33), construct the coninus stability region;

[0033] 35) Calculate the minimum distance from the steady-state concentric center state to the boundary of the concentric center stability domain;

[0034] 36) Based on the minimum distance obtained in step 35), construct the maximum allowable energy ellipse area within the coninocaloric stability region;

[0035] 37) Based on the maximum allowable energy ellipse area obtained in step 36), the coninstituent center stability margin is quantified.

[0036] Further, step 4) specifically includes:

[0037] 41) Define the participants in a bimodal virtual game based on translation and rotation modes;

[0038] 42) Based on the instantaneous center stability margin obtained in step 3), construct a neural network mode switching strategy;

[0039] 43) Determine the master-slave game relationship between the translation mode and the rotation mode based on the final master-slave structure switching variables.

[0040] Further, step 42) specifically includes:

[0041] A neural network mode switching strategy is constructed, which refers to a mode switching decision strategy that takes the concentric center stability margin, the change in concentric center stability margin, the vehicle polar coordinate concentric center state, and the vehicle longitudinal velocity as inputs, and takes the master-slave structure selection result between translation mode and rotation mode as output. The neural network mode switching strategy includes: input vector construction, feedforward neural network mapping, offline label generation, network parameter training, hysteresis switching mechanism construction, and stability safety fallback mechanism construction; specifically as follows:

[0042] 421) Construct the input vector for the neural network mode switching strategy;

[0043] 422) Construct a feedforward neural network to implement the neural network mode switching strategy;

[0044] 423) The offline evaluation cost required to construct modality switching label generation;

[0045] 424) Generate modality switching tags;

[0046] 425) A feedforward neural network is trained using a binary cross-entropy loss function;

[0047] 426) Construct a hysteresis switching mechanism to convert the rotation priority factor into a discrete mode switching variable;

[0048] 427) Based on the instantaneous center stability margin, a stability safety fallback mechanism is constructed to determine the safety fallback state based on the instantaneous center stability margin;

[0049] 428) Determine the final master-slave structure switching variables based on the discrete mode switching variables and the safety fallback state.

[0050] Furthermore, step 5) specifically includes:

[0051] Based on the steering collaboration model established in step 2), a bimodal Stackelberg game predictive controller is constructed. This bimodal Stackelberg game predictive controller includes a discrete-time prediction model, a translational mode optimization objective function, a rotational mode optimization objective function, a set of prediction constraints, a follower optimal response solution module, a leader optimization solution module, and a rolling time-domain control output module. The translational mode and rotational mode serve as two virtual participants in the Stackelberg game, and the leader and follower are determined based on the master-follower game relationship obtained in step 4. Specifically:

[0052] 51) Based on the steering coordination model established in step 2), establish the discrete-time prediction model required for bimodal Stackelberg game predictive control;

[0053] 52) Construct translational mode predictive control sequences and rotational mode predictive control sequences;

[0054] 53) Based on the vehicle's predicted pose and reference trajectory, construct the lateral tracking error and vehicle motion direction error in the prediction time domain.

[0055] 54) Construct the objective function for translational mode optimization;

[0056] 55) Construct the objective function for rotational mode optimization;

[0057] 56) Apply stability region constraints to the predicted steady-state concentric center state based on the concentric center stability region;

[0058] 57) Construct the feasible region of the bimodal Stackelberg game predictive controller;

[0059] 58) Based on the master-slave game relationship in step 4), determine the leader control sequence, the follower control sequence, and the corresponding optimization objective function;

[0060] 59) Given a leader control sequence, construct a follower optimal response problem and solve for the follower optimal response mapping;

[0061] 510) Based on the Stackelberg master-slave game mechanism, the leader makes decisions based on the prediction of the follower's optimal response, constructs the leader optimization problem, and obtains the leader's optimal control sequence;

[0062] 511) Based on the follower's optimal response mapping and the leader's optimal control sequence, obtain the local Stackelberg equilibrium in the current prediction time domain and the current master-slave game relationship;

[0063] 512) Based on the final master-slave structure switching variables, recover the optimal control sequences for translation and rotation modes;

[0064] 513) Using the rolling time-domain control method, the first control variable in the optimal control sequence of translation mode and the optimal control sequence of rotation mode is selected as the optimal control input at the current sampling time.

[0065] Furthermore, step 6) specifically includes:

[0066] 61) Based on the optimal control inputs for translation mode and rotation mode in step 5), determine the target polar coordinate concentric variable at the current sampling time;

[0067] 62) Based on the mapping relationship between the steering axis angles and the concentric center state established in step 22), map the target polar coordinate concentric center variables to the target steering axis angles;

[0068] 63) Based on the target steering angles of each steering axis obtained in step 62), construct a multi-axis steering target angle vector;

[0069] 64) The multi-axis steering target angle vector obtained in step 63) is sent to each steering axis control steering actuator, so that each steering axis control steering actuator tracks the corresponding target angle and outputs the corresponding actual steering axis angle response; thereby, the optimal control input of translation mode and rotation mode is converted into the target angle of each steering axis through the polar coordinate common instantaneous center angle mapping relationship, realizing the common instantaneous center cooperative control of the multi-axis control steering system of heavy-duty vehicles.

[0070] The beneficial effects of this invention are:

[0071] 1. This invention transforms the high-dimensional optimization problem of multi-axis steering angle into a low-dimensional control problem of translation and rotation modes by constructing a steering coordination model of a multi-axis steering system based on polar coordinate common instantaneous center, thereby reducing the difficulty of multi-axis steering coordination optimization and improving control real-time performance.

[0072] 2. This invention decomposes the motion of a multi-axis steering system into translational and rotational modes, respectively describing the vehicle's lateral translational and rotational responses. It also constructs a common center stability domain by combining vehicle yaw and rollover constraints, and quantifies the common center stability margin, enabling the vehicle's stability state to participate in steering cooperative control decisions.

[0073] 3. This invention defines translation mode and rotation mode as two virtual participants in a Stackelberg game, and adaptively determines the master-slave game relationship through a neural network mode switching strategy. This allows for priority suppression of lateral slip and rollover risks when the stability margin is low, and improvement of vehicle motion direction adjustment capability and trajectory tracking performance when the stability margin is sufficient. Attached Figure Description

[0074] Figure 1This is a schematic diagram of the method of the present invention. Detailed Implementation

[0075] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present invention.

[0076] Reference Figure 1 As shown, the present invention provides a method for coordinated control of the instantaneous center of gravity of a multi-axis steering system for heavy-duty vehicles, comprising the following steps:

[0077] 1) Establish a dynamic model of the multi-axis steering system for heavy-duty vehicles, specifically including:

[0078] 11) Determine the modeling object of the multi-axle steering system of the heavy-duty vehicle, which includes: the vehicle body, multiple steering axes, the steer-by-wire actuators corresponding to each steering axis, and the wheels; equivalently combine the lateral forces of the left and right wheels of the same steering axis to obtain the first... Equivalent lateral force of each steering axle ,in , Indicates the number of steering shafts;

[0079] 12) Establish the lateral-yaw dynamics relationship of the multi-axle steering system of heavy-duty vehicles;

[0080] make Indicates the equivalent mass of the whole vehicle. This represents the equivalent yaw inertia of the entire vehicle. Indicates the first The longitudinal distance from the steering axis to the vehicle's center of gravity. Indicates the first Given the equivalent lateral forces on each steering axle, the expression for the lateral-yaw dynamics of the multi-axle steering system of a heavy-duty vehicle is as follows:

[0081] ;

[0082] in,

[0083] ;

[0084] ;

[0085] In the formula, Indicates the longitudinal speed of the vehicle. Indicates the lateral speed of the vehicle. This represents the first derivative of the vehicle's lateral velocity with respect to time. Indicates the yaw rate of the vehicle. This represents the first derivative of the vehicle's yaw rate with respect to time. Indicates the first The equivalent shaft group mass corresponding to each steering shaft Indicates the first The equivalent yaw inertia corresponding to each steering axis Indicates vehicle body mass. This represents the moment of inertia of the vehicle body during yaw.

[0086] 13) Establish the first The relationship between tire slip angle and equivalent lateral force for each steering axle;

[0087] No. The tire slip angle of each steering axle is expressed as:

[0088] ;

[0089] No. The equivalent lateral force of each steering axle is expressed as:

[0090] ;

[0091] In the formula, Indicates the first One steering axle tire slip angle, Indicates the first One steering axis angle, Indicates the first The lateral force function of the steering axle tire. Indicates the first The road surface adhesion coefficient corresponding to each steering axle Indicates the first Vertical load on each steering axle tire Indicates the first Steering axle tire lateral stiffness;

[0092] 14) Establish the global kinematic relationship of the vehicle, expressed as:

[0093] ;

[0094] In the formula, Indicates the vehicle's yaw angle. This represents the first derivative of the vehicle's yaw angle with respect to time. This indicates the longitudinal position of the vehicle's center of gravity in the inertial coordinate system. This represents the first derivative of the longitudinal position of the vehicle's center of gravity with respect to time. This indicates the lateral position of the vehicle's center of gravity in the inertial coordinate system. This represents the first derivative of the lateral position of the vehicle's center of mass with respect to time.

[0095] 15) Establish a dynamic model of the multi-axle steering system for heavy-duty vehicles;

[0096] By selecting the vehicle's lateral velocity, yaw rate, yaw angle, and center of gravity position as state variables, and selecting the steering axis angles as control inputs, we obtain:

[0097] ;

[0098] in,

[0099] ;

[0100] ;

[0101] In the formula, This represents the first derivative of the state vector of a multi-axle steering system for heavy-duty vehicles with respect to time. This represents the state vector of a multi-axle steering system for heavy-duty vehicles. This represents the control input vector composed of the steering angles of each steering axis. This represents a nonlinear dynamic function determined by the lateral-yaw dynamic relationship, the tire slip angle and equivalent lateral force relationship, and the vehicle's global kinematic relationship; thus, a dynamic model of the multi-axle steering system of a heavy-duty vehicle with the steering angle of each steering axle as input is obtained.

[0102] 2) Based on the dynamic model of the multi-axis steering system for heavy-duty vehicles established in step 1), construct a steering coordination model of the multi-axis steering system based on the polar coordinate concentric center, and decompose the motion of the multi-axis steering system into translational and rotational modes; specifically including:

[0103] 21) Based on the dynamic model of the multi-axle steering system of the heavy-duty vehicle established in step 1), a polar coordinate concentric center variable is introduced to describe the cooperative steering state of the multi-axle steering system; the polar coordinate concentric center variable includes: concentric center lateral translation variable. and common instantaneous center of curvature variable ,in, Used to characterize the lateral translational synergy of multi-axis steering systems Used to characterize the yaw-rotation synergy of multi-axis steering systems;

[0104] 22) Establish the mapping relationship between the rotation angle of each steering axis and the state of the concentric center based on the polar coordinate concentric center variables, as follows:

[0105] ;

[0106] In the formula, Indicates the first One steering axis angle, Indicates the first The longitudinal distance from each steering axis to the vehicle's center of gravity; thus, the steering angle of each steering axis is uniformly generated through the two-dimensional polar coordinate concentric center variable;

[0107] 23) Define the polar coordinate concentric center state variable corresponding to the actual motion of the vehicle as follows:

[0108] ;

[0109] ;

[0110] In the formula, The lateral translation state variable represents the actual motion of the vehicle. The yaw rate state variable represents the actual motion of the vehicle. Indicates the vehicle's sideslip angle. Indicates the actual curvature of the vehicle's motion;

[0111] 24) Based on the polar coordinate concentric center state variables corresponding to the actual vehicle motion, rewrite the lateral-yaw dynamic relationship in step 1) into a polar coordinate concentric center dynamic form, as follows:

[0112] ;

[0113] In the formula, This represents the first derivative of the lateral translation state variable with respect to time. This represents the first derivative of the yaw curvature state variable with respect to time; thus, the lateral translation response of the multi-axis steering system is derived from... Characterization, transforming the yaw rotation response by Characterization;

[0114] 25) Based on the definition of tire slip angle and the mapping relationship between the steering axle angles and the concentric center state in step 22), establish the first... The relationship between the tire slip angle of each steering axle and the polar coordinate concentricity variable is as follows:

[0115] ;

[0116] In the formula, Indicates the first Each steering axle has a tire slip angle; thus, the lateral force response of each steering axle is correlated with the polar coordinate concentric center control variable;

[0117] 26) Construct a steering coordination model for a multi-axis steering system based on the polar coordinate common instantaneous center, as follows:

[0118] ;

[0119] in,

[0120] ;

[0121] ;

[0122] In the formula, This represents the first derivative of the polar coordinate concentric center state vector with respect to time. Represents the polar coordinate concentric center state vector. This represents the polar coordinate common instantaneous center control input vector. This represents a nonlinear steering coordination function jointly determined by the polar coordinate concentric center dynamics, tire slip angle, and vehicle global kinematics.

[0123] 27) Decompose the motion of the multi-axis steering system into translational and rotational modes, based on the lateral translational state variables of the actual vehicle motion. and their corresponding control variables The motion component characterized is defined as the translation mode, used to describe and regulate the lateral translation response of a multi-axis steering system; the yaw rate state variable is determined by the actual vehicle motion. and their corresponding control variables The motion component characterized is defined as the rotational mode, which is used to describe and regulate the yaw rotational response of the multi-axis steering system; thereby, the translational and rotational modes of the multi-axis steering system motion are decomposed in the polar coordinate concentric center frame.

[0124] 3) Based on the steering coordination model of the multi-axis axial steering system with concentric polar coordinates constructed in step 2), and combined with vehicle sideslip and rollover constraints, a concentric stability domain is constructed, and the concentric stability margin is quantified; specifically including:

[0125] 31) Based on the steering coordination model of the multi-axis steering system based on polar coordinate common instantaneous center constructed in step 2), determine the steady-state common instantaneous center state corresponding to the dual-modal common instantaneous center control input; the steady-state common instantaneous center state is expressed as:

[0126] ;

[0127] And satisfy the following:

[0128] ;

[0129] in,

[0130] ;

[0131] In the formula, Represents the steady-state concentric central state vector. Represents the steady-state lateral translation variable. Represents the steady-state yaw rate variable. This represents the steady-state coninstituent center mapping function determined by the steering cooperative model. This represents the polar coordinate common instantaneous center control input vector. Indicates the longitudinal speed of the vehicle;

[0132] 32) Based on the vehicle's sideslip safety requirements, construct steady-state lateral translation variable constraints; set the upper limit of the vehicle's center of gravity sideslip angle as follows: Then the upper limit of the steady-state horizontal translation variable is expressed as:

[0133] ;

[0134] The following set of steady-state lateral translation variable constraints is obtained:

[0135] ;

[0136] In the formula, This represents the upper limit of the steady-state lateral translation variable determined by vehicle roll safety requirements. Represents the set of constraints for steady-state lateral translation variables;

[0137] 33) Based on vehicle rollover safety requirements, construct steady-state yaw rate variable constraints; set the upper limit of load transfer rate as follows: The lateral acceleration satisfies The load transfer rate satisfies ,in,

[0138] ;

[0139] The upper limit of the steady-state yaw curvature variable is then expressed as:

[0140] ;

[0141] The following set of steady-state yaw curvature variable constraints is obtained:

[0142] ;

[0143] In the formula, This represents the upper limit of the steady-state yaw rate variable determined by vehicle rollover safety requirements. Represents the set of steady-state yaw curvature variable constraints. Indicates the load transfer rate coefficient. Indicates the height of the vehicle's center of gravity. Indicates the vehicle's track width. Represents gravitational acceleration;

[0144] 34) Based on the steady-state lateral translation variable constraint set obtained in step 32) and the steady-state yaw curvature variable constraint set obtained in step 33), the coninoculation center stability region is constructed as follows:

[0145] ;

[0146] In the formula, This represents the common instantaneous center stability region determined by the vehicle's lateral deviation constraint and rollover constraint; thus, the lateral deviation safety boundary and rollover safety boundary of the multi-axle steering system of heavy-duty vehicles are uniformly transformed into steady-state common instantaneous center state constraints.

[0147] 35) Calculate the minimum distance from the steady-state concentric center state to the boundary of the concentric center stability domain;

[0148] The boundary distance in the direction of steady-state lateral translation variable is expressed as:

[0149] ;

[0150] The boundary distance in the direction of the steady-state yaw curvature variable is expressed as:

[0151] ;

[0152] In the formula, This represents the minimum distance from the steady-state concentric center state to the boundary of the steady-state transverse translation variable. It represents the minimum distance from the steady-state concentric center state to the boundary of the steady-state yaw curvature variable;

[0153] 36) Based on the minimum distance obtained in step 35), construct the area of ​​the maximum allowable energy ellipse within the concentric center stable region; define the concentric center energy distance index as:

[0154] ;

[0155] The maximum allowable energy ellipse area is obtained as follows:

[0156] ;

[0157] In the formula, This index represents the energy distance between the vehicle's current polar coordinate concentric center state and its steady-state concentric center state. It represents the area of ​​the maximum allowable energy ellipse centered on the steady-state coninctuator state and not exceeding the boundary of the coninctuator stability domain;

[0158] 37) Based on the maximum allowable energy ellipse area obtained in step 36), the coninoculation center stability margin is quantized; the reference energy ellipse area is defined as:

[0159] ;

[0160] The instantaneous center stability margin is then expressed as:

[0161] ;

[0162] In the formula, This represents the area of ​​the reference energy ellipse used for normalization. This represents the coninocene stability margin; therefore, based on the area of ​​the maximum allowable energy ellipse within the coninocene stability domain, the coninocene stability margin is quantified. The larger the value, the farther the steady-state concentric center of gravity is from the vehicle's yaw-rollover coupling safety boundary, and the greater the remaining stability margin of the multi-axle steering system of heavy-duty vehicles.

[0163] 4) Based on the coninstituent center stability margin obtained in step 3), construct a neural network mode switching strategy to determine the master-slave game relationship between translation and rotation modes; specifically including:

[0164] 41) Define the participants in a bimodal virtual game based on translation and rotation modes;

[0165] The translational modal control input is defined as:

[0166] ;

[0167] The rotational modal control input is defined as:

[0168] ;

[0169] The translation modality is defined as a virtual participant. The rotation mode is defined as a virtual participant. ;in, This indicates the translation mode control input. Indicates rotational mode control input. This represents a virtual participant in the translation modality. Represents a virtual participant in a rotating modal;

[0170] 42) Based on the instantaneous center stability margin obtained in step 3), construct a neural network mode switching strategy;

[0171] A neural network mode switching strategy is constructed, which refers to a mode switching decision strategy that takes the concentric center stability margin, the change in concentric center stability margin, the vehicle polar coordinate concentric center state, and the vehicle longitudinal velocity as inputs, and takes the master-slave structure selection result between translation mode and rotation mode as output. The neural network mode switching strategy includes: input vector construction, feedforward neural network mapping, offline label generation, network parameter training, hysteresis switching mechanism construction, and stability safety fallback mechanism construction; specifically as follows:

[0172] 421) The input vector for constructing the neural network mode switching strategy is expressed as:

[0173] ;

[0174] in,

[0175] ;

[0176] In the formula, Indicates the first The neural network input vector at each sampling time point, Indicates the first The instantaneous center stability margin at each sampling time, Indicates the first The change in the coninal stability margin at each sampling time. Indicates the first The lateral translation state variable at each sampling time, Indicates the first The yaw curvature state variable at each sampling time. Indicates the first The longitudinal speed of the vehicle at each sampling time;

[0177] 422) Construct a feedforward neural network to implement the neural network mode switching strategy;

[0178] Feedforward neural networks receive input vectors Output rotation priority factor The rotation priority factor characterizes whether the current sampling time is suitable for a translation-dominated structure or a rotation-dominated structure, and is expressed as:

[0179] ;

[0180] ;

[0181] In the formula, Indicates the first Rotation priority factor at each sampling time, This represents the weight matrix from the input layer to the hidden layer of the neural network. This represents the weight matrix from the hidden layer to the output layer of the neural network. This represents the hidden layer bias vector. This represents the output layer bias vector. This represents the activation function of the hidden layer. Represents the Sigmoid function; The larger the value, the more inclined the structure is to adopt rotational mode dominance. The smaller the value, the more likely it is to adopt a translation mode-dominated structure;

[0182] 423) The offline evaluation cost required to construct modality switching label generation;

[0183] Let the candidate master-slave structure ,in This indicates a translation-dominant structure where the translation mode acts as the leader and the rotation mode acts as the follower. This represents a rotation-dominated structure where the rotation mode acts as the leader and the translation mode acts as the follower. For each candidate leader-slave structure, the finite-time offline evaluation cost is calculated as follows:

[0184] ;

[0185] In the formula, Indicates candidate master-slave structure The corresponding offline evaluation cost, Indicates a finite evaluation time domain. This represents the common instantaneous center stability margin weighting coefficient. This represents the weighting coefficient for the penalty of decreasing the instantaneous center stability margin. This represents the load transfer rate weighting coefficient. This represents the tracking error weighting coefficient. Indicates candidate master-slave structure Next The load transfer rate at each sampling time. Indicates candidate master-slave structure Next The overall trajectory tracking error at each sampling time point, superscript This indicates the vehicle response under the corresponding candidate master-slave structure;

[0186] 424) Generate mode switching labels for training the feedforward neural network based on the finite-time offline evaluation cost obtained in step 423), as follows:

[0187] ;

[0188] In the formula, Indicates the first Modal switching labels at each sampling time; This indicates that the translation-dominant structure has a lower offline evaluation cost. This indicates that the rotation-dominant structure has a lower offline evaluation cost;

[0189] 425) The feedforward neural network is trained using the binary cross-entropy loss function, expressed as:

[0190] ;

[0191] In the formula, This represents the training loss function for mode switching in a neural network. This indicates the number of training samples; after training, the parameters of the feedforward neural network are fixed, and the input vector is used to define the parameters. Feedforward neural network mapping relationship and rotation priority factor The neural network decision-making part that constitutes the online neural network mode switching strategy;

[0192] 426) Based on the rotation priority factor obtained in step 422), a hysteresis switching mechanism is constructed. This hysteresis switching mechanism is used to convert the rotation priority factor into a discrete mode switching variable, expressed as:

[0193] ;

[0194] In the formula, Indicates the first Discrete mode switching variables obtained at each sampling time through a hysteresis switching mechanism; This represents the discrete mode switching variable at the previous sampling time. Indicates the upper threshold of hysteresis. This represents the lower threshold of hysteresis, and ;when At that time, the hysteresis switching mechanism outputs , indicating the use of a rotation-dominant structure; when At that time, the hysteresis switching mechanism outputs This indicates that a translation-dominant structure is used; when At that time, the hysteresis switching mechanism outputs the discrete mode switching variable of the previous sampling time. To maintain the current dominant structure unchanged; thereby, the hysteresis switching mechanism suppresses frequent switching between translational and rotational dominant structures near the threshold.

[0195] 427) Based on the instantaneous center stability margin obtained in step 3), a stability safety fallback mechanism is constructed. This mechanism is used to determine the safety fallback state based on the instantaneous center stability margin, and is expressed as:

[0196] ;

[0197] in, Satisfy: When hour, Accumulation; when hour, Reset to zero; Indicates the first The safety fallback state obtained at each sampling time through the stability safety fallback mechanism This indicates the safety fallback status at the previous sampling time. This indicates the safety fallback threshold. This indicates the safety net release threshold, and , Indicates the instantaneous center stability margin Greater than The number of consecutive sampling steps, Indicates the number of consecutive recovery steps required for a safe bottom-line release; when At that time, the stability and safety fallback mechanism outputs... This indicates that the system has entered a safety net state; when At that time, the stability and safety fallback mechanism outputs... This indicates that the safety fallback state has been lifted; otherwise, the stability safety fallback mechanism outputs the safety fallback state at the previous sampling time. To maintain a safety net in place;

[0198] 428) Based on the discrete mode switching variables and the safety fallback state, the final master-slave structure switching variables are determined as follows:

[0199] ;

[0200] In the formula, Indicates the first The final master-slave structure switching variable at each sampling time; when When, a translation-dominant structure is adopted; when At that time, a rotation-dominant structure is adopted; thus, the rotation priority factor, hysteresis switching mechanism, and stability safety fallback mechanism output by the feedforward neural network together form the online switching result of the neural network mode switching strategy;

[0201] 43) Determine the master-slave game relationship between the translation mode and the rotation mode based on the final master-slave structure switching variables;

[0202] when At this time, the vehicle operates in a stability-first structure, with the translation mode acting as the leader and the rotation mode as the follower. The master-slave game relationship is as follows:

[0203] ;

[0204] when At this time, the vehicle operates in a follower-first structure, with the rotation mode acting as the leader and the translation mode as the follower. The master-slave game relationship is as follows:

[0205] ;

[0206] In the formula, Indicates the first The leader at each sampling moment, Indicates the first The followers at each sampling time point; thus, based on the common instantaneous center stability margin, a neural network mode switching strategy is constructed, and the master-slave game relationship between translation mode and rotation mode is determined.

[0207] 5) Construct a bimodal Stackelberg game predictive controller and solve for the optimal control inputs in the translation and rotation modes; specifically including:

[0208] Based on the steering collaboration model established in step 2), a bimodal Stackelberg game predictive controller is constructed. This bimodal Stackelberg game predictive controller includes a discrete-time prediction model, a translational mode optimization objective function, a rotational mode optimization objective function, a set of prediction constraints, a follower optimal response solution module, a leader optimization solution module, and a rolling time-domain control output module. The translational mode and rotational mode serve as two virtual participants in the Stackelberg game, and the leader and follower are determined based on the master-follower game relationship obtained in step 4. Specifically:

[0209] 51) Based on the steering coordination model established in step 2), establish the discrete-time prediction model required for bimodal Stackelberg game predictive control, expressed as:

[0210] ;

[0211] in,

[0212] ;

[0213] In the formula, Indicates the first The prediction at the nth sampling time Polar coordinate coninal state vector at each sampling time point Indicates the first The prediction at the nth sampling time Polar coordinate coninal state vector at each sampling time point Indicates the first The prediction at the nth sampling time The dual-modal concentric center control input vector at each sampling time point This represents the nonlinear steering cooperative function in step 2). The prediction model function obtained by discretization This indicates the translation mode control input. Indicates rotational mode control input;

[0214] 52) Construct the translational mode predictive control sequence and the rotational mode predictive control sequence, represented as follows:

[0215] ;

[0216] ;

[0217] In the formula, Indicates the first Translational mode prediction control sequence constructed at each sampling time point Indicates the first A rotating mode predictive control sequence constructed at each sampling time point. Indicates the prediction time domain;

[0218] 53) Based on the vehicle's predicted pose and reference trajectory, construct the lateral tracking error and vehicle motion direction error in the prediction time domain.

[0219] Let the reference trajectory be at the th The reference position at each prediction step is:

[0220] ;

[0221] The lateral tracking error of the reference trajectory in the prediction time domain is expressed as:

[0222] ;

[0223] The vehicle's direction angle is expressed as:

[0224] ;

[0225] At small angles, there are The error in predicting the vehicle's motion direction in the time domain is expressed as:

[0226] ;

[0227] In the formula, Indicates the vehicle's direction of motion angle. Indicates the prediction of the first time domain The error in the vehicle's direction of motion at each sampling time. Indicates the predicted yaw angle. This represents the predicted lateral translation state variable. Indicates the tangential direction angle of the reference trajectory;

[0228] 54) Construct the objective function for translational mode optimization, expressed as:

[0229] ;

[0230] In the formula, Indicates the first The objective function for shift mode optimization at each sampling time point Indicates the prediction of the first time domain Lateral tracking error at each sampling time, Indicates the translational mode control increment. This represents the weighting coefficient for the lateral tracking error in the translation mode. This represents the weighting coefficient for the translational mode motion direction error. This represents the incremental weighting coefficient for translational mode control;

[0231] 55) Construct the objective function for rotational modal optimization, expressed as:

[0232] ;

[0233] In the formula, Indicates the first The objective function for rotating mode optimization at each sampling time point Indicates the increment of rotating modal control. This represents the weighting coefficient for the lateral tracking error of the rotating mode. This represents the weighting coefficient for the direction error of rotational mode motion. This represents the weighting coefficient of the lateral translation state variable. This represents the incremental weighting coefficient for rotating modal control;

[0234] 56) Apply stability domain constraints to the predicted steady-state concentric center state based on the concentric center stability domain in step 3).

[0235] The predicted steady-state concentric center state generated by the dual-modal concentric center control input is represented as:

[0236] ;

[0237] And satisfy:

[0238] ;

[0239] In the formula, Indicates the prediction of the first time domain The steady-state concentric center state at each sampling time. Indicates the common instantaneous center stability region;

[0240] 57) Construct the feasible region of the bimodal Stackelberg game predictive controller;

[0241] make and They represent the first The feasible regions of the translation mode and the rotation mode at each sampling time include: discrete-time prediction model constraints, control input amplitude constraints, control input increment constraints, target rotation angle constraints of each steering axis, and common instantaneous center stability region constraints.

[0242] 58) Based on the master-slave game relationship in step 4), determine the leader control sequence, the follower control sequence, and the corresponding optimization objective function;

[0243] when When the translation mode acts as the leader and the rotation mode acts as the follower, it is represented as follows:

[0244] ;

[0245] ;

[0246] ;

[0247] when When the rotation mode acts as the leader and the translation mode as the follower, it is represented as follows:

[0248] ;

[0249] ;

[0250] ;

[0251] In the formula, Indicates the leader control sequence. Indicates the follower control sequence. This indicates that the leader optimizes the objective function. This indicates that the follower optimizes the objective function. Indicates the feasible domain of the leader. Indicates the feasible domain of the followers;

[0252] 59) In a given leader control sequence In this case, we construct the follower optimal response problem and solve the follower optimal response mapping as follows:

[0253] ;

[0254] In the formula, Indicates a given leader control sequence The optimal response control sequence of the follower obtained under the given conditions. This represents the objective function for the follower in the current master-slave game relationship;

[0255] 510) Based on the Stackelberg master-slave game mechanism, the leader makes decisions based on predicting the optimal response of the followers. Constructing a leader optimization problem, the leader's optimal control sequence is obtained as follows:

[0256] ;

[0257] In the formula, Indicates the first The optimal control sequence for the leader is obtained at each sampling time point. This represents the leader's objective function in the current master-slave game relationship. This represents the follower's optimal response to the leader's control sequence;

[0258] 511) Based on the follower optimal response mapping obtained in step 59) and the leader optimal control sequence obtained in step 510), the local Stackelberg equilibrium under the current prediction time domain and the current master-slave game relationship is obtained as follows:

[0259] ;

[0260] In the formula, This represents the equilibrium control sequence of translation and rotation modes under the current master-slave game relationship;

[0261] 512) Based on the final master-slave structure switching variables in step 428), restore the optimal control sequences for translation and rotation modes;

[0262] when hour:

[0263] ;

[0264] when hour:

[0265] ;

[0266] In the formula, Indicates the first The optimal control sequence for translation mode obtained at each sampling time point. Indicates the first The optimal control sequence for the rotating mode obtained at each sampling time;

[0267] 513) Using a rolling time-domain control method, the first control variable in the optimal control sequence of the translation mode and the optimal control sequence of the rotation mode is selected as the optimal control input at the current sampling time, expressed as:

[0268] ;

[0269] ;

[0270] In the formula, This represents the optimal control input for the translation mode at the current sampling time. This represents the optimal control input for the rotation mode at the current sampling time. Based on this, a bimodal Stackelberg game predictive controller is constructed, and the optimal control inputs for the translation and rotation modes are obtained by solving the problem.

[0271] 6) Based on the optimal control inputs for the translation and rotation modes obtained in step 5), the target steering angles of each steering axis are generated through the polar coordinate concentric center of rotation angle mapping relationship, thereby realizing the concentric center of rotation coordinated control of the multi-axis steering system of heavy-duty vehicles; specifically including:

[0272] 61) Based on the optimal control inputs for translational and rotational modes in step 5), determine the target polar coordinate concentricity variable at the current sampling time, as follows:

[0273] ;

[0274] ;

[0275] In the formula, Indicates the first The horizontal translation variable of the target concentric center at each sampling time. Indicates the first The target coninal yaw curvature variable at each sampling time. Indicates the first The optimal control input for the translation mode at each sampling time. Indicates the first Optimal control input for rotational mode at each sampling time;

[0276] 62) Based on the mapping relationship between the steering axis angles and the concentric center state established in step 22), map the target polar coordinate concentric center variables to the target steering axis angles. The target steering angle of each steering axis is represented as:

[0277] ;

[0278] In the formula, Indicates the first The sampling time of the first sampling moment Target steering angle of the steering axis Indicates the first The longitudinal distance from the steering axis to the vehicle's center of gravity. Indicates the number of steering shafts;

[0279] 63) Based on the target steering angles of each steering axis obtained in step 62), construct the multi-axis steering target angle vector as follows:

[0280] ;

[0281] In the formula, Indicates the first The multi-axis steering target angle vector is generated by the translation mode optimal control input and the rotation mode optimal control input at each sampling time.

[0282] 64) The multi-axis steering target angle vector obtained in step 63) The signal is sent to each steering axis control steering actuator, enabling each steering axis control steering actuator to track its corresponding target steering angle. The corresponding actual steering axis angle response is output; thus, the optimal control inputs of translation mode and rotation mode are converted into target steering angles of each steering axis through the polar coordinate common instantaneous center angle mapping relationship, realizing the common instantaneous center coordinated control of the multi-axis steering system of heavy-duty vehicles.

[0283] This invention has many specific applications. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1. A method for coordinated control of the instantaneous center of gravity of a multi-axis steering system for heavy-duty vehicles, characterized in that, The steps are as follows: 1) Establish a dynamic model of the multi-axis steering system for heavy-duty vehicles; 2) Construct a steering coordination model for a multi-axis steering system based on polar coordinate common instantaneous center, and decompose the motion of the multi-axis steering system into translational and rotational modes; 3) Based on the polar coordinate concentric center of gravity (CNC) model of a multi-axis traction control system, the CNC stability domain is constructed by combining vehicle side slip constraints and rollover constraints, and the CNC stability margin is quantified. 4) Based on the stability margin of the consensual center, construct a neural network mode switching strategy and determine the master-slave game relationship between the translation mode and the rotation mode; 5) Construct a bimodal Stackelberg game predictive controller and solve for the optimal control inputs for the translation and rotation modes; 6) Based on the optimal control input of translation mode and rotation mode, the target steering angle of each steering axis is generated through the polar coordinate common instantaneous center of rotation angle mapping relationship, so as to realize the common instantaneous center of rotation coordinated control of the multi-axis steering system of heavy-duty vehicle.

2. The method for coordinated control of the instantaneous center of gravity of a multi-axis steering system for heavy-duty vehicles according to claim 1, characterized in that, Step 1) specifically includes: 11) Determine the modeling object for the multi-axle steering system of heavy-duty vehicles; 12) Establish the lateral-yaw dynamics relationship of the multi-axle steering system of heavy-duty vehicles; 13) Establish the first The relationship between tire slip angle and equivalent lateral force for each steering axle; 14) Establish the global kinematic relationships of the vehicle; 15) Establish a dynamic model of the multi-axle steering system for heavy-duty vehicles.

3. The method for coordinated control of the instantaneous center of gravity of a multi-axis steering system for heavy-duty vehicles according to claim 2, characterized in that, Step 2) specifically includes: 21) Based on the dynamic model of the multi-axle steering system of heavy-duty vehicles established in step 1), polar coordinate concentric center variables are introduced to describe the cooperative steering state of the multi-axle steering system. 22) Establish the mapping relationship between the rotation angle of each steering axis and the state of the concentric center based on the polar coordinate concentric center variables; 23) Define the polar coordinate concentric center state variable corresponding to the actual motion of the vehicle; 24) Based on the polar coordinate concentric center state variables corresponding to the actual motion of the vehicle, rewrite the lateral-yaw dynamic relationship in step 1) into a polar coordinate concentric center dynamic form; 25) Based on the definition of tire slip angle and the mapping relationship between the steering axle angles and the concentric center state, establish the first... The relationship between the tire slip angle of each steering axle and the polar coordinate concentricity variable; 26) Construct a steering coordination model for a multi-axis steering system based on the common instantaneous center of polar coordinates; 27) The motion of the multi-axis steering system is decomposed into translational and rotational modes. The motion part characterized by the lateral translational state variables of the actual vehicle motion and their corresponding control variables is defined as the translational mode, which is used to describe and adjust the lateral translational response of the multi-axis steering system. The motion part characterized by the yaw curvature state variables of the actual vehicle motion and their corresponding control variables is defined as the rotational mode, which is used to describe and adjust the yaw rotational response of the multi-axis steering system.

4. The method for coordinated control of the instantaneous center of gravity of a multi-axis steering system for heavy-duty vehicles according to claim 3, characterized in that, Step 3) specifically includes: 31) Based on the steering coordination model of the multi-axis steering system based on polar coordinate common instantaneous center constructed in step 2), determine the steady-state common instantaneous center state corresponding to the dual-modal common instantaneous center control input; 32) Based on the vehicle lateral slip safety requirements, construct steady-state lateral translation variable constraints and obtain the set of steady-state lateral translation variable constraints; 33) Based on the vehicle rollover safety requirements, construct steady-state yaw curvature variable constraints and obtain the set of steady-state yaw curvature variable constraints; 34) Based on the steady-state lateral translation variable constraint set obtained in step 32) and the steady-state yaw curvature variable constraint set obtained in step 33), construct the coninus stability region; 35) Calculate the minimum distance from the steady-state concentric center state to the boundary of the concentric center stability domain; 36) Based on the minimum distance obtained in step 35), construct the maximum allowable energy ellipse area within the coninocaloric stability region; 37) Based on the maximum allowable energy ellipse area obtained in step 36), the coninstituent center stability margin is quantified.

5. The method for coordinated control of the instantaneous center of gravity of a multi-axis steering system for heavy-duty vehicles according to claim 4, characterized in that, Step 4) specifically includes: 41) Define the participants in a bimodal virtual game based on translation and rotation modes; 42) Based on the instantaneous center stability margin obtained in step 3), construct a neural network mode switching strategy; 43) Determine the master-slave game relationship between the translation mode and the rotation mode based on the final master-slave structure switching variables.

6. The method for coordinated control of the instantaneous center of gravity of a multi-axis steering system for heavy-duty vehicles according to claim 5, characterized in that, Step 42) specifically includes: A neural network mode switching strategy is constructed, which refers to a mode switching decision strategy that takes the common instantaneous center stability margin, the change in the common instantaneous center stability margin, the state of the vehicle's polar coordinate common instantaneous center, and the vehicle's longitudinal velocity as inputs, and takes the master-slave structure selection result between translation mode and rotation mode as output. The neural network mode switching strategy includes: input vector construction, feedforward neural network mapping, offline label generation, network parameter training, hysteresis switching mechanism construction, and stability safety fallback mechanism construction.

7. The method for coordinated control of the instantaneous center of gravity of a multi-axis steering system for heavy-duty vehicles according to claim 6, characterized in that, Step 42) specifically also includes: 421) Construct the input vector for the neural network mode switching strategy; 422) Construct a feedforward neural network to implement the neural network mode switching strategy; 423) The offline evaluation cost required to construct modality switching label generation; 424) Generate modality switching tags; 425) A feedforward neural network is trained using a binary cross-entropy loss function; 426) Construct a hysteresis switching mechanism to convert the rotation priority factor into a discrete mode switching variable; 427) Based on the instantaneous center stability margin, a stability safety fallback mechanism is constructed to determine the safety fallback state based on the instantaneous center stability margin; 428) Determine the final master-slave structure switching variables based on the discrete mode switching variables and the safety fallback state.

8. The method for coordinated control of the instantaneous center of gravity of a multi-axis steering system for heavy-duty vehicles according to claim 7, characterized in that, Step 5) specifically includes: Based on the steering collaboration model established in step 2), a bimodal Stackelberg game predictive controller is constructed. The bimodal Stackelberg game predictive controller includes a discrete-time prediction model, a translation mode optimization objective function, a rotation mode optimization objective function, a set of prediction constraints, a follower optimal response solution module, a leader optimization solution module, and a rolling time-domain control output module. The translation mode and the rotation mode are respectively used as two virtual participants in the Stackelberg game, and the leader and follower are determined according to the master-follower game relationship obtained in step 4).

9. The method for coordinated control of the instantaneous center of gravity of a multi-axis steering system for heavy-duty vehicles according to claim 8, characterized in that, Step 5) specifically also includes: 51) Based on the steering coordination model established in step 2), establish the discrete-time prediction model required for bimodal Stackelberg game predictive control; 52) Construct translational mode predictive control sequences and rotational mode predictive control sequences; 53) Based on the vehicle's predicted pose and reference trajectory, construct the lateral tracking error and vehicle motion direction error in the prediction time domain. 54) Construct the objective function for translational mode optimization; 55) Construct the objective function for rotational mode optimization; 56) Apply stability region constraints to the predicted steady-state concentric center state based on the concentric center stability region; 57) Construct the feasible region of the bimodal Stackelberg game predictive controller; 58) Based on the master-slave game relationship in step 4), determine the leader control sequence, the follower control sequence, and the corresponding optimization objective function; 59) Given a leader control sequence, construct a follower optimal response problem and solve for the follower optimal response mapping; 510) Based on the Stackelberg master-slave game mechanism, the leader makes decisions based on the prediction of the follower's optimal response, constructs the leader optimization problem, and obtains the leader's optimal control sequence; 511) Based on the follower's optimal response mapping and the leader's optimal control sequence, obtain the local Stackelberg equilibrium in the current prediction time domain and the current master-slave game relationship; 512) Based on the final master-slave structure switching variables, recover the optimal control sequences for translation and rotation modes; 513) Using the rolling time-domain control method, the first control variable in the optimal control sequence of translation mode and the optimal control sequence of rotation mode is selected as the optimal control input at the current sampling time.

10. The method for coordinated control of the instantaneous center of gravity of a multi-axis steering system for heavy-duty vehicles according to claim 9, characterized in that, Step 6) specifically includes: 61) Based on the optimal control inputs for translation mode and rotation mode in step 5), determine the target polar coordinate concentric variable at the current sampling time; 62) Based on the mapping relationship between the steering axis angles and the concentric center state established in step 22), map the target polar coordinate concentric center variables to the target steering axis angles; 63) Based on the target steering angles of each steering axis obtained in step 62), construct a multi-axis steering target angle vector; 64) The multi-axis steering target angle vector obtained in step 63) is sent to each steering axis control steering actuator, so that each steering axis control steering actuator tracks the corresponding target angle and outputs the corresponding actual steering axis angle response; thereby, the optimal control input of translation mode and rotation mode is converted into the target angle of each steering axis through the polar coordinate common instantaneous center angle mapping relationship, realizing the common instantaneous center cooperative control of the multi-axis control steering system of heavy-duty vehicles.

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