A path tracking control method considering uncertain torque loss of a wheel hub motor

Abstract

This invention relates to a path tracking control method considering uncertain torque loss of in-wheel motors. Based on a hierarchical control architecture, it includes an upper-level tracking target module and a lower-level torque distribution module. The upper-level tracking target module establishes a vehicle dynamics model considering DTTER (Due Difference of Target Torque) and obtains DTTER estimates using the MIEKF algorithm. It also employs a path tracking control strategy based on an improved MADDPG, utilizing two agents—Active Front Steering (AFS) and Rear Differential Steering (RDS)—to output front wheel steering angle and rear wheel differential torque signals, respectively. The lower-level torque distribution module, based on the DTTER estimate and the rear wheel differential torque signal, obtains the optimal torque distribution signal through quadratic programming. Combined with the front wheel steering angle signal, this signal controls the torque of all four wheels of the vehicle, achieving path tracking. Compared with existing technologies, this invention effectively improves the path tracking accuracy and stability of distributed in-wheel motor driven electric vehicles.

Description

Technical Field

[0001] This invention relates to the field of vehicle control technology, and in particular to a path tracking control method that takes into account the uncertain torque loss of the hub motor. Background Technology

[0002] Distributed in-wheel motor drive systems have become an ideal platform for path tracking control algorithms in intelligent vehicles due to their ability to independently decouple the in-wheel motors, flexibly output driving torque, and improve the control range and accuracy of all four wheels. However, the dynamic seals of the in-wheel motors generate additional damping torque due to contact friction and fluid shear resistance, causing the actual output torque to be less than the command torque issued by the controller, resulting in uncertain dynamic torque errors. This uncertain torque loss further affects path tracking accuracy and lateral stability. Therefore, quantifying the uncertain torque loss caused by dynamic seals is crucial for improving the torque control accuracy of in-wheel motors, reducing path tracking deviations, suppressing yaw torque fluctuations caused by uneven torque, and enhancing the lateral stability and driving safety of the vehicle. However, current research lacks solutions to this problem.

[0003] To mitigate the adverse effects of hub motor torque loss on path tracking accuracy and yaw stability, it is necessary to observe the location and magnitude of the torque loss in real time, i.e., vehicle state estimation. Common state estimation methods include model-based Kalman filtering (EKF), data-driven machine learning algorithms, and optimization estimation combining mechanism and data-driven approaches. Among these, EKF, as a standard method for nonlinear system state estimation, achieves linearization through a first-order Taylor expansion of the nonlinear system and has been widely used. However, the truncation error introduced during EKF linearization can lead to filter divergence in strongly nonlinear systems or under conditions of large initial estimation errors. Furthermore, when hub motor-driven vehicles travel at high speeds, the increased unsprung mass intensifies vibration, and the time-varying characteristics of nonlinear dynamics couple with unsprung vibration, amplifying the transient nonlinear effects of tire forces and affecting estimation accuracy. Even when data-driven mechanisms are incorporated, generalization is limited by the scarcity of data under extreme conditions.

[0004] Currently, there is a lack of research proposing solutions to the problems of insufficient path tracking accuracy and deteriorated yaw stability caused by uncertain in-wheel motor torque losses. This problem is similar to the vehicle control problem caused by in-wheel motor failures / malfunctions. It requires real-time detection and estimation of abnormal in-wheel motor indicators and reallocation of torque among the four motors to maintain the vehicle's desired motion state to the greatest extent possible. However, current torque reallocation methods all employ passive compensation control. This method uses the actual torque error as a feedback condition for "post-hoc compensation" and has a lag, making it difficult to cope with real-time disturbances caused by uncertain torque losses.

[0005] Furthermore, path tracking control requires tracking the desired path with minimal lateral displacement and heading angle errors while ensuring yaw stability. Essentially, it involves collaborative optimization of multiple systems under multiple constraints. Currently, collaborative methods mainly fall into two categories: one is dividing the working region based on the vehicle dynamics phase plane. However, this method largely relies on the assumption of zero front wheel steering angle, failing to consider the impact of steering angle changes during lateral movement on vehicle dynamics and the phase plane region, thus limiting the applicability of the collaborative strategy. The other method is dividing the working region based on tire condition. However, tire lateral force is difficult to measure directly in real vehicles, and the measuring equipment is expensive. Although the tire condition region can be divided by fitting the magic tire formula, this method is difficult to apply directly when tire parameters are unknown. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a path tracking control method that considers the uncertain torque loss of the hub motor.

[0007] The objective of this invention can be achieved through the following technical solution: a path tracking control method considering the uncertain torque loss of the hub motor, based on a hierarchical control architecture, which includes an upper-level tracking target module and a lower-level torque distribution module. The upper-level tracking target module, on the one hand, establishes a vehicle dynamics model considering DTTER (dynamic torque tracking error rate) and uses the MIEKF (multi-innovation extended Kalman filter) algorithm to obtain the DTTER estimate. On the other hand, it adopts a path tracking control strategy based on the improved MADDPG (multi-agent deep deterministic policy gradient), and uses two agents, AFS (active front-wheel steering) and RDS (rear-wheel differential steering), to output the front wheel angle and rear wheel differential torque signals respectively. The lower-level torque distribution module obtains the optimal torque distribution signal based on the DTTER estimate and the rear wheel differential torque signal through a quadratic programming method. Combined with the front wheel steering angle signal, it controls the torque of the four wheels of the vehicle accordingly to achieve path tracking.

[0008] Furthermore, the process of establishing a vehicle dynamics model considering DTTER includes: The dynamic torque tracking deviation rate is defined as a quantitative indicator of uncertainty to characterize the real-time uncertainty of motor torque loss, as follows: in, For the first Taiwan hub motor The actual output torque at any given moment. These correspond to the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. For the controller in Send to the first Torque command of the motor, For the first Taiwan hub motor Dynamic torque tracking deviation rate at any given time. The larger the value, the more severe the motor torque loss and the greater the uncertainty. A physical model is established to reflect the vehicle dynamics under the torque loss of the hub motors. Based on the seven-degree-of-freedom vehicle model, considering the driving torque loss of the four hub motors, the specific form of the continuous-time nonlinear state equation is as follows: in, For longitudinal vehicle speed, Lateral speed, , , , These represent the lateral forces from the ground acting on the left front, right front, left rear, and right rear wheels of the vehicle, respectively. , , , These represent the longitudinal forces from the ground acting on the left front, right front, left rear, and right rear wheels of the vehicle, respectively. and These are the distances from the center of mass to the front and rear axles, respectively. and These are the slip angles of the front and rear wheels, respectively. For the front wheel steering angle, It is half the track width between the left and right wheels. The sideslip angle is the angle of the center of mass. The yaw rate is angular velocity. For the sprung mass, For vehicles to bypass Moment of inertia of the shaft, For the moment of inertia of the wheel, The angular velocity of the wheel's rotation. The effective rolling radius of the wheel, The rolling resistance torque, i.e. , The rolling resistance coefficient, For process noise, It is random noise used to characterize the uncertainty of measurements and models.

[0009] Furthermore, the process of obtaining the DTTER estimate using the MIEKF algorithm includes: The vehicle dynamics model is discretized, and the vehicle acceleration, yaw rate, wheel speed and actual torque are used as observations to establish observation equations. The multi-innovation theory and extended Kalman filtering are fused together. Multi-time-time innovation vectors and extended measurement matrices are constructed through sliding time windows. The state prediction is completed based on numerical differentiation to calculate the Jacobian matrix, and the covariance is updated using the Joseph form. The DTTER estimates of the four wheels are output in real time.

[0010] Furthermore, the multi-time innovation vector is specifically as follows: in, For the first The new information of the moment, that is , For the observation vector, For the nonlinear function of the observation model, This is the current predicted state. The innovation length is the number of sampling points contained in the sliding time window. To measure the dimension of a vector, This represents the current discrete time step. The extended measurement matrix is ​​specifically as follows: in, For the first The Jacobian matrix for measuring time, i.e. , The dimension is the state vector.

[0011] Furthermore, the improved MADDPG path tracking control strategy specifically employs the idea of ​​approximate fitting to construct policy approximation functions for other agents, and obtains an approximate policy by maximizing entropy regularization, thereby realizing indirect information interaction between the two agents, AFS and RDS; and introduces an integrated policy structure, so that the two agents, AFS and RDS, each contain multiple sub-policies and randomly select them, and obtains an approximate optimization result by maximizing the overall reward of the integrated policy.

[0012] Furthermore, the formula for calculating the entropy regularization is: in, Let be the cost function of entropy. For the first The first agent fits the first... An approximate strategy for each agent For strategy parameters, For strategy distribution weight factors, The entropy of the policy distribution; The objective function for the integration strategy is: in, The objective function that needs to be optimized for the integration strategy is... The state distribution of the strategy, For the first Individual strategies For the first The total expected return for each agent As a discount factor, For the first An intelligent agent in The reward value at any given moment.

[0013] Furthermore, the state space of the AFS agent Action space and reward function The definition is as follows: in, These are the lateral displacement error, lateral velocity error, heading angle error, and heading angular velocity error, respectively. This is the distribution coefficient for the front wheel steering angle. , , , The weighting coefficients are used to adjust the path tracking accuracy.

[0014] Furthermore, the state space of the RDS agent Action space and reward function The definition is as follows: in, This is the distribution coefficient for the rear wheel differential torque. , , To adjust the weighting coefficients for stability, These are the yaw rate error, the centroid sideslip angle error, and the longitudinal velocity error, respectively.

[0015] Furthermore, the method of obtaining the optimal torque distribution signal through quadratic programming specifically involves incorporating the estimated DTTER values ​​of the four wheels into the constraints of control input, tire utilization rate, and hub motor torque output capability, thereby rewriting the standard form of quadratic programming and solving for the optimal torque distribution signal.

[0016] Furthermore, the specific constraints on the control input, tire utilization rate, and hub motor torque output capability are as follows: in, The coefficient of friction of the tire. The vertical force on the wheel, This represents the maximum torque of the hub motor.

[0017] Compared with the prior art, the present invention has the following advantages: This invention designs a hierarchical control architecture, which includes an upper-level target tracking module and a lower-level torque distribution module. In the upper-level target tracking module, on the one hand, a vehicle dynamics model considering DTTER is established, and the DTTER estimate is obtained using the MIEKF algorithm. On the other hand, a path tracking control strategy based on an improved MADDPG is adopted, using two agents, AFS and RDS, to output the front wheel steering angle and rear wheel differential torque signals, respectively. In the lower-level torque distribution module, based on the DTTER estimate and the rear wheel differential torque signal, the optimal torque distribution signal is obtained through a quadratic programming method. This signal is then combined with the front wheel steering angle signal to control the torque of the four wheels of the vehicle accordingly. This effectively improves the path tracking accuracy and stability of electric vehicles driven by distributed hub motors.

[0018] This invention proposes a DTTER index that reflects the uncertain torque loss caused by the dynamic seal of the hub motor. Based on this, a vehicle dynamics model considering DTTER is established, and a DTTER estimation method based on the MIEKF algorithm is proposed. The method deeply integrates the concept of multiple innovations with extended Kalman filtering. By introducing measurement information from multiple moments within the sliding time window, the collaborative optimization and updating of the state estimate is achieved. This method can output high-precision estimates of the dynamic torque loss rate of the four wheels in real time, providing a reliable state input for subsequent feedforward optimal torque distribution and path tracking control.

[0019] This invention improves the measurement update of the MIEKF algorithm by constructing a new information vector from the measurement residuals (new information) of the current time and multiple previous time steps. It utilizes more historical information for state updates and improves data utilization and estimation accuracy by introducing multiple new information vectors. Furthermore, under the multiple new information framework, the measurement Jacobian matrix of all historical time steps is calculated based on the current predicted state. Although this approach introduces approximation, the compensation effect of multiple new information can significantly reduce computational complexity while ensuring accuracy.

[0020] This invention proposes a path tracking control strategy based on an improved MADDPG. An AFS agent is used to control path tracking accuracy, while an RDS agent is used to control stability. This enables adaptive optimization among different control objectives, overcoming the limitations of single-agent training. In this invention, the improved MADDPG employs an approximation fitting approach to construct policy approximation functions for other agents and maximizes these functions through entropy regularization, achieving indirect information interaction between agents. Furthermore, to mitigate environmental non-stationarity caused by dynamic policy changes, an ensemble policy structure is introduced into the improved MADDPG framework. This structure allows both the AFS and RDS agents to each contain multiple sub-policies, which are randomly selected. Maximizing the overall reward of the ensemble policy improves algorithm stability and optimization performance.

[0021] This invention treats torque loss as a feedforward variable, taking it into account in advance during the torque distribution process. By incorporating the estimated DTTER values ​​of the four wheels into the constraints of control input, tire utilization rate, and hub motor torque output capability, the standard form of the quadratic programming is rewritten, and the optimal torque distribution signal is obtained by solving the problem. This allows the control system to complete the optimal torque distribution while considering motor torque loss, avoiding "post-control" that would affect real-time performance. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the hierarchical control architecture of the present invention; Figure 2 This is a schematic diagram illustrating the application process of the embodiment; Figure 3 This is a schematic diagram of the path tracking control design based on the improved MADDPG in the embodiment; Figure 4 This is a schematic diagram of the DTTER estimation effect of the left front wheel under the slalom driving condition in the embodiment. Figure 5 This is a schematic diagram of the DTTER estimation effect of the right rear wheel under the slalom driving condition in the embodiment. Figures 6-9 This is a schematic diagram illustrating the path tracking control effect considering the uncertain torque loss of the hub motor under the serpentine slalom condition in the embodiment. Detailed Implementation

[0023] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0024] Example This proposal suggests a path tracking control method that considers the uncertain torque loss of the hub motor, implemented based on a hierarchical control architecture, such as... Figure 1 As shown, the hierarchical control architecture includes an upper-level target tracking module and a lower-level torque distribution module. The upper-level target tracking module, on the one hand, establishes a vehicle dynamics model that considers the dynamic torque tracking deviation rate (DTTER) and uses the multi-innovation extended Kalman filter (MIEKF) algorithm to obtain the DTTER estimate. On the other hand, it adopts a path tracking control strategy based on the improved multi-agent deep deterministic policy gradient (MADDPG), using two agents, Active Front Steering (AFS) and Rear Wheel Differential Steering (RDS), to output the front wheel steering angle and rear wheel differential torque signals, respectively. The lower-level torque distribution module obtains the optimal torque distribution signal based on the DTTER estimate and the rear wheel differential torque signal through a quadratic programming method. Combined with the front wheel steering angle signal, it controls the torque of the four wheels of the vehicle accordingly to achieve path tracking.

[0025] This embodiment applies the above-described solution, such as Figure 2As shown, the main process includes establishing a vehicle dynamics model that considers DTTER, estimating DTTER based on MIEKF, performing path tracking control based on MADDPG, and achieving optimal torque distribution control considering motor torque loss.

[0026] Specifically: I. Establishing a vehicle dynamics model considering DTTER Based on the Newton-Euler equations and assuming a small front wheel steering angle, a three-degree-of-freedom vehicle dynamics model is established: in, For the sprung mass, For vehicles to bypass Moment of inertia of the shaft.

[0027] Considering load transfer, the vertical load on each tire is: in, The wheelbase is, i.e. . The height of the center of mass. It is the lateral acceleration, that is, . , , , These are the vertical forces from the ground acting on the left front, right front, left rear, and right rear wheels of the vehicle, respectively.

[0028] Using the Pacejka magic formula and the cutoff method to build a tire model, tire forces can be approximated: in, and These represent the stiffness of the front and rear tires, respectively. For slip ratio, It is the slip angle. and The calculation formulas are as follows: in, and These are the longitudinal and lateral velocities at the center of the tire, respectively, and their corresponding calculation formulas are as follows: To address the torque loss caused by the inconsistency of torque characteristics among the four hub motors in the DDEV during real-time operation, this solution focuses on the dynamic tracking characteristics of the "control command - actual output," thus defining a dynamic torque tracking deviation rate. As a quantitative indicator of uncertainty, to characterize the real-time uncertainty of motor torque loss, it is defined as follows: in, For the first Taiwan hub motor The actual output torque at any given moment. For the controller in Send to the first Torque command of the motor For the first Taiwan hub motor Dynamic torque tracking deviation rate at any given time. The larger the value, the more severe the motor torque loss and the greater the uncertainty.

[0029] The reasonable quantification of dynamic torque tracking deviation rate needs to be combined with actual driving conditions to avoid misjudging "normal torque adjustment" as "torque loss". Since this embodiment mainly considers path tracking under low-adhesion conditions such as ice and snow, torque loss can easily increase. Therefore, the following settings are used... The numerical fluctuation range is less than 1.5%, that is, the difference between adjacent time points. ≤1.5% to avoid misjudgment of torque loss caused by instantaneous impact.

[0030] Dynamic torque tracking deviation rate It exhibits time-varying and nonlinear characteristics, and is therefore represented as: in, This is the steady-state deviation. This is a time-varying dynamic deviation, which can be caused by factors such as sudden changes in temperature and load. This represents random noise, characterizing the uncertainty of measurements and models.

[0031] Considering the dynamic torque tracking deviation rate, the rotational dynamics equations for each wheel are established as follows: in, For the moment of inertia of the wheel, The angular velocity of the wheel's rotation. This is the effective rolling radius of the wheel. The rolling resistance torque is, i.e. . This is the rolling resistance coefficient.

[0032] In order to accurately estimate The dynamic torque tracking deviation rate is used as an extended state for joint estimation, and the extended state vector is defined as follows: The continuous-time nonlinear state equation can be expressed as: in, To control the input, that is, . The process noise is assumed to be zero-mean Gaussian white noise, i.e., Assuming that the noise components are independent and the covariance matrix is ​​a diagonal matrix: Therefore, the specific form of the continuous-time nonlinear state equation is: in, The first-order time constant of the dynamic torque tracking deviation rate is used to characterize its dynamic characteristics. For longitudinal vehicle speed, Lateral speed, , , , These are the lateral forces from the ground acting on the left front, right front, left rear, and right rear wheels of the vehicle, respectively. , , , These are the longitudinal forces from the ground acting on the front left, front right, rear left, and rear right wheels of the vehicle, respectively. and These are the distances from the center of mass to the front and rear axles, respectively. and These are the slip angles of the front and rear wheels, respectively. For the front wheel steering angle, It is half the track width between the left and right wheels. The sideslip angle is the angle of the centroid. ω represents the yaw rate.

[0033] Therefore, by designing a dynamic torque tracking deviation rate index to reflect the uncertain torque loss caused by the dynamic seal of the hub motor, and establishing a vehicle dynamics model that considers the dynamic torque tracking deviation rate, a model basis can be provided for subsequent motor torque loss estimation.

[0034] II. Path Tracking Control Method Based on MADDPG The parameters that need to be set for MADDPG are the state space, action space, reward function, and hyperparameters. Some parameters for the two different agents, AFS and RDS, need to be designed according to the driving conditions, such as... Figure 3 As shown.

[0035] Agent 1, i.e., the state space of AFS Action space and reward function The definition is as follows: in, These are the lateral displacement error, lateral velocity error, heading angle error, and heading angular velocity error, respectively. This is the distribution coefficient for the front wheel steering angle. , , and The weighting coefficients are used to adjust the path tracking accuracy.

[0036] Agent 2, i.e., the state space of RDS Action space and reward function The definition is as follows: in, This is the distribution coefficient for the rear wheel differential torque. , ,and The weighting coefficients are used to adjust stability. These are the yaw rate error, the centroid sideslip angle error, and the longitudinal velocity error, respectively.

[0037] The MADDPG experience replay pool stores the state, actions, and reward information of the AFS and RDS agents at each time step. That is, at each time step, the current states of both the AFS and RDS agents are stored in the same matrix, resulting in the information shown below: in, The state matrices of two agents, AFS and RDS, are stored. The action matrices of the two agents are stored. The reward value matrix of the two agents is stored. This stores the state matrices of the two agents for the next time step. These four matrices are then combined to form an empirical sample dataset. in, It contains information about all agents at every moment, superscript. For the first Empirical sample data at any given time.

[0038] To address the issue that information cannot be directly shared between two agents, we use an approximate fitting approach to infer the policies of other agents. This approximate policy is obtained by maximizing entropy regularization, as shown below: in, Let be the cost function of entropy. For the first The first agent fits the first... An approximate strategy for each agent, For strategy parameters, For strategy distribution weight factors, Let be the entropy of the policy distribution.

[0039] To further address the non-stationarity of the environment caused by the continuous changes in the policies of different agents, MADDPG uses an ensemble policy. The two agents, AFS and RDS, each contain multiple sub-policies, and only one sub-policy is randomly used in each training round. Assume... yes The ensemble strategy of individual sub-policies for an agent An approximate optimization result can be obtained by maximizing the overall reward of the ensemble strategy, as shown below: in, The objective function that needs to be optimized for the integration strategy is... The state distribution of the strategy, For the first Individual strategies For the first Total expected return for each agent As a discount factor, For the first An intelligent agent in The reward value at any given moment.

[0040] Assumption It is the set of parameters for the online Q network of critics. Let be the set of parameters for the actor's online policy network for all agents. The parameters for the critic's online network can also be minimized using a loss function. To achieve this, see the following: in, To recycle from the experience pool The number of random samples is empirical sample data, For the first The online value function of an agent. For approximate online strategies of other intelligent agents The output action, For the first Real online strategies of individual agents The output action, To approximate the target action value, For the first The objective value function of an agent. For approximate target strategies of other intelligent agents The output action, For the first The real target strategy of an agent The output action.

[0041] Since different actor sub-policies in the agent will be executed in different training rounds, the obtained empirical sample data will be different. Therefore, in the MADDPG algorithm, the agent... Each sub-strategy has its own separate experience replay pool. (Integrated strategy) Equivalent to the first The online value network parameters corresponding to the execution of each sub-strategy gradient The details are as follows: in, The total number of sub-strategies For the first Individual strategies This serves as the experience replay pool for the corresponding sub-strategy. For the first The gradient of each sub-policy This represents the gradient of the online value function.

[0042] III. DTTER Estimation Method Based on MIEKF To identify the dynamic torque tracking deviation rate, the vehicle dynamics equations considering motor torque loss are discretized. In this embodiment, the forward Euler method is used for discretization. in, For state vectors, For the input vector, Sampling time, It is a nonlinear state transition function. This is discrete process noise, i.e. . It is usually assumed to be zero-mean Gaussian white noise.

[0043] In actual driving, , , , , , , , , , , All of these can be measured using onboard sensors. Therefore, the measurement vector is defined as: The measurement nonlinear state equation can be expressed as: in, For the observation vector, For the nonlinear function of the observation model, To measure noise, i.e. Assuming all measurements are independent, and the noise covariance matrix is ​​a diagonal matrix: Therefore, measuring nonlinear state equations The specific form is as follows: The prediction steps are the same as the traditional EKF algorithm, based on nonlinear state equations for state prediction and error covariance propagation: Furthermore, the error covariance is predicted: in, Let be the Jacobian matrix of the state transition matrix, i.e.: The analytical calculation of the Jacobian matrix involves complex partial derivative operations. This embodiment uses a numerical differentiation method to achieve this: in, For small perturbations, the value is 10. -6 , For the first A standard unit vector.

[0044] Measurement updates are the core innovation of the MIEKF algorithm, which involves updating measurements at each time step within the sliding window. Calculate the new information: It should be noted that all new information uses the current forecast state. Calculating the predicted values ​​of measurements at historical moments reflects MIEKF's reinterpretation and utilization of historical information.

[0045] The MIEKF improves data utilization and estimation accuracy by introducing multiple innovation vectors. The core idea of ​​MIEKF is to construct an innovation vector from the measurement residuals (innovations) of the current time step and multiple previous time steps, utilizing more historical information for state updates. The innovation length is defined as... Then the multiple information vector is: in, For the first The new information of the moment, that is, . The length of the information is the number of sampling points contained in the sliding time window. To measure the dimension of a vector, This represents the current discrete time step.

[0046] The innovation sequence contains information about the difference between measured and predicted values, reflecting the dynamic characteristics and model uncertainties of the system. The construction of multiple innovation vectors allows the filtering algorithm to simultaneously consider measurement residual information at multiple time points, mining the continuity and correlation of state changes from a time series perspective, effectively suppressing random disturbances from measurement noise, and enhancing the ability to track slowly changing states. Corresponding to the multiple innovation vectors, an extended measurement matrix needs to be constructed: in, For the first The Jacobian matrix for measuring time, i.e., , The dimension is the state vector.

[0047] It is worth noting that, under the multiple innovation framework, the measurement Jacobian matrix for all historical moments is based on the current prediction state. Calculation. Although this approach introduces approximation, it can significantly reduce computational complexity while maintaining accuracy through the compensation effect of multiple innovations.

[0048] Accordingly, the measurement noise covariance matrix is ​​expanded to a block diagonal form: in, The original measurement noise covariance matrix is ​​assumed to be independent and distributed at each time step, which is consistent with the typical characteristics of vehicle sensor noise.

[0049] Next, we need to calculate the extended innovation covariance matrix and the Kalman gain matrix separately: Wherein, the Kalman gain matrix The increased dimensionality reflects the weighted fusion of multiple measurement residuals in multi-information updates.

[0050] The state correction is a linear combination of multiple innovation vectors, and the innovation at each historical time step contributes to the state update through the corresponding gain submatrix: To further ensure the stability of the values, this embodiment uses the Joseph form for updating: IV. Optimal Torque Distribution Control Method Considering Motor Torque Loss In this solution, the vehicle's yaw moment response requirements are mainly twofold: firstly, the rear-wheel differential drive torque output by the RDS requires the vehicle to generate an additional yaw moment during path tracking to ensure stability; secondly, the additional yaw moment generated by unbalanced forces due to torque loss in the wheel hub motors requires the vehicle to have the ability to eliminate or balance this additional yaw moment. Therefore, to improve the vehicle's path tracking accuracy and stability after motor torque loss, torque distribution is performed based on optimal tire adhesion utilization combined with dynamic torque tracking deviation rate.

[0051] Controlling the combined lateral and longitudinal forces of the vehicle to not exceed the tire friction circle is crucial for stability and for maximizing tire adhesion.

[0052] The peak value of the longitudinal force is limited not only by the tires but also by the motor's torque output capability. Based on the actual output capability of the hub motor, the maximum output torque of the hub motor is limited to its rated torque. Considering that the hub motor can switch to a generator for kinetic energy recovery under braking conditions, this scheme also takes braking capability into account. However, given that the efficiency of kinetic energy recovery is typically around 0.8, the lower limit of the motor torque is proportionally adjusted. Therefore, the range of longitudinal force under the limitation of the hub motor's torque output capability is: The yaw moment caused by steering and unbalanced longitudinal forces on both sides can be expressed as: The total longitudinal force on the four wheels is: To ensure dynamic performance, the desired total longitudinal force is obtained from the desired driving torque derived from the driver model: Quadratic programming is used as the optimization method for torque distribution. The standard form of quadratic programming is as follows: in, , , , They are shown below: By incorporating the dynamic torque loss rate of the hub motor into the control input, tire utilization rate, and hub motor torque output capability limits, we obtain: By rewriting the standard form of the quadratic programming in this way, the control system can complete the optimal torque distribution while taking into account the motor torque loss, thereby solving the problem of decreased path tracking accuracy and stability caused by the uncertain torque loss caused by the dynamic seal of the wheel hub motor during long-term driving.

[0053] To demonstrate the effectiveness of the path tracking control method considering the uncertain torque loss of the hub motor proposed in this scheme, this embodiment is simulated and verified under the scenario of slalom driving, vehicle speed of 80km / h, and road adhesion coefficient of 0.85. Figure 4 and Figure 5 It can be seen that the DTTER value of the left front wheel oscillates significantly compared to the right rear wheel. This is because the left front wheel, as both a drive and steering wheel, bears the steering torque, driving torque fluctuations, and tire nonlinear characteristics, resulting in a drastic dynamic response of the system. Although the estimation results for the left front wheel are relatively less stable, the estimation error is within a reasonable range and more consistent with actual losses. Compared with experimental data, the maximum estimation errors of EKF, Transformer, and MIEKF for the left front and right rear wheels are 0.24124, 0.23088, and 0.00648, and 0.02862, 0.00562, and 0.00514, respectively. Compared with Transformer, the estimation accuracy of MIEKF for the left front and right rear wheels is improved by 97.19% and 8.54%, respectively.

[0054] Furthermore, this embodiment also compares with the traditional MAPPO path tracing algorithm, from... Figures 6 to 8The comparison shows that, compared with MAPDO, the maximum path tracking error and RMSE under the proposed MADDPG control scheme are reduced by 2.40% and 5.43% respectively, a relatively small improvement. This is because MADDPG, in conjunction with AFS and RDS, sacrifices some path tracking accuracy to ensure lateral stability and safe vehicle operation. The maximum error and RMSE of yaw rate are reduced by 69.32% and 82.97% respectively, and these two indicators of sideslip angle are reduced by 46.84% and 36.98% respectively, indicating that MADDPG has better control performance. Similarly, from... Figure 9 As can be seen, the optimal torque distribution control strategy can impose higher torque output demands on the left rear wheel and right front wheel to meet path tracking and stability requirements.

[0055] In summary, this scheme utilizes rear-wheel differential steering technology to propose a path tracking control method that considers the uncertain torque loss of the hub motor. It designs a DTTER index to reflect the uncertain torque loss caused by the dynamic seal of the hub motor and establishes a vehicle dynamics model considering DTTER. A path tracking control architecture based on an improved multi-agent deep deterministic strategy gradient algorithm is proposed, which improves vehicle stability during path tracking without adding actuators through RDS. A DTTER estimation method based on MIEKF is proposed, deeply integrating the multi-innovation concept with the EKF framework. By introducing multi-time measurement information within a sliding time window, it achieves collaborative optimization and updating of the state estimate. Furthermore, torque loss is treated as a feedforward variable, taking it into account in advance during torque distribution to avoid "post-control" affecting real-time performance.

[0056] This solution effectively addresses the issues of insufficient path tracking accuracy and deteriorated yaw stability in distributed drive vehicles under the influence of uncertain torque loss disturbances caused by the dynamic seal of the hub motor, thereby improving the reliability of distributed hub drive vehicles.

Claims

1. A path tracking control method considering the uncertain torque loss of a hub motor, characterized in that, The system is based on a hierarchical control architecture, which includes an upper-level target tracking module and a lower-level torque distribution module. The upper-level target tracking module establishes a vehicle dynamics model that considers the dynamic torque tracking deviation rate (DTTER) and uses the multi-innovation extended Kalman filter (MIEKF) algorithm to obtain the DTTER estimate. On the other hand, it adopts a path tracking control strategy based on the improved multi-agent deep deterministic policy gradient (MADDPG), and uses two agents, Active Front Steering (AFS) and Rear Wheel Differential Steering (RDS), to output the front wheel steering angle and rear wheel differential torque signals, respectively. The lower-level torque distribution module obtains the optimal torque distribution signal based on the DTTER estimate and the rear wheel differential torque signal through a quadratic programming method. Combined with the front wheel steering angle signal, it controls the torque of the four wheels of the vehicle accordingly to achieve path tracking.

2. The path tracking control method considering uncertain torque loss of the hub motor according to claim 1, characterized in that, The process of establishing a vehicle dynamics model that considers DTTER includes: The dynamic torque tracking deviation rate is defined as a quantitative indicator of uncertainty to characterize the real-time uncertainty of motor torque loss, as follows: in, For the first Taiwan hub motor The actual output torque at any given moment. These correspond to the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. For the controller in Send to the first Torque command of the motor, For the first Taiwan hub motor Dynamic torque tracking deviation rate at any given time. The larger the value, the more severe the motor torque loss and the greater the uncertainty. A physical model is established to reflect the vehicle dynamics under the torque loss of the hub motors. Based on the seven-degree-of-freedom vehicle model, considering the driving torque loss of the four hub motors, the specific form of the continuous-time nonlinear state equation is as follows: in, For longitudinal vehicle speed, Lateral speed, , , , These represent the lateral forces from the ground acting on the left front, right front, left rear, and right rear wheels of the vehicle, respectively. , , , These represent the longitudinal forces from the ground acting on the left front, right front, left rear, and right rear wheels of the vehicle, respectively. and These are the distances from the center of mass to the front and rear axles, respectively. and These are the slip angles of the front and rear wheels, respectively. For the front wheel steering angle, It is half the track width between the left and right wheels. The sideslip angle is the angle of the centroid. The yaw rate is angular velocity. For the sprung mass, For vehicles to bypass Moment of inertia of the shaft, For the moment of inertia of the wheel, The angular velocity of the wheel's rotation. The effective rolling radius of the wheel, The rolling resistance torque, i.e. , The rolling resistance coefficient, For process noise, It is random noise, used to characterize the uncertainty of measurement and model.

3. The path tracking control method considering uncertain torque loss of the hub motor according to claim 2, characterized in that, The process of obtaining the DTTER estimate using the MIEKF algorithm includes: The vehicle dynamics model is discretized, and the vehicle acceleration, yaw rate, wheel speed and actual torque are used as observations to establish observation equations. The multi-innovation theory and extended Kalman filtering are fused together. Multi-time-time innovation vectors and extended measurement matrices are constructed through sliding time windows. The state prediction is completed based on numerical differentiation to calculate the Jacobian matrix, and the covariance is updated using the Joseph form. The DTTER estimates of the four wheels are output in real time.

4. The path tracking control method considering uncertain torque loss of the hub motor according to claim 3, characterized in that, The multi-time innovation vector is specifically: in, For the first The new information of the moment, that is , For the observation vector, For the nonlinear function of the observation model, This is the current predicted state. The innovation length is the number of sampling points contained in the sliding time window. To measure the dimension of a vector, This represents the current discrete time step. The extended measurement matrix is ​​specifically as follows: in, For the first The Jacobian matrix for measuring time, i.e. , The dimension is the state vector.

5. The path tracking control method considering uncertain torque loss of the hub motor according to claim 2, characterized in that, The improved MADDPG path tracking control strategy specifically employs the idea of ​​approximation fitting to construct a strategy approximation function for other agents, and obtains an approximate strategy by maximizing entropy regularization, thereby realizing indirect information interaction between the two agents AFS and RDS. Furthermore, an integrated policy structure is introduced, which allows the two agents, AFS and RDS, to each contain multiple sub-policies that are randomly selected. By maximizing the overall reward of the integrated policy, an approximate optimization result can be obtained.

6. The path tracking control method considering uncertain torque loss of the hub motor according to claim 5, characterized in that, The formula for calculating entropy regularization is: in, Let be the cost function of entropy. For the first The first agent fits the first... An approximate strategy for each agent For strategy parameters, For strategy distribution weight factors, The entropy of the policy distribution; The objective function for the integration strategy is: in, The objective function that needs to be optimized for the integration strategy is... The state distribution of the strategy, For the first Individual strategies For the first The total expected return for each agent As a discount factor, For the first An intelligent agent in The reward value at any given moment.

7. The path tracking control method considering uncertain torque loss of the hub motor according to claim 6, characterized in that, The state space of the AFS agent Action space and reward function The definition is as follows: in, These are the lateral displacement error, lateral velocity error, heading angle error, and heading angular velocity error, respectively. This is the distribution coefficient for the front wheel steering angle. , , , The weighting coefficients are used to adjust the path tracking accuracy.

8. The path tracking control method considering uncertain torque loss of the hub motor according to claim 7, characterized in that, The state space of the RDS agent Action space and reward function The definition is as follows: in, This is the distribution coefficient for the rear wheel differential torque. , , To adjust the weighting coefficients for stability, These are the yaw rate error, the centroid sideslip angle error, and the longitudinal velocity error, respectively.

9. A path tracking control method considering uncertain torque loss of a hub motor according to claim 2, characterized in that, The method of obtaining the optimal torque distribution signal through quadratic programming involves incorporating the estimated DTTER values ​​of the four wheels into the constraints of control input, tire utilization rate, and hub motor torque output capability. This rewrites the standard form of quadratic programming and then solves to obtain the optimal torque distribution signal.

10. A path tracking control method considering uncertain torque loss of a hub motor according to claim 9, characterized in that, The specific constraints on the control input, tire utilization rate, and hub motor torque output capability are as follows: in, The coefficient of friction of the tire. The vertical force on the wheel, This represents the maximum torque of the hub motor.

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