A longitudinal and vertical motion vector control method for tracked vehicles considering linear parameter time-varying model

Abstract

The application discloses a longitudinal-vertical motion vector control method of a tracked vehicle considering a linear parameter time-varying model, which firstly establishes a 6-DOF (degree of freedom) half-vehicle dynamics model considering time-varying tracked ground rigidity, tracks the nonlinear change of tracked-ground interaction in real time through a time-varying parameter correction mechanism based on the Bekker-Wong theory, and constructs a linear parameter time-varying state space equation. Secondly, a multi-objective model predictive controller is designed, a comprehensive objective function containing vertical acceleration suppression, pitch angle optimization and vehicle speed tracking is constructed, and through the rolling time domain optimization, an optimal driving torque and an active suspension force distribution strategy are solved in combination with hard constraint conditions such as suspension stroke and actuator output. Finally, through real-time data collection of sensors, time-varying tracked rigidity parameters are identified on line based on the recursive least square method, and the linear time-varying model is dynamically updated. The application realizes the comprehensive improvement of motion performance, driving comfort and stability.

Description

[0001] This invention belongs to the field of unmanned tracked vehicle control, specifically relating to a longitudinal-vertical motion vector control method for tracked vehicles that considers a time-varying model with linear parameters. Background Technology

[0002] With the transformation and upgrading of agricultural mechanization towards full-process, comprehensive, high-quality, and efficient operation, tracked vehicles are widely used in unstructured road operations due to their advantages such as low ground pressure and good climbing and obstacle-crossing performance. Traditional tracked vehicles mostly adopt independent control architectures for their longitudinal drive system and vertical suspension system: longitudinal control mainly focuses on drive torque distribution to achieve vehicle speed tracking and steering control; vertical control relies on passive suspension or simple active suspension to suppress road vibration.

[0003] However, tracked vehicles are highly nonlinear systems with multiple inputs and outputs and complex non-holonomic constraints, and they operate under complex and ever-changing field conditions, resulting in significant time-varying characteristics. Existing technologies mainly suffer from the following problems: (1) The longitudinal and vertical control systems are designed independently and lack collaborative optimization; (2) Insufficient handling of time-varying parameters such as track ground stiffness and slip ratio, resulting in poor model adaptability; (3) Insufficient real-time response capability of the control algorithm to terrain changes; (4) Failure to achieve a systematic trade-off among multiple objectives such as vehicle speed tracking, ride comfort, and driving stability. Summary of the Invention

[0004] This invention aims to provide a longitudinal-vertical motion vector control method and system for tracked vehicles that considers a time-varying model with linear parameters, solving the problems of independent longitudinal-vertical control, insufficient processing of time-varying parameters, and lack of collaborative optimization in the prior art, and achieving a comprehensive improvement in the motion performance, driving comfort, and stability of tracked vehicles in complex terrain.

[0005] This invention is implemented as follows: a longitudinal-vertical motion vector control method for tracked vehicles considering a time-varying model with linear parameters, comprising the following steps:

[0006] (1) Establish a 6-DOF half-vehicle dynamics model that considers time-varying track ground stiffness. This model coupled describes the longitudinal drive and longitudinal and vertical suspension motion characteristics of the tracked vehicle.

[0007] (2) Based on the Bekker-Wong theory, a time-varying parameter correction mechanism for track ground stiffness is constructed, and the time-varying stiffness and slip ratio parameters are integrated into the linear parameter time-varying state space equation.

[0008] (3) Design a multi-objective model predictive controller, construct a comprehensive objective function including vehicle speed tracking error term, track slip ratio control term and vertical comfort term, and set hard constraints on driving torque, active suspension force, ground pressure, suspension travel and slip ratio;

[0009] (4) Discretize the continuous-time dynamics model;

[0010] (5) The comprehensive objective function is solved by rolling time-domain optimization at each sampling time, and the optimal driving torque and active suspension force are calculated online;

[0011] (6) Based on the real-time vehicle operating status data collected by the sensors, the time-varying track stiffness parameters are identified online, and the linear parameter time-varying model is dynamically updated.

[0012] Compared with the prior art, the present invention has the following significant advantages:

[0013] 1. Longitudinal-vertical coordinated control: By integrating longitudinal drive and vertical suspension control, comprehensive optimization of motion performance is achieved, solving the coordination problem of traditional independent control architecture.

[0014] 2. Time-varying parameter adaptive control: By introducing a time-varying linear parameter model combined with an online identification mechanism, the control system can adapt to changes in terrain in real time, thereby improving its robustness under complex working conditions.

[0015] 3. Multi-objective optimization balance: By using the MPC framework to uniformly optimize vehicle speed tracking, ride comfort and driving stability, the best balance is achieved among multiple competing objectives.

[0016] 4. Superior real-time performance: The recursive least squares method and efficient QP solver are adopted to ensure the real-time performance of the control algorithm on the embedded platform (single-step solution time <10ms).

[0017] 5. Safety assurance: Through systematic hard constraint settings, the vehicle's operational safety under various working conditions is ensured, preventing actuator overload, vehicle instability and other problems. Attached Figure Description

[0018] Figure 1 is a kinematic model of the dual-motor tracked vehicle of the present invention;

[0019] Figure 2 is a vertical dynamics model of the dual-motor tracked vehicle of the present invention;

[0020] Figure 3 shows the MPC control system of the present invention;

[0021] Figure 4 is a flowchart of the overall system of the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this invention will be described in more detail below with reference to the accompanying drawings.

[0023] A longitudinal-vertical vector control method considering a time-varying model with linear parameters includes the following steps:

[0024] (1) Establish a 6-DOF half-vehicle dynamics model that considers time-varying track ground stiffness. This model coupled describes the longitudinal drive and longitudinal and vertical suspension motion characteristics of the tracked vehicle.

[0025] (2) Based on the Bekker-Wong theory, a time-varying parameter correction mechanism for track ground stiffness is constructed, and the time-varying stiffness and slip ratio parameters are integrated into the linear parameter time-varying state space equation.

[0026] (3) Design a multi-objective model predictive controller, construct a comprehensive objective function including vehicle speed tracking error term, track slip ratio control term and vertical comfort term, and set hard constraints on driving torque, active suspension force, ground pressure, suspension travel and slip ratio;

[0027] (4) Discretize the continuous-time dynamics model;

[0028] (5) The comprehensive objective function is solved by rolling time-domain optimization at each sampling time, and the optimal driving torque and active suspension force are calculated online;

[0029] (6) Based on real-time vehicle operating status data collected by sensors, the time-varying track stiffness parameters are identified online, and the linear parameter time-varying model is dynamically updated. Specifically:

[0030] Step (1): Establishing the dynamic model

[0031] A 6-DOF (DoF) half-vehicle dynamics model considering time-varying track ground stiffness was established based on a tracked vehicle. This model considers the vertical motion of the vehicle's center of gravity, pitch motion, and the vertical motion of the left and right track suspension systems. It accurately describes the coupled motion characteristics of the longitudinal drive and vertical suspension of the tracked vehicle. The model establishment process is as follows: A modified Bekker-Wong model is used to describe the mechanical relationship between the track and the ground. Track speeds are measured. longitudinal speed of tracked vehicles Calculate the track slip ratio The kinematic model of the tracked vehicle is shown in Figure (1).

[0032] Based on the ground adhesion coefficient μ, the vertical load of the track Slip ratio influence coefficient λ, track slip ratio The longitudinal driving force of the tracks is obtained. .

[0033] Considering the coupling of the longitudinal and pitch movements of the tracked vehicle, based on the overall vehicle mass... Spring load mass Vertical velocity Pitch angle The longitudinal driving force of the left and right tracks is obtained. and And the following longitudinal dynamic model is established:

[0034] (1)

[0035] The vertical motion equation of the sprung mass for the 6-DOF semi-vehicle active suspension system model is expressed as:

[0036]

[0037] (2)

[0038] In the formula, This represents the vertical displacement of the vehicle's center of gravity. , For the stiffness of the left and right suspension springs, , This is the suspension damping coefficient. , The vertical displacement of the left and right spring-loaded masses. , The vertical displacement of the unsprung mass is represented by the left and right sides. , The active suspension force is shown in Figure (2). The model of the 6-DOF semi-vehicle active suspension system is shown in Figure (2).

[0039] The equation of motion for the unsprung mass is expressed as:

[0040]

[0041] (3)

[0042] In the formula, , For left and right unsprung masses, , This is the equivalent vertical stiffness of the track ground contact section.

[0043] Based on the magnitude of the left and right suspension forces and the distance from the left and right suspension systems to the center of gravity. Calculate the torques of the left and right suspensions about the center of gravity. (i=1,2)

[0044] Torque of the center of mass:

[0045] (4)

[0046] The equation of motion for the vehicle's pitch is:

[0047] (5)

[0048] In the formula, Let y be the moment of inertia of the vehicle about the y-axis.

[0049] Step (2): Processing time-varying state parameters.

[0050] The ground stiffness of the track varies significantly with changes in vehicle load, speed, and ground conditions, exhibiting obvious time-varying characteristics. To accurately describe these time-varying characteristics, an improved time-varying parameter model is used to correct the equivalent stiffness of the track in real time.

[0051] Based on Bekker's pressure-sinking theory, the track ground stiffness can be expressed as:

[0052] (6)

[0053] In the formula, As the reference stiffness, For time-varying corrections, It is a function of slip ratio, travel speed, and vertical load.

[0054] A linear parameter time-varying model is introduced. Time-varying parameters such as track stiffness, slip ratio, and speed are expressed as functions of measurable variables, thereby transforming the nonlinear time-varying system into a linear parameter time-varying system, which facilitates subsequent controller design.

[0055] Combining the above longitudinal and vertical dynamic equations, and considering the influence of time-varying parameters, the state-space equation of the tracked vehicle can be expressed as:

[0056] (7)

[0057] In the formula, x is the state vector, and u is the control input vector. and For time-varying parameter matrices, This is a time-varying vector containing parameters such as slip ratio and velocity. To facilitate linear parameter time-varying (LTV) modeling and online controller updates, the state vector and control input are preferably selected as follows:

[0058] , ;in For the longitudinal speed of the vehicle, Let φ be the vertical displacement of the center of mass of the sprung mass, φ be the pitch angle, and z_u1 and z_u2 be the vertical displacements of the left and right unsprung masses. , The output torque of the left and right drive motors. , It is the active suspension force on both sides.

[0059] The time-varying parameter vector θ(t) includes at least the left and right slip rates of the tracks. , Vehicle speed and the equivalent vertical stiffness of the left and right track ground contact sections Time-varying parameter matrix and This is achieved by associating the system matrix elements with the aforementioned parameters: for example, in the equations for the vertical acceleration of the left and right unsprung masses. by Form of entry and The relevant state matrix elements cause the corresponding elements in matrix A to change in real time with the ground stiffness; similarly, the equivalent gain of longitudinal traction force on driving torque and the sensitivity of traction force to slip ratio change with... The changes are incorporated into the corresponding elements of matrix B and matrix A, thus forming a time-varying linear parameter model.

[0060] Step 2 Supplementary Explanation: Online Recursive Least Squares Identification and LTV Model Update

[0061] (1) Identification model construction and measurement quantity selection. To achieve adaptive effect, it is preferable to select the equivalent vertical stiffness of the left and right track ground contact sections. Online identification is performed, and the result is embedded as a time-varying parameter into formula (7). , In the middle. Online identification can construct a regression model based on the Bekker pressure-sinking relationship and the balance relationship of unsprung mass vertical force: in the left and right track contact sections, the equivalent normal force With equivalent settlement i satisfies an approximately linear relationship ≈ (i=1,2). Wherein It can be estimated from the suspension travel sensor and the actuator force sensor: , = - , . It can be estimated from vehicle attitude (IMU), suspension displacement, and geometric parameters, or directly measured by displacement sensors at the support rollers / carrier rollers. Vehicle longitudinal velocity. With left and right track slip ratio The data is obtained through the fusion of the encoder, odometer, and IMU. Considering the time-varying characteristics of ground stiffness with respect to slip ratio and velocity, further... Represented as a linear combination of measurable variables, for example: Therefore, the linear regression form can be obtained: , .

[0062] (2) Recursive Least Squares Update and θ(t) Construction. Let the sampling time be k, and the forgetting factor be λ∈(0,1], then the RLS recursion is: ; ; .Depend on get Then, construct the time-varying parameter vector in formula (7): .

[0063] (3) How time-varying parameters are embedded in A(θ(t)) and B(θ(t)). Taking the vertical subsystem as an example, the vertical dynamic equations for the left and right unsprung masses can be written as: Select the state as This yields the standard second-order form: Where M is the mass matrix and C is the damping matrix. At this point, the diagonal elements in K(θ) related to the left and right ground segments contain... Thus, in the state matrix A(θ) it corresponds to The coefficient term is reflected as and ; corresponding to The coupling terms are manifested as Etc. The above relationships ensure Changes can directly alter the corresponding elements of A(θ), enabling the model to be updated in real time according to ground conditions. For the longitudinal subsystem, the vehicle's longitudinal dynamics can be expressed as... Treating the equivalent gain of traction force on driving torque and the linearization coefficient of traction force on slip ratio as time-varying parameters, then B(θ) and Related elements As the equations change and are updated, the linearization terms in A(θ) related to slip ratio and velocity also change accordingly, thus forming a longitudinally-vertically coordinated LTV state-space model.

[0064] (4) Online update process. Within each sampling period, the following steps are executed sequentially: 1. Acquire sensor data. 2. Calculate... , and 3. Update according to the RLS above. And calculate 4. Construction And update A(θ) and B(θ). 5. Discretize according to formula (16) to obtain 6. Solve the MPC rolling optimization problem based on the updated discrete LTV model and output the results. .

[0065] Step (3): Design of a longitudinal-vertical motion vector controller based on MPC

[0066] First, the control objective is clearly defined as achieving coordinated optimization of the longitudinal and vertical motion of the tracked vehicle, which mainly includes the following aspects:

[0067] a) Longitudinal control objective: Track the desired vehicle speed to ensure vehicle power and driving efficiency.

[0068] b) Vertical control objective: Improve the driving comfort and operability of the operator by reducing the vertical displacement and acceleration of the vehicle's center of gravity.

[0069] c) Stability objective: To control the slip ratio of the tracks within a reasonable range, avoid slippage and instability, and improve the vehicle's driving stability and safety in complex terrain.

[0070] Based on the above research objectives, a comprehensive optimization function is constructed:

[0071] (8)

[0072] Vehicle speed tracking error term:

[0073] (9)

[0074] In the formula, For the predicted longitudinal velocity, For the desired speed, This is the weight matrix. Track slip ratio control term:

[0075] (10)

[0076] In the formula, , The slip ratio of the left and right tracks. The slip ratio weight matrix

[0077] Vertical comfort items:

[0078] (11)

[0079] In the formula, Let the vertical acceleration of the center of mass be , The pitch angle, , This is the comfort weight matrix.

[0080] Step (4): Set constraints

[0081] Considering the physical limitations of the drive motor and active suspension system, the drive torque is set. Active suspension Upper and lower limits:

[0082]

[0083] (12)

[0084] In the formula, These are the upper and lower limits of the driving torque. These are the upper and lower limits of the active suspension force.

[0085] Secondly, to ensure the safety of tracked vehicles during operation, track ground pressure constraints are set. Suspension system travel constraints and track slip ratio constraints

[0086] Track ground pressure constraint:

[0087] (13)

[0088] In the formula, For track ground pressure, , Within the permissible ground pressure range, avoid causing excessive damage to the ground or causing vehicles to sink.

[0089] Suspension system travel constraints:

[0090] (i=1,2)(14)

[0091] In the formula, This is the maximum permissible travel of the suspension system to prevent overloading.

[0092] Track slip ratio constraint:

[0093] In equation (i=1,2)(15), , To maintain a reasonable slip ratio and avoid excessive track slippage or lockup.

[0094] Step (5): Discretize the model

[0095] To achieve model predictive control, the continuous-time dynamics model of the tracked vehicle is first discretized. Here, the zero-order hold method is used to transform the continuous state-space equations into a discrete form:

[0096] (16)

[0097] In the formula, and These are the discretized state matrix and input matrix.

[0098] Step (6): Rolling optimization and online solution

[0099] Solve the finite-time optimization problem at each sampling time: The optimal active suspension force is calculated online using a quadratic programming algorithm. and driving torque .

[0100] Furthermore, based on the vehicle's operating status, time-varying parameters such as track stiffness are estimated online and updated into the LTV model, improving the controller's adaptability to terrain changes.

[0101] In a preferred embodiment, a multibody dynamics model of the RecurDyn tracked vehicle is established, including track-ground contact, track roller and suspension geometry. The online RLS identification and MPC controller of this invention are implemented in MATLAB / Simulink, and closed-loop verification is performed through a co-simulation interface. Typical rugged road surfaces and different adhesion and soil hardness variations are selected, and the vehicle is tested at the same desired speed. The following compares two control strategies:

[0102] 1. Fixed parameter model integrates conventional MPC, without online identification or updating LTV model.

[0103] 2. The method of this invention (online identification) The simulation or experimental statistical indicators (including updating the LTV model) include: vehicle speed tracking error, root mean square value of vehicle vertical acceleration, peak or root mean square value of pitch angle, track slip ratio exceeding limit rate, and suspension travel utilization rate. The results show that when ground stiffness and adhesion coefficient change, this invention can maintain consistency between model parameters and actual working conditions through online identification, thereby significantly suppressing vehicle speed tracking error, vehicle vertical vibration, and pitch response. Furthermore, the slip ratio is more easily constrained within the set range, verifying the technical effectiveness of this invention.

[0104] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make several improvements without departing from the principles of the present invention, and these improvements should also be considered within the scope of protection of the present invention.

Claims

1. A method for longitudinal-vertical motion vector control of a tracked vehicle considering a time-varying model with linear parameters, characterized in that, Includes the following steps: (1) Establish a 6-DOF half-vehicle dynamics model that considers time-varying track ground stiffness. This model coupled describes the longitudinal drive and longitudinal and vertical suspension motion characteristics of the tracked vehicle. (2) Based on the Bekker-Wong theory, a time-varying parameter correction mechanism for track ground stiffness is constructed, and the time-varying stiffness and slip ratio parameters are integrated into the linear parameter time-varying state space equation. (3) Design a multi-objective model predictive controller, construct a comprehensive objective function including vehicle speed tracking error term, track slip ratio control term and vertical comfort term, and set hard constraints on driving torque, active suspension force, ground pressure, suspension travel and slip ratio; (4) Discretize the continuous-time dynamics model; (5) The comprehensive objective function is solved by rolling time-domain optimization at each sampling time, and the optimal driving torque and active suspension force are calculated online; (6) Based on the real-time vehicle operating status data collected by the sensors, the time-varying track stiffness parameters are identified online, and the linear parameter time-varying model is dynamically updated.

2. The method according to claim 1, characterized in that, In step (1), a 6-DOF half-vehicle dynamics model considering time-varying track ground stiffness is established to accurately describe the coupled motion characteristics of the longitudinal drive and vertical suspension of the tracked vehicle. The model establishment process is as follows: Measure track speed longitudinal speed of tracked vehicles Calculate the track slip ratio : Track slip ratio is defined as: （1） Based on the ground adhesion coefficient μ, the vertical load of the track Slip ratio influence coefficient λ, track slip ratio The longitudinal driving force of the tracks is obtained. : （2） Considering the coupling of the longitudinal and pitch movements of the tracked vehicle, based on the overall vehicle mass... Spring load mass Vertical velocity Pitch angle This yields the longitudinal driving force of the left and right tracks. and And the following longitudinal dynamic model is established: （3） The equation of motion for the sprung mass can be expressed as: （4） In the formula, This represents the vertical displacement of the vehicle's center of gravity. , For the stiffness of the left and right suspension springs, , This is the suspension damping coefficient. , The vertical displacement of the left and right spring-loaded masses. , The vertical displacement of the unsprung mass is represented by the left and right sides. , For active suspension force; The equation of motion for the unsprung mass is: （5） In the formula, , For left and right unsprung masses, , The equivalent vertical stiffness of the track ground contact section; Based on the magnitude of the left and right suspension forces and the distance from the left and right suspension systems to the center of gravity. Calculate the torques of the left and right suspensions about the center of gravity. (i=1,2) Torque of the center of mass: （6） The equation of motion for the vehicle's pitch is: （7） In the formula, Let be the moment of inertia of the vehicle about the y-axis.

3. The method according to claim 1, characterized in that: In step (2), based on Bekker's pressure-sinking theory, the track ground stiffness is expressed as: （8） In the formula, As the reference stiffness, For time-varying corrections, It is a function of slip ratio, travel speed, and vertical load; The state-space equation of a tracked vehicle can be expressed as: （9） In the formula, x is the state vector, and u is the control input vector. and For time-varying parameter matrices, It is a time-varying vector containing slip ratio and velocity.

4. The method according to claim 1, characterized in that: In step (3), the design of the multi-objective model predictive controller specifically involves: firstly, clarifying that the control objective is to achieve coordinated optimization of the longitudinal and vertical motion of the tracked vehicle, including the following aspects: a) Longitudinal control objective: Track the desired vehicle speed to ensure vehicle power and driving efficiency; b) Vertical control objective: Improve the driving comfort and operability of the operator by reducing the vertical displacement and acceleration of the vehicle's center of gravity; c) Stability objective: To control the slip ratio of the tracks within a reasonable range, avoid slippage and instability, and improve the vehicle's driving stability and safety in complex terrain; Based on the above research objectives, a comprehensive optimization function is constructed: （10） Vehicle speed tracking error term: （11） In the formula, For the predicted longitudinal velocity, For the desired speed, This is the weight matrix; Track slip ratio control item: （12） In the formula, , The slip ratio of the left and right tracks. This is the slip ratio weight matrix; Vertical comfort items: （13） In the formula, Let the vertical acceleration of the center of mass be , The pitch angle, , This is a comfort weighting matrix used to reduce the vehicle's vertical vibration and pitch motion.

5. The method according to claim 1, characterized in that: In step (3), the hard constraint condition is set as follows: considering the physical limitations of the drive motor and the active suspension system, the drive torque is set. Active suspension Upper and lower limits: （14） In the formula, These are the upper and lower limits of the driving torque. This refers to the upper and lower limits of the active suspension force. Secondly, to ensure the safety of tracked vehicles during operation, track ground pressure constraints are set. Suspension system travel constraints and track slip ratio constraints , Track ground pressure constraint: （15） In the formula, For track ground pressure, , Within the permissible ground pressure range, to avoid excessive damage to the ground or causing the vehicle to sink; Suspension system travel constraints: （i=1,2）（16） In the formula, This is the maximum permissible travel of the suspension system to prevent overloading. Track slip ratio constraint: (i=1,2)（17） In the formula, , To maintain a reasonable slip ratio and avoid excessive track slippage or lockup.

6. The method according to claim 1, characterized in that: Step (4) is as follows: First, the continuous-time dynamics model of the tracked vehicle should be discretized. Here, the zero-order hold method is used to transform the continuous state-space equations into a discrete form: （18） In the formula, and These are the discretized state matrix and input matrix.

7. The method according to claim 1, characterized in that: The specific steps of step (6) are as follows: Solve the finite-time optimization problem at each sampling time: The optimal active suspension force is calculated online using a quadratic programming algorithm. and driving torque ; Furthermore, based on the vehicle's operating status, time-varying parameters such as track stiffness are estimated online and updated into the LTV model, improving the controller's adaptability to terrain changes.

8. The method according to claim 1, characterized in that, It also includes the following steps: finally, data is collected in real time through sensors, time-varying track stiffness parameters are identified online, the linear time-varying model is dynamically updated, and the control algorithm is made to respond to terrain changes in real time.

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