An articulated vehicle design optimization method and device that cooperates optimal design and optimal control

Abstract

The application discloses a kind of articulated vehicle design optimization method and device of optimal design and optimal control cooperation, it is related to vehicle design optimization technical field, the method comprises: first, based on the construction of articulated vehicle multiple degree-of-freedom dynamics model obtained from Lagrange dynamics theory, then determine residual error constraint, and according to driving cycle and articulated vehicle each subsystem operating boundary boundary constraint is established, subsequently design parameter and control parameter are simultaneously as optimization variable, and construct multi-objective collaborative optimization problem;Finally, multi-objective collaborative optimization problem is converted into nonlinear optimization problem, and problem solving is carried out using solver, and optimal control parameter set and optimal design parameter set are obtained, for the development of articulated vehicle and the development of its control algorithm.The application constructs an optimal design and optimal control cooperative problem for articulated vehicle, can realize the simultaneous optimization of design parameter and control parameter based on articulated vehicle multiple degree-of-freedom dynamics model.

Description

Technical Field

[0001] This application relates to the field of vehicle design optimization technology, and in particular to an articulated vehicle design optimization method and apparatus that combines optimal design and optimal control. Background Technology

[0002] Articulated vehicles, with their unique design and functionality, have demonstrated significant advantages in the transportation sector. Firstly, they possess a powerful carrying capacity, capable of transporting large quantities of goods, thus significantly improving transportation efficiency. Secondly, the flexible interchangeability of trailers makes them suitable for various transportation scenarios, from long-distance logistics to urban delivery, enhancing adaptability and flexibility. Furthermore, the high transportation efficiency of articulated vehicles not only reduces transportation time but also lowers overall costs, enabling companies to maintain a competitive edge in a highly competitive market. Moreover, their energy-saving and emission-reduction effects are significant, aligning with modern society's demands for environmental protection and sustainable development. Therefore, articulated vehicles have a significant advantage in improving the overall economic benefits of road transportation and are widely used in trunk logistics, port hubs, and large logistics centers.

[0003] Due to rapid technological advancements and evolving market demands in the automotive industry, manufacturers are continuously investing in research and development and introducing new technologies to meet consumers' ever-increasing demands for performance, safety, and environmental friendliness. Simultaneously, intense market competition forces manufacturers to accelerate product updates to maintain competitiveness. These factors collectively drive the rapid evolution of articulated vehicles. Therefore, new R&D processes are needed to shorten production cycles in platform connectivity and software.

[0004] Traditional new vehicle development typically employs an experience-based design-testing approach. However, articulated vehicle structures are extremely complex, and during the design process, it's often impossible to determine whether local and overall strength meet design requirements. Improvements can only be achieved through repeated testing, resulting in lengthy design cycles and high prototyping costs, making it difficult to adapt to market demands. Furthermore, traditional vehicle development methods calculate design parameters based on requirements, optimize parameters using static models, and then perform control optimizations for specific operating conditions. This leads to limited optimization space, poor dynamic performance, and the independent design of each subsystem, restricting overall vehicle performance. Therefore, to improve the development efficiency and quality of articulated vehicles, it is necessary to develop more advanced simulation-based vehicle optimization methods to shorten development cycles and reduce costs. Summary of the Invention

[0005] The purpose of this application is to provide a design optimization method and apparatus for articulated vehicles that combines optimal design and optimal control, which can simultaneously optimize the design parameters and control parameters of articulated vehicles based on a multi-degree-of-freedom dynamic model of the vehicle.

[0006] To achieve the above objectives, this application provides the following solution:

[0007] In a first aspect, this application provides a method for optimizing the design of articulated vehicles through collaborative optimal design and optimal control, comprising the following steps:

[0008] A multi-degree-of-freedom dynamic model of the articulated vehicle was constructed based on Lagrange dynamics theory.

[0009] The residual constraints are determined based on the multi-degree-of-freedom dynamic model, and the boundary constraints are established based on the driving conditions and the working boundaries of each subsystem of the articulated vehicle.

[0010] The design parameters and control parameters are used as optimization variables simultaneously, and a multi-objective collaborative optimization problem is constructed based on residual constraints, boundary constraints, and optimization variables.

[0011] The multi-objective collaborative optimization problem is transformed into a nonlinear optimization problem, and a nonlinear optimization problem solver is used to solve the problem, obtaining the optimal control parameter set and the optimal design parameter set. The optimal control parameter set is used for the development of articulated vehicle control algorithms, and the optimal design parameter set is used for the development of articulated vehicles.

[0012] Secondly, this application provides an articulated vehicle design optimization device for collaborative optimal design and optimal control, comprising the following modules:

[0013] The dynamics model construction module is used to construct a multi-degree-of-freedom dynamics model of an articulated vehicle based on Lagrange dynamics theory.

[0014] The relevant constraint establishment module is used to determine residual constraints based on the multi-degree-of-freedom dynamic model and to establish boundary constraints based on the driving conditions and the working boundaries of each subsystem of the articulated vehicle.

[0015] The multi-objective optimization problem construction module is used to construct a multi-objective collaborative optimization problem by simultaneously using design parameters and control parameters as optimization variables, and based on residual constraints, boundary constraints and optimization variables.

[0016] The problem transformation and NLP solving module is used to transform multi-objective collaborative optimization problems into nonlinear optimization problems, and to solve the problems using a nonlinear optimization problem solver to obtain the optimal control parameter set and the optimal design parameter set. The optimal control parameter set is used for the development of articulated vehicle control algorithms, and the optimal design parameter set is used for the development of articulated vehicles.

[0017] According to the specific embodiments provided in this application, the following technical effects are disclosed:

[0018] This application provides a method and apparatus for designing and optimizing articulated vehicles through coordinated optimal design and control. The method first constructs a multi-degree-of-freedom dynamic model of the articulated vehicle based on Lagrange dynamics theory. Then, residual constraints are determined based on the multi-degree-of-freedom dynamic model, and boundary constraints are established according to driving conditions and the working boundaries of each subsystem of the articulated vehicle. Subsequently, design parameters and control parameters are simultaneously used as optimization variables, and a multi-objective coordinated optimization problem is constructed based on residual constraints, boundary constraints, and optimization variables. Finally, the multi-objective coordinated optimization problem is transformed into a nonlinear optimization problem, and a nonlinear optimization problem solver is used to solve the problem, obtaining the optimal control parameter set and the optimal design parameter set. This can be used for the development of articulated vehicles and their control algorithms. This application constructs a coordinated optimal design and optimal control problem for articulated vehicles, enabling the simultaneous optimization of design and control parameters based on the multi-degree-of-freedom dynamic model of the articulated vehicle. The optimal design parameters can be used for vehicle design, and the optimal control parameters can serve as a reference for subsequent online control strategy formulation. The scheme of this application can apply gradient information to expand the optimization space and has good optimization performance. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating a collaborative optimal design and optimal control method for articulated vehicle design optimization, provided as an embodiment of this application.

[0021] Figure 2 A detailed flowchart of step S4 in an articulated vehicle design optimization method for collaborative optimal design and optimal control provided in an embodiment of this application.

[0022] Figure 3 This is a schematic diagram of the functional modules of an articulated vehicle design optimization device for collaborative optimal design and optimal control, provided in an embodiment of this application.

[0023] Figure 4 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0024] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0025] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0026] In one exemplary embodiment, such as Figure 1 As shown, a design optimization method for articulated vehicles that combines optimal design and optimal control is provided, including the following steps:

[0027] S1. A multi-degree-of-freedom dynamic model of the articulated vehicle is constructed based on Lagrange dynamics theory. In this embodiment, the multi-degree-of-freedom dynamic model of the articulated vehicle can be expressed by the following equation:

[0028]

[0029] Among them, T t Q represents the kinetic energy of the tractor unit. t,b Q represents the generalized force acting on the sprung mass of the tractor unit. t,u q represents the generalized force acting on the unsprung mass of the tractor unit. t,b The generalized coordinate q represents the sprung mass of the tractor. t,u The generalized coordinate T represents the unsprung mass of the tractor. s Q represents the kinetic energy of the trailer. s,b Q represents the generalized force acting on the sprung mass of the trailer. s,u q represents the generalized force acting on the unsprung mass of the trailer. s,b The generalized coordinate q represents the sprung mass of the trailer. s,u The generalized coordinates represent the unsprung mass of the trailer, and the point signs on the parameters are the derivative symbols.

[0030]

[0031] Among them, M t,u and J t,u These are the mass matrix and moment of inertia matrix of the unsprung mass of the tractor, M. t,b and J t,b These are the mass matrix and moment of inertia matrix of the sprung mass of the tractor, M. s,u and J s,u These are the mass matrix and moment of inertia matrix of the unsprung mass of the trailer, M. s,b and J s,bThese are the mass matrix and moment of inertia matrix of the trailer's sprung mass, respectively.

[0032] Kinetic energy T of the tractor t This includes the kinetic energy of the sprung mass and the unsprung mass of the tractor unit; and the kinetic energy T of the trailer. s This includes the kinetic energy of the trailer's sprung mass and the kinetic energy of the trailer's unsprung mass.

[0033] The kinetic energy of the sprung mass of the tractor unit can be expressed by the following formula:

[0034]

[0035] Among them, T t,b V is the kinetic energy of the sprung mass of the tractor. t,b V is the generalized velocity of the tractor vehicle. t,u,i M represents the component of the unsprung mass velocity of the tractor in the vehicle coordinate system. t,u,i Let h be the mass matrix of the unsprung mass of the tractor. A,b with h b,u,i M is the transformation matrix corresponding to the sprung mass and the unsprung mass. gb To assemble the generalized mass matrix.

[0036] The kinetic energy of the unsprung mass of the tractor unit can be expressed by the following formula:

[0037]

[0038] Among them, T t,u V is the kinetic energy of the unsprung mass of the tractor. t,uz Let ω be the vertical velocity of the unsprung mass of the tractor. t,u J is the rotational angular velocity of the unsprung mass of the tractor. t,u Let be the moment of inertia matrix of the unsprung mass of the tractor.

[0039] The calculation methods for the kinetic energy of the trailer's sprung mass and unsprung mass are similar to those for the tractor's sprung mass and unsprung mass, and will not be repeated here.

[0040] Specifically, in this embodiment, the generalized forces acting on the sprung mass of the tractor, the unsprung mass of the tractor, the sprung mass of the trailer, and the unsprung mass of the trailer can be obtained through the principle of virtual work:

[0041]

[0042] Where F is the total generalized force matrix, r t,b F represents the virtual displacement of the sprung mass of the tractor. t,b Let r be the generalized force matrix acting on the sprung mass of the tractor.t,u F represents the virtual displacement of the unsprung mass of the tractor. t,u Let r be the generalized force matrix acting on the unsprung mass of the tractor. s,b F represents the virtual displacement of the trailer's sprung mass. s,b r is the generalized force matrix acting on the sprung mass of the trailer. s,u F represents the virtual displacement of the unsprung mass of the trailer. s,u The generalized force matrix is ​​the matrix of forces acting on the unsprung mass of the trailer.

[0043] Specifically, in this embodiment, the generalized force matrix of the sprung mass of the tractor is shown in the following equation:

[0044]

[0045] Among them, F t,x,i Let δ be the longitudinal force at the contact point between the i-th tire of the tractor and the ground. t,i For the steering angle input of the i-th tire of the tractor, F t,y,i Let ψ be the lateral force at the point of contact between the i-th tire of the tractor and the ground. t F is the yaw angle of the tractor unit. t,wx F is the longitudinal component of aerodynamic drag. hitch,x For longitudinal hinge force, F t,wy F is the lateral component of aerodynamic drag. hitch,y For the lateral hinge force, F t,bs,i F is the suspension force acting on the i-th tire of the tractor. t,wz The downforce of aerodynamic drag, m t,b Let g be the sprung mass of the tractor, g be the acceleration due to gravity, and F be the speed of motion. hitch,z For vertical hinge force, y t,u,i Let Z be the lateral coordinate of the suspension mounting point in the vehicle coordinate system. t T is the height of the sprung mass center of the tractor. t,d,i M is the torque input for the i-th tire of the tractor. t,wx M is the component of the aerodynamic drag torque about the x-axis. hitch,x Let x be the hinge torque about the x-axis. t,u,i M represents the longitudinal coordinate of the suspension mounting point in the vehicle coordinate system. t,wy M is the component of the aerodynamic drag torque about the y-axis. hitch,y M is the hinge torque about the y-axis. t,z,i Let x be the restoring torque at the contact point between the i-th tire of the tractor and the ground. t,w,i Let y be the longitudinal coordinate of the tire center in the vehicle coordinate system. t,w,i M is the lateral coordinate of the tire center in the vehicle coordinate system. t,wz M is the component of the aerodynamic drag torque about the z-axis. hitch,z The hinge torque is about the z-axis.

[0046] The generalized force matrix of the unsprung mass of the tractor is shown in the following equation:

[0047]

[0048] Among them, T t,d,fr M is the torque input for the right front tire of the tractor. t,y,fr F is the rolling resistance torque of the right front tire of the tractor. t,x,fr z is the longitudinal force at the contact point between the right front tire of the tractor and the ground. t,u,fr T is the center height of the right front tire of the tractor. t,d,rr M is the torque input for the right rear tire of the tractor. t,y,rr F is the rolling resistance torque of the right rear tire of the tractor. t,x,rr z is the longitudinal force at the contact point between the right rear tire of the tractor and the ground. t,u,rr F is the center height of the right rear tire of the tractor. t,z,fr F is the vertical force acting on the right front tire of the tractor. t,bs,fr The suspension force acting on the right front tire of the tractor unit, m t,u,fr For the mass of the right front tire of the tractor, F t,z,rr F is the vertical force acting on the right rear tire of the tractor. t,bs,rr The suspension force acting on the right rear tire of the tractor unit, m t,u,rr Let g be the mass of the right rear tire of the tractor, and g be the acceleration due to gravity.

[0049] S2. Determine residual constraints based on the multi-degree-of-freedom dynamic model, and establish boundary constraints based on driving conditions and the working boundaries of each subsystem of the articulated vehicle.

[0050] S3. Using both design parameters and control parameters as optimization variables, and based on residual constraints, boundary constraints, and optimization variables, construct a multi-objective collaborative optimization problem. In this embodiment, the constructed multi-objective collaborative optimization problem is shown in the following equation:

[0051]

[0052] Where J is the objective function value; t f t0 is the terminal time, t0 is the start time, and J is the terminal time. p The penalty function is used to constrain acceleration and braking to not be performed simultaneously; w is the weighting factor of the penalty function; f[] is the multi-degree-of-freedom dynamic model; and x is the set of state parameters. min and x max The upper and lower bounds of the state parameters; u is the set of control parameters, u min and u max The upper and lower bounds of the state parameters; t is the time step, p is the design parameter set, p min and p maxThe upper and lower bounds of the state parameters are defined by g[], which represents the path constraint function. min and g max b[] represents the upper and lower bounds of the path constraint function; b[] represents the boundary constraint function. min and b max These are the upper and lower bounds of the boundary constraint function.

[0053] S4. The multi-objective collaborative optimization problem is transformed into a nonlinear optimization problem, and a nonlinear optimization problem solver is used to solve the problem, obtaining the optimal control parameter set and the optimal design parameter set. The optimal control parameter set is used for the development of articulated vehicle control algorithms, and the optimal design parameter set is used for the development of articulated vehicles. In an exemplary embodiment, any one of the following methods—local collocation, finite difference, or autoscaling—is used to transform the multi-objective collaborative optimization problem into a nonlinear optimization problem.

[0054] In this embodiment, as Figure 2 The flowchart shown includes the following steps in step S4:

[0055] S41. Perform linear interpolation on the state parameters and control parameters respectively to obtain the state parameters and control parameters at each interpolation time, so as to reconstruct the optimization variables and obtain the reconstructed optimization variables; the interpolation time includes the start time, the end time, and several intermediate times between the start time and the end time; the reconstructed optimization variables include the design parameters and the state parameters and control parameters at each interpolation time.

[0056] S42. Calculate the gradient of the objective function with respect to the reconstructed optimization variables.

[0057] S43. Based on the reconstructed optimization variables, the residual constraints, boundary constraints, and path constraints are reconstructed respectively to obtain the reconstructed residual constraints, reconstructed path constraints, and reconstructed boundary constraints.

[0058] S44. Calculate the first Jacobian matrix of the reconstructed residual constraints, the second Jacobian matrix of the reconstructed path constraints, and the third Jacobian matrix of the reconstructed boundary constraints, respectively.

[0059] S45. Based on the above results, call the nonlinear programming solver to solve the problem and obtain the optimal control parameter set and the optimal design parameter set. Using the reconstructed optimization variables, objective function, gradient of the objective function with respect to the reconstructed optimization variables, reconstructed residual constraints, reconstructed path constraints, reconstructed boundary constraints, the first Jacobian matrix, the second Jacobian matrix, and the third Jacobian matrix as input, use the nonlinear programming solver to solve the problem and obtain the optimal control parameter set and the optimal design parameter set.

[0060] To better understand the articulated vehicle design optimization method based on collaborative optimal design and optimal control proposed in the above embodiments of this application, the following example uses an articulated commercial vehicle with a configuration of a three-axle rear-wheel drive tractor and a three-axle trailer to illustrate the application of the above-mentioned articulated vehicle design optimization method based on collaborative optimal design and optimal control, including the following steps:

[0061] Step 1: Construction of a multi-degree-of-freedom vehicle dynamics model.

[0062] The inputs for the articulated commercial vehicle model are the steering wheel angle and the driving or braking torque of each wheel. Tire rotation is driven by wheel torque and longitudinal ground forces. The tire model module's inputs are the wheel rotational angular velocity and wheel center velocity, and its outputs are tire forces and torques. The vertical motion of the unsprung mass is generated by the tire vertical force and suspension force. The articulation point is equivalent to a spring-damped system, and the articulation force is calculated based on the motion of the tractor and trailer. The motion of the vehicle body is determined by the combined effects of longitudinal and lateral tire forces, aerodynamic forces, suspension forces, and articulation forces. To improve computational efficiency, a vectorized programming method is used to establish a vehicle dynamics model that supports vectorized calculations.

[0063] A multi-degree-of-freedom vehicle model is used to represent the dynamic behavior of a simplified vehicle composed of multiple rigid components. The tractor and trailer bodies have longitudinal, lateral, and vertical movement, as well as rotation about the x, y, and z axes. The 12 wheels have 12 rotational degrees of freedom, and due to the suspension system, the 12 wheels also have 12 vertical degrees of freedom. This totals 36 degrees of freedom.

[0064] In the modeling process, O-xyz represents the geodetic coordinate system, O1-x1y1z1 represents the tractor body coordinate system, and O2-x2y2z2 represents the trailer body coordinate system. The multi-degree-of-freedom generalized coordinates are represented by vectors as follows:

[0065]

[0066] Where q represents the generalized coordinates of the vehicle model; the subscript t represents the tractor unit, and the subscript s represents the trailer unit. bv The vector representing the position of the vehicle's center of mass, where X, Y, and Z are the absolute displacements of the center of mass along the global coordinate system; q bω This indicates the angle of rotation of the vehicle's center of gravity. φ and ψ are the rotation angles of the vehicle body about the three axes of the global coordinate system; q uθ θ represents the sequence of angular velocities generated by the rotational motion of the six tires on both sides. i q represents the angular velocity of the tire rotation. uz This represents the vertical displacement sequence of the six tires on both sides, z. iThis indicates the vertical displacement of the tires; the six tires are distinguished by subscripts: u,fr represents the right front tire of the first axle, u,fl represents the left front tire of the first axle, u,mr represents the right middle tire of the second axle, u,ml represents the left middle tire of the second axle, u,rr represents the right rear tire of the third axle, and u,rl represents the left rear tire of the third axle.

[0067] The coordinates of the six tire centers of the tractor in the x1-y1 plane within the tractor's body coordinate system are shown in the following formula:

[0068]

[0069] Among them, l t w represents the longitudinal distance between the three axles of the tractor and its center of gravity. t This indicates the wheelbase of the three axles, with the subscript f representing the first axle, m representing the second axle, and r representing the third axle.

[0070] Accordingly, the coordinates of the six tire centers of the trailer in the x2-y2 plane within the trailer's body coordinate system are as follows:

[0071]

[0072] Unsprung mass, i.e., the relative vertical position of the tire in the vehicle coordinate system, can be represented by its absolute coordinates, vehicle roll angle, pitch angle, and xy coordinates in the vehicle coordinate system, as shown in the following formula:

[0073]

[0074] The 36-DOF dynamic equations of the vehicle are derived based on Lagrange dynamics, as shown in the following equation:

[0075]

[0076] Among them, T t T represents the kinetic energy of the tractor unit. s Q represents the kinetic energy of the trailer. t,b Q represents the generalized force acting on the sprung mass of the tractor unit. t,u q represents the generalized force acting on the unsprung mass of the tractor unit. t,b The generalized coordinate q represents the sprung mass of the tractor. t,u The generalized coordinate system representing the six tires of the tractor unit, i.e., the unsprung mass, includes tire rotation angles and vertical positions; Q s,b Q represents the generalized force acting on the sprung mass of the trailer. s,u q represents the generalized force acting on the unsprung mass of the trailer. s,b The generalized coordinate q represents the sprung mass of the trailer. s,uA generalized coordinate system representing the unsprung mass of the trailer's six tires, including tire rotation angle and vertical position.

[0077] The calculation process of kinetic energy is introduced by taking the tractor unit in an articulated vehicle as an example. The calculation of kinetic energy of the trailer is exactly the same, so it will not be repeated here.

[0078] When calculating the kinetic energy of the sprung mass, the kinetic energy of the tire's lateral and longitudinal motion is considered, as shown in the following formula:

[0079]

[0080] Among them, V t,b V t,ui These are the components of the generalized velocity of the tractor body and the unsprung mass velocity in the vehicle body coordinate system, M. t,b M t,ui Let be the mass matrices of the tractor body and the unsprung mass, respectively. Through coordinate transformation and matrix calculation, the kinetic energy of the sprung mass can be expressed as follows:

[0081]

[0082] The kinetic energy of the unsprung mass consists of the rotation and vertical motion of the tire, as shown in the following equation:

[0083]

[0084] Among them, V t,uz ω t,u The vertical velocity and angular velocity of the six unsprung tires are M, respectively. t,u J t,u Let these be the mass matrix and moment of inertia matrix of the unsprung mass, respectively. Based on matrix calculations, the above equation can be transformed into the form of generalized coordinates and a generalized mass matrix:

[0085]

[0086] In addition, the vertical forces acting on the sprung mass (vehicle body) include vehicle weight, suspension forces, vertical air resistance, and vertical articulation forces. The longitudinal forces include the lateral forces generated between the tires and the ground, the components of the longitudinal forces and air resistance in the global coordinate system, and the longitudinal articulation forces. The lateral forces include the components of the lateral and longitudinal forces acting on the tires from the ground, and the lateral articulation forces. The triaxial torques include the torques of the above forces about the center of mass, the tire self-aligning torque, the air resistance torque, the reaction torque of the driving tires, and the torque at the articulation points.

[0087] The vertical force acting on a tire consists of the tire's own weight and the suspension force, as shown in the following formula:

[0088] F t,z,i =F t,bs,i +mt,u,i g.

[0089] The longitudinal slip ratio at the tire-ground contact point is calculated using the following formula:

[0090]

[0091] The tire magic formula is used to calculate the tire's longitudinal force, lateral force, self-aligning torque, rolling resistance torque, and yaw resistance torque.

[0092] Suspension force consists of spring force and damping force. When the stiffness and damping ratio are constant, the suspension force can be expressed as follows:

[0093]

[0094] The calculation of air resistance begins with calculating the air resistance sideslip angle. Assuming the air is still and the wind speed is 0, the air resistance sideslip angle is the same as the vehicle's center of gravity sideslip angle. Then, based on the air resistance sideslip angle, the air resistance coefficient is calculated using linear interpolation and cubic spline interpolation. Finally, the air resistance factor is calculated using the following formula:

[0095]

[0096] Air resistance can be calculated based on the air resistance factor.

[0097] Based on the above calculations of tire forces and suspension model, the generalized force matrix of the sprung mass of the tractor is shown in the following equation:

[0098]

[0099] The forces acting on the unsprung mass of the tractor unit include suspension forces, vertical ground forces, and the weight of the tires themselves; the torques acting on it include driving torque and tire rolling resistance torque. Its generalized force matrix is ​​expressed as follows:

[0100]

[0101] Similarly, the generalized force matrix for the sprung and unsprung masses of the trailer can be derived. Based on force analysis and the principle of virtual work, the generalized forces can be derived as shown in the following equations:

[0102]

[0103] According to Lagrange's mechanics and d'Alembert's principle, the generalized equation of motion for the sprung mass of the tractor is as follows:

[0104]

[0105] The generalized equation of motion for the unsprung mass of the tractor is shown below:

[0106]

[0107] The generalized equation of motion for the sprung mass of the trailer is shown below:

[0108]

[0109] The generalized equation of motion for the unsprung mass of the trailer is shown below:

[0110]

[0111] The second-order differentials of all state variables can be obtained from the above generalized equations of motion, which can be transformed into residual constraints as the basis for constructing the subsequent optimal control problem.

[0112] Step 2: Construct a multi-objective collaborative optimization problem for collaborative optimal design and optimal control.

[0113] This section requires defining the objective function, upper and lower bounds of constraints, and guessing initial values. It also requires setting some optimization-related parameters, such as the transformation method m. trans Differential method m diff , allocation point number N n , scaling settings (scal), plot parameters to be plotted during iteration, and weights (w) of the control parameters to be smoothed. u wait.

[0114] Based on the vehicle dynamics model established in step 1, provide the inputs to the problem, including the initial guesses of the state variables x0, the initial guesses of the control variables u0, and the terminal time t. f0 And design variable p0.

[0115]

[0116] Where N x,usr It is the number of nodes for the user-provided state variables, where t is the number of nodes from 0 to t. f Discretized into N x,usr Time series of N points u,usr It is the number of nodes for the user-provided control variables, n. x n is the number of state variables in the dynamic equation. u This refers to the number of control variables. If the terminal time is also a parameter to be optimized, then n... tf It is 1, otherwise it is 0, n p It refers to the number of design parameters. Let represent a two-dimensional matrix with i rows and j columns. For the global transformation method, the initial values ​​of the start and end times for each stage will be generated by the optimal control framework.

[0117] The upper and lower bounds of the state variables, control variables, terminal time, and design variables, as well as the inequality constraint g, are given by the following formula:

[0118]

[0119] Where, n g This represents the number of path constraints. In addition to the initial values ​​and upper and lower bound constraints mentioned above, the problem input also includes the Lagrange term of the cost function. Meyer First-order dynamic constraint function f, path constraint function g, boundary constraint function b.

[0120] Step 3: Perform nonlinear transformation and solution of the multi-objective collaborative optimization problem.

[0121] Before solving the problem, it needs to be transformed into a large-scale NLP problem, and then the underlying NLP solver is called to solve the problem.

[0122] In the problem transformation section, the format of variables and functions in the problem input is converted into the format required by the NLP solver. In this embodiment, local collocation methods, difference methods, and scaling methods are developed for this part.

[0123] Step 3.1: Local point allocation method.

[0124] Step 3.1.1: NLP solver variables.

[0125] In the local collocation method, the continuous state and control variables over the entire time interval can be discretized into N using linear interpolation. n The new variables obtained from the given nodes are given by the following formula:

[0126]

[0127] Where x0 represents the initial guess value of the state variable, u0 represents the initial guess value of the control variable, and t f0 p0 represents the initial guess of the terminal time, and N represents the initial guess of the design variables. x,usr It is the number of nodes for the state variable, where t is the number of nodes from 0 to t. f Discretized into N x,usr Time series of N points, u,usr It is the number of nodes for the user-provided control variables, n. x n is the number of state variables in the dynamic equation. u This refers to the number of control variables. If the terminal time is also a parameter to be optimized, then n... tf It is 1, otherwise it is 0, n p It refers to the number of design parameters. Let represent a two-dimensional matrix with i rows and j columns.

[0128] Then, the discrete state variables, control variables, and static variables are reconstructed into NLP column vectors:

[0129]

[0130] Where, x i Let u represent the state variable at the i-th node. i t represents the control quantity at the i-th node. f 'p' represents the terminal time, and 'p' represents the design variable.

[0131] The upper and lower bounds of the variables in step 2 should also be reconstructed based on the reconstructed NLP variables.

[0132] Step 3.1.2: Constraints.

[0133] 1) Residual constraints of the Trapezoidal method:

[0134] Residual constraint ζ of the Trapezoidal method k It can be represented as:

[0135]

[0136] Where, ζ k Let x represent the residual constraint at the k-th node. k Let x represent the state variable at the k-th node. k+1 This represents the state quantity at the (k+1)th node.

[0137] The matrix calculation is as follows:

[0138]

[0139] Where the transformation matrix T s1 and T s2 As shown in the following formula:

[0140]

[0141] 2) Path constraints and boundary constraints:

[0142] The path constraint g(x,u,p,t) is a function of the state variables, control variables, design variables, and time. The boundary constraints are functions of the initial state and the terminal state, as shown in the following equations:

[0143]

[0144] Boundary constraint b(x0,t0,x) f ,t f ,p) is a function of initial state variables, initial time, terminal state variables, terminal time, and design variables.

[0145] Finally, after all constraint calculations are completed, the NLP constraints are represented as follows:

[0146]

[0147] All residual constraints have upper and lower bounds of 0.

[0148] Step 3.1.3: Jacobian matrix.

[0149] 1) Jacobian matrix of residual constraints:

[0150] Residual constraints when the state and control variables at the midpoint of each discrete time interval are not considered It is x a ,u a ,x b ,u b ,t f A function of p, x a ,u a ,x b ,u b ,t f The specific values ​​of p are as follows:

[0151]

[0152] To avoid redundant calculations, matrix calculations are performed. First, the derivative of ζ with respect to x, u, and p is calculated. and

[0153] Therefore, the Jacobian matrix can be simplified to:

[0154]

[0155] In the formula Let T be a matrix where the i-th column is 1 and all other elements are 0. a ,T b It is given by the following formula:

[0156] 2) Jacobian matrix of path constraints and boundary constraints:

[0157] First, calculate the derivative of the path constraint g with respect to x, u, p, t.

[0158]

[0159] Then calculate the boundary constraint b for x0, x f The derivatives of p and t:

[0160]

[0161] Step 3.1.4: Cost function.

[0162] The input cost function consists of Meyer and Lagrange terms, and can be expressed as follows:

[0163]

[0164] Step 3.1.5: Gradient of the cost function.

[0165] The cost function is [x,u,t] f The function is defined as [p], therefore its gradient with respect to the state variable and the control variable is as follows:

[0166]

[0167] Then, the gradient of the cost function with respect to the terminal time and design variables is calculated, and finally the NLP gradient is obtained:

[0168]

[0169] Step 3.2: Difference method.

[0170] Most NLP solvers require constraints on the first derivative of c(y), and accurate calculation of these derivatives contributes to faster convergence. The difference method implemented in this patent is central difference. The central finite difference approximation method is as follows:

[0171]

[0172] Step 3.3: Scaling.

[0173] Step 3.3.1: Variable scaling.

[0174] Apply linear scaling to scale state variables, control variables, terminal time, and design variables:

[0175]

[0176]

[0177] Step 3.3.2: Constrain scaling.

[0178] Applying a gradient-based mean norm method to scale the constraint function and cost function achieves faster convergence:

[0179] The scaling of the residual constraints is as follows:

[0180]

[0181] Scaling for path constraints is similar and will not be listed further.

[0182] Step 3.3.3: Scaling of the Jacobian matrix.

[0183] The scaling of the Jacobian matrix takes into account the relationship between the scaling variable and the scaling constraint. The scaling of the residual-constrained Jacobian matrix is ​​defined as follows:

[0184]

[0185] Similarly, the scaling of the Jacobian matrix for path constraints is:

[0186]

[0187] After the problem is transformed as described above, the transformed problem is input into the underlying solver for solving, which can simultaneously determine the optimal control parameters and the optimal design parameters. The design parameters are defined according to requirements; the control parameters are the tire steering angle and torque input. This can be used for the development of articulated vehicles and their control algorithms.

[0188] The embodiments described above construct a collaborative optimal design and control problem for articulated vehicles. This allows for the simultaneous optimization of design and control parameters based on the dynamic model of the articulated vehicle. The optimal design parameters can be used for vehicle design, while the optimal control parameters can serve as a reference for subsequent online control strategy formulation. This framework can utilize gradient information to expand the optimization space, exhibiting good optimization performance and improving the development efficiency of articulated commercial vehicles. This is mainly related to the construction of the optimal design and control problem, the rationality of vehicle dynamics modeling, and the efficient solution of the problem. Furthermore, this embodiment significantly improves the stability and efficiency of solving large-scale, multi-degree-of-freedom optimal design and control problems. This is primarily due to the vectorized dynamics modeling method for the vehicle, and the improved direct collocation method and application of an automatic normalization algorithm in the optimal problem solution, achieving stable and rapid solutions to large-scale collaborative optimal problems.

[0189] Based on the same inventive concept, this application also provides an apparatus for implementing the articulated vehicle design optimization method involving cooperative optimal design and optimal control as described above. The solution provided by this apparatus is similar to the implementation scheme described in the above method; therefore, the specific limitations in one or more apparatus embodiments provided below can be found in the limitations of the articulated vehicle design optimization method involving cooperative optimal design and optimal control described above, and will not be repeated here.

[0190] In one exemplary embodiment, such as Figure 3As shown, an articulated vehicle design optimization device for collaborative optimal design and optimal control is provided, comprising the following modules:

[0191] The dynamics model construction module is used to construct a multi-degree-of-freedom dynamics model of an articulated vehicle based on Lagrange dynamics theory.

[0192] The relevant constraint establishment module is used to determine residual constraints based on the multi-degree-of-freedom dynamic model and to establish boundary constraints based on the driving conditions and the working boundaries of each subsystem of the articulated vehicle.

[0193] The multi-objective optimization problem construction module is used to construct a multi-objective collaborative optimization problem by simultaneously using design parameters and control parameters as optimization variables, and based on residual constraints, boundary constraints and optimization variables.

[0194] The problem transformation and NLP solving module is used to transform multi-objective collaborative optimization problems into nonlinear optimization problems, and to solve the problems using a nonlinear optimization problem solver to obtain the optimal control parameter set and the optimal design parameter set. The optimal control parameter set is used for the development of articulated vehicle control algorithms, and the optimal design parameter set is used for the development of articulated vehicles.

[0195] certainly, Figure 3 The architecture shown is merely exemplary; it can be omitted as needed when implementing different functionalities. Figure 3 One or at least two components of the system shown.

[0196] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 4 As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operating system and computer programs stored in the non-volatile storage media to run. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communicating with external terminals via a network connection. When the computer program is executed by the processor, it implements a collaborative optimal design and optimal control method for articulated vehicle design optimization.

[0197] Those skilled in the art will understand that Figure 4The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0198] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0199] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0200] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0201] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A design optimization method for articulated vehicles based on collaborative optimal design and optimal control, characterized in that, include: A multi-degree-of-freedom dynamic model of the articulated vehicle was constructed based on Lagrange dynamics theory. The residual constraints are determined based on the multi-degree-of-freedom dynamic model, and the boundary constraints are established according to the driving conditions and the working boundaries of each subsystem of the articulated vehicle. The design parameters and control parameters are used as optimization variables simultaneously, and a multi-objective collaborative optimization problem is constructed based on the residual constraints, the boundary constraints, and the optimization variables. The multi-objective collaborative optimization problem is transformed into a nonlinear optimization problem, and a nonlinear optimization problem solver is used to solve the problem, obtaining the optimal control parameter set and the optimal design parameter set. The optimal control parameter set is used for the development of articulated vehicle control algorithms, and the optimal design parameter set is used for the development of articulated vehicles. The multi-degree-of-freedom dynamic model of an articulated vehicle can be expressed by the following equation: ； in, T t Indicates the kinetic energy of the tractor unit. This represents the generalized force acting on the sprung mass of the tractor unit. This represents the generalized force acting on the unsprung mass of the tractor unit. A generalized coordinate system representing the sprung mass of the tractor unit. A generalized coordinate system representing the unsprung mass of the tractor unit. T s This indicates the kinetic energy of the trailer. This represents the generalized force acting on the sprung mass of the trailer. This represents the generalized force acting on the unsprung mass of the trailer. A generalized coordinate system representing the sprung mass of a trailer. The generalized coordinates represent the unsprung mass of the trailer, and the point signs on the parameters are the derivative symbols; , ； , ； in, M t,u and J t,u These are the mass matrix and moment of inertia matrix of the unsprung mass of the tractor, respectively. M t,b and J t,b These are the mass matrix and moment of inertia matrix of the tractor's sprung mass, respectively. M s,u and J s,u These are the mass matrix and moment of inertia matrix of the unsprung mass of the trailer, respectively. M s,b and J s,b These are the mass matrix and moment of inertia matrix of the trailer's sprung mass, respectively. The multi-objective collaborative optimization problem is shown in the following equation: ； in, J The objective function value; t f For terminal time, t 0 represents the start time. J p This is a penalty function used to constrain acceleration and braking to prevent them from occurring simultaneously. w Let f[] be the weighting factor of the penalty function, f[] be the multi-degree-of-freedom dynamic model, and x be the set of state parameters. min and x max The upper and lower bounds of the state parameters; u is the set of control parameters, u min and u max These are the upper and lower bounds of the state parameters; t p is the time step, p is the design parameter set, p min and p max The upper and lower bounds of the state parameters are defined by g[], which represents the path constraint function. min and g max b[] represents the upper and lower bounds of the path constraint function; b[] represents the boundary constraint function. min and b max These are the upper and lower bounds of the boundary constraint function; The multi-objective collaborative optimization problem is transformed into a nonlinear optimization problem, and a nonlinear optimization problem solver is used to solve the problem, obtaining the optimal control parameter set and the optimal design parameter set, specifically including: Linear interpolation is performed on the state parameters and control parameters respectively to obtain the state parameters and control parameters at each interpolation time, so as to reconstruct the optimization variables and obtain the reconstructed optimization variables; the interpolation time includes the start time, the end time, and several intermediate times between the start time and the end time; the reconstructed optimization variables include the design parameters and the state parameters and control parameters at each interpolation time. Calculate the gradient of the objective function with respect to the reconstructed optimization variables; Based on the reconstructed optimization variables, the residual constraints, the boundary constraints, and the path constraints are reconstructed respectively to obtain the reconstructed residual constraints, the reconstructed path constraints, and the reconstructed boundary constraints. Calculate the first Jacobian matrix of the reconstructed residual constraints, the second Jacobian matrix of the reconstructed path constraints, and the third Jacobian matrix of the reconstructed boundary constraints, respectively. Using the reconstructed optimization variables, the objective function, the gradient of the objective function with respect to the reconstructed optimization variables, the reconstructed residual constraints, the reconstructed path constraints, the reconstructed boundary constraints, the first Jacobian matrix, the second Jacobian matrix, and the third Jacobian matrix as inputs, a nonlinear programming solver is used to solve the problem and obtain the optimal control parameter set and the optimal design parameter set.

2. The articulated vehicle design optimization method based on collaborative optimal design and optimal control according to claim 1, characterized in that, The kinetic energy of the tractor unit includes the kinetic energy of the tractor unit's sprung mass and the kinetic energy of the tractor unit's unsprung mass; the kinetic energy of the trailer unit includes the kinetic energy of the trailer unit's sprung mass and the kinetic energy of the trailer unit's unsprung mass. The kinetic energy of the sprung mass of the tractor unit can be expressed by the following formula: ； in, T t,b The kinetic energy of the sprung mass of the tractor unit. V t,b For the generalized speed of the tractor body, V t,u,i Let be the component of the unsprung mass velocity of the tractor in the vehicle coordinate system. M t,u,i The mass matrix of the unsprung mass of the tractor. h A,b and h b,u,i This is the transformation matrix corresponding to the sprung mass and the unsprung mass. M gb To organize the obtained generalized mass matrix; The kinetic energy of the unsprung mass of the tractor unit can be expressed by the following formula: ； in, T t,u The kinetic energy of the unsprung mass of the tractor unit. V t,uz The vertical velocity of the unsprung mass of the tractor unit. ω t,u The rotational angular velocity of the unsprung mass of the tractor unit. J t,u Let be the moment of inertia matrix of the unsprung mass of the tractor; The calculation methods for the kinetic energy of the trailer's sprung mass and unsprung mass are similar to those for the tractor's sprung mass and unsprung mass.

3. The articulated vehicle design optimization method based on collaborative optimal design and optimal control according to claim 1, characterized in that, The generalized forces acting on the sprung mass of the tractor, the unsprung mass of the tractor, the sprung mass of the trailer, and the unsprung mass of the trailer can be obtained through the principle of virtual work: ； in, F For the total generalized force matrix, r t,b This represents the virtual displacement of the sprung mass of the tractor unit. F t,b The generalized force matrix is ​​the force matrix acting on the sprung mass of the tractor. r t,u This represents the virtual displacement of the unsprung mass of the tractor. F t,u Let be the generalized force matrix acting on the unsprung mass of the tractor. r s,b This represents the virtual displacement of the trailer's sprung mass. F s,b The generalized force matrix is ​​the force matrix acting on the sprung mass of the trailer. r s,u This represents the virtual displacement of the unsprung mass of the trailer. F s,u The generalized force matrix is ​​the matrix of forces acting on the unsprung mass of the trailer.

4. The articulated vehicle design optimization method based on collaborative optimal design and optimal control according to claim 3, characterized in that, The generalized force matrix of the sprung mass of the tractor is shown in the following equation: ； in, F t,x,i For the tractor unit i The longitudinal force at the contact point between the tire and the ground δ t,i For the tractor unit i Input the steering angle of each tire. F t,y,i For the tractor unit i Lateral force at each tire contact point with the ground ѱ t The yaw angle of the tractor unit. F t,wx This represents the longitudinal component of aerodynamic drag. F hitch,x For longitudinal hinge force, F t,wy This represents the lateral component of aerodynamic drag. F hitch,y For lateral hinge force, F t,bs,i For the action of the tractor i Suspension force on each tire F t,wz The downforce that causes aerodynamic drag. m t,b For the sprung mass of the tractor, g It is the acceleration due to gravity. F hitch,z For vertical hinge force, y t,u,i Let be the lateral coordinate of the suspension mounting point in the vehicle coordinate system. Z t The height of the sprung mass center of the tractor unit. T t,d,i For the tractor unit i Torque input to each tire, M t,wx Let x be the component of the aerodynamic drag torque about the x-axis. M hitch,x The hinge torque about the x-axis, x t,u,i Let be the longitudinal coordinate of the suspension mounting point in the vehicle coordinate system. M t,wy Let be the component of the aerodynamic drag torque about the y-axis. M hitch,y The hinge torque about the y-axis, M t,z,i For the tractor unit i The restoring torque at each tire contact point with the ground x t,w,i Let be the longitudinal coordinate of the tire center in the vehicle coordinate system. y t,w,i Let be the lateral coordinate of the tire center in the vehicle coordinate system. M t,wz Let be the component of the aerodynamic drag torque about the z-axis. M hitch,z The hinge torque is about the z-axis.

5. The articulated vehicle design optimization method based on collaborative optimal design and optimal control according to claim 3, characterized in that, The generalized force matrix of the unsprung mass of the tractor is shown in the following equation: ； in, T t,d,fr This is the torque input to the right front tire of the tractor. M t,y,fr The rolling resistance torque of the right front tire of the tractor unit. F t,x,fr This refers to the longitudinal force at the point of contact between the right front tire of the tractor and the ground. z t,u,fr The center height of the right front tire of the tractor unit. T t,d,rr This is the torque input for the right rear tire of the tractor. M t,y,rr The rolling resistance torque of the right rear tire of the tractor unit. F t,x,rr The longitudinal force at the point of contact between the right rear tire of the tractor and the ground. z t,u,rr The center height of the right rear tire of the tractor unit. F t,z,fr This refers to the vertical force acting on the right front tire of the tractor. F t,bs,fr The suspension force acting on the right front tire of the tractor unit. m t,u,fr The mass of the right front tire of the tractor unit. F t,z,rr The vertical force acting on the right rear tire of the tractor unit. F t,bs,rr The suspension force acting on the right rear tire of the tractor unit. m t,u,rr The mass of the right rear tire of the tractor unit. g This is the acceleration due to gravity.

6. The articulated vehicle design optimization method based on collaborative optimal design and optimal control according to claim 1, characterized in that, The multi-objective collaborative optimization problem can be transformed into a nonlinear optimization problem by using any one of the following methods: local collocation method, difference method, or automatic scaling method.

7. An articulated vehicle design optimization device for collaborative optimal design and optimal control, characterized in that, The articulated vehicle design optimization method for implementing the collaborative optimal design and optimal control as described in any one of claims 1-6, wherein the articulated vehicle design optimization device for collaborative optimal design and optimal control comprises: The dynamics model construction module is used to construct a multi-degree-of-freedom dynamics model of an articulated vehicle based on Lagrange dynamics theory. The relevant constraint establishment module is used to determine residual constraints based on the multi-degree-of-freedom dynamic model, and to establish boundary constraints based on the driving conditions and the working boundaries of each subsystem of the articulated vehicle. A multi-objective optimization problem construction module is used to construct a multi-objective collaborative optimization problem by simultaneously using design parameters and control parameters as optimization variables, and based on the residual constraints, the boundary constraints, and the optimization variables. The problem transformation and NLP solving module is used to transform the multi-objective collaborative optimization problem into a nonlinear optimization problem, and to solve the problem using a nonlinear optimization problem solver to obtain the optimal control parameter set and the optimal design parameter set. The optimal control parameter set is used for the development of articulated vehicle control algorithms, and the optimal design parameter set is used for the development of articulated vehicles.

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