Multi-body system processing method and device, multi-body system and medium

Abstract

The embodiment of the invention provides a multi-body system processing method and device, a multi-body system and a medium. The method comprises the following steps: determining an integral step length corresponding to each subsystem model according to at least two subsystem models corresponding to the multi-body system at the current moment; and predicting the prediction state of the multi-body system at the next moment based on the integral step length corresponding to each subsystem model and the corresponding current state of the multi-body system at the current moment. And based on the prediction state, determining a target control instruction from the plurality of control instructions through the at least two subsystem models. And at the next moment, executing the target control instruction to control the multi-body system. Wherein the dynamic components corresponding to different subsystem models have different time scale characteristics, and the faster the time scale characteristics are, the smaller the integral step corresponding to the subsystem model is. The method is used for achieving the effects of improving calculation efficiency and saving calculation resources.

Description

Technical Field

[0001] This application relates to the field of power system technology, and in particular to a multibody system processing method, apparatus, multibody system and medium. Background Technology

[0002] Multibody dynamics plays an important role in modeling, simulation, and control in fields such as spacecraft, robotics, and vehicle engineering. Its core challenge lies in how to efficiently and accurately solve the differential equations describing the motion of the system.

[0003] Currently, fixed-step integrators are the traditional method for handling the dynamic equations of multibody systems. During simulation initialization, it is necessary to first identify the fastest variable dynamic component in the multibody system and preset a fixed step size much smaller than the characteristic time of that component. During the simulation, regardless of whether the multibody system is a slow-changing rigid body on the order of seconds or a fast-changing flexible body on the order of microseconds, the state of all degrees of freedom is updated synchronously using this uniform step size.

[0004] However, the above methods suffer from low computational efficiency and waste of computational resources. Summary of the Invention

[0005] This application provides a multi-body system processing method, apparatus, multi-body system, and medium to achieve the technical effects of improving computing efficiency and saving computing resources.

[0006] In a first aspect, embodiments of this application provide a multi-body system processing method, including:

[0007] At the current moment, based on at least two subsystem models corresponding to the multibody system, determine the integration step size for each subsystem model; where the dynamic components corresponding to different subsystem models have different time scale characteristics, and the subsystem model with faster time scale characteristics corresponds to a smaller integration step size;

[0008] Based on the integration step size corresponding to each subsystem model and the current state of the multibody system at the current time, predict the predicted state of the multibody system at the next time.

[0009] Based on the predicted state, the target control command is determined from multiple control commands using the at least two subsystem models;

[0010] At the next moment, the target control command is executed to control the multibody system.

[0011] In one possible implementation, before determining the integration step size corresponding to each subsystem model based on at least two subsystem models corresponding to the multibody system at the current moment, the method further includes:

[0012] Identify the time-scale characteristics corresponding to each dynamic component of the multibody system;

[0013] Based on the aforementioned time scale characteristics, the dynamic model of the multibody system is decomposed into at least two subsystem models.

[0014] In one possible implementation, identifying the time-scale characteristics corresponding to each dynamic component of the multibody system includes:

[0015] The corresponding timescale feature is determined based on the characteristic frequency or characteristic time constant corresponding to each dynamic component;

[0016] The characteristic frequency is obtained by performing eigenvalue decomposition on the dynamic equations of the multibody system, and the characteristic time constant is obtained by performing spectral analysis on the response signal of the multibody system.

[0017] In one possible implementation, the at least two subsystem models include a first subsystem model and a second subsystem model, wherein the integration step size corresponding to the first subsystem model is a first integration step size, the integration step size corresponding to the second subsystem model is a second integration step size, and the time scale feature corresponding to the first subsystem model is slower than the time scale feature of the second subsystem model.

[0018] Accordingly, predicting the predicted state of the multi-body system at the next time step based on the integration step size corresponding to each subsystem model and the current state of the multi-body system at the current time step includes:

[0019] Integrate the first subsystem model with the first integration step size to obtain the first intermediate state;

[0020] Within the integration interval corresponding to the first integration step size, the second subsystem model is integrated at least once with the second integration step size to obtain the second intermediate state;

[0021] Based on the coupling relationship between the first intermediate state and the second intermediate state, the predicted state of the multibody system is determined.

[0022] In one possible implementation, determining the target control command from multiple control commands based on the predicted state using the at least two subsystem models includes:

[0023] Using the predicted state as the initial state, the future state trajectory of the multibody system under different control commands is simulated through the at least two subsystem models.

[0024] Based on the future state trajectory corresponding to different control commands, the control commands that satisfy the preset constraints and can optimize the preset optimization target are determined as the target control commands.

[0025] In one possible implementation, determining the predicted state of the multi-body system based on the coupling relationship between the first intermediate state and the second intermediate state includes:

[0026] Based on the first intermediate state and the second intermediate state, the candidate prediction state is determined;

[0027] Perform physical quantity conservation verification and / or geometric constraint satisfaction verification on the candidate predicted states, and determine the verification results;

[0028] If the verification result indicates that the candidate prediction state has passed the verification, then the candidate prediction state is determined as the prediction state.

[0029] In one possible implementation, determining the integration step size corresponding to each subsystem model based on at least two subsystem models corresponding to the multibody system includes:

[0030] Based on the current state of the multibody system, the corresponding integration step size is dynamically determined for each subsystem model through the adaptive decision module;

[0031] The decision-making basis of the adaptive decision-making module includes constraints related to numerical stability and optimization objectives related to computational efficiency.

[0032] Secondly, embodiments of this application provide a multi-body system processing apparatus, comprising:

[0033] The first determining module is used to determine the integration step size corresponding to each subsystem model at the current time, based on at least two subsystem models corresponding to the multibody system; wherein, the dynamic components corresponding to different subsystem models have different time scale characteristics, and the integration step size corresponding to the subsystem model with faster time scale characteristics is smaller.

[0034] The prediction module is used to predict the predicted state of the multibody system at the next time step based on the integral step size corresponding to each subsystem model and the current state of the multibody system at the current time.

[0035] The second determining module is used to determine the target control command from multiple control commands based on the predicted state and through the at least two subsystem models;

[0036] An execution module is configured to execute the target control command at the next moment to control the multibody system.

[0037] In one possible implementation, the multi-body system processing apparatus further includes an identification module, which, before determining the integration step size corresponding to each subsystem model based on at least two subsystem models corresponding to the multi-body system at the current moment, is configured to:

[0038] Identify the time-scale characteristics corresponding to each dynamic component of the multibody system;

[0039] Based on the aforementioned time scale characteristics, the dynamic model of the multibody system is decomposed into at least two subsystem models.

[0040] In one possible implementation, the identification module is specifically used for:

[0041] The corresponding timescale feature is determined based on the characteristic frequency or characteristic time constant corresponding to each dynamic component;

[0042] The characteristic frequency is obtained by performing eigenvalue decomposition on the dynamic equations of the multibody system, and the characteristic time constant is obtained by performing spectral analysis on the response signal of the multibody system.

[0043] In one possible implementation, the at least two subsystem models include a first subsystem model and a second subsystem model, wherein the integration step size corresponding to the first subsystem model is a first integration step size, the integration step size corresponding to the second subsystem model is a second integration step size, and the time scale feature corresponding to the first subsystem model is slower than the time scale feature of the second subsystem model.

[0044] Accordingly, the prediction module is specifically used for:

[0045] Integrate the first subsystem model with the first integration step size to obtain the first intermediate state;

[0046] Within the integration interval corresponding to the first integration step size, the second subsystem model is integrated at least once with the second integration step size to obtain the second intermediate state;

[0047] Based on the coupling relationship between the first intermediate state and the second intermediate state, the predicted state of the multibody system is determined.

[0048] In one possible implementation, the second determining module is specifically used for:

[0049] Using the predicted state as the initial state, the future state trajectory of the multibody system under different control commands is simulated through the at least two subsystem models.

[0050] Based on the future state trajectory corresponding to different control commands, the control commands that satisfy the preset constraints and can optimize the preset optimization target are determined as the target control commands.

[0051] In one possible implementation, the prediction module is specifically used for:

[0052] Based on the first intermediate state and the second intermediate state, the candidate prediction state is determined;

[0053] Perform physical quantity conservation verification and / or geometric constraint satisfaction verification on the candidate predicted states, and determine the verification results;

[0054] If the verification result indicates that the candidate prediction state has passed the verification, then the candidate prediction state is determined as the prediction state.

[0055] In one possible implementation, the first determining module is specifically used for:

[0056] Based on the current state of the multibody system, the corresponding integration step size is dynamically determined for each subsystem model through the adaptive decision module;

[0057] The decision-making basis of the adaptive decision-making module includes constraints related to numerical stability and optimization objectives related to computational efficiency.

[0058] Thirdly, embodiments of this application provide a multibody system, including: a multibody system body, a memory, and a processor;

[0059] The memory stores computer-executed instructions;

[0060] The processor executes computer execution instructions stored in the memory, causing the processor to perform the first aspect and / or various possible implementations of the first aspect as described above.

[0061] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the first aspect and / or various possible implementations of the first aspect.

[0062] Fifthly, embodiments of this application provide a computer program product, including a computer program that, when executed by a processor, implements the first aspect and / or various possible implementations of the first aspect.

[0063] The multibody system processing method, apparatus, multibody system, and medium provided in this application's embodiments configure different integration step sizes for subsystem models with different time scale characteristics. Based on these differentiated step sizes, the future state trajectory of the multibody system is predicted, and the target control command is determined based on this predicted state, ultimately achieving precise control of the multibody system. The entire process allows simulation computing resources to be intelligently allocated according to the actual needs of dynamic changes. Larger step sizes are used to improve efficiency for slowly changing processes, while smaller step sizes are used to ensure accuracy for rapidly changing processes. This provides a solution for achieving real-time control and efficient simulation of multibody systems while maintaining high-fidelity simulation of the physical process, thereby improving computational efficiency and saving computing resources. Attached Figure Description

[0064] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0065] Figure 1 Flowchart of the multibody system processing method provided in this application Figure 1 ;

[0066] Figure 2 Flowchart of the multibody system processing method provided in this application Figure 2 ;

[0067] Figure 3 Flowchart of the multibody system processing method provided in this application Figure 3 ;

[0068] Figure 4 This is a schematic diagram of the structure of the multibody system processing system provided in this application;

[0069] Figure 5 Flowchart of the multibody system processing method provided in this application Figure 4 ;

[0070] Figure 6 A schematic diagram illustrating the principle of the multibody system processing method provided in this application;

[0071] Figure 7 Flowchart of the multibody system processing method provided in this application Figure 5 ;

[0072] Figure 8 A schematic diagram of the multibody system processing device provided in this application;

[0073] Figure 9 A schematic diagram of the structure of the multibody system provided in this application.

[0074] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0075] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0076] 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. Furthermore, the collection, use and processing of the relevant data must comply with relevant laws, regulations and standards, and corresponding operation entry points are provided for users to choose to authorize or refuse.

[0077] First, the application scenarios involved in this application will be explained:

[0078] Multibody dynamics plays an important role in modeling, simulation and control in fields such as spacecraft, robotics and vehicle engineering. Its core challenge lies in how to efficiently and accurately solve the differential equations describing the motion of multibody systems.

[0079] However, the dynamics of multibody systems typically range from slow, variable rigid body motion on the order of seconds or even minutes to fast, variable flexible vibrations or instantaneous contact collisions on the order of milliseconds or even microseconds, exhibiting significantly separated timescale characteristics. For example, in a flexible robotic arm system, the elastic vibration of the arm occurs on the order of milliseconds or even microseconds, while the posture motion of the base spans from seconds to minutes. This multiscale characteristic stems from the huge differences in stiffness and inertia between components within the system, as well as the complex coupling of external forces, which makes the governing equations generally numerically rigid, posing a long-standing challenge to computational simulation.

[0080] Currently, fixed-step integrators, such as the classic fourth-order Runge-Kutta method, are one of the commonly used fundamental methods for handling the dynamic equations of multibody systems. This method requires the integration step size to satisfy numerical stability conditions. When the multibody system has significantly separated timescales, to ensure the simulation stability and accuracy of the fastest dynamic component, the integration step size needs to be set according to the characteristic time of that fastest component, typically less than 1 / 10 to 1 / 50 of its characteristic time. During the simulation, all degrees of freedom of the multibody system, regardless of their actual rate of dynamic change, are forced to use this uniform small step size for synchronous state updates.

[0081] However, in order to ensure numerical stability, the above method requires the selection of the integration step size to meet the minimum step size required by the dynamic component with the fastest time scale characteristics in the system. This results in the part describing the dynamic component with slower time scale characteristics also having to use an integration step size that is extremely mismatched with its dynamic changes, thus causing inefficient use of computing resources, low computational efficiency, and difficulty in meeting the needs of scenarios such as real-time control and fast simulation.

[0082] Based on the aforementioned technical problems, the technical concept of this application is as follows: If appropriate integration step sizes are configured for subsystem models describing different dynamic components according to the inherent different time scale characteristics within the multibody system, differentiated processing of fast and slow physical processes can be achieved at the mathematical simulation level, thereby improving computational efficiency and saving computational resources. Therefore, the inventors propose that, based on at least two subsystem models corresponding to the multibody system, a smaller integration step size can be configured for the model with faster time scale characteristics; then, based on this differentiated step size system and the current state, the future trajectory of the system can be predicted; and using this predicted state as the basis for decision-making, the target control command can be determined from multiple control commands, and finally, the command can be executed at the next moment to achieve control.

[0083] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0084] Figure 1 Flowchart of the multibody system processing method provided in this application Figure 1 ,like Figure 1 As shown, the method includes:

[0085] S11. At the current moment, based on at least two subsystem models corresponding to the multibody system, determine the integration step size corresponding to each subsystem model.

[0086] The execution subject of this application embodiment is a controller in a multibody system, which can be a spacecraft, robot, vehicle, etc.

[0087] It should be understood that the embodiments of this application are applied after the multi-body system has started automatic control. For example, the application scenario of the embodiments of this application is after the vehicle has started autonomous driving.

[0088] A multibody system is a complex dynamic system composed of multiple interconnected physical components (such as rigid bodies and flexible bodies), whose overall motion needs to be described by solving coupled differential equations. For example, a car can be regarded as a multibody system, which includes components such as the body, suspension, and tires.

[0089] In this context, a subsystem model refers to an independent mathematical model obtained by decomposing the overall dynamics model of a multibody system according to its physical properties, and used to describe the dynamic components at a specific time scale. Specifically, the dynamic components corresponding to different subsystem models have different time scale characteristics, and the faster the time scale characteristics of the subsystem model, the smaller the integration step size.

[0090] It should be understood that the method of decomposing the dynamic model of a multibody system into at least two subsystem models can be referred to Figure 2 The embodiments shown are not described in detail here.

[0091] Here, the integration step size refers to the time increment used to advance the simulation time during numerical integration. In this step, the integration step size specifically refers to the time interval configured individually for each subsystem model to update its state. This integration step size is used to determine the time resolution of the corresponding dynamic components in the simulation.

[0092] For example, an integration step of 0.1 seconds is configured for the subsystem model describing vehicle body motion, while an integration step of 0.005 seconds is configured for the subsystem model describing suspension vibration.

[0093] In one possible implementation, based on the current state of the multibody system, an adaptive decision module dynamically determines the corresponding integration step size for each subsystem model. The decision-making criteria of the adaptive decision module include constraints related to numerical stability and optimization objectives related to computational efficiency.

[0094] The current state refers to the physical condition of the multibody system at the current moment, which is a set of generalized coordinates and generalized momentum.

[0095] For example, for a space robotic arm multibody system, the current state includes the position and orientation of the base, the angles and angular velocities of each joint, and the modal coordinates and vibration velocities of the flexible extension arm.

[0096] The adaptive decision-making module takes the current state of the multi-body system as input, performs a series of internal calculations and judgments, and outputs a suggested integral step size tailored to each subsystem model. Essentially, the adaptive decision-making module is a real-time optimizer, whose decision logic is based on a comprehensive consideration of system stability boundaries, accuracy requirements, and computational load.

[0097] Specifically, the adaptive decision-making module performs real-time analysis of the current state of the input multi-body system, extracting key physical characteristics such as the rate of change of total energy, the rate of change of momentum, and trajectory curvature to quantify the intensity of the dynamics. Subsequently, based on these characteristics, the adaptive decision-making module performs two parallel calculations: firstly, based on numerical stability theories (such as Lyapunov exponential analysis or the Courant–Friedrichs–Lewy condition (CFL)), it calculates the maximum allowable step size for each subsystem model to maintain stability under the current conditions, reserving a safety margin; secondly, the adaptive decision-making module also estimates the computational load of each subsystem model using different step sizes. Finally, the adaptive decision-making module solves a multi-objective optimization problem that comprehensively considers stability constraints, accuracy requirements, and computational efficiency, with the integration step size of each subsystem model as the decision variable. By solving this optimization problem (using a hybrid strategy such as gradient descent or genetic algorithms), the adaptive decision-making module outputs a set of integration step size configurations that optimize overall performance under the current state.

[0098] This implementation automatically increases the integration step size to maximize computational efficiency when the multibody system is moving smoothly; when the multibody system enters a dynamic or complex stage such as contact or collision, it automatically shrinks the integration step size to prioritize numerical stability and computational accuracy. It eliminates the dependence on fixed, conservative parameters and achieves a dynamic balance between simulation accuracy, numerical stability, and computational efficiency.

[0099] S12. Based on the integral step size corresponding to each subsystem model and the current state of the multibody system at the current moment, predict the predicted state of the multibody system at the next moment.

[0100] In this context, the predicted state refers to the estimated state of the multibody system at the next moment, calculated by numerical integration based on the current state and the subsystem model, and after advancing forward by a specified time span (i.e., from the current moment to the next moment). For example, based on the current state of a car, predict how its position, speed, attitude, and suspension state will change in 0.1 seconds.

[0101] In one possible implementation, the first subsystem model is integrated with a first integration step size to obtain a first intermediate state. Within the integration interval corresponding to the first integration step size, the second subsystem model is integrated at least once with a second integration step size to obtain a second intermediate state. Finally, based on the coupling relationship between the first and second intermediate states, the predicted state of the multibody system is determined.

[0102] It should be understood that the specific implementation process and principles of this step will be explained later. Figure 3 The embodiments shown are described in detail here, and will not be repeated here.

[0103] S13. Based on the predicted state, determine the target control command from multiple control commands using at least two subsystem models.

[0104] Among them, multiple control commands are preset or generated in real time for controlling the multibody system, and each control command represents a generalized force or generalized torque plan applied to the multibody system over a period of time.

[0105] For example, for an autonomous driving multi-body system, multiple control commands include different steering and braking combinations such as turning the steering wheel 3 degrees and holding the accelerator, turning the steering wheel 5 degrees and lightly applying the brakes, and turning the steering wheel 1 degree and heavily applying the brakes.

[0106] Among them, the target control instruction refers to the optimal control instruction selected from multiple control instructions based on preset optimization criteria and constraints, which will be executed at the next moment.

[0107] In one possible implementation, the predicted state is used as the initial state, and the future state trajectories of the multibody system under different control commands are simulated using at least two subsystem models. Based on the future state trajectories under different control commands, the control commands that satisfy preset constraints and can optimize the preset optimization objective are determined as the target control commands.

[0108] Among them, the preset constraints refer to the physical limits or safety boundaries that must be strictly followed in the control decision-making process. They define the range of feasible solutions, and any control instructions that violate the constraints will be excluded.

[0109] For example, the preset constraints include path constraints and control quantity constraints. Path constraints include preventing the vehicle from crossing the lane boundary and ensuring that the joint angle of the robotic arm does not exceed the mechanical limit, while control quantity constraints include ensuring that the motor output torque does not exceed its peak value and that the braking pressure does not exceed the system's maximum value.

[0110] Among them, the preset optimization target refers to the pre-set mathematical index used to measure the quality of control. The goal of control decision is to make it optimal (usually minimized).

[0111] For example, preset optimization objectives include minimizing tracking error (such as the deviation between the actual trajectory and the desired trajectory), minimizing control energy consumption (such as the sum of the squares of the torques of all motors), and optimizing comfort indicators (such as the smoothness of acceleration changes). Multiple sub-optimization objectives can be combined into a preset optimization objective through weighted summation.

[0112] This implementation ensures that the final selected target control command is not only feasible, but also has the best global performance over a period of time, thus enhancing the intelligence and stability of multibody system control in complex dynamic environments.

[0113] S14. At the next moment, execute the target control command to control the multibody system.

[0114] In one possible implementation, when the multibody system clock reaches the next time step, the controller (such as an onboard computer) sends the target control command to the corresponding actuator via a communication bus (such as a CAN bus). After receiving the command, the actuator drives a motor or hydraulic mechanism with its internal servo driver to precisely generate the required force or motion.

[0115] It should be understood that the next moment can be determined as the new current moment. In addition to executing the target control command, it is necessary to repeat the above S11-S14 until the control of the multibody system is no longer required.

[0116] The multibody system processing method provided in this application determines the integration step size for each subsystem model based on at least two subsystem models corresponding to the multibody system at the current moment. Based on the integration step size of each subsystem model and the current state of the multibody system at the current moment, the predicted state of the multibody system at the next moment is predicted. Based on the predicted state, a target control command is determined from multiple control commands using at least two subsystem models. At the next moment, the target control command is executed to control the multibody system. The dynamic components corresponding to different subsystem models have different time-scale characteristics; the faster the time-scale characteristic, the smaller the integration step size of the subsystem model. In this technical solution, by configuring different integration step sizes for subsystem models with different time-scale characteristics, the future state trajectory of the multibody system is predicted based on these differentiated step sizes, and the target control command is decided based on this predicted state, ultimately achieving precise control of the multibody system. The entire process enables intelligent allocation of simulation computing resources according to the actual needs of dynamic changes. Large step sizes are used to improve efficiency for slow-changing processes and small step sizes are used to ensure accuracy for fast-changing processes. Thus, while maintaining high-fidelity simulation of the physical process, it provides a solution for real-time control and efficient simulation of multibody systems, thereby improving computational efficiency and saving computing resources.

[0117] Furthermore, this scheme first identifies the time-scale characteristics of different dynamic components within the multibody system and decomposes the overall dynamic model into at least two subsystem models accordingly. This decomposition based on physical characteristics provides a better problem structure for numerical processing. Then, during multi-rate integration, variational coupling terms ensure state coordination between subsystems, and stability constraints in adaptive decision-making (such as analysis based on Lyapunov exponents) jointly guarantee the coupled numerical stability during integration processes with different time lengths, effectively improving the robustness of the simulation under complex conditions.

[0118] Figure 2 Flowchart of the multibody system processing method provided in this application Figure 2 ,like Figure 2 As shown, the method further includes the following steps before S11:

[0119] S21. Identify the time-scale characteristics corresponding to each dynamic component of a multibody system.

[0120] In this context, dynamic components refer to the components that constitute the overall dynamic behavior of a multibody system and have specific physical meanings and characteristic rates of change. For example, for a flexible spatial robotic arm, its dynamic components include the slow orbital and postureal motion of the base, the rotation of the joints, and the multi-order elastic vibrations of the arm.

[0121] The time-scale characteristic refers to the physical property used to quantify how fast a dynamic component changes, usually expressed as a characteristic frequency or the reciprocal of its characteristic time. A high characteristic frequency indicates that the component changes rapidly; conversely, a low characteristic frequency indicates that the component changes slowly.

[0122] For example, the vibration of a vehicle suspension has a characteristic frequency of 10 Hz (time scale of approximately 0.1 seconds), while the yaw motion of the vehicle body has a characteristic frequency of only 1 Hz (time scale of approximately 1 second).

[0123] The characteristic frequency is a scalar value obtained by linearizing and performing eigenvalue analysis on the differential equations describing the dynamics of a multibody system. Its unit is Hertz (Hz). It quantitatively describes the oscillation frequency of the corresponding dynamic component when it undergoes free vibration near the equilibrium point of the multibody system.

[0124] In one possible implementation, the corresponding time scale characteristics are determined based on the characteristic frequency or characteristic time constant corresponding to each dynamic component. The characteristic frequency is obtained by eigenvalue decomposition of the dynamic equations of the multibody system, and the characteristic time constant is obtained by spectral analysis of the response signal of the multibody system.

[0125] The characteristic time constant is a time parameter extracted from the dynamic response signal of a multibody system to external excitation or initial disturbance through spectral analysis, and its unit is seconds (s). It quantitatively describes the time required for the corresponding dynamic component to complete its typical change process or decay to a specific proportion.

[0126] For example, spectral analysis of the vibration decay signal after the end of the robotic arm is subjected to an impact identifies a dominant 50Hz component with a corresponding characteristic time constant of approximately 0.02 seconds, which characterizes the rapid decay of this vibration.

[0127] Specifically, the nonlinear dynamic equations of the multibody system are linearized at a certain operating point (such as the equilibrium position or typical motion state) to obtain the state matrix or Jacobian matrix of the multibody system. Then, eigenvalue analysis is performed on the state matrix or Jacobian matrix to obtain the characteristic frequencies of each mode. Finally, the characteristic frequencies of each mode are determined as the time-scale characteristics of the corresponding dynamic component. Alternatively, response signals (such as acceleration and displacement) of key parts of the multibody system can be collected during actual operation or high-precision simulation, and then spectral analysis techniques are applied to identify frequency bands with concentrated energy in the response signals. Subsequently, the frequency corresponding to each significant spectral peak is determined as the characteristic frequency of a dynamic component of the multibody system, and its reciprocal is determined as the characteristic time constant, thereby determining the time-scale characteristics of that dynamic component.

[0128] In the above implementation, the accuracy of time-scale feature recognition is improved by using eigenvalue decomposition or spectral analysis, which in turn improves the accuracy of subsequent calculation of the integral step size corresponding to each subsystem model.

[0129] S22. Based on the time scale characteristics, the dynamic model of the multibody system is decomposed into at least two subsystem models.

[0130] Among them, the dynamic model refers to a set of equations that completely describe the motion laws of a multibody system in mathematical form. It is usually based on the principles of analytical mechanics (such as Lagrange mechanics or Hamiltonian mechanics) and includes the kinetic energy function, potential energy function, dissipation function and generalized force of the multibody system.

[0131] In one possible implementation, based on the degree of participation of each generalized coordinate in the main characteristic modes and its associated potential stiffness, they are divided into a set of slowly varying coordinates (a set of coordinates with slower time-scale characteristics) and a set of rapidly varying coordinates (a set of coordinates with faster time-scale characteristics). Subsequently, terms in the original system's Lagrangian that depend only on the slowly varying coordinates and their velocities are categorized to form a slowly varying subsystem model; terms that depend only on the rapidly varying coordinates and their velocities are categorized to form a rapidly varying subsystem model.

[0132] In another possible implementation, the modal coordinates of the multibody system are obtained through modal analysis. Then, the modal coordinates are grouped according to their frequency. The dynamic equations of the low-frequency modes are integrated into a slow-varying subsystem model, and the dynamic equations of the high-frequency modes are integrated into a fast-varying subsystem model.

[0133] In this technical solution, by identifying the inherent time-scale characteristics of each dynamic component in a multibody system, and decomposing the complex dynamic model into multiple subsystem models accordingly, a foundation is laid for allocating different integration step sizes to different subsystems, thereby improving the efficiency and control accuracy of the multibody system processing scheme.

[0134] In scenarios where at least two subsystem models include a first subsystem model and a second subsystem model, the integration step size corresponding to the first subsystem model is the first integration step size, the integration step size corresponding to the second subsystem model is the second integration step size, and the timescale feature corresponding to the first subsystem model is slower than the timescale feature of the second subsystem model, the implementation process of S12 can be achieved through... Figure 3 The illustrated embodiments are explained below.

[0135] Figure 3 Flowchart of the multibody system processing method provided in this application Figure 3 ,like Figure 3 As shown, S12 includes:

[0136] S31. Integrate the first subsystem model with the first integration step size to obtain the first intermediate state.

[0137] In one possible implementation, the current state of the multibody system is used as the initial input, but only those state variables belonging to the first subsystem model are extracted and updated. The integration process strictly follows the dynamic equations of the first subsystem model itself and is advanced using a first integration step size within one time step. After the calculation is completed, the first intermediate state of the first subsystem model is determined.

[0138] S32. Within the integration interval corresponding to the first integration step size, integrate the second subsystem model at least once with the second integration step size to obtain the second intermediate state.

[0139] In one possible implementation, the second subsystem model is numerically integrated one or more times in units of the second integration step size. Each integration is based on the state of the second subsystem model at the current moment and usually needs to consider the coupling effects from the first intermediate state. Through such multiple integrations, the second intermediate state of the second subsystem model after the first integration step size is finally obtained.

[0140] S33. Based on the coupling relationship between the first intermediate state and the second intermediate state, determine the predicted state of the multibody system.

[0141] The coupling relationship refers to the mathematical expression that exists between the first subsystem model and the second subsystem model, describing their interaction. It originates from the energy and momentum exchange terms between different degrees of freedom in the original undecomposed multibody system model.

[0142] In one possible implementation, candidate prediction states are determined based on a first intermediate state and a second intermediate state. The candidate prediction states are then subjected to physical quantity conservation verification and / or geometric constraint satisfaction verification to determine the verification results. If the verification results indicate that the candidate prediction state has passed verification, then the candidate prediction state is determined as the prediction state.

[0143] Among them, the verification of the conservation of physical quantities refers to checking whether the changes of certain physical quantities (such as total energy, total momentum, and angular momentum) of a multibody system that should remain unchanged under ideal conditions exceed the acceptable error range during the process of evolving from the current state to the candidate predicted state.

[0144] For example, for a conservative system, its total mechanical energy should be approximately conserved during numerical integration. During verification, the total energy in the candidate predicted state needs to be calculated and compared with the total energy in the current state to determine whether the relative error is less than a preset threshold.

[0145] Among them, geometric constraint satisfaction verification refers to checking whether the candidate predicted state satisfies the inherent kinematic relationship of the multibody system, which is determined by the connection method or contact conditions between the components.

[0146] For example, for two rigid bodies connected by a hinge, the displacements at the hinge point must be consistent; for a rotary joint, the relevant quaternion must maintain the unit norm; and for a contact state, penetration between the objects is not allowed.

[0147] Specifically, based on the first intermediate state and the second intermediate state, the candidate prediction state can be determined in any of the following ways:

[0148] Method 1: Extract the state variable values ​​belonging to the first subsystem model from the first intermediate state, extract the state variable values ​​belonging to the second subsystem model from the second intermediate state, combine them together according to the inherent order of the multibody system state vector, and determine the complete state vector formed by the combination as the candidate prediction state.

[0149] Method 2: Adjust the overlapping or related parts of the first and second intermediate states based on the coupling relationship, and then combine the adjusted first and second intermediate states to determine the complete state vector formed by the combination as the candidate prediction state.

[0150] Optionally, if the verification result indicates that the candidate prediction state verification failed, the verification result can be recorded and the integral step size corresponding to each subsystem model can be reduced. Based on the adjusted integral step size, the prediction state of the multibody system at the next time step can be re-predicted.

[0151] In this implementation, by verifying the conservation laws of energy and momentum and checking geometric constraints on candidate predicted states, non-physical solutions caused by the accumulation of numerical errors or extreme operating conditions can be effectively intercepted. If the verification passes, it indicates that the predicted state is highly reliable, and subsequent target control commands can be determined based on it; if the verification fails, an alarm or correction mechanism can be triggered, improving the robustness and safety fault tolerance of the multibody system in long-term operation and high-risk tasks.

[0152] In the above embodiments, the computation frequency of slow-varying dynamics is reduced, saving computational resources. The final predicted state is determined based on the coupling relationship of intermediate states, ensuring that the decomposed subsystem model is still a physically coordinated whole, laying the foundation for subsequent state prediction.

[0153] To further illustrate the multibody system processing method provided in this application, four embodiments will be used to explain its implementation.

[0154] The multibody system processing method provided in this application can be applied to a multibody system processing system, the structure of which can be... Figure 4 The illustrated embodiments are explained below.

[0155] Figure 4 This is a schematic diagram of the structure of the multi-body system processing system provided in this application, such as... Figure 4 As shown, the multibody system processing system includes a top-level intelligent dynamic splitting module and a multi-rate variational integral engine, a mid-level intelligent adaptive decision engine and intelligent control actuators, and a bottom-level actuator and environment. The functions and specific processing procedures of each of these components will be described in detail below.

[0156] 1. Power Intelligent Splitting Module

[0157] The dynamic intelligent splitting module includes a feature scale recognizer, a physical operator decomposer, and a Lie group structure processor.

[0158] The feature scale recognizer performs eigenvalue decomposition on the dynamic equations of a multibody system to obtain the characteristic frequencies of the system modes, or performs spectral analysis on the response signal of the multibody system to extract the dominant frequency components to calculate the characteristic time constant. Based on the characteristic frequencies and the aforementioned characteristic time constant, the quantized time scale characteristics of each dynamic component are determined.

[0159] The physics operator decomposer reconstructs the total Lagrangian or Hamiltonian of a multibody system based on the time-scale features provided by the feature scale recognizer, according to the meaning of the physical process. For example, it decomposes the system into a slowly varying subsystem model describing large-scale rigid body motion, a rapidly varying subsystem model describing high-frequency vibration and flexible effects, and a rigid subsystem model describing instantaneous interactions such as contact and collision.

[0160] The Lie group structure processor is a submodule that processes the rigid body attitude dynamics in a multibody system. It ensures that in all subsequent model representations and numerical integrations, the rigid body's attitude variables and their update algorithms remain on the Lie group manifold structure to which it belongs, thereby avoiding problems such as Euler angle singularity and guaranteeing the geometric correctness of the rigid body dynamics.

[0161] 2. Multi-rate variational integral engine

[0162] The inputs to the multi-rate variational integral engine include: at least two subsystem models from the dynamic intelligent splitting module and the current state of the multibody system at the current moment.

[0163] The multi-rate variational integral engine first dynamically determines the integration step size for each subsystem model based on its characteristics and current state. This decision-making process is based on multi-objective optimization principles, comprehensively considering numerical stability, physical accuracy, and computational efficiency. The core is to solve for the optimal step size ratio {H,M,N}, where the subsystem model with faster time scale characteristics corresponds to a smaller integration step size.

[0164] Specifically, when determining the integration step size, the multi-rate variational integration engine tracks four key physical quantities: the rate of change of energy ΔE / Δt, the momentum flux Δp / Δt, the trajectory curvature κ, and the numerical error ε, in order to capture the dynamic characteristics of the multibody system. Based on this, the multi-rate variational integration engine performs stability boundary calculations and accuracy requirement quantification in parallel.

[0165] Stability boundary calculation: using Lyapunov exponent analysis (calculating the maximum Lyapunov exponent λ of the Jacobian matrix J of the many-body system). max Using the CFL condition, the maximum allowable step size to ensure numerical stability is derived, and a stability safety factor γ (e.g., 0.6-0.8) is multiplied to set a safety margin.

[0166] Precision requirement quantification: by evaluating energy conservation error Momentum conservation error And trajectory tracking accuracy (requiring tracking error) Establish accuracy indicators.

[0167] Subsequently, the multi-rate variational integral engine models the efficiency objective, predicting the computational load of each subsystem model at different step sizes. Next, the core multi-objective optimization solution process is initiated. This process unifies the three objectives of stability, accuracy, and efficiency into a single optimization problem: .in, It is a stability objective function based on the Lyapunov exponent. The accuracy objective function is based on the aforementioned conservation law error. It is an efficiency objective function based on computation time; , , All are dynamically adjusted weight coefficients. Under the constraints of stability, accuracy, and efficiency, the multi-rate variational integral engine uses a hybrid algorithm (such as gradient descent, genetic algorithm, and sequential quadratic programming) to solve this problem and finally decides the optimal step size ratio {H,M,N}, where the subsystem model with faster time scale characteristics is assigned a smaller integration step size (i.e., H>H / M>H / (M×N)).

[0168] Based on the determined step size ratio {H,M,N}, the multi-rate variational integral engine executes a structured multi-rate integral loop to achieve prediction. This loop employs a three-layer nested architecture:

[0169] The outer loop integrates the slow-varying subsystem model (such as a model describing large-scale rigid body motion) with the maximum step size H to obtain the intermediate state.

[0170] The middle-level loop executes M loops within each outer-level step size H, integrating the model of the fast-changing subsystem with rapid time-scale characteristics (such as a model describing structural vibration) with a step size H / M to obtain the intermediate state.

[0171] The inner loop can execute N loops within each intermediate step size H / M, integrating the rigid subsystem model describing instantaneous contact collision with the minimum step size H / (M×N) to obtain the intermediate state.

[0172] Each cyclic level is based on the discrete variational principle of its subsystem model, and achieves state updates by solving the discrete Euler-Lagrange equations, thereby algorithmically preserving the geometric properties of the system, such as symplectic structure and momentum conservation. Inter-level interactions are transmitted through variational coupling terms, ensuring physically consistent state transfer and energy-momentum exchange, and ultimately coordinating to determine a complete and physically self-consistent predicted state.

[0173] This innovative method, which decomposes complex multi-scale dynamics into single-scale sub-problems with multiple time-scale feature sets and employs optimal step-size collaborative processing for each, enables the multi-rate variational integral engine to automatically decrease H or increase M and N to improve the sampling rate when the system is dynamically volatile, and increase H or decrease M and N to improve efficiency when the dynamics are stable. This overcomes the technical bottleneck of traditional simulations where efficiency or accuracy is sacrificed to achieve stability, achieving a dynamic optimal balance among numerical stability, physical accuracy, and computational efficiency. It provides a reliable technical foundation for real-time high-fidelity simulation and control of complex multibody systems.

[0174] 3. Intelligent Adaptive Decision Engine

[0175] The intelligent adaptive decision engine includes a physical quantity monitoring unit, a step size optimizer, and a load balancer.

[0176] The physical quantity monitoring unit performs at least one of the following verifications:

[0177] (1) Verification of energy and momentum conservation: Due to the use of the variational integral principle, the total energy of the system should theoretically exhibit bounded small-amplitude oscillations rather than monotonically drifting. This unit calculates the change in total energy before and after a complete integration step. It checks whether the generalized momentum of the system exceeds a preset acceptable threshold δE_max. Simultaneously, it checks whether the generalized momentum of the system remains conserved in the direction corresponding to the system's symmetry; any non-physical momentum change is considered a potential indicator of numerical error or model mismatch.

[0178] (2) Geometric Constraint Verification: Perform geometric integrity checks on specific components in a multibody system. For rigid body subsystems, verify whether the rotation matrix describing their attitude satisfies the orthogonality requirement to prevent non-physical distortion caused by numerical integration. For constrained systems, verify whether their generalized coordinates strictly satisfy all complete constraint equations (such as the positional consistency of hinge connection points and the contact non-penetration condition), calculate the constraint residuals, and determine whether they are within the allowable tolerance.

[0179] (3) Numerical Error Estimation: This unit estimates the numerical error introduced by the current simulation step using technical means. Common methods include: comparing the differences between the results obtained by using different precision schemes (such as variational integrators of different orders) within the same integration step; or directly evaluating the magnitude of the residuals of the discrete Euler-Lagrange equations. The local truncation error estimated in this way is one of the key inputs for judging whether the current integration step size is appropriate and whether it needs to be adjusted.

[0180] The step-size optimizer monitors actual performance metrics (such as final state error and control effectiveness) and compares them with predicted performance. Based on the discrepancies generated by this real-time comparison, adaptive learning is performed: successful parameter configurations and their corresponding system states are recorded in an experience database for rapid initialization and decision optimization under similar future operating conditions, and the parameters of the dynamic model are dynamically adjusted to reduce deviations.

[0181] Meanwhile, multiple safety protection mechanisms are built-in to prevent decision instability: including limiting the rate of parameter change to avoid violent oscillations; pre-setting backup configurations so that performance indicators can be switched quickly and smoothly when deterioration is detected; and performing physical rationality checks on all decided parameters to ensure that they are within the preset safety range.

[0182] The load balancer is used to dynamically adjust resource allocation based on the real-time computing overhead of each subsystem model, ensuring maximum computing efficiency.

[0183] 4. Intelligent control actuator

[0184] The intelligent control actuator includes a model predictive controller, a real-time optimizer, and a feedback corrector.

[0185] Specifically, the model prediction controller is used to receive validated predicted states from the intelligent adaptive decision engine. This serves as the sole starting point for all scenario simulations. The model predictive controller integrates subsystem models derived from the multi-rate variational integral engine. For each control command to be evaluated, the controller utilizes these subsystem models, starting from the initial... Initially, the state evolution of the multi-body system is simulated and deduced over a period of time in the future, thereby obtaining the corresponding future state trajectory.

[0186] The real-time optimizer receives the future state trajectories corresponding to different control commands provided by the model predictive controller. Based on the preset optimization objective (such as minimizing tracking error and energy consumption) and preset constraints (such as actuator physical limits and safety boundaries), it solves a constrained numerical optimization problem to determine the control command that satisfies the constraints and optimizes the objective from all control commands, and then identifies that control command as the target control command to be executed.

[0187] The feedback corrector is used at the end of a control cycle to perform two corrections based on the difference between the processed predicted state and the new state read from the actual sensors: first, as immediate feedback, it can be used to update or calibrate the parameters of the dynamic model to reduce future prediction bias; second, it records this difference, along with the corresponding system state, control commands, and decision parameters, into an empirical database, providing data for the adaptive learning mechanism, thereby enabling the decision-making quality of the entire system to continuously optimize with the accumulation of operational experience. This ensures the long-term robustness and adaptability of the closed-loop control.

[0188] 5. Actuator and Environment

[0189] In this process, when the multi-body system clock reaches the next instant, the feedback corrector in the intelligent control actuator sends the finalized target control command to the corresponding actuator via a real-time communication interface (such as CAN bus, EtherCAT, or real-time shared memory). The actuator then drives the physical mechanism to produce the corresponding action based on the command. For example, in an autonomous vehicle, the actuator controls the steering motor to adjust the front wheel angle, controls the braking system to adjust the braking torque, and controls the drive motor to adjust the output torque.

[0190] Simultaneously and subsequently, the sensor network deployed within the multibody system and its environment begins to operate, collecting data on the actual physical state of the multibody system at the new current moment, such as position, velocity, acceleration, attitude, and contact force.

[0191] Figure 5 Flowchart of the multibody system processing method provided in this application Figure 4 ,like Figure 5 As shown, the multibody system processing method includes:

[0192] S31. Multibody system state initialization.

[0193] At the present moment To obtain the current state of a multibody system, the current state is composed of generalized coordinates qs and generalized momentum ps.

[0194] S32. Dynamic characteristics analysis and subsystem model construction.

[0195] Based on the overall dynamics model of the multibody system, the time-scale characteristics of its different dynamic components are identified. Subsequently, according to the time-scale characteristics, the overall dynamics model is decomposed into at least two subsystem models.

[0196] S33, Adaptive integral step size decision.

[0197] Based on at least two subsystem models and the current state, the corresponding integration step size is dynamically determined for each subsystem model. The subsystem model with a faster time scale characteristic has a smaller corresponding integration step size.

[0198] Specifically, we solve a multi-objective optimization problem that comprehensively considers numerical stability, computational accuracy, and computational efficiency, and determine a set of optimal integration step size ratios {H,M,N} for subsystem models with different time scale characteristics.

[0199] Where H is the integration step size of the first subsystem model, H / M is the integration step size of the second subsystem model, and H>H / M. If there is a third subsystem model describing instantaneous interactions, its integration step size is H / (M×N), satisfying H>H / M>H / (M×N).

[0200] S34, Multirate Variational Integral Prediction.

[0201] Based on the current state and the integration step size determined for each subsystem model, multi-rate numerical integration is performed to predict the multibody system at the next time step. The predicted state.

[0202] This step specifically executes a structured integration loop: The first subsystem model is integrated with a step size H to obtain the first intermediate state. Within the time interval corresponding to step size H, the second subsystem model is integrated M times with a step size H / M to obtain the second intermediate state. Optionally, within each integration interval of step size H / M, the third subsystem model can be integrated N times with a step size H / (M×N) to obtain the third intermediate state.

[0203] Candidate prediction states are determined based on the coupling relationship between the first intermediate state and the second intermediate state, as well as the coupling relationship between the second intermediate state and the third intermediate state.

[0204] S35, Physical Audit and Status Verification.

[0205] The candidate predicted states are verified for physical quantity conservation and / or geometric constraint satisfaction. If the verification passes, the candidate predicted state is determined as a high-confidence predicted state. Then proceed to step S36. If the verification fails, record the event and trigger the feedback adjustment mechanism (such as reducing the integration step size), and return to step S32 to re-determine the integration step size and make predictions.

[0206] S36, Intelligent control command generation.

[0207] Predicted state Starting from the decision-making point, at least two subsystem models are used to simulate the future state trajectory of the multibody system as it executes multiple preset control commands over a future period. Based on preset optimization objectives and preset constraints, the target control command is determined from the multiple preset control commands.

[0208] S37, Instruction Execution and Closed-Loop Update.

[0209] In the next moment The target control command is sent to the physical actuator to control the multibody system. At the same time, the actual new state of the multibody system after the control is executed is collected, and this actual new state is used as the current state of the next control cycle. Then, the process returns to step S31 to start a new cycle until the control task ends.

[0210] Figure 6 A schematic diagram illustrating the principle of the multibody system processing method provided in this application, as shown below. Figure 6 As shown, the principle of decomposing the dynamic model of the multibody system into at least two subsystem models (three in this embodiment) in this multibody system processing method includes:

[0211] 1. Mechanical modeling of continuous systems.

[0212] The multibody system is modeled using analytical mechanics methods. The overall dynamic behavior of the multibody system is fully described by its Lagrange quantity L, which can be expressed as the sum of multiple components:

[0213] L=L slow +L fast +L stiffL

[0214] Among them, L slow L fast L stiffL These correspond to the Lagrangian components that describe dynamics with slower timescale characteristics (such as large-scale motion of rigid bodies), dynamics with faster timescale characteristics (such as structural vibration), and instantaneous strong interactions (such as contact collisions), respectively.

[0215] 2. Discrete variational principle.

[0216] According to Hamilton's principle, the actual trajectory of a multibody system within any time interval causes its action to take a stationary value. For numerical calculations, this continuous principle is discretized.

[0217] 3. Calculate the discrete action quantity.

[0218] Wherein, discrete action S d It is the summation of discrete Lagrange quantities along time nodes:

[0219] S d=∑[L d slow +L d fast +L d stiff ]

[0220] 4. Discrete Hamiltonian principle.

[0221] 5. Discrete Euler-Lagrange equations.

[0222] For discrete action S d Applying the Discrete Hamiltonian principle (i.e., requiring S...) d (If the variation is zero), the discrete control equations for the motion of the multibody system can be derived—the discrete Euler-Lagrange equations:

[0223] D1L d (q k ,q k+1 )+D2L d (q k−1 ,q k )=0

[0224] Where D1 and D2 represent the partial derivatives with respect to the first and second variables of the discrete Lagrange, respectively.

[0225] 6. Operator splitting technique.

[0226] The operator splitting technique is used to split the total discrete Lagrangian L d Decompose according to its physical components:

[0227] L d ≈L d slow +L d fast +L d stiff

[0228] Based on operator splitting technology, complex global dynamic problems are decomposed into a series of subsystem model solving problems.

[0229] 7. Solve the sequence by splitting.

[0230] Based on the determined integration step size {H,M,N}, construct and execute an independent but coordinated solution sequence for each subsystem model:

[0231] Solving the slow-varying subsystem model: Based on the discrete Lagrange L d slowThe corresponding discrete Euler-Lagrange equations (DEL) are solved independently with a large integration step size H to update the state of the slowly varying dynamics.

[0232] Solving the model of a rapidly changing subsystem: Based on the discrete Lagrange L d fast The corresponding DEL equation is solved independently with a small integration step size H / M. This process is repeated M times within each slowly varying step size H.

[0233] Solving the rigid subsystem model: Based on the discrete Lagrange L d stiff The corresponding DEL equations are solved independently with smaller integration steps H / (M×N). This process can be repeated N times within each rapidly varying step size H / M.

[0234] Since the entire derivation strictly follows the discrete variational principle, the obtained numerical solution inherits and preserves the key physical properties of the original continuous system:

[0235] Momentum conservation: If the original system has a certain symmetry on the continuous level (such as translation or rotation invariance), then the discrete solution maintains momentum conservation in the corresponding direction.

[0236] Energy conservation: The total energy of the discrete solution system (Hamiltonian) exhibits bounded, small-amplitude oscillations (nearly conservation) in long-term simulations, rather than monotonically drifting, and has excellent long-term stability.

[0237] Geometric structure preservation: In particular, for state variables such as rigid body attitude defined on manifolds (such as rotation group SO(3)), the discrete variational integral algorithm can ensure that its solution always stays on the correct geometric manifold, avoiding parameterization singularity and numerical drift problems.

[0238] The multibody system processing method starts from the mechanical description of continuous systems and adopts the discrete variational principle based on Lagrange quantities. This fundamental choice ensures that the discretized numerical algorithm inherently preserves the core geometric structure and physical conservation laws of the continuous system. Its core construction involves transforming the integral of continuous action into a discrete summation, constructing a corresponding discrete Lagrange quantity for each subsystem model, and then applying the discrete Hamiltonian principle to derive the discrete Euler-Lagrange equations, providing a mathematical basis for numerical updates.

[0239] At the technical implementation level, the multi-body system processing method decomposes the overall dynamic model of the multi-body system into three subsystem models based on the identified time-scale characteristics. Using operator splitting techniques, discrete dynamic descriptions are constructed for each of the three subsystem models. Based on this, a corresponding integration step size is dynamically determined for each subsystem model, with smaller integration step sizes for subsystem models with faster time-scale characteristics, and multi-rate numerical integration is performed accordingly. Specifically, this method employs a multi-rate advancement strategy: for the first subsystem model with the slowest time-scale characteristics, an integration step size H is used; for the second subsystem model with faster time-scale characteristics, multiple integrations are performed within the integration interval corresponding to step size H / M, thus forming a hierarchical integration loop.

[0240] Its discrete variational construction preserves the key physical properties of the multibody system: its numerical scheme automatically maintains the symplectic structure, ensuring long-term numerical stability; it accurately preserves the momentum conservation quantities corresponding to the system's symmetry; it provides long-term bounded energy evolution behavior; and it naturally maintains the inherent geometric constraints of the multibody system. This, in principle, guarantees that in multibody system simulations, high physical accuracy and numerical stability are maintained while improving computational efficiency.

[0241] Figure 7 Flowchart of the multibody system processing method provided in this application Figure 5 ,like Figure 7 As shown, the process of determining the integration step size corresponding to each subsystem model in this multibody system processing method includes the following steps:

[0242] S71, Real-time monitoring and sensing of multiple physical quantities.

[0243] Real-time monitoring of four key physical quantities of a multibody system enables a comprehensive understanding of the system's dynamic state.

[0244] The key physical quantities include: the rate of change of energy ΔE / Δt, the rate of change of momentum Δp / Δt, the trajectory curvature κ, and the estimated value of numerical integration error ε.

[0245] S72. Multi-objective optimization decision modeling and solution.

[0246] Based on the monitored input, a multi-objective optimization problem is constructed and solved to determine the optimal integration step size configuration. This optimization comprehensively considers the following three objectives:

[0247] Stability objective: Quantitative analysis of the system's local stability is conducted using Lyapunov stability theory, providing a theoretical stability boundary for selecting the integration step size. Simultaneously, the numerical damping introduced by the numerical integration algorithm itself is monitored to prevent non-physical excessive dissipation or energy explosions during optimization.

[0248] Accuracy objective: Ensure that the numerical integration algorithm maintains the algorithmic conservation of physical quantities such as energy and momentum (i.e., the discrete conservation law is preserved), and control the local truncation error or global cumulative error of the numerical solution.

[0249] Efficiency objective: To evaluate the computational load of each subsystem model in real time under different integration steps, and to meet the hard real-time or soft real-time application constraints required by the multi-body system processing task.

[0250] S73, Output optimal step size configuration and adaptive adjustment.

[0251] Solve the above multi-objective optimization problem and output the optimal integration step size ratio {H,M,N} at the current time step. This ratio is used to dynamically adjust the time resolution of the three-level loop in multi-rate numerical integration.

[0252] (1) H is determined as the integration step size corresponding to the first subsystem model with the slowest time scale feature;

[0253] (2) H / M is determined as the integration step size corresponding to the second subsystem model with faster time scale characteristics;

[0254] (3) H / (M×N) is determined as the integration step size corresponding to the third subsystem model with faster time scale characteristics.

[0255] Meanwhile, based on the system dynamic characteristics reflected in this optimization, feedback information (i.e., splitting strategy adjustment) is provided for the subsystem model partitioning in subsequent control cycles, and the computing resources allocated to each subsystem model can be reallocated accordingly to further optimize the overall computing efficiency.

[0256] By deeply integrating the aforementioned physical perception, multi-objective optimization, and intelligent decision-making, the fidelity, efficiency, and adaptability of multibody system dynamics simulation can be improved.

[0257] In summary, the multi-body system processing method provided in the above embodiments has the following innovations compared with the prior art:

[0258] Innovation Point 1: Intelligent Decomposition Mechanism of Dynamic Model Based on Time Scale Characteristics

[0259] Traditional approach: Dynamic equations are usually decomposed based on simplified mathematical forms or fixed engineering experience, lacking adaptive consideration of the system’s inherent time-varying physical characteristics.

[0260] This application aims to automatically identify and quantify the time-scale characteristics of different dynamic components within a multibody system by analyzing the eigenvalues ​​of the system's dynamic equations in real time or monitoring the spectrum of the system's response signal.

[0261] For example, it can be characterized by calculating its characteristic frequencies or characteristic time constants. Based on the identified timescale characteristics, the overall dynamic model (Lagrangian or Hamiltonian) of the multibody system is decomposed into at least two subsystem models. For example, it can be decomposed into a subsystem model describing the slower dynamic components with slower timescale characteristics (such as large-scale motion of a rigid body) and a subsystem model describing the faster dynamic components with faster timescale characteristics (such as structural vibration).

[0262] How to solve the technical problem: By accurately separating the dynamics at different time scales, a foundation is laid for subsequent divide-and-conquer simulations using differentiated integration step sizes, avoiding the efficiency bottleneck caused by using an extremely small step size globally to adapt to the fastest dynamics. Furthermore, decomposition based on physical time scale characteristics better aligns with the inherent dynamic laws of the system, providing a more robust problem structure for subsequent numerical integration and helping to ensure numerical stability.

[0263] Innovation Point Two: Structure-Preserving Multirate Variational Integral Method

[0264] Traditional methods, such as using fixed step sizes or simple multi-rate operator splitting for integration, often fail to preserve the original system's geometry and physical conservation laws.

[0265] This application applies the discrete variational principle to each subsystem model, constructs a corresponding discrete Lagrangian for it, and derives the discrete equations of motion (discrete Euler-Lagrangian equations) from this. Furthermore, it dynamically configures different integration step sizes for different subsystem models and executes a structured multi-rate integration loop.

[0266] For example, an integration step size H (first integration step size) is configured for the first subsystem model with the slowest time-scale characteristics, and an integration step size H / M (second integration step size) is configured for the second subsystem model with faster time-scale characteristics. Within the interval of step size H, the second subsystem model undergoes M integration updates. The subsystems are coordinated through variational coupling terms.

[0267] How to solve the technical problems: For dynamic components with slow time-scale characteristics, a large step size is used, significantly reducing the computational load; for dynamic components with fast time-scale characteristics, a small step size is used, but limited to local degrees of freedom. Overall, computational acceleration is achieved while maintaining accuracy. Furthermore, because the numerical solution algorithm in the integration process organically preserves the key physical properties of the original system, such as symplectic structure and momentum conservation, the physical realism and numerical stability of long-term simulations are ensured.

[0268] Innovation Point 3: A Unified Integral Framework for Heterogeneous Systems Based on Geometric Structure Preservation

[0269] Traditional approach: For variables such as rigid body attitude defined on non-Euclidean space (manifold), parameterization (such as Euler angles) combined with conventional integration methods is often used, which is prone to singularity or numerical drift and violates geometric constraints.

[0270] This application extends the variational integral method of innovation point two to manifold spaces such as Lie groups. Specifically, when constructing the discrete Lagrangian of the subsystem model, variables such as rigid body attitude are given discrete forms defined on their respective Lie groups (such as SO(3), SE(3)). This allows multibody systems containing heterogeneous components such as rigid bodies and flexible bodies to be processed within a unified multirate variational integral framework, and the integration process automatically maintains the inherent geometric constraints of each component (such as the orthogonality of the rotation matrix).

[0271] How to solve the technical problems: avoid numerical instability caused by parameter singularity and constraint violation, and ensure the numerical robustness and geometric accuracy of complex multibody system simulation, especially in scenarios with large-scale rigid body motion and fine flexible deformation coupling.

[0272] Innovation Point 4: Adaptive Decision Engine Based on Multi-Physical Quantity Sensing

[0273] Traditional approach: Parameters such as integral step size rely heavily on manual presets or simple error control, which cannot be optimized and adjusted in real time and globally according to changes in the dynamic characteristics of the system.

[0274] This application aims to continuously monitor key physical quantities reflecting the dynamic state of a system, such as the rate of change of energy, the rate of change of momentum, the trajectory curvature, and numerical error estimation. Based on the monitoring data, a multi-objective optimization problem is constructed and solved in real time, with the decision variables being the integration step size (or step size ratio {H,M,N}) of each subsystem model.

[0275] The optimization objectives encompass numerical stability, computational accuracy (e.g., conservation law preservation, trajectory tracking), and computational efficiency (e.g., computational load, real-time constraints). Based on the optimization results, the corresponding integration step size is dynamically determined for each subsystem model. Simultaneously, the decision model is continuously optimized based on historical performance data.

[0276] How to solve the technical problems: Through real-time sensing and optimization, the step size is automatically increased to improve efficiency when the system dynamics are smooth, and automatically decreased to ensure stability and accuracy when the dynamics are drastic or high precision requirements are needed, thus realizing intelligent allocation of computing resources. The entire multibody system processing method can automatically adapt to different working conditions, changes in model parameters, and external disturbances, enhancing the robustness and practicality of the method.

[0277] Figure 8 This is a schematic diagram of the structure of the multibody system processing device provided in this application, as shown below. Figure 8 As shown, the multi-body system processing device 80 provided in this embodiment includes:

[0278] The first determining module 801 is used to determine, at the current moment, the integration step size corresponding to each subsystem model based on at least two subsystem models corresponding to the multibody system. The dynamic components corresponding to different subsystem models have different timescale characteristics; the subsystem model with a faster timescale characteristic corresponds to a smaller integration step size.

[0279] The prediction module 802 is used to predict the predicted state of the multibody system at the next time step based on the integral step size corresponding to each subsystem model and the current state of the multibody system at the current time step.

[0280] The second determining module 803 is used to determine the target control command from multiple control commands based on the predicted state and through at least two subsystem models.

[0281] The execution module 804 is used to execute target control instructions to control the multibody system at the next moment.

[0282] In one possible implementation, the multi-body system processing device 80 further includes an identification module, which, before determining the integration step size corresponding to each subsystem model based on at least two subsystem models corresponding to the multi-body system at the current moment, is used to:

[0283] Identify the time-scale characteristics of each dynamic component of a multibody system.

[0284] Based on the time scale characteristics, the dynamic model of a multibody system is decomposed into at least two subsystem models.

[0285] In one possible implementation, the identification module is specifically used for:

[0286] The corresponding time scale characteristics are determined based on the characteristic frequency or characteristic time constant of each dynamic component.

[0287] Among them, the characteristic frequency is obtained by eigenvalue decomposition of the dynamic equation of the multibody system, and the characteristic time constant is obtained by spectral analysis of the response signal of the multibody system.

[0288] In one possible implementation, at least two subsystem models include a first subsystem model and a second subsystem model, the first subsystem model has an integration step size of the first integration step size, the second subsystem model has an integration step size of the second integration step size, and the time scale feature of the first subsystem model is slower than the time scale feature of the second subsystem model.

[0289] Accordingly, the prediction module 802 is specifically used for:

[0290] Integrate the first subsystem model with the first integration step size to obtain the first intermediate state.

[0291] Within the integration interval corresponding to the first integration step size, the second subsystem model is integrated at least once with the second integration step size to obtain the second intermediate state.

[0292] Based on the coupling relationship between the first intermediate state and the second intermediate state, the predicted state of the multibody system is determined.

[0293] In one possible implementation, the second determining module 803 is specifically used for:

[0294] Using the predicted state as the initial state, the future trajectory of the multibody system under different control commands is simulated through at least two subsystem models.

[0295] Based on the future state trajectory corresponding to different control commands, the control commands that satisfy the preset constraints and can optimize the preset optimization target are determined as the target control commands.

[0296] In one possible implementation, the prediction module 802 is specifically used for:

[0297] Based on the first intermediate state and the second intermediate state, candidate prediction states are determined.

[0298] Verify the physical quantity conservation and / or geometric constraint satisfaction of the candidate predicted states, and determine the verification results.

[0299] If the verification result indicates that the candidate prediction state has passed the verification, then the candidate prediction state is determined as the prediction state.

[0300] In one possible implementation, the first determining module 801 is specifically used for:

[0301] Based on the current state of the multibody system, the corresponding integration step size is dynamically determined for each subsystem model through an adaptive decision module.

[0302] The adaptive decision-making module's decision-making criteria include constraints related to numerical stability and optimization objectives related to computational efficiency.

[0303] The multibody system processing device provided in this embodiment can execute the method provided in the above method embodiment. Its implementation principle and technical effect are similar, and will not be described in detail here.

[0304] Figure 9 A schematic diagram of the structure of the multibody system provided in this application. (See attached diagram.) Figure 9As shown, the multi-body system 90 provided in this embodiment includes: a multi-body system body 901, at least one processor 902, and a memory 903. Optionally, the multi-body system 90 further includes a communication component 904. The processor 902, memory 903, and communication component 904 are connected via a bus 905.

[0305] In a specific implementation, at least one processor 902 executes computer execution instructions stored in memory 903, causing at least one processor 902 to perform the above-described method.

[0306] The specific implementation process of processor 902 can be found in the above method embodiments, and its implementation principle and technical effect are similar. It will not be repeated here.

[0307] In the above embodiments, it should be understood that the processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor.

[0308] The memory may include random access memory (RAM) and may also include non-volatile memory (NVM), such as at least one disk storage device.

[0309] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, the buses shown in the accompanying drawings are not limited to a single bus or a single type of bus.

[0310] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0311] This application also provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the above-described method.

[0312] The aforementioned readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random-Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The readable storage medium can be any available medium accessible to a general-purpose or special-purpose computer.

[0313] An exemplary readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the readable storage medium. Of course, the readable storage medium can also be a component of the processor. The processor and the readable storage medium can reside in an application-specific integrated circuit (ASIC). Alternatively, the processor and the readable storage medium can exist as discrete components in the device.

[0314] The division of units is merely a logical functional division; in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or units, and may be electrical, mechanical, or other forms.

[0315] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0316] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0317] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, ROM, RAM, magnetic disks, or optical disks.

[0318] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0319] Furthermore, while the operations are described in a specific order, this should not be construed as requiring these operations to be performed in the specific order shown or in a sequential order. Multitasking and parallel processing may be advantageous in certain environments. Similarly, while several specific implementation details are included in the above discussion, these should not be construed as limiting the scope of this application. Certain features described in the context of individual embodiments may also be implemented in combination in a single embodiment. Conversely, various features described in the context of a single embodiment may also be implemented individually or in any suitable sub-combination in multiple embodiments.

[0320] Finally, it should be noted that other embodiments of this application will readily conceive of by those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein, and is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and alterations may be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A method for processing multi-body systems, characterized in that, include: At the current moment, based on at least two subsystem models corresponding to the multibody system, determine the integration step size for each subsystem model; where the dynamic components corresponding to different subsystem models have different time scale characteristics, and the subsystem model with faster time scale characteristics corresponds to a smaller integration step size; Based on the integration step size corresponding to each subsystem model and the current state of the multibody system at the current time, predict the predicted state of the multibody system at the next time. Based on the predicted state, the target control command is determined from multiple control commands using the at least two subsystem models; At the next moment, the target control command is executed to control the multibody system.

2. The method according to claim 1, characterized in that, before determining the integration step size corresponding to each subsystem model based on at least two subsystem models corresponding to the multibody system at the current time, the method further includes: Identify the time-scale characteristics corresponding to each dynamic component of the multibody system; Based on the aforementioned time scale characteristics, the dynamic model of the multibody system is decomposed into at least two subsystem models.

3. The method according to claim 2, characterized in that, The identification of the time-scale features corresponding to each dynamic component of the multibody system includes: The corresponding timescale feature is determined based on the characteristic frequency or characteristic time constant corresponding to each dynamic component; The characteristic frequency is obtained by performing eigenvalue decomposition on the dynamic equations of the multibody system, and the characteristic time constant is obtained by performing spectral analysis on the response signal of the multibody system.

4. The method according to any one of claims 1-3, characterized in that, The at least two subsystem models include a first subsystem model and a second subsystem model. The integration step size corresponding to the first subsystem model is a first integration step size, and the integration step size corresponding to the second subsystem model is a second integration step size. The time scale feature corresponding to the first subsystem model is slower than the time scale feature of the second subsystem model. Accordingly, predicting the predicted state of the multi-body system at the next time step based on the integration step size corresponding to each subsystem model and the current state of the multi-body system at the current time step includes: Integrate the first subsystem model with the first integration step size to obtain the first intermediate state; Within the integration interval corresponding to the first integration step size, the second subsystem model is integrated at least once with the second integration step size to obtain the second intermediate state; Based on the coupling relationship between the first intermediate state and the second intermediate state, the predicted state of the multibody system is determined.

5. The method according to any one of claims 1-3, characterized in that, The determination of the target control command from multiple control commands based on the predicted state using the at least two subsystem models includes: Using the predicted state as the initial state, the future state trajectory of the multibody system under different control commands is simulated through the at least two subsystem models. Based on the future state trajectory corresponding to different control commands, the control commands that satisfy the preset constraints and can optimize the preset optimization target are determined as the target control commands.

6. The method according to claim 4, characterized in that, Determining the predicted state of the multi-body system based on the coupling relationship between the first intermediate state and the second intermediate state includes: Based on the first intermediate state and the second intermediate state, the candidate prediction state is determined; Perform physical quantity conservation verification and / or geometric constraint satisfaction verification on the candidate predicted states, and determine the verification results; If the verification result indicates that the candidate prediction state has passed the verification, then the candidate prediction state is determined as the prediction state.

7. The method according to any one of claims 1-3 and 6, characterized in that, The step of determining the integration step size corresponding to each subsystem model based on at least two subsystem models corresponding to the multibody system includes: Based on the current state of the multibody system, the corresponding integration step size is dynamically determined for each subsystem model through the adaptive decision module; The decision-making basis of the adaptive decision-making module includes constraints related to numerical stability and optimization objectives related to computational efficiency.

8. A multi-body system processing device, characterized in that, include: The first determining module is used to determine the integration step size corresponding to each subsystem model at the current time, based on at least two subsystem models corresponding to the multibody system; wherein, the dynamic components corresponding to different subsystem models have different time scale characteristics, and the integration step size corresponding to the subsystem model with faster time scale characteristics is smaller. The prediction module is used to predict the predicted state of the multibody system at the next time step based on the integral step size corresponding to each subsystem model and the current state of the multibody system at the current time. The second determining module is used to determine the target control command from multiple control commands based on the predicted state and through the at least two subsystem models; An execution module is configured to execute the target control command at the next moment to control the multibody system.

9. A multibody system, characterized in that, include: Multibody system main body, memory and processor; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory, causing the processor to perform the method as described in any one of claims 1-6.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the method as described in any one of claims 1-6.

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