KR100876642B1 - The analysis method of the multibody dynamics system using parallel processing - Google Patents

Abstract

A method for analyzing an object dynamic mechanics system having multiple degree-of-freedom is provided to reduce analyzing time by disassembling the object mechanics system into a plurality of pieces and processing respective processes in parallel. A turnaround time of processes calculating Jacobian is computed for each entity. An intrinsic thread ID is given to each entity. A nonlinear motion equation of the object dynamic mechanics system is linearized through Jacobian computation by distributing the processes having the intrinsic thread to the threads in parallel according to the intrinsic thread ID. Jacobian of the motion equation of the system is converted into product of lower and top triangular matrixes with triangular matrix decomposition by distributing the processes of the part disassembling the motion equation of the linearized system to a plurality of threads generated in a CPU. A solution of the motion equation of the linearized system, which is converted through the triangular matrix decomposition, is output by distributing the processes of the part disassembling the linearized motion equation to the threads generated in the CPU.

Description

Analysis method of the multibody dynamics system using parallel processing

The present invention relates to an analysis method for a multibody dynamics system and to a processing method using parallel computer programming or processing. More specifically, the present invention relates to an analysis method of a multibody dynamics system using parallel processing in a multibody dynamics system in which rigid bodies are connected by joints, forces, and contact elements.

Multibody dynamics system deals with the dynamics of a system in which rigid bodies are connected by joints, forces, and contact elements.In recent years, the system is complicated and enlarged, which complicates the configuration. It's getting very long.

The degrees of freedom in the above means the minimum number of coordinates required to represent the moving shape of the multibody system.

The most important factor in the analysis of multibody dynamics system is the speed and accuracy, but it increases the degree of freedom of the system in order to improve the accuracy, and thus processes many processes when analyzing the dynamics of multibody systems with more than tens of thousands of complex degrees of freedom. As a lot of time is required, the problem of the speed of interpretation is caused.

1 is a flowchart illustrating an analysis process of a multibody dynamics system according to the prior art, and the system is analyzed through entities such as rigid bodies, joints, forces, and contacts, which constitute the multibody dynamics system.

The multibody dynamics system composed of the above-mentioned entities can be expressed by the following nonlinear equations of motion and constraints.

In order to solve the equation of motion of the multibody dynamics system expressed as described above, to obtain the solution of the desired multibody dynamics system, it is necessary to linearize the equation of motion F.

In order to linearize the equations of motion of the multibody dynamics system, the Jacobian and residuals are calculated using the Newton-Rapson method to convert the linearized linear equations into a matrix form as follows. (Step S1)

Ax = b

A: Jacobian

b: residual

x: Solutions of Multibody Dynamics Systems

In addition, a numerical factorizing step of converting Jacobian of the converted determinant into a Jacobian A = LU ( L: lower triangular matrix, U: upper triangular matrix) form using triangular matrix decomposition (step S2) And a back-substitution step (step S3) of calculating the dynamic solution of the multi-body system using the converted LU matrix and a step of updating the obtained solution (step S4).

Since the LU decomposition method and the back extraction method mentioned above are generally used in numerical analysis, detailed descriptions are omitted here.

In the above, in particular, in the case of calculating Jacobian and residual (step S1), the calculation of the equation F is performed by partial derivative of the general equation and the Lagrange multiplier, which are independent of the entities necessary for interpretation. You lose.

However, in the case of calculating Jacobian and residual for the entities in order to linearize the equation of motion when tens of thousands of entities are included, the step (S1) requires a very long processing time, thereby substantially reducing the multi-body dynamics system. This is a problem for the speed of analysis time.

In other words, in the processing of each of the above steps, in the case of processing the process of each step through the computer in a sequential manner, the analysis process of the multi-degree of freedom complex multi-body dynamics system which is very complicated and the system is enlarged as in recent years The problem is that a very long analysis time is required.

In other words, the method of grasping the state of the system by minimizing the analysis time of the multibody dynamics system is actually the most important issue in the multibody dynamics system.

In order to solve the above problems, an object of the present invention is to reduce the analysis time of a multibody dynamics system by disassembling the system into a plurality of processes in parallel and processing the processes of the respective decomposed parts in parallel. .

In addition, the present invention is to process the process for each entity of the multi-body dynamics system in the process of calculating Jacobian using the Newton-Lapson method in the linearization of the non-linear dynamics of the multi-body dynamics system. It aims to reduce the analysis time of multibody dynamics system by creating multiple threads.

In addition, the present invention, in the process of calculating Jacobian using the Newton-Lapson method in the linearization step of the non-linear dynamic equation of the multibody dynamics system, allocates processes for calculating Jacobian for each entity to threads. In this case, it is aimed to minimize the analysis time of the multibody dynamics system by maximizing the efficiency of parallel processing by minimizing the gap of parallel processing time between multiple threads.

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In order to achieve the above object, in the method of analyzing a multibody dynamics system having multiple degrees of freedom and a plurality of entities connected to each other, (a) linearizing a nonlinear equation of motion of the multibody dynamics system using the Newton-Lapson method In the case of calculating Jacobian for the purpose of computing the time required for the processes of calculating Jacobian for each entity, and assigning a unique thread ID so that the processes for calculating Jacobian for each entity are distributed to a specific thread. Linearizing the nonlinear equations of motion of the multi-body dynamics system by calculating Jacobian by distributing the processes for each entity to which a unique thread ID is assigned to the threads according to the unique thread ID to perform parallel processing; (b) linearizing the nonlinear equations of motion of the multibody dynamics system in step (a), and then converting the Jacobian to the product of the upper and lower triangles by triangular matrix decomposition. Decompose the kinematic equation of and divide the processes of each decomposed part into multiple threads created by the central processing unit, and convert the Jacobian of the kinematic equation of the system into the product of the upper triangular matrix and the lower triangular matrix by triangular matrix decomposition. Doing; (c) after constructing the transformed linearized equation of motion through the triangular matrix decomposition method of step (b), in order to derive a solution of the transformed linearized equation of motion, the linearized motion transformed through the triangular matrix decomposition method Decomposing the equations and distributing the processes of each decomposed portion to a plurality of threads generated in the central processing unit to derive a solution of the equation of motion of the linearized system transformed by the triangular matrix decomposition. This paper presents a dynamic analysis method for multi-objective systems with multiple degrees of freedom.
In order to achieve the above object, the present invention is a multi-body dynamics system analysis method having a number of degrees of freedom and is connected to a plurality of entities, the system is divided into a plurality of parts to interpret the system, each part The present invention proposes an analysis method of a multi-body dynamics system having multiple degrees of freedom including parallel processing by distributing a plurality of processes to a plurality of threads generated in a central processing unit.
When the plurality of threads are in parallel in the process of parallel processing, the memory sharing between the threads to affect each other may further comprise the step of synchronizing the thread processing for sequential processing.

In addition, in order to achieve the above object, the present invention in the multi-body dynamics system analysis method having multiple degrees of freedom and connected a plurality of entities, the Newton-Lapson method of the nonlinear kinematic equation of the system to interpret the system The calculation of Jacobian to linearize using the step of: generating a plurality of threads in the central processing unit to perform parallel processing; Assigning a unique ID to each of the processes for calculating Jacobian for each entity; And distributing processes for calculating Jacobian for each entity to which the unique ID has been assigned to the plurality of threads in an equal number to the plurality of threads. The multi-body dynamics system having the multiple degrees of freedom to which parallel processing is applied is included. Provide an interpretation method.

In addition, in order to achieve the above object, the present invention in the multi-body dynamics system analysis method having multiple degrees of freedom and connected a plurality of entities, the Newton-Lapson method of the nonlinear kinematic equation of the system to interpret the system The process of calculating Jacobian to linearize using the step includes: generating a plurality of threads in the central processing unit to perform parallel processing; Calculating a time required for each process of calculating Jacobian for each entity; Assigning a unique thread ID so that processes for calculating Jacobian for each entity are distributed to specific threads; And distributing the processes for each entity to which the unique thread ID is assigned to the thread according to the unique thread ID. The present invention provides a method of interpreting a multibody dynamics system having multiple degrees of freedom including parallel processing. .

In addition, in order to achieve the above object, the present invention is a method of analyzing a multi-body dynamics system having a multiple degree of freedom and a plurality of entities are connected, (a) to linearize the non-linear equation of motion of the multi-body system, Disassembling the system to distribute the processes of each disassembled portion to a plurality of threads for parallel processing;

(b) disassembling the system, distributing the processes of each of the decomposed parts to a plurality of threads generated in a central processing unit and performing parallel processing to convert the linear equations of the system using triangular matrix decomposition; (c) disassembling the system, distributing the processes of each of the decomposed parts to a plurality of threads generated in a central processing unit and performing parallel processing to derive a solution of a linear equation converted using the triangular matrix decomposition; ; And (d) updating the derived solutions in parallel by updating the derived solutions. The present invention provides a dynamic analysis method for a multi-object system having multiple degrees of freedom including the parallel processing.

Steps (b) and (c) may further include synchronizing thread processing for sequential processing when the plurality of threads share a memory and influence each other in parallel processing.

In addition, in the step (a), the Newton-Lapson method is used to linearize the nonlinear equation of motion, and when the Newton-Lapson method is used, the Jacobian calculation is performed by a central processing unit. Creating a thread; Assigning a unique ID to each of the processes for calculating Jacobian for each entity; And distributing processes for calculating Jacobian for each entity to which the unique ID has been assigned, in equal numbers to the plurality of threads.

In addition, in the step (a), the Newton-Lapson method is used to linearize the nonlinear equation of motion, and when the Newton-Lapson method is used, the Jacobian calculation is performed by a central processing unit. Creating a thread; Calculating a time required for each process of calculating Jacobian for each entity; Assigning a unique thread ID so that processes for calculating Jacobian for each entity are distributed to specific threads; And distributing the processes for each entity to which the unique thread ID is assigned to the thread according to the unique thread ID.

Through the analysis method of the multi-body dynamics system having the multiple degree of freedom applying the parallel processing according to the present invention, the following effects can be obtained.

First, the analysis speed of the multibody dynamics system can be improved drastically, and the processing speed can be significantly improved compared to the conventional sequential processing method, thereby reducing design time and development cost.

Secondly, when obtaining Jacobian using Newton-Lapson method in the linearization stage of multibody dynamics system, parallel processing that allocates and processes the Jacobian for each entity to multiple threads. Through this, the analysis time of multibody dynamics system can be reduced.

Third, when obtaining Jacobian using Newton-Lapson method in the linearization stage of multibody dynamics system, it calculates in advance the time required to calculate Jacobian for each entity, and Jacobian for each entity. By assigning a unique thread ID to each of the processes for calculating the value and assigning it to a specific thread, it minimizes the gap of parallel processing time between a plurality of threads and has the effect of maximizing the efficiency of parallel processing.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

Figure 2 shows a simplified flow diagram of the process of analyzing the multi-body dynamics system of the present invention, as shown in the present invention is configured to perform parallel processing for multi-body dynamics system analysis.

Elements that make up a multibody dynamics system include entities such as rigid bodies, joints, forces, and contact elements. Depending on the system, the entities may include tens of thousands or more.

In more detail, in the parallel processing method, calculating Jacobian and residual in order to linearize the equation of motion of the system (S1), and numerical factorizing (S2), In the back-substituion step (S3) for obtaining a solution of the object dynamics system and the step (S4) for updating the solution of the obtained system, at each step, a plurality of threads are generated and generated in the central processing unit. By disassembling the multibody dynamics system into threads, the processes of each step can be configured to perform parallel processing so that all steps of the system analysis can be parallelized.

The parallel processing method creates a plurality of processing units called threads in the central processing unit (CPU) in order to process the process, decomposes the process to be processed into elements, and distributes them to the threads created in the central processing unit for the disassembled process. To perform the processing in parallel.

That is, the parallel processing method that is processed in each step of the multi-body dynamics system allows a thread to be generated, and the multi-body dynamics system is decomposed into a plurality of generated threads, and a process to be processed in a decomposed system unit is provided to the threads. Allocate and parallelize threads simultaneously.

Therefore, in the conventional multi-body dynamics analysis method, the processing method for each analysis is applied to the sequential method rather than parallel processing, which requires a great amount of time in the analysis step. The present invention can solve the problem by introducing a parallel processing method has the effect of reducing the enormous time required for system analysis.

FIG. 3 illustrates Jacobian in units of a plurality of entities in step S1 of calculating Jacobian and residual in order to linearize a multibody dynamics system according to a first embodiment of the present invention. And a method of allocating a process for calculating a residual and a residual to a thread for parallel processing, wherein the central processing unit (CPU) generates a certain number of threads, and multiplies the generated multiple threads. Divide and distribute the entities of the dynamics system and configure them to parallelize the entities with each thread.

The calculation of Jacobian and Residue is calculated by partial derivative of the system's equation of motion with respect to general coordinates and Lagrange multipliers, which are performed separately for the entities needed for interpretation, and for each entity calculated for each entity. There is no memory sharing with each other on the process.

In other words, parallel processing means processing that processes multiple processes in parallel by allocating each process to a plurality of threads in order to rapidly process a plurality of processors for each entity calculating a Jacobian and a residual.

As shown in the illustrated embodiment, if three threads (P1, P2, P3) are generated, when the number of processes per entity to be processed is N, each thread has an entity-specific process for each of the three threads created. By distributing them evenly and collectively, parallelizing the process by each entity in each thread at the same time, it is possible to quickly linearize the equations of motion of a multibody dynamics system.

To this end, each entity-specific process is assigned a unique ID, and the entity-specific processes to which the unique ID is assigned are distributed to an equal number of generated threads so as to perform parallel processing.

FIG. 4 shows Jacobian in units of a plurality of entities in step S1 of calculating Jacobian and residual in order to linearize a multibody dynamics system according to a second embodiment of the present invention. And a method of allocating a process for calculating a process and a residual to a thread for parallel processing, and each entity has its own thread id.

In the case of parallel processing in the same manner as in FIG. 3 mentioned above, since the parallel processing is performed by randomly equally distributing the processes by entity to the threads, the time according to the parallel processing of the processes by the entity allocated to each thread. Eventually, there will be a gap in parallelism completion time for each thread.

In more detail, in the process of calculating Jacobian to linearize the equation of motion of a multibody dynamics system, nonlinear equations of motion are computed by partial derivatives of the general and Lagrangian multipliers. , Joints, forces, contacts, etc.).

Therefore, the calculation time of the Jacobian and the residual differs depending on the type of joint, the type of force, the type of contact, and the like.

와

는 바디 i와 j를 연결하는 조인트의 자세를 나타내기 위한 단위 방향벡터로서, 서로 직각을 이루고 있는 좌표이며,

는 두 좌표간의 거리를 나타내는 벡터이다. 또한 r 과 A는 각각의 바디들의 위치와 자세를 나타내는 벡터와 행렬이다. 이하에서 기재하는 수학식 자체의 정확한 의미는 당해분야의 당업자 등만이 이해할 수 있을 것이며, 다만, 본 발명의 다물체 동역학 시스템을 해석하는 방법의 구성상 구현하고자하는 바를 설명하기 위한 하나의 예시로서 기재할 뿐이지 수학식 자체의 의미는 본 발명과는 크게 관련이 없을 것임은 당해분야의 당업자 입장에서 자명한 것일 것이다.5 is a state diagram in which the bodies and joints of the multibody dynamics system are shown in a vector.

Wow

Is a unit direction vector for indicating the posture of the joint connecting the bodies i and j, and the coordinates are perpendicular to each other.

Is a vector representing the distance between two coordinates. Also, r and A are vectors and matrices representing the positions and postures of the respective bodies. The exact meaning of the equations described below will be understood only by those skilled in the art, but as an example for explaining what is intended to be implemented in the construction of a method for interpreting the multibody dynamics system of the present invention. It will be apparent to those skilled in the art that the meanings of the equations themselves are not related to the present invention.

For example, in the case of a translational joint, the translational joint is only one direction, and the joint cannot rotate. Therefore, there are five constraint expressions as follows.

In the case of a spherical joint, three joint constraints are shown below.

를 계산하게 된다.To calculate Jacobian and Residue for the above joints,

Will be calculated.

In this process, the difference between the joints and the constraints of the respective joints causes a time difference in the process of calculating the Jacobian and the residual.

Therefore, if the process of entity that calculates Jacobian where such temporal difference occurs is simply distributed equally to each thread and parallelized by each thread, the time difference occurs when the constraints process the processes of other entities. As a result, the parallel processing time is different for each thread, which can reduce the efficiency of parallel processing. That is, as the time required for the calculation process in each thread is different, a problem may occur that a waiting thread is generated after the calculation process is finished first.

To improve this, a configuration may be added to minimize the time gap of processes computed in each thread in view of the difference in constraint of each entity.

In other words, in order to calculate Jacobian, it includes a step of precomputing the time required for each process for all the entities forming the multibody dynamics system, and the process for each entity having such different time is allocated to a specific thread. Configure to have information about whether

To this end, in order to be distributed to specific threads P1, P2, and P3, each entity-specific process is configured to have its own thread id, P1, P2, and P3, so that processes for each entity are individually allocated. Go to the thread and configure it to process.

That is, by allocating the computational time required by the process of each entity processed in each thread of a plurality of threads through the operation time of the process per entity, the efficiency of parallel processing can be maximized. As the time required for the calculation process is different, the problem that the waiting thread is generated after the calculation process is finished first can be prevented, which greatly reduces the analysis speed of the multi-body dynamics system.

6A and 6B are simplified diagrams illustrating a decomposition method of a multibody dynamics system and a parallel processing method for processing a process in a decomposed system unit.

In more detail, in the step S2 of numerical multiplication of the multibody dynamics system of the present invention, the back-substituion step S3 of obtaining a solution of the multibody dynamics system may be performed in parallel. As shown in the figure, a multibody dynamics system can be decomposed into 3, 2, and 1 and parallelized in steps.

FIG. 6A is a simplified diagram of a method for decomposing a multibody dynamics system of the present invention, with a plurality of rigid bodies and connecting elements representing the forces, contacts, joints, etc. connecting the rigid bodies as shown, ie a plurality of entities. A method of decomposing a multibody dynamics system with rigid-body connectivity information for parallel processing is shown.

FIG. 6B is a diagram illustrating a method for parallelizing a disassembled system process by element. If the CPU generates two threads P1 and P2 as shown in FIG. Parallelize processes one, two, and one.

First, erase three times and distribute them to threads P1 and P2 so that they are processed in parallel, and then erase the second times and distribute them to P1 and P2 to process them in parallel, and finally, distribute one time to P1 and P2. By using the parallel processing method, the processing speed can be greatly improved.

However, when there is a part that shares the processes of steps 3, 2, and 1 at the time of processing, that is, when the memory is shared between threads and affects each other, the thread processing is synchronized for sequential processing. A step is necessary.

That is, when the memory is shared in the process of sharing the number 2 and 1 in the process of erasing 3 times, in the process of sharing the number 1 in the process of erasing 2 times, preventing simultaneous processing between threads; In other words, it includes a synchronous step that restricts thread access.

For this purpose, when other threads share memory, the processing order must be set between threads. For example, when erasing 3 times, the thread that accesses the memory of the shared part first for the part shared with 1 and 2 times. Parallel processing should be performed while configuring to prohibit access to the memory for all threads except.

More specifically, the mutex function can be used as such a synchronization method, and the creation and destruction of threads can be configured through the windows function or OpenMP.

Finally, the solution solved through the above steps is updated to update the accuracy of the solution of the multibody system dynamics analysis.

This process does not require any shared memory between entity-specific processes, as in the case of obtaining Jacobian and Residue, and does not require any work on shared memory. To perform.

In addition, the analysis method of the multi-body dynamics system having the multiple degree of freedom to which the parallel processing processing of the present invention described above is applied may be recorded in a computer-operated intermediate apparatus and used to analyze the multi-body dynamics system through a computer. .

In particular, if the central processing unit (CPU) of the computer has multiple cores, it will enable faster processing.

In the above detailed description of the present invention, specific embodiments have been described, but the present invention is not limited thereto, and various modifications may be made without departing from the scope of the technical idea of the present invention to those skilled in the art. Will be self explanatory.

1 is a flow chart showing an analysis process of a multibody dynamics system according to the prior art.

Figure 2 is a simplified flow diagram of the analysis process of the multi-body dynamics system of the present invention.

3 is a flowchart illustrating a method of allocating a process to threads for parallel processing in units of entities in order to linearize a multibody dynamics system according to a first embodiment of the present invention.

4 is a flowchart illustrating a method of allocating a process to threads for parallel processing in units of entities in order to linearize a multibody dynamics system according to a first embodiment of the present invention.

5 is a state diagram in which the body and the joint of the multi-body dynamics system of the present invention are represented by a vector.

6A and 6B are simplified diagrams illustrating a decomposition method of a multibody dynamics system and a parallel processing method for processing a process in a decomposed system unit.

Claims (8)

delete delete delete delete In the analysis method of a multibody dynamics system having multiple degrees of freedom and a plurality of entities connected to each other, (a) In the case of calculating Jacobian to linearize the nonlinear equation of motion of the multibody dynamics system using the Newton-Lapson method, the time required for the processes of calculating Jacobian for each entity is calculated, and for each entity. By assigning a unique thread ID so that processes calculating Jacobian are distributed to a specific thread, and calculating the Jacobian by distributing the processes for each entity to which the unique thread ID is assigned to the thread according to the unique thread ID and performing parallel processing Linearizing the nonlinear equations of motion of the multibody dynamics system; (b) linearizing the nonlinear equations of motion of the multibody dynamics system in step (a), and then converting the Jacobian to the product of the upper and lower triangles by triangular matrix decomposition. Decompose the kinematic equation of and divide the processes of each decomposed part into multiple threads created by the central processing unit, and convert the Jacobian of the kinematic equation of the system into the product of the upper triangular matrix and the lower triangular matrix by triangular matrix decomposition. Doing; (c) after constructing the transformed linearized equation of motion through the triangular matrix decomposition method of step (b), in order to derive a solution of the transformed linearized equation of motion, the linearized motion transformed through the triangular matrix decomposition method Decomposing the equations and distributing the processes of each decomposed portion to a plurality of threads generated in the central processing unit to derive a solution of the equation of motion of the linearized system transformed by the triangular matrix decomposition. Dynamic Analysis Method of Multibody Systems with Multiple Degrees of Freedom. According to claim 1, wherein step (b) and (c), Synchronizing thread processing for sequential processing when the plurality of threads share a memory in the process of parallel processing and influence each other. The multi-body dynamics having the multiple degree of freedom to which parallel processing is applied is further included. How to interpret the system. delete delete

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