CN114660958A - Physical simulation method for crane boom with complex structure - Google Patents

Abstract

The invention discloses a physical simulation method of a crane boom with a complex structure, which comprises the following steps: 1) carrying out simulation on the multi-degree-of-freedom compound motion of the suspension arm by using a quaternion-based compound rotation processing method; 2) the rotation or displacement of the suspension arm can cause the swing of the attached rigid rope, and a PBD (particle beam detector) and procedural grid generation method-based simulation method is used for simulating the rigid rope; 3 the swinging of the rope causes the motion of the object suspended by the rope, and the simulation of the object attached to the bottom of the rope is carried out by using a rigid body-based simulation method. On the basis of meeting the requirement of physical simulation effect, the method greatly improves the efficiency of the method on time and space, and can meet the requirement of real-time rendering software application on real-time performance.

Description

Physical simulation method for crane boom with complex structure

Technical Field

The invention belongs to the field of physical simulation of mechanical structures, and particularly relates to a physical simulation method of a crane boom with a complex structure.

Background

In the field of physical simulation, a boom system with multiple degrees of freedom is difficult to perform physical simulation, which mainly refers to the realistic simulation of compound motion of the system and soft motion such as ropes existing in the system by combining related subject fields such as computer graphics, physics and the like, and rendering and outputting the realistic simulation on target display equipment in a three-dimensional graph mode, wherein related application fields mainly comprise virtual auxiliary training, education, industrial design, electronic games and the like.

The rapid development of the related application field puts higher demands on the virtual simulation technology in terms of reality and real-time performance, and demands that not only the real motion trajectory and the real motion law of the related object can be really simulated, but also the real-time performance of the system can be improved as much as possible.

The existing crane jib simulation method has low efficiency in physical calculation, which is mainly because the traditional simulation method based on physics needs complex traversal operation for many times when simulating software, and in large scene real-time rendering application, the time spent by the physical simulation part needs less time to ensure the application instantaneity, so an efficient crane jib physical simulation method is urgently needed.

Disclosure of Invention

The invention aims to provide a physical simulation method of a crane boom with a complex structure, which can accurately simulate the physical motion track of the crane boom during engineering operation and simultaneously ensure the real-time performance of the crane boom by using an efficient physical simulation scheme.

The invention is realized by adopting the following technical scheme:

a physical simulation method of a crane boom with a complex structure comprises the following steps:

1) carrying out simulation on the multi-degree-of-freedom compound motion of the suspension arm by using a quaternion-based compound rotation processing method;

2) the rotation or displacement of the suspension arm can cause the swing of the attached rigid rope, and a PBD (particle beam detector) and procedural grid generation method-based simulation method is used for simulating the rigid rope;

3) the swinging of the rope causes the motion of an object suspended by the rope, and a rigid body-based simulation method is used for carrying out simulation on the attached object at the bottom of the rope.

The further improvement of the invention is that the simulation of the multiple-degree-of-freedom compound motion of the suspension arm based on quaternion in the step 1) comprises the following steps:

step 1.1) constructing a crane model of the simulation platform according to the crane physical model;

step 1.2) initializing position rotation and scaling information of each large arm and each small arm of a crane arm and a support arm thereof in a world space for a crane model;

step 1.3) setting the hierarchical relation of each part of the crane boom;

step 1.4) reading external input information, converting the external input information into numerical values of a floating point group type for the input of displacement operation so as to represent the moving speed of the operated suspension arm in a simulation environment, and converting the external input information into numerical values of a quaternion type for the input of rotation operation so as to represent the rotating shaft direction and the rotating angular speed of the operated suspension arm in the rotating process;

step 1.5) updating the positions and the rotations of the suspension arms in the world space according to the input numerical values in the step 1.4);

step 1.6) updating the position and rotation of the supporting arm under the world space according to the position of the suspension arm.

The further improvement of the invention is that in the step 1.1), the grid of the crane boom model is formed by combining a plurality of sub-grids, and the plurality of sub-grids are combined into an integral crane boom model in the simulation platform based on the displacement and rotation under different world spaces.

A further improvement of the present invention is that in step 1.4), the read external input is converted into two data types, namely a floating point array type and a quaternion type, for respectively representing the boom movement speed and the rotation speed in the world space.

A further improvement of the invention is that in step 1.6), the position of the supporting arm is updated only after the boom position is updated, and the position of the supporting arm is completely dependent on the position of the boom rather than external input and any other control method.

The invention further improves that the simulation method of the rigid rope generated based on the PBD and the procedural grid in the step 2) comprises the following steps;

step 2.1) determining the starting position of the rope in the world space, and generating a bundle of vertex sets towards the lower direction in the world space;

step 2.2) constraining the positions of the vertexes contained in the vertex set in the step 2.1) by using a PBD (provider-based decomposition) method, and taking the distance between the adjacent vertexes as a constraint quantity;

step 2.3) taking the vertex in the step 2.2) as a path point and approximating by using a catmull-rom curve to obtain a curve;

and 2.4) carrying out process grid generation by taking the triangle as a basic primitive based on the world coordinate, the normal and the tangent of each point on the curve in the step 2.3) to obtain a generated three-dimensional grid model.

A further improvement of the invention is that in step 2.2), the PBD based method only simulates a bundle of vertex sets.

A further improvement of the invention is that in step 2.3) the catmull-rom spline method is used to fit the set of points in step 2.2).

A further improvement of the invention is that in step 2.4) a mesh model of the rope is generated based on the coordinates of the points on the curve in step 2.3) and the normal and tangent data.

The invention has the further improvement that the simulation method of the rope bottom attached object based on the rigid body simulation method in the step 3) comprises the following steps:

step 3.1) determining an attachment point of the rope on a rigid object, and setting a tail end point of the rope as a coordinate of the attachment point in a world space all the time;

step 3.2) carrying out stress analysis on the attached rigid object, and calculating the new speed and angular speed of the object by a rigid body simulation method, wherein the stress analysis comprises the elastic force of the rope, the self gravity and the force generated by collision;

step 3.3) updating the object state of the object based on the velocity and the angular velocity.

The invention has at least the following beneficial technical effects:

1. the rotation problem is processed by using a quaternion-based method, so that the problems of memory waste when a rotation matrix is used and universal lock when an Euler angle is used for processing rotation are avoided;

2. the method for simulating line segments and process grid generation is adopted for simulating the rigid rope, main calculated amount is put on the quick grid generation, and less calculation resources are consumed on the physical simulation, so that the efficiency is improved under the condition of ensuring the physical simulation effect, and meanwhile, the process rope grid generation also supports the dynamic change of the length of the rope during the operation, so that the method is more suitable for the application scene of a crane;

3. the collision of the object is processed by using a method for solving impulse, so that the displacement rotation condition of the complex grid object under the collision stress can be processed, and the effect is more real compared with a collision detection method of a regular bounding box.

Drawings

FIG. 1 is a schematic illustration of an example boom in three-dimensional space;

FIG. 2 is a simplified diagram of a crane arm model and the movement of the boom and arm in an embodiment;

FIG. 3 is a variation of the support arm in a single rotation of the large arm;

FIG. 4 is a schematic diagram of determining the location of a set of points of a rigid rope, wherein FIG. 4(a) is a schematic diagram of a top view, FIG. 4(b) is a schematic diagram of a front view, FIG. 4(c) is a schematic diagram of a right view, and FIG. 4(d) is a schematic diagram of the location of points after production;

FIG. 5 is a graph showing the position update trend of particles in a spring system;

FIG. 6 is a schematic diagram of a catmull-rom spline curve generated for a certain set of vertices;

FIG. 7 is a schematic diagram of a rope lattice produced in the example;

FIG. 8 is a schematic view of the attachment point of the cord to a rigid object according to an embodiment;

FIG. 9 is a schematic view of a single spring system;

FIG. 10 is a force analysis of an object to which a rope is attached;

fig. 11 shows a specific stress situation of the embodiment when simulating the movement of a rigid object.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

The invention relates to a physical simulation method for the movement of a crane arm with a complex structure, which mainly comprises the following three parts:

firstly, processing displacement rotation of a large arm and a small arm of a suspension arm and a supporting arm thereof by using a quaternion-based composite motion simulation method:

1) a crane model of a simulation platform is constructed according to the crane model, fig. 1 is a schematic diagram of a crane arm in a three-dimensional space of an embodiment, fig. 2 is a simplified schematic diagram of the crane arm model and the activity modes of various large and small arms in the embodiment, all parts of the crane arm do not share the same grid in the embodiment, and the point is marked by using discontinuous material colors in the diagram. If OpenGL is used as a graphics rendering API for the simulation platform, this means that each part of the boom corresponds to a separate VAO.

2) Initializing the position rotation and scaling information of each small arm and the supporting arm of the suspension arm in the world space, initializing by using different displacement matrixes and rotation matrixes when initializing the model position, ensuring that the grid models of the large arm, the small arm and the supporting arm have correct joint relation after being converted into the world space, and if vectors are used

The position of the grid i in the world space is represented, and the coordinates of each vertex of the grid i are T x v_jWherein v is_jFor the local coordinate of the jth vertex of grid i, T is a displacement matrix of 3 rows and 3 columns, whose value is

The invention uses quaternion to process the rotation of the model, with quaternion

Representing grid i around an arbitrary axis of rotation

By rotating by theta degrees (in radians), the coordinates of each vertex of the grid i after rotation are R x v_jR is a 3-row and 3-column rotation matrix having a value of

Wherein the content of the first and second substances,

only 4 floating point numbers need to be stored when the rotation is performed by physical simulation calculation after the rotation is processed by using the quaternion, namely four components of the quaternion, and compared with a rotation matrix using three-dimensional three columns, the storage overhead on the rotation operation is reduced

3) And setting the hierarchical relation of the grid models of all parts of the crane boom. FIG. 2 is a schematic diagram of a hierarchical relationship of a boom model in an embodiment, in the hierarchical relationship shown in the embodiment, if the local coordinates and rotations of the whole boom, the big arm, the small arm, the big arm of the support arm, and the small arm of the support arm are p respectively_i,q_iAnd i is 0,1,2,3,4 (i.e. the position and rotation of a certain mesh model are respectively expressed by a three-dimensional vector and a quaternion), then in the hierarchical relationship of the embodiment, the displacement and rotation of each part of the boom in the world space are

4) And reading an input signal of an external device and converting the input signal into displacement increment or rotation increment of each part of the crane arm. In the boom structure shown in the embodiment, the rotation of the large arm and the expansion and contraction of the small arm are conversion states which can be directly operated, and the RotateSpeed E-1, 1 is input signal for the rotation of the large arm]To renew the rotation of the large arm

Wherein

Is the rotation axis of the large arm, Δ t is the rendering interval between every two frames, q_oldThe rotation of the large arm in the previous frame. Translatespeeed ∈ [ -1,1 ] input signal for telescopic displacement of forearm]Updating the position p of the forearm_new＝p_old+ Δ t × translated × Direction, where Direction is the Direction in which the forearm changes in extension and retraction.

5) The rotation of the support arm is updated according to the rotation of the large arm. FIG. 3 shows the change of the supporting arm in one rotation of the boom, before the rotation the supporting arm boom is at an angle beta to the boom chassis₁The included angle between the small arm and the large arm of the supporting arm is alpha₁After the rotation, the two angles are respectively updated to beta₂、α₂. In the embodiment, the model displacement and the rotation are both expressed by local variables in a hierarchical relationship, so that the change of the local rotation amount of the large arm and the small arm of the supporting arm in the current movement only needs to be analyzed respectively. For the rotation variation shown in FIG. 3, the partial rotation of the large arm of the support arm

Wherein q is_oldFor the partial rotation of the large arm of the support arm before the rotation operation,

Is a rotating shaft of a big arm of the supporting arm. Local rotation of the small arms of the supporting arms

Wherein q is_oldA small partial rotation of the support arm before the rotation operation,

Is the rotation axis of the small arm of the supporting arm. Obtaining new coordinates and rotation values of the support arm in the world space according to the relationship between the local space coordinates and rotation in the hierarchical relationship and the coordinate rotation in the world space in the 3).

Secondly, using a rope physical simulation algorithm generated based on the PBD and the procedural grid to process the state update of the boom rigid rope:

1) determining the starting point position of the rigid rope, wherein the starting point positions p of the rigid rope in the embodiment are shown in fig. 4(a), (b) and (c) respectively₁、p₂、p₃、p₄Position under plan view, front view, right view, indicated by p₁、p₂、p₃、p₄Generating i points in the downward direction as the starting point, and marking as

FIG. 4(d) gives a schematic of this process;

2) point p is aligned using the PBD method_jkAnd (6) carrying out constraint. The PBD method comprises the following processes that 1) the stress motion condition of each mass point in the system is simulated in a single particle mode; 2) all particles in the system are constrained by certain constraint quantities; 3) the positions of all particles in the system are updated. For a rigid rope, the initial distance of adjacent particles may be used as the amount of restraint.

The PBD method is further explained herein using a system containing only two particles, and FIG. 5 shows the position update trend of the particles in this system, when the particles are currentlyWhen the distance is less than the threshold value, the PBD method will drive the particles to move in the direction that can make the distance between them larger, and when the distance is greater than the threshold value, the particles will be driven to move in the direction that can make the distance between them smaller, so the constraint used here is that

The location update function is:

obtaining the solution

The location update functions are:

for a system containing multiple particles, traversing each pair of adjacent particles in the system and updating their positions, the pseudo-code is described as follows:

or a Jacobi method is used to obtain a global better solution, and pseudo codes are described as follows:

so far, the set of vertices generated in 1) has had a simple rope-like physical simulation effect, but has not yet constituted a line segment.

3) Curve fitting is carried out on the vertex set in the step 2.2), in the embodiment, a catmull-rom spline curve method is used for fitting, the catmull-rom method ensures that the fitted curve can pass through all points between the second point of the control point and the penultimate point, and fig. 6 shows an example of a curve segment obtained by using the catmull-rom spline curve method for a certain vertex set.

4) Carrying out process generation on the mesh model of the rope according to the curve c obtained in the step 3), and knowing that the coordinates of each point on the curve c are

The tangential direction of each point is

The mesh generation process is as follows: 1) obtaining the right direction unit vector in world space

2) For each vertex

Projection (projector)

To the normal plane to obtain the projected unit vector

3) For each projected unit vector

Make it around the tangential direction

Rotate n times, each rotation

Degree (in radians), and the vector after each rotation is recorded as

The projection operation in the process and 2) will generate n +1 new vectors on the normal plane of each vertex, and will respectively connect these vectors with the corresponding normal plane

Adding to obtain i x (n +1) new vertexes in world space, wherein the vertexes are used as vertexes of the procedural rope grid; 4) generating a corresponding rope mesh model by taking the triangle as a basic primitive and taking the coordinates of the vertex generated in the step 3) as the coordinates of the vertex of the mesh; the procedure for implementing the above steps is as follows, first, finding an additional set of vertices mesvertics on the normal plane for each vertex on the curve, which will contain i × (n +1) vertices, and the pseudo code is described as follows:

after all the vertices of the mesh are obtained, we will set a mesh triangle primitive index set, mesltrians, in which the index of each triangle primitive of the mesh in mesltrians is stored, for example,

which are the coordinates of the three vertices of the first triangle primitive of the mesh, the mesltriangles is set by the following way, for each vertex, two triangle faces will be generated, and the pseudo code is described as follows:

fig. 7 presents a schematic diagram of a rope grid generated using the above-described procedural generation method in an embodiment.

And thirdly, performing physical simulation on the motion of a rigid object attached to the bottom of the rope.

1) The attachment point of the rope on the rigid object is determined and the end point of the rope is always set as the coordinate of the attachment point in world space, and fig. 8 shows a schematic diagram of the attachment point of the rope on the rigid object in the embodiment.

2) And (5) carrying out stress analysis on the attached rigid object. First, the object is influenced by its own weight, and because 1) the bottom vertex of the rope is always set to the position of the attachment point on the rigid object, when the object falls downward by the gravity, the rope is stretched to cause the object to receive the spring force, and the spring force changes along with the change of the length of the rope, specifically, in the single-spring system shown in fig. 9, the spring force received by the two mass points is respectively the spring force

Where k is a constant representing the spring constant of the spring system.

In an embodiment, force analysis of a rigid object as shown in FIG. 10, the object is subjected to its own weight

And spring force

The influence of (c). Of these forces, gravity acts on the center of gravity of the object and thus only on the physical displacement, whereas the spring force acts on the attachment point, which will have an effect on the rotation of the object.

First, for a displacement of an object, it is subjected to a resultant force of

The acceleration of the object can be obtained as

Where m is the mass of the object. The linear velocity of the object is updated to

The displacement p of the object is thus updated to

Spring force for rotation of an object

Will result in the rotation of the object, the sum of the torques they generate on the object being

τ＝∑τ_i

The angular velocity increment resulting from the torque τ is

Δω＝ΔtI^-1τ

Where I is the moment of inertia, represented here as a matrix of four rows and four columns, with values of

I＝RI_refR^T

Wherein m is_iThe mass of a particle i on the grid, r_iIs the offset of the position of vertex i relative to the centroid position.

Thus, the angular velocity of the object is updated to

ω＝ω+Δω

After obtaining the new angular velocity, the quaternion for representing the rotation of the object is updated in each frame by

Thus, the embodiment is processed for the movement of the rigid object to which the rope is attached, and fig. 11 is a special case of the embodiment when simulating the movement of the rigid object, so as to show the simulation effect of the invention.

Although the invention has been described in detail hereinabove with respect to a general description and specific embodiments thereof, it will be apparent to those skilled in the art that modifications or improvements may be made thereto based on the invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.

Claims (10)

1. A physical simulation method for a cargo boom with a complex structure is characterized by comprising the following steps:

1) carrying out simulation on the multi-degree-of-freedom compound motion of the suspension arm by using a quaternion-based compound rotation processing method;

2) the rotation or displacement of the suspension arm can cause the swing of the attached rigid rope, and a PBD (particle beam detector) and procedural grid generation method-based simulation method is used for simulating the rigid rope;

3) the swinging of the rope causes the motion of an object suspended by the rope, and a rigid body-based simulation method is used for carrying out simulation on the attached object at the bottom of the rope.

2. The physical simulation method of a crane boom with a complex structure as claimed in claim 1, wherein the simulation of the complex motion of multiple degrees of freedom of the crane boom based on quaternion in step 1) comprises:

step 1.1) constructing a crane model of the simulation platform according to the crane physical model;

step 1.2) initializing position rotation and scaling information of each large arm and each small arm of a crane arm and a support arm thereof in a world space for a crane model;

step 1.3) setting the hierarchical relation of each part of the crane boom;

step 1.4) reading external input information, converting the external input information into numerical values of a floating point group type for the input of displacement operation so as to represent the moving speed of the operated suspension arm in a simulation environment, and converting the external input information into numerical values of a quaternion type for the input of rotation operation so as to represent the rotating shaft direction and the rotating angular speed of the operated suspension arm in the rotating process;

step 1.5) updating the positions and the rotations of the suspension arms in the world space according to the input numerical values in the step 1.4);

step 1.6) updating the position and rotation of the supporting arm under the world space according to the position of the suspension arm.

3. The physical simulation method of the crane boom with the complex structure as claimed in claim 2, wherein in step 1.1), the grid of the crane boom model is composed of a plurality of sub-grids, and the plurality of sub-grids are combined into an integral crane boom model in the simulation platform based on displacement and rotation under different world spaces.

4. The method for simulating the physical simulation of the crane boom with the complex structure as claimed in claim 2, wherein in the step 1.4), the read external input is converted into two data types, namely a floating point group type and a quaternion type, which are respectively used for representing the moving speed and the rotating speed of the crane boom in the world space.

5. The method for simulating the physics of a crane boom with a complicated structure as claimed in claim 2, wherein in step 1.6), the position of the supporting arm is updated only after the update of the boom position is finished, and the position of the supporting arm is completely dependent on the position of the boom and not external input and any other control modes.

6. The physical simulation method of a crane boom with a complex structure according to claim 1, wherein the simulation method of the rigid rope generated based on the PBD and the procedural grid in the step 2) comprises;

step 2.1) determining the starting position of the rope in the world space, and generating a bundle of vertex sets towards the lower direction in the world space;

step 2.2) restraining the positions of vertexes contained in the vertex set in the step 2.1) by using a method based on PBD, and taking the distance between adjacent vertexes as a restraint quantity;

step 2.3) taking the vertex in the step 2.2) as a path point and approximating by using a catmull-rom curve to obtain a curve;

and 2.4) carrying out process grid generation by taking the triangle as a basic primitive based on the world coordinate, the normal and the tangent of each point on the curve in the step 2.3) to obtain a generated three-dimensional grid model.

7. The physical simulation method of a crane boom with a complex structure as claimed in claim 6, wherein in step 2.2), the PBD-based method only simulates a bundle of vertex sets.

8. The method for simulating the physical simulation of the crane boom with the complex structure as claimed in claim 6, wherein in the step 2.3), a catmull-rom spline method is used for fitting the point set in the step 2.2).

9. The method for simulating physical simulation of a crane boom with a complex structure as claimed in claim 6, wherein in step 2.4), the mesh model of the rope is generated based on the coordinates of each point on the curve in step 2.3) and the data of the normal line and the tangent line.

10. The physical simulation method of a crane boom with a complex structure as claimed in claim 1, wherein the simulation method of the rope bottom attached object based on the rigid body simulation method in step 3) comprises:

step 3.1) determining an attachment point of the rope on a rigid object, and setting a tail end point of the rope as a coordinate of the attachment point in a world space all the time;

step 3.2) carrying out stress analysis on the attached rigid object, and calculating the new speed and angular speed of the object by a rigid body simulation method, wherein the stress analysis comprises the elastic force of the rope, the self gravity and the force generated by collision;

step 3.3) updating the object state of the object based on the velocity and the angular velocity.

Images