JP2003089082A - Method for detecting force of constraint acting between objects and system thereof - Google Patents

Abstract

PROBLEM TO BE SOLVED: To detect a force of constraint acting between objects even when an inner point of the object comes into contact with a vertex of the other object as in the case where an inner point of foot rear interferes with a vertex on an unprepared ground when a walking robot moves on the unprepared ground. SOLUTION: According to this invention, a point of constraint is obtained by analyzing mutual positional relation of object shapes as they are instead of a simple method in which processing for obtaining the point of constraint is performed by analyzing positional relation between a representative point and a face. When considering the case where two rectangular parallelopiped boxes come into contact mutually, an intersection of two rectangular parallelopiped is obtained, and interference depth of this intersection and normal vector at the intersection are obtained together. A force of constraint is calculated based on the interference information. Consequently, a force of constraint can be calculated even when two objects interfere mutually on the halfway of a side.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to the contact between the inner point of an object and the other vertex, such as when the inside point of the foot interferes with the apex on the irregular ground when the walking robot moves on the irregular ground. The present invention also relates to a binding force detection method and system capable of detecting a binding force acting between objects even in the case of doing so.

[0002]

2. Description of the Related Art A small number of points called representative points are designated in advance on a target object, interference inspection between each representative point and another object is performed, and the interference position / interference depth / Obtain interference information such as the restraint direction. The conventional technique is to calculate the binding force acting between the objects based on the interference information at the representative point and the dynamic model. For example, in the DADS of LMS CADSI, which is a typical dynamics simulation software,
This method is used. Here, the binding force is a force generated by a drag force or a frictional force acting between the two objects when two objects are in contact with each other, and the motion of the object is determined by gravity and the binding force. Considering the dynamic simulation of humanoid robot motion as an example, the vertex of the bottom of the foot of the robot is selected as a representative point, and the interference inspection between this representative point and the floor surface is performed, and based on the information such as the interference position and depth. Calculate the binding force. Since the process of the interference inspection is limited to the analysis of the positional relationship between the points and the surface, the required process is greatly simplified. The basic idea is to simplify processing at the expense of versatility. In addition, considering the case where the reaction force is calculated when the object is operated by the haptic interface, it is common to use the vertex of the operated object as the representative point. In this case as well, the interference inspection between the representative point and the environmental object is performed, but the processing required is simplified because it is still limited to the analysis of the positional relationship between the point and the surface. In the example of FIG. 11, the point with an arrow is the representative point.

[0003]

In the case of using the conventional technique, the binding force acting between the objects cannot be calculated when the object interferes with other objects at a representative point other than the designated representative point.
For example, consider the case where the shape of an object is a rectangular parallelepiped and its vertices are selected as representative points. If the inside points of any surface interfere with the vertices of other objects, It is not possible to calculate the binding force that acts between objects. From an application point of view, when a walking robot moves on an irregular ground, the binding force cannot be calculated if the inner point of the sole and the apex on the irregular ground interfere. In the haptic interface, the binding force cannot be calculated when the inner point of the object contacts the other vertex. Even in a video game, the binding force cannot be calculated in the same case. Therefore, the present invention, even when the inner point of the object and the other vertex contact, such as when the inner point of the sole and the vertex of the irregular ground interfere when the walking robot moves on the irregular ground, The purpose is to detect the binding force acting between objects.

[0004]

The problem of the prior art has arisen because the processing for obtaining the constraint point is realized by a simple method of analyzing the positional relationship between the representative point and the surface. In the present invention, the constraint point is obtained by analyzing the positional relationship between the object shapes as they are without performing such simplification, so that the problem of the conventional technique can be solved. For example, considering the case where two rectangular parallelepiped boxes contact each other, the intersection of the two rectangular parallelepipeds is obtained, and the interference depth of this intersection and the normal vector at the intersection are obtained together. Then, the binding force is calculated based on the interference information. FIG. 15 shows a two-dimensional schematic diagram. It is a feature of the present invention that the binding force can be calculated even when two objects interfere with each other in the middle of the side like this example. Figure 1
FIG. 6 is a diagram illustrating detection of a restraining force acting between objects based on the present invention. The input is the shape / position / physical property data of the object. In the present invention, the shape of the object can be expressed or approximated by a set of polygons or a set of polyhedra.
The present invention obtains interference information by shape processing between geometric models of an object represented by a set of polygons or a set of polyhedra given a position (step S1), and uses a dynamic model based on physical property data, The binding force acting between the objects is calculated from the interference information (step S2). It is characterized in that interference information is obtained by highly versatile shape processing without setting a representative point on the object as in the past, and it is possible to calculate the binding force when the object interferes in any state. Become. The shape representation is limited to a set of polygons or a set of polyhedra, but since the shapes of many objects can be approximated by these representations, the range of applicable objects is very wide. Further, since the binding force can be calculated for an arbitrary interference state, the binding force can be calculated even when the above-described conventional technique cannot be applied.

[0005]

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 2 is a diagram for explaining the flow of the embodiment. Hereinafter, the present invention will be specifically described based on examples. The target object is represented by a set of polygons or a set of polyhedra. The surfaces of these objects are represented by a set of triangles (step S10). It is assumed that the normal vector of each triangle points out of the object. It should be noted that instead of a set of triangles, a set of other shapes such as a polygon or a tetrahedron can be used.

Interference inspection is performed between a set of triangles representing each object to obtain a pair of interfering triangles (step S11). This can be obtained at high speed using software called RAPID developed at the University of North Carolina, USA.

Interference information is obtained for each of the pair of interfering triangles by the following procedure. First, it is determined whether one triangle penetrates the inside of the other triangle or mutually penetrates the inside (step S12). Figure 3
Shows each case.

Interference information is acquired based on the determined interference state (step S13). When one triangle penetrates the inside of the other triangle, when the interference point is close enough to the interference vertex, the normal vector of the penetrating triangle is set as the constraint normal vector, and the interference depth in the direction of this vector. Ask for. The interference position is the apex that penetrates. This case is shown in FIG.

When a point obtained by projecting the vertices of a penetrating triangle on the surface containing the other triangle is not on the other triangle,
The normal vector of the penetrating triangle is used as the constraint normal vector, and the interference depth is obtained in the direction of this vector. The interference position is the intersection of two triangles. This case is shown in FIG.

When the rule of FIG. 4 or FIG. 5 cannot be determined, the shallower interference depth along the normal vectors of the two triangles is defined as the constraint normal vector, and the interference depth and the interference position are It shall be determined in the same manner as in the case of FIG. 4 or FIG.

When two triangles penetrate each other, the outer product of the penetrating sides of each triangle is the direction of the constraint normal vector. The interference depth is the distance between two feet of a common perpendicular to the two penetrating sides, and the interference position is the midpoint of the two feet. The direction of the constraint normal vector is determined by the following method.

First, when the inner product of the normal vectors of the two triangles is positive, the two triangles are removed from the object of interference inspection. This is shown in FIG. The same applies when the inner product between the vectors from the interference point to the third vertex is positive. This is shown in FIG. These two conditions do not need to be processed because they are tests of whether the two triangles are “facing” each other, and if they are not facing, there is always a pair of stronger triangles.

When the inner product between the outer product vector of the two penetrating sides and the vector directed from the interference point to the third vertex of each triangle has the same sign, two pairs of triangles are subject to interference inspection. Remove. This is a separability test of two triangles near the interference point. This is shown in FIG.

For pairs of triangles not rejected by FIGS. 6-8, the angle between the constraint normal vector and the vector from the interference point to the third vertex, the constraint normal vector and the triangle normal vector. 0 degree or 1 for angle
The angle closer to 80 degrees is selected, and the orientation of the constraint normal vector is determined by the sign of the inner product of the two selected vectors. The case where the former or the latter is selected is shown in FIG.

By the above method, the interference information can be obtained from the geometric model of the object. An example of a humanoid robot stepping on a plate on the floor is shown in FIG. Thus, even when the plate is stepped on the sole of the humanoid robot, it is possible to obtain the interference information such as the position of the constraint normal vector and the interference depth.

From this interference information, the constraint force acting between the objects is determined based on the dynamic model by the following method. As an example, a method of obtaining the binding force based on the spring damper model will be described. In addition to this, there is also a method of obtaining the binding force based on the law of conservation of momentum.

The component of the restraint force corresponding to the spring is, for example, a minute translation and rotation of an object such that the interference depth in the direction of the restraint normal vector at each interference position is closest to the obtained value in the meaning of least squares. The components are calculated, and these are calculated as force and torque with the independent variables. However, restraint between objects is generally one-sided restraint, so that it works in one direction but may not occur in the opposite direction. For example, considering the case where the box is placed on a plane, the upward restraining force acts on the box from the floor, but the reverse does not occur. Such force generation conditions are expressed by simultaneous linear inequalities. For example, such a solution is obtained by orthographically projecting the minute translational and rotational components obtained above so as to satisfy the simultaneous linear inequalities (step S
14). Alternatively, there is a method of formulating the above problem as a non-linear programming problem and obtaining a solution.

FIG. 11 is a two-dimensional explanatory view showing a case where one box is embedded in another box. The arrow in the figure is the constraint normal vector. In this case, the two boxes can be fitted closely by translating in the upward direction of the figure and rotating counterclockwise. The force and torque proportional to such translation and rotation are set as the restraining force acting between the two boxes. Further, when considering the saturation characteristic, the force and the torque are calculated by an appropriate non-linear function rather than simply making them proportional.

In the example of FIG. 11, the constraint normal vector can be obtained by first expressing each box by a set of triangles and then applying the above-mentioned method of obtaining interference information from the geometric model of the object. FIG. 12 shows how each box is represented by a set of triangles on a two-dimensional explanatory diagram.

The component of the restraint force corresponding to the damper is, for example, a vector obtained by multiplying the velocity of the object by an appropriate negative coefficient,
It can be obtained by the method of giving the difference from the vector orthogonally projected to the convex polyhedron corresponding to the solution set of the simultaneous linear inequalities. This physically corresponds to giving the damper reaction force only in the direction constrained by the interfering object in the velocity component of the object. FIG. 13 shows an example in which one box has a diagonal downward speed and interferes with another box. In this case, the constraint normal vectors obtained by the above method for obtaining the interference information from the geometric model of the object are the two upward vectors in the figure, and only the middle and downward velocity components are constrained by the constraint normal vector. , Drag is generated upward. A drag force is not generated with respect to the horizontal component, and a friction force is generated according to the friction coefficient between the boxes. By the above method, the component corresponding to the damper is obtained (step S15). Alternatively, there is also a method of generating a non-linear damper in the drag force direction and a linear damper in the tangential force direction. In this case, the calculation is performed by obtaining the projection matrix of the matrix expressing the constraint on the null space.

FIG. 14 shows a simulation result of the vertical floor reaction force when the humanoid robot shown in FIG. 10 walks,
The experimental result by the corresponding robot hardware is shown.
It is observed that there is good agreement.

[0022]

As described above, according to the present invention, it becomes possible to calculate the binding force when an object interferes at an arbitrary position, which is not possible with the conventional representative point method. It can be applied to a case where a humanoid robot walks on an irregular ground, a feedback force is calculated by a haptic interface device, and a reaction force is calculated by video game software.

[Brief description of drawings]

FIG. 1 is a diagram illustrating “detection of a restraining force acting between objects” of the present invention.

FIG. 2 is a diagram illustrating a flow of an embodiment.

FIG. 3 is a diagram showing a case where one triangle penetrates the inside of the other and a case where it penetrates each other.

FIG. 4 is a diagram showing a case where an interference point is sufficiently close to a penetration apex.

FIG. 5 is a diagram showing a case where a projection point of a penetrating apex does not fall on the other triangle.

FIG. 6 is a diagram illustrating that when the inner product of the normal vectors of two triangles is positive, it is excluded from the targets of interference inspection.

FIG. 7 is a diagram for explaining that when the inner product between the vectors from the interference point to the third vertex is positive, it is not the target of interference inspection.

FIG. 8 is a diagram illustrating a separability test of two triangles in the vicinity of an interference point.

FIG. 9 is a diagram showing a case where an angle between a constraint normal vector and a vector from an interference point to a third vertex is selected and a case where an angle between a constraint normal vector and a triangle normal vector is selected.

FIG. 10 is a diagram showing an example in which a humanoid robot steps on a plate on the floor.

FIG. 11 is a diagram showing an example in which two boxes are embedded.

FIG. 12 is a diagram showing an example of two boxes represented by a set of triangles.

FIG. 13 is an explanatory diagram of a direction in which a damper force is generated.

FIG. 14 is a diagram showing an example of simulation and experimental results.

FIG. 15 shows a two-dimensional schematic diagram.

   ─────────────────────────────────────────────────── ─── Continued front page    (72) Kenji Kaneko             1-1-1 Higashi 1-1-1 Tsukuba City, Ibaraki Prefecture             Inside the Tsukuba Center, National Institute of Advanced Industrial Science and Technology (72) Inventor Kiyoshi Fujiwara             1-1-1 Higashi 1-1-1 Tsukuba City, Ibaraki Prefecture             Inside the Tsukuba Center, National Institute of Advanced Industrial Science and Technology (72) Inventor Fumio Kanehiro             1-1-1 Higashi 1-1-1 Tsukuba City, Ibaraki Prefecture             Inside the Tsukuba Center, National Institute of Advanced Industrial Science and Technology F-term (reference) 3C007 AS36 CS08 WA03 WA13 WA24                       WB01

Claims (4)

[Claims] 1. A method for obtaining interference information by shape processing between geometric models of an object represented by a set of polygons or a set of polyhedra, and detecting a binding force acting between the objects from the interference information based on a dynamic model. 2. The restraining force acting between the objects is a restraining force acting when an inner point of the foot and an apex on the irregular ground interfere when the walking robot moves on the irregular ground. A method to detect the binding force acting between objects. 3. A means for obtaining interference information by shape processing between geometric models of an object represented by a set of polygons or a set of polyhedra, and a constraint force acting between the objects based on the dynamic model from the obtained interference information. System to detect. 4. The restraining force acting between the objects is a restraining force acting when an inner point of the sole of the foot and an apex on the irregular ground interfere when the walking robot moves on the irregular ground. A system that detects the binding force that acts between objects.