1 Introduction
Collision Detection (CD) is used to determine whether one or more pairs of objects occupy the same area at a certain time in a given time domain. At present, common real-time collision detection algorithms are discrete collision detection algorithms. These algorithms can be roughly divided into graphics-based and image-based collision detection algorithms. The graph-based real-time collision detection algorithm is mainly divided into two types: Hierarchical BoundingBlumes and SpaceDecomposition. The core idea of ​​the hierarchical bounding box method is to approximate a complex geometric object with a bounding box that is slightly larger and has a simple geometrical feature, so that only the objects intersecting the bounding boxes are subjected to further intersection testing. In addition, by constructing a tree-like hierarchy, the geometric properties of the object can be increasingly approached. Typical hierarchical trees include AABB (axis2alignedboundingbox) hierarchical tree, spheres hierarchical tree, OBB (orien2tedboundingbox) hierarchical tree, and κ2DOPs (discreteorientationpolytope) hierarchical tree.
In order to improve the efficiency of collision detection, some simple geometry is used to approach the robot arm to develop a more efficient algorithm to quickly detect the collision between the robot and the robot, between the robot and the obstacle. For example, some scholars have simplified the robot joint into a spherical solid model, and used a set of balls and tables to approach the robot system. In addition, some scholars have simplified the robot joint into a solid model with hemispheres at both ends of the cylinder, and used the minimum distance algorithm for interference detection.
2. Simplified modeling of multi-degree-of-freedom robot joint entities
The collision detection between the joints of multi-degree-of-freedom robots is mainly the collision detection between the robot arms at all levels. In order to reduce the complexity of the collision detection algorithm and improve the detection efficiency, we can consider the joint rods without affecting the detection results. Simplify the pieces and build a simplified model of each joint. In general, the joints of the robot arm can be considered to consist of cylindrical rods, so we can simplify the joint rods into a cylinder of radius r and a hemisphere with radius r at both ends. The simplified model is shown in Figure 1.
3. The three-dimensional interference problem is transformed into a two-dimensional interference problem.
In order to transform the three-dimensional interference problem into a two-dimensional interference problem, we can first find the orthographic projection of the simplified joint member in the xoy plane, as shown in Figure 2.
In the three-dimensional coordinate system, the simplified joint member entity Q(R, C1, C2) is a cylinder and two hemispheres with a radius r connected to each other. The possible states of the entity are vertical, horizontal or inclined; The orthographic projection, that is, in a plane rectangular coordinate system, may be a circle or a rectangle and a union of two circles. For ease of description, we define these two cases in a plane Cartesian coordinate system. If it is a circle, we define it as C'(x0, y0, r), where the center of the circle is (x0, y0) and the radius is r; if it is a combination of a rectangle and two circles, we define it as Q'(R', C '1, C'2), where R'(A', B', |A'B'|, 2r, θ) is a rectangle, A'(x'1, y'1), B(x'2, Y'2) is the coordinates of the midpoint of the two ends of the rectangle, |A'B'|, 2r is the length and width of the rectangle, and θ is the angle between the length of the rectangle and the x-axis. C'1(x'1, y'1, r), C'2(x'2, y'2, r) is a circle at both ends.
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