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A Forward Kinematics Modeling and Calculation Method of Multi-axis Robot System Based on Axis Invariants

A multi-axis robot and forward kinematics technology, applied in the field of robotics, can solve the problems of lack of design framework calculation and control methods

Active Publication Date: 2020-01-07
居鹤华
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

[0006] Therefore, although there are many robot-related theories, there is still a lack of a complete and effective design framework and corresponding calculation and control methods, which can solve all aspects of modeling in the actual development process of various robots. The operation structure and rules, to forward kinematics, inverse kinematics, and related issues of mechanical calculations

Method used

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  • A Forward Kinematics Modeling and Calculation Method of Multi-axis Robot System Based on Axis Invariants
  • A Forward Kinematics Modeling and Calculation Method of Multi-axis Robot System Based on Axis Invariants
  • A Forward Kinematics Modeling and Calculation Method of Multi-axis Robot System Based on Axis Invariants

Examples

Experimental program
Comparison scheme
Effect test

example 22

[1147] Example 2.2 Given axis sequence A = (i, c1, c2, c3, c4, c5, c], parent axis sequence The axis type sequence is recorded as K=(F, R, R, R, P, P, P], and the joint coordinate sequence is recorded as q (i,c] =(φ c1 ,φ c2 ,φ c3 ,r c4 ,r c5 ,r c ]; so the kinematic chain is recorded as i l c =(i,c1,c2,c3,c4,c5,c]. And there are

[1148] i no c1 = c5 no c = 1 [z] , c1 no c2 = c4 no c5 = 1 [y] , c2 no c3 = c3 no c4 = 1 [x] . (1.157)

[1149] What the kinematic chain expresses is: first execute the "3-2-1" rotation, and then execute the "1-2-3" translation. then there is

[1150]

[1151]

[1152]

[1153]

[1154] From formula (1.157)~(1.160), we get

[1155]

[1156] Obviously,

[1157]

[1158] Therefore there

[1159]

[1160] By formula (1.163) get

[1161]

[1162] By formula (1.164) get

[1163]

[1164] in:

[1165]

[1166] For precision electromechanical systems, due to machining and assembly errors, ortho...

example 23

[1175] Example 2.3: The installation relationship of the camera system c relative to the patrol system r is determined by the angle between the coordinate axes of the two systems: in: represented by the axis x r to axis x c angle, and so on.

[1176] begging r Q c .

[1177] Solution: The projection of the camera coordinate axis x in the inspector system is The projection of the camera coordinate axis y in the inspector system is The projection of the camera coordinate axis z in the inspector system is Therefore there

[1178]

[1179] Solution finished.

[1180] This example applies the direction cosine to calculate the rotation transformation matrix, which is correct in principle. However, there is an important shortcoming in engineering: due to errors in the measurement of nine angles, the "orthogonal normalization" constraint of the rotation transformation matrix is ​​destroyed. Examples are as follows:

example 24

[1181] Example 2.4: Continuation of Example 2.3, measured by engineering

[1182]

[1183] Calculated by the formula

[1184]

[1185] It can be seen from the calculation results r Q c Sick, the precision is only 6 digits.

[1186] Apply formula (1.144) or formula (1.146) to calculate the attitude angle It is established in theory; the premise is: the rotation transformation matrix must satisfy the "orthonormalization" constraint, when this constraint cannot be satisfied, The calculation error may be large. for sick Formula (1.144) and formula (1.146) are not fully utilized components, resulting in a sequence of attitude angles The accuracy is worse than the measurement accuracy of the cosine angle.

[1187] In addition to the engineering measurement error, the digital truncation error of the computer also leads to the ill-conditioning of the rotation transformation matrix. for the kinematic chain k l j , because There is a certain pathology that leads ...

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Abstract

The invention proposes a multi-axis system forward kinematics modeling and solving method based on axis invariants. This method realizes inherently compact, real-time and functional reuse and simplified layering and complete parameter modeling and real-time calculation. It has the function of pseudo-code and symbol analysis, and can be set into circuits, codes, direct or indirect, partial Or do it all inside the multi-axis machine system. In addition, the present invention also includes an analysis and verification system constructed on these principles for designing and verifying multi-axis machine systems.

Description

technical field [0001] The present invention relates to a robot, a robot autonomous control system and a method used in the robot autonomous control system, and particularly relates to a multi-axis robot, a multi-axis robot autonomous control system and a method used in the multi-axis robot autonomous control system. Background technique [0002] Robotics is a very hot field right now. This field has invested a lot of scientific and engineering manpower in the past few decades, and it has been studied for many years. However, once the number of axes and degrees of freedom increase to a certain number, according to the existing textbooks and known observation, modeling, calculation and control methods, it will often fall into complex and out-of-control problems, or even unsolvable problems. [0003] First, past practices lack the ability to generalize. For different robots, it is often necessary to re-study and establish corresponding kinematics and mechanics models. [00...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G05B19/414
CPCG05B19/4142G05B2219/34013B25J19/007G05B2219/41413B25J9/1605B25J9/163B25J9/1664B25J19/0037
Inventor 居鹤华
Owner 居鹤华
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