A Dynamics Modeling Method of Multi-axis Robot Based on Axis Invariant

A multi-axis robot and dynamic equation technology, applied in CAD numerical modeling, instruments, manipulators, etc., can solve the problems of lack of design framework calculation and control methods

Active Publication Date: 2020-02-21
居鹤华
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  • 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 Dynamics Modeling Method of Multi-axis Robot Based on Axis Invariant
  • A Dynamics Modeling Method of Multi-axis Robot Based on Axis Invariant
  • A Dynamics Modeling Method of Multi-axis Robot Based on Axis Invariant

Examples

Experimental program
Comparison scheme
Effect test

example 22

[1145] 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

[1146] 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)

[1147] What the kinematic chain expresses is: first execute the "3-2-1" rotation, and then execute the "1-2-3" translation. then there is

[1148]

[1149]

[1150]

[1151]

[1152] From formula (1.157)~(1.160), we get

[1153]

[1154] Obviously,

[1155]

[1156] Therefore there

[1157]

[1158] By formula (1.163) get

[1159]

[1160] By formula (1.164) get

[1161]

[1162] in:

[1163]

[1164] For precision electromechanical systems, due to machining and assembly errors, ortho...

example 23

[1173] 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.

[1174] beg r Q c .

[1175] 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

[1176]

[1177] Solution finished.

[1178] 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

[1179] Example 2.4: Continuation of Example 2.3, measured by engineering

[1180]

[1181] Calculated by the formula

[1182]

[1183] It can be seen from the calculation results r Q cSick, the precision is only 6 digits.

[1184] 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.

[1185] 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 present invention proposes a multi-axis system dynamics modeling and calculation principle based on axis invariants, and realizes the iterative display of multi-axis systems with tree chains, closed chains, joints with friction and stickiness, and moving bases. Dynamics modeling, the established model has an elegant chain symbol system, has the function of pseudocode, and realizes complete parameterization including "topology, coordinate system, polarity, structural parameters, mass inertia, etc.". This principle can be implemented as a circuit, as code, directly or indirectly, partially or fully within 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): B25J9/16
CPCB25J9/1607B25J9/1605G05B2219/40527G06F2111/10B25J9/1671G05B17/02G05B2219/50391
Inventor 居鹤华
Owner 居鹤华
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