General inverse solution modeling and solving method of 7R manipulator based on axis invariant

A robotic arm and variable technology, applied in the field of robotics, can solve problems such as the inability to calculate the inverse solution of a 7R robotic arm

Active Publication Date: 2018-12-18
居鹤华
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

[0004] The technical problem to be solved by the present invention is to provide a general-purpose 7R manipulator inverse solution modeling and ca

Method used

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  • General inverse solution modeling and solving method of 7R manipulator based on axis invariant
  • General inverse solution modeling and solving method of 7R manipulator based on axis invariant
  • General inverse solution modeling and solving method of 7R manipulator based on axis invariant

Examples

Experimental program
Comparison scheme
Effect test

Embodiment 1

[0197] Given 2 2D row vector polynomials On the one hand, from formula (4) we get

[0198]

[0199] on the other hand,

[0200]

[0201] The above results verify the correctness of formula (4).

[0202] Give the determinant computation theorem for block matrices:

[0203] If the square matrix whose size is (n+m)·(n+m) is recorded as M, the matrix whose size is n·n It is a sub-matrix composed of the first n rows and any n columns of elements of the square matrix M, and the size of the matrix is ​​m m It is a sub-matrix composed of m rows and remaining m columns after the square matrix M; the sequence cn and cm composed of the matrix column numbers arranged in ascending order is a subset of the sequence [1:m+n], [cn,cm]∈, and there is cm∪cn=[1:m+n]; then the square matrix M determinant and block matrix and The determinant relationship of

[0204]

[0205] The principle of row stepping calculation of determinant:

[0206] For an S×S matrix, each item is abo...

Embodiment 2

[0209] Through the elementary row transformation of the matrix, we get The row echelon matrix of .

[0210] The steps are: rk represents the kth row. have to

[0211]

[0212] then have

[0213] N-order polynomial system based on "N-carry word":

[0214] If n "n-ary 1st order" polynomial power product If the independent variable appears repeatedly N times, then n "n-element N-order" polynomial systems are obtained "N-element N-order polynomial system" and "n-bit N-carry word" isomorphic.

[0215]

[0216]

[0217]

[0218]

[0219] Dixon polynomials of a system of n "n-ary n-order" polynomials:

[0220] Introduce auxiliary variable [y 2 ,y 3 ,...,y n ], with

[0221]

[0222] In the multivariate polynomial (8), with the auxiliary variable Y m The first m in turn replace the original variables (OriginalVariables) X n For the m variables in , record "|" as the replacement operator to get the extended (Extended) polynomial

[0223]

[0224...

Embodiment 3

[0287] Perform Dixon elimination on the polynomial system (39).

[0288]

[0289] The steps are as follows: the formula is a polynomial system of 4 "quaternary 1st order", which satisfies the Dixon elimination condition. From formula (19) and formula (22), get

[0290]

[0291] in:

[0292]

[0293] Five solutions are obtained from formula (34) and formula (40):

[0294]

[0295]

[0296]

[0297] in: is not a solution to this system of equations. Substitute other solutions into formula (35). when , from equation (35) we get

[0298]

[0299] Solved: τ 3 = 1, τ 4 =-2. Will τ 3 and τ 4 Substitute into equation (39) to get τ 2 =1. Similarly, the other three sets of solutions can be obtained. Obviously, the dependent variable does not satisfy the formula (26), and the Dixon matrix shown in the formula (40) is not symmetrical. This example shows that the Dixon determinant being zero is sufficient for multilinear polynomial systems.

[0300]...

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Abstract

The invention discloses an inverse solution modeling and calculation method of a universal 7R manipulator based on axis invariant. The manipulator is a universal 7R manipulator, which is provided withseven rotational axes, the picking point is located on the seventh axis, and the fifth axis and the sixth axis are not coaxial. The universal 7R manipulator aligns the seventh axis with the desired position and attitude through the first six axes, so that the seventh axis infinitely rotates or the seventh axis satisfies the radial alignment. The kinematics equation of 7R manipulator is derived bymeans of the population function, and the kinematics equation of 7R manipulator is solved by using the population function. Gibbs quaternion expression, the sixth axis takes the point which is a certain distance from the picking point as the nominal picking point, first calculates the inverse solution of the universal 6R manipulator, and then completes the kinematic planning and inverse solutioncalculation of the universal 7R manipulator by using the numerical iteration method, thus solving the problem that the inverse solution of the universal 7R manipulator cannot be calculated in the prior art.

Description

technical field [0001] The invention relates to a multi-axis robot 7R mechanical arm inverse modeling and calculation method, belonging to the field of robot technology. Background technique [0002] An important aspect of autonomous robot research is the need to solve the problem of kinematic modeling of robots with variable topology. In MAS, there is a dynamic graph structure (Dynamic Graph Structure), which can dynamically establish a directed Span tree based on the motion axis, which lays the foundation for the study of robot modeling and control of variable topology structure (Variable Topology Structure). To this end, it is necessary to propose a general-purpose manipulator inverse solution principle based on axis invariants. It is necessary to establish a fully parameterized forward kinematics model including coordinate system, polarity, structural parameters, and joint variables, and to calculate the pose equation in real time. ; On the one hand, the autonomy of the...

Claims

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Application Information

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IPC IPC(8): G06F17/50B25J9/16
CPCB25J9/1605G06F30/17G06F30/20
Inventor 居鹤华
Owner 居鹤华
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