A Mechanized Mechanics Modeling Method for Nonholonomic Constrained Systems

A non-holonomic constraint and mechanical modeling technology, which is applied in the field of robot dynamics modeling, can solve problems such as redundant and complicated output, low calculation efficiency, and repeated calculation of variables, so as to reduce complexity, reduce calculation time, and extend Effect of Die Depth

Active Publication Date: 2019-06-28
GUILIN UNIV OF ELECTRONIC TECH
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Problems solved by technology

However, the above-mentioned modeling methods for nonholonomic constrained systems usually have problems such as repeated calculation of variables, long and complicated output, and low computational efficiency.

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  • A Mechanized Mechanics Modeling Method for Nonholonomic Constrained Systems
  • A Mechanized Mechanics Modeling Method for Nonholonomic Constrained Systems
  • A Mechanized Mechanics Modeling Method for Nonholonomic Constrained Systems

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Embodiment Construction

[0030] The following describes the present invention with reference to the drawings and embodiments, but it does not limit the content of the present invention.

[0031] Assuming that a certain mechanical system is a nonholonomic constraint system, the position of the system at any time is represented by n generalized coordinates q s (s=1, 2,...,n) to determine that the system is subject to g nonholonomic constraints of the following form,

[0032]

[0033] According to Chapleykin’s equation,

[0034]

[0035] Where It is called kinetic energy floating, which means the kinetic energy after substituting non-holonomic constraints. q ν , Q σ Are independent generalized coordinates, Is an independent generalized speed, Is the independent generalized speed, B ε+β,σ , B ε+β,ν Is the independent generalized velocity in the velocity constraint equation Coefficient of Is the kinetic energy of the system after substituting the nonholonomic constraint equation, V is the potential energ...

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Abstract

The invention discloses a mechanized mechanics modeling method of a non-holonomic constraint system. During the constraint analysis, intermediate variables are introduced to describe the non-holonomic constraint relationship according to the complex situation of the non-holonomic constraint; the independent generalized velocity contained in the kinetic energy is revealed through the constraint analysis Information, extract the coefficient of the independent generalized velocity product term and define it as an intermediate variable, and rewrite the kinetic energy into a new form of expression; The total derivative of , can be solved by analyzing the subordination structure of variables, establishing a function-variable implication relationship table and introducing compound derivatives; calculating the influence items of non-holonomic constraints on the system is more complicated, and several structure arrays can be defined to store calculation results. In order to avoid the problem of model expansion caused by the back substitution of intermediate variables, the calculation expressions of the model need to be output in reverse order.

Description

Technical field [0001] The invention relates to the technical field of robot dynamics modeling, in particular to a mechanized mechanical modeling method of a non-holonomic constraint system. Background technique [0002] Robot dynamics model is mainly used in the optimization design of robot mechanism, system dynamics simulation and motion control. Accuracy, simplicity, efficiency and reliability are the basic requirements of robot dynamics modeling. Wheeled robots and spherical robots are two important forms of mobile robots. These two types of robots belong to non-holonomic systems due to non-holonomic constraints between the wheels (or spherical shells) and the ground. Common dynamic modeling methods for nonholonomic constrained systems mainly include the first-type Lagrange equations with multipliers, Chapleykin (Чаплыгин) equations, Boltzmann-Hammer (Boltzmann- Hamel equation, Appell equation, etc. However, the above modeling methods of nonholonomic constraint systems usu...

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F17/50
CPCG06F30/17G06F30/20
Inventor 庄未黄用华余记华王昌盛黄美发孙永厚匡兵钟永全
Owner GUILIN UNIV OF ELECTRONIC TECH
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