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Mechanical modeling method for nonholonomic constraint system

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

Active Publication Date: 2017-02-08
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.

Method used

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  • Mechanical modeling method for nonholonomic constraint system
  • Mechanical modeling method for nonholonomic constraint system
  • Mechanical modeling method for nonholonomic constraint system

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Embodiment Construction

[0030] The present invention will be described below in conjunction with the accompanying drawings and embodiments, but not to limit the content of the present invention.

[0031] Assuming that a mechanical system is a nonholonomic constrained system, the position shape of the system at any time is composed of n generalized coordinates q s (s=1,2,…,n) to determine, the system is subject to g nonholonomic constraints of the following form,

[0032]

[0033] According to the Chaprekin equation,

[0034] d d t ∂ T ~ ∂ q · σ - ∂ T ~ ∂ q σ + ∂ V ∂ q ...

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Abstract

The invention discloses a mechanical modeling method for a nonholonomic constraint system. The mechanical modeling method comprises the steps of introducing an intermediate variable to describe a nonholonomic constraint relation according to the complexity of nonholonomic constraints when constraint analysis is carried out; revealing independent generalized velocity information included in kinetic energy through the constraint analysis, extracting a coefficient of a product item of independent generalized velocity and defining the coefficient as the intermediate variable, and changing the kinetic energy into a new form of expression; in a modeling process, calculating partial derivatives of some function variables to generalized coordinates or total derivatives of the function variables to time massively, establishing a function-variable implication relation table and introducing composite derivation to solve by analyzing a variable subordinate structure; and defining several structural arrays to store calculation results since the calculation of the influence of the nonholonomic constraints on the system is more complex. In order to avoid a model expansion problem caused by back substitution of the intermediate variable, the calculation expression of the model needs to be outputted in a reverse order.

Description

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

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Application Information

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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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