Formalized analyzing method and system for mechanical arm motion planning on basis of conformal geometric algebra

A technique of geometric algebra and motion planning, applied in the field of computer science, can solve problems such as complex calculations and inaccurate results

Inactive Publication Date: 2016-07-13
CAPITAL NORMAL UNIVERSITY
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[0004] In view of this, the object of the present invention is to provide a formal analysis method and system for manipulator motion planning based on conformal geometric algebra, mainly to establish a formal model of the CGA system in the h...

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  • Formalized analyzing method and system for mechanical arm motion planning on basis of conformal geometric algebra
  • Formalized analyzing method and system for mechanical arm motion planning on basis of conformal geometric algebra
  • Formalized analyzing method and system for mechanical arm motion planning on basis of conformal geometric algebra

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[0106] Various embodiments of the invention will be described in more detail below with reference to the accompanying drawings. In the various drawings, the same elements are denoted by the same or similar reference numerals. For the sake of clarity, various parts in the drawings have not been drawn to scale.

[0107] The currently developed conformal geometric algebra system can theoretically be extended to any dimension of space. The main application is 5-dimensional conformal space, which is composed of 3-dimensional Euler space and 2-dimensional Min's space. Conformal geometric algebra provides a representation The Grassmann structure of geometry, the unified screw action representing geometric transformation, the bracket system and invariant system representing geometric quantities have shown significant advantages in geometric data processing and geometric calculation. Under the framework of geometric algebra, different transformation expressions and operation forms are...

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Abstract

The invention discloses a formalized analyzing method and system for mechanical arm motion planning on the basis of conformal geometric algebra.The method comprises the steps that corresponding geometric models are built for basic elements and motion planning constrains of a robot on the basis of a conformal geometric algebra theory, and the built geometric models are described with a high-order logical language to form a basic geometric logical model system of the robot; specific structure parameters and motion planning parameters of the robot are determined; formalized modeling is performed on the specific robot motion process on the basis of the basic geometric logical model system to obtain a geometric relationship logical model of the specific robot motion process; the robot motion process constraints or attributes needing to be verified are described with a logical formula; the geometric relationship logical model of the specific robot motion process and the motion process constraints or attributes to be verified form a logical proposition; whether the logical proposition is valid or not is proved through a logical inference engine.

Description

【Technical field】 [0001] The invention relates to a formalized analysis method and system for manipulator motion planning based on conformal geometric algebra, belonging to the technical field of computer science. 【Background technique】 [0002] Conformal Geometric Algebra (CGA), as an advanced geometric representation and computation system, provides a concise, intuitive and unified homogeneous algebra framework for classical geometry. CGA introduces two extra dimensional datum origins (e 0 ) and the point at infinity (e ∞ ), so that the Euclidean space is embedded in the conformal space, and endowed with Min’s inner product structure, which not only retains the Grassmann structure of the outer product in the homogeneous space, but also makes the inner product have a clear geometry representing basic metrics such as distance and angle. significance. CGA not only successfully solves geometric calculations using geometric language, but also new methods and algorithms based...

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Application Information

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IPC IPC(8): G06F17/50
CPCG06F30/3323B25J9/1605B25J9/1664G05B2219/40519B25J9/1602B25J9/1682B25J19/0029G05B2219/39079G05B2219/40371
Inventor 施智平马莎关永邵振洲张倩颖王瑞李晓娟李黎明
Owner CAPITAL NORMAL UNIVERSITY
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