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

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...

AI Technical Summary

Problems solved by technology

[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 high-level logic proof tool HOL-Light, And based on the established conformal geometric logic model, the robot's motion planning is formally modeled and verified to solve the problems of complex calculations and inaccurate results in the prior art

Images