The Solution Of Analyzing A Redundant Robot Configuration With A Built-In Safety System

The reliability analysis on the Redundant Robot Configuration is one of the study objects in the reliability Mathemetical Theory,which makes quantitative study on the reliability of the products(units or systems) using theories and methods of probability,statistics and operations research and so on.It is one of reliable theory foundations.Many scholars,both domestic or abroad,have made massive researches concerning this kind of questions.Generally,they have set up a repairable system's mathematical model of which can repair time to be obedient to distributes,using the supplement variable method,then using Laplace method gives the proof to system's evolution stability,but to such related questions as system reliablility and system characteristic value,they haven't given good proof,yet.This article mainly studies this question.The system studied in this article is the redundant machine system which has the internal structure safety control system's,in which two same machines' parallel operating and an independently-running safety control system constitute a stochastic mathematical model.When being applied,the machine that is being repaired and the safety control system are almost new,but when these two machines both break down,then the whole system breaks down.In this article,the system solution existence uniqueness was firstly obtained by transforming the system into Banach under the spatial Volterra operator equation,then through functional analysis processing,the system solution existence,and also the only one, was obtained using the operator semi-group method to establish one is compressing C₀-semigroup, thus this system's stability has been proven.Based on the above,the analysis to this system's spectrum's characteristic has been carried on,so that the system operator spectrum that was located at the left half plane of the complex planes was known,and also there was no other spectrum spot besides 0 spots on the axis of imaginaries.And through a concrete example,it is explained that the system's non-vanishing characteristic value is in existence, and the characteristic value and the feature vector are in correspondences,finally it is shown that this system solution's reliability,namely the transient state reliability is not smaller than the reliable reliability had.