Reliability and Numerical Analysis of a Robot Safety System

This paper discusses a model for a repairable robot safety system composed of a safety component and two redundant robots according to a semi-group approach. The development of the model is divided into three phases: (I) The use of pure analysis to prove the uniqueness of a classical solution to the model; (II) The verification of this uniqueness by providing a non-negative solution to the model; and (III) the formulation of reliability indices for the model, along with numerical examples to explain the results. The existence, uniqueness, and exponential stability of the solution of the repairable robot safety system is studied using Volterra-type integral-differential-equation theory, and the spectral distribution of the ACP operator is discussed. Moreover, the authors propose a method to investigate the steady-state indicator of the robot safety system with the safety component working, and with or without the component revolving, to make use of the correspondence of the eigenvector to the eigenvalue zero. The authors show that the robot’s operation, with or without the safety component revolving and with fractional motion, is superior to that with the safety component working. The novelty of the approach lies in its examination of a unique solution to the system and its exponential stability based on C0-semi-group theory, the co-final relative theory, and the functional analysis method.