Stochastic error propagation in robot arms

Abstract

Static error propagation in positioning robot arms has been extensively analyzed based on linearized error propagation models. These models are used for robot design and calibration. Most results were calculated using normally distributed errors in the different robot joints and links. In reality not all joints and links errors are normally distributed, and a mix of suitable symmetric and nonsymmetric probability distributions should be used in the error propagation model. The paper presents the general model for propagating errors with different distributions applicable to any system whose model can be linearized. Numerical examples are given for a general beta distribution of errors, and for a mix of symmetric and nonsymmetric distributions. Within the work-volume, the different configurations that a robot arm may attain during its life span can be expressed by a probability distribution. The paper includes the analysis of the effect of this distribution on the position error of the end-effector.