Combined interval analysis - Monte Carlo simulation approach for the analysis of uncertainties in parallel manipulators

The quantification of the impact of uncertainties may increase the reliability and robustness of parallel manipulators. Monte Carlo simulation (MCS) and interval analysis are among the most common techniques used in uncertainty quantification. Interval analysis provides guaranteed performance since the interval evaluation of a function always contains the exact result. Nevertheless, interval analysis estimations are very conservative, frequently yielding overestimated results. Conversely, Monte Carlo Simulation avoids overestimation, but does not provide guaranteed performance. This paper proposes a novel hybrid algorithm combining the best features of interval analysis and Monte Carlo simulation for estimating probabilities of failure in the positioning error of parallel manipulators. A 3RRR manipulator is employed as case-study. The hybrid approach provides information on the bounds (minimum and maximum values) and estimated values of failure probabilities. The simulations herein compare the hybrid approach with pure interval analysis and pure Monte Carlo simulation. The results reveal that the hybrid technique may estimate not only the probability of failure in a continuous region, but also the worst and best case probabilities, much faster than interval analysis based approaches.