Adaptive quasi-Monte Carlo method for uncertainty evaluation in centroid measurement of planetary rovers

The measurement of the centroid is of great significance to improve the control performance and reduce the energy consumption of the planetary rover (PR). The uncertainty is an essential indicator of the reliability of centroid measurement results. The purpose of the current study is to evaluate the uncertainty of centroid measurement in the multi-configuration rover. For the measurement of the centroid, the model with 37 parameters of two measurements as the input and the centroid coordinates as the output is derived. Further, the mechanical and electrical integrated system is developed, which can measure the centroid of PRs in different configurations and sizes. Moreover, to overcome the shortcomings of the Monte Carlo method (MCM) in uncertainty evaluation, an adaptive algorithm that automatically determines the number of input sequences is proposed. On this basis, an adaptive quasi-Monte Carlo method (AQMCM) is presented in order to accelerate the uncertainty evaluation, which is characterized by the randomized Sobol sequence. Besides, experiments are performed to compare the uncertainty evaluation process and results of the AQMCM and the adaptive Monte Carlo method (AMCM) in multiple configurations. The result shows that the standard uncertainty of the AQMCM is almost the same as that of the AMCM, but the sequence size of AQMCM is evidently smaller than that of AMCM. Taken together, we identify that the AQMCM evaluates the uncertainty of CM for the multi-configuration rover in an efficient and fast way. Furthermore, the AQMCM provides a new method for uncertainty evaluation, particularly for nonlinear models in different states.

An Improved Measurement Uncertainty Calculation Method of Profile Error for Sculptured Surfaces

The current researches mainly adopt “Guide to the expression of uncertainty in measurement (GUM)” to calculate the profile error. However, GUM can only be applied in the linear models. The standard GUM is not appropriate to calculate the uncertainty of profile error because the mathematical model of profile error is strongly non-linear. An improved second-order GUM method (GUMM) is proposed to calculate the uncertainty. At the same time, the uncertainties in different coordinate axes directions are calculated as the measuring points uncertainties. In addition, the correlations between variables could not be ignored while calculating the uncertainty. A k-factor conversion method is proposed to calculate the converge factor due to the unknown and asymmetrical distribution of the output quantity. Subsequently, the adaptive Monte Carlo method (AMCM) is used to evaluate whether the second-order GUMM is better. Two practical examples are listed and the conclusion is drawn by comparing and discussing the second-order GUMM and AMCM. The results show that the difference between the improved second-order GUM and the AMCM is smaller than the difference between the standard GUM and the AMCM. The improved second-order GUMM is more precise in consideration of the nonlinear mathematical model of profile error.