Uncertainty propagation in attitude dynamics
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We present some recent results on the propagation of initial condition uncertainty in the description of attitude of rigid bodies performing prescribed motions (angular velocities). The Euler 3-2-1 angles, Rodrigues parameters and modified Rodrigues parameter sets are considered as the candidate three dimensional attitude coordinates and we compare the results of propagation of the same initial condition errors in each of these three coordinate sets. The prescribed angular velocities are such that neither of these coordinates become singular at any time. The state-transition matrix which maps the initial uncertainty to instantaneous uncertainty is obtained by direct numerical integration in all three sets of attitude coordinates under consideration. Certain measures of nonlinearity are computed to give a quantitative comparison of the performance of linear propagation in the respective coordinates. Error covariance surfaces of constant probability are displayed to demonstrate the results. Monte-Carlo simulations are also performed to compare with the linearization approximations. The results strongly favor the modified Rodrigues parameters over other three parameter sets and validate the applicability of the nonlinearity indices for problems in rotational dynamics.
author list (cited authors)
Akella, M. R., & Junkins, J. L.