Design and analysis of attitude observers based on the Lagrange-d'Alembert principle applied to constrained three-vehicle formations

Constrained formations of vehicles are interesting in a variety of space mission scenarios for their potential ability to solve complex problems with relatively simple and specialized individual systems. However, the analysis of such formations can present some challenges. In this paper, an attitude observer is designed with the intent of applying it to three-vehicle heterogeneous formations with no line of sight between two of the vehicles. Each vehicle measures directions to other vehicles and independent inertial reference vectors. The relative direction between the two vehicles with no line of sight cannot be measured. Under some assumptions, these relative measurements yield a reconstructed attitude, which, together with the angular velocities measured by rate gyros, drive the observers. The attitude observers are identical and independently applied to each vehicle. Their design is based on the Lagrange-d'Alembert principle of variational mechanics, considering only kinematic models. The attitude observers are locally exponentially stable and each estimation error is shown to converge to zero error for almost all initial conditions. Finally, a series of numerical Monte Carlo simulations of the discrete-time form of the observers validate the stability and convergence characteristics of the observers under the appropriate assumptions on the availability of a reconstructed attitude.