Attitude observers for three-vehicle heterogeneous formations based on the Lagrange-d'Alembert principle

This paper considers the problem of attitude estimation in three-vehicle heterogeneous formations with no line of sight between two of the vehicles. Each vehicle measures different inertial reference vectors and directions to other vehicles. The relative direction between the two vehicles with no line of sight cannot be measured. Moreover, rate gyros measure the angular velocity of each vehicle. An attitude observer is designed based on the Lagrange-d'Alembert principle of variational mechanics, considering only kinematic models. This design is driven by the angular velocity measurement and a reconstructed attitude computed from the direction measurements. The attitude reconstruction follows a deterministic algorithm, which has a unique solution under appropriate assumptions. The attitude observer is locally exponentially stable and the estimation error is shown to converge to zero for almost all initial conditions. The discrete-time form of the observer is obtained for practical implementation. Lastly, numerical simulations validate the stability and convergence characteristics of the observer.