ABSTRACT
ABSTRACT Stable estimation of rigid body rotational and translational motion states from noisy measurements, without any knowledge of the dynamics model, is treated using the Lagrange-d’Alembert principle from variational mechanics. With body-fixed sensor measurements, a Lagrangian is obtained as the difference between a kinetic energy-like term that is quadratic in velocity estimation errors and an artificial potential function of configuration (attitude and position) estimation errors. An additional dissipation term that is linear in the velocity estimation errors is introduced, and the Lagrange-d’Alembert principle is applied to the Lagrangian with this dissipation. This estimation scheme is shown to be almost globally asymptotically stable in the state space of rigid body motions. It is discretized for computer implementation using the discrete Lagrange-d’Alembert principle, as a first-order Lie group variational integrator (LGVI). In the presence of bounded measurement noise in the measurements, numerical simulations show that the estimated states converge to a bounded neighborhood of the actual states.
