Measurement Observers for Pose Estimation on SE(3)

This thesis develops a nonlinear observer for the problem of pose estimation; that is, the determination of the position and attitude of a rigid body from sensor measurements. The observer is derived on the Special Euclidean group, SE (3), and exploits the natural Lie groups geometry of the space in the structure of the observer. The observer uses body fixed frame measurements of known landmarks for the primary position measurement, and implements body fixed frame measurements of velocity, both angular and linear, as feed forward terms. A Lyapunov argument is used to prove local exponential stability of the error system, assuming that there are at least three non-collinear landmark reference points measured. The observer is well-behaved and stable with only one or two landmark reference points measured; however, the pose estimate is not guaranteed to converge to the true value in these cases. The characteristics of the observer and its stability are demonstrated by a series of simulations.