Abstract:

Pose estimation is central to several robotics applications such as registration, manipulation, SLAM, etc. In this thesis, we develop probabilistic approaches for fast and accurate pose estimation. A fundamental contribution of this thesis is formulating pose estimation in a parameter space in which the problem is truly linear and thus globally optimal solutions can be guaranteed. It should be stressed that the approaches developed in this thesis are indeed inherently linear, as opposed to linearization or other approximations commonly made by existing techniques, which are known to be computationally expensive and highly sensitive to initial estimation error.

This thesis will demonstrate that the choice of probability distribution significantly impacts performance of the estimator. The distribution must respect the underlying structure of the parameter space to ensure any optimization, based on such a distribution, produces a globally optimal estimate, despite the inherent nonconvexity of the parameter space.

Furthermore, in applications such as registration and three-dimensional reconstruction, the correspondence between the measurements and the geometric model is typically unknown. In this thesis we develop probabilistic methods to deal with cases of unknown correspondence.

We plan to extend our approaches to applications requiring dynamic pose estimation. We also propose to incorporate probabilistic means for finding the data association, inspired by recent work of Billings et. al. Finally, we will develop a filtering approach using a Gilitschenski distribution, that considers the constraints of both rotation and translation parameters without decoupling them.

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Thesis Committee Members:

Howie Choset, Chair
Michael Kaess
Simon Lucey
Russell H. Taylor, Johns Hopkins University
Nabil Simaan, Vanderbilt University