Particle filtering on the Euclidean group: framework and applications

Authors:
Junghyun Kwon;Minseok Choi;F. C. Park;Changmook Chun
Affiliations:
School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, Korea;School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, Korea;School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, Korea;Intelligent Robotics Research Center, Korea Institute of Science and Technology, Seoul 136-791, Korea
Venue:
Robotica
Year:
2007

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Abstract

We address general filtering problems on the Euclidean group SE(3). We first generalize, to stochastic nonlinear systems evolving on SE(3), the particle filter of Liu and West for simultaneous estimation of the state and covariance. The filter is constructed in a coordinate-invariant way, and explicitly takes into account the geometry of SE(3) and P(n), the space of symmetric positive definite matrices. Some basic results for bilinear systems on SE(3) with linear and quadratic measurements are also derived. Three examples—GPS attitude estimation, needle tip location, and vision-based robot end-effector pose estimation—are presented to illustrate the framework.