Particle filtering on the Euclidean group: framework and applications

Abstract

SUMMARYWe address general filtering problems on the Euclidean groupSE(3). We first generalize, to stochastic nonlinear systems evolving onSE(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 ofSE(3) andP(n), the space of symmetric positive definite matrices. Some basic results for bilinear systems onSE(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.

6-DOF Model Based Tracking via Object Coordinate Regression

“…The definition of probability distributions and calculation of average rotations is not straight forward. A theoretical analysis of these issues can be found in [6] and [17]. While earlier methods relied on simple random walk motion models, Choi et al [9] used autoregressive models that assume a more or less constant pose velocity and were thus able to deal with faster motion.…”

Monocular SLAM with locally planar landmarks via geometric rao-blackwellized particle filtering on Lie groups

“…The efficient gradient-descent algorithm to obtain the sample mean of SL(3) is presented in [2] while the sample mean formula of SO(3) is given in [14]. For SL (3) and SO (3), with the sample meanμ of {X 1 , .…”

Tracking a Swinging Target with a Robot Manipulator using Visual Sensing

“…For robotic visual servoing it is specially interesting to look at the work on tracking of rigid bodies in Cartesian space. Particle filter based tracking on the SE(3) group has been investigated using different assumptions on the underlying dynamical model in Kwon et al (2007), Choi et al (2011) and Choi and Christensen (2012). In particular, the particle filters were Figure 1: Manual loading of objects onto a swinging conveyor trolley is a common task in industry.…”

“…The main motivation for this is to simplify and improve the parameter estimation algorithm. The benefits of a coordinate invariant representation with the particle filter was thoroughly discussed in Kwon et al (2007). In the use case that is presented in this paper, it is unrealistic to consider swinging motions with amplitudes larger than 10…”