1,959 research outputs found
Incremental Sparse GP Regression for Continuous-time Trajectory Estimation & Mapping
Recent work on simultaneous trajectory estimation and mapping (STEAM) for
mobile robots has found success by representing the trajectory as a Gaussian
process. Gaussian processes can represent a continuous-time trajectory,
elegantly handle asynchronous and sparse measurements, and allow the robot to
query the trajectory to recover its estimated position at any time of interest.
A major drawback of this approach is that STEAM is formulated as a batch
estimation problem. In this paper we provide the critical extensions necessary
to transform the existing batch algorithm into an extremely efficient
incremental algorithm. In particular, we are able to vastly speed up the
solution time through efficient variable reordering and incremental sparse
updates, which we believe will greatly increase the practicality of Gaussian
process methods for robot mapping and localization. Finally, we demonstrate the
approach and its advantages on both synthetic and real datasets.Comment: 10 pages, 10 figure
Batch Nonlinear Continuous-Time Trajectory Estimation as Exactly Sparse Gaussian Process Regression
In this paper, we revisit batch state estimation through the lens of Gaussian
process (GP) regression. We consider continuous-discrete estimation problems
wherein a trajectory is viewed as a one-dimensional GP, with time as the
independent variable. Our continuous-time prior can be defined by any
nonlinear, time-varying stochastic differential equation driven by white noise;
this allows the possibility of smoothing our trajectory estimates using a
variety of vehicle dynamics models (e.g., `constant-velocity'). We show that
this class of prior results in an inverse kernel matrix (i.e., covariance
matrix between all pairs of measurement times) that is exactly sparse
(block-tridiagonal) and that this can be exploited to carry out GP regression
(and interpolation) very efficiently. When the prior is based on a linear,
time-varying stochastic differential equation and the measurement model is also
linear, this GP approach is equivalent to classical, discrete-time smoothing
(at the measurement times); when a nonlinearity is present, we iterate over the
whole trajectory to maximize accuracy. We test the approach experimentally on a
simultaneous trajectory estimation and mapping problem using a mobile robot
dataset.Comment: Submitted to Autonomous Robots on 20 November 2014, manuscript #
AURO-D-14-00185, 16 pages, 7 figure
Learning the dynamics of articulated tracked vehicles
In this work, we present a Bayesian non-parametric approach to model the motion control of ATVs. The motion control model is based on a Dirichlet Process-Gaussian Process (DP-GP) mixture model. The DP-GP mixture model provides a flexible representation of patterns of control manoeuvres along trajectories of different lengths and discretizations. The model also estimates the number of patterns, sufficient for modeling the dynamics of the ATV
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