On the representation and estimation of spatial uncertainly
International Journal of Robotics Research
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
Computing MAP trajectories by representing, propagating and combining PDFs over groups
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
A comparison of loop closing techniques in monocular SLAM
Robotics and Autonomous Systems
A robust approach for ego-motion estimation using a mobile stereo platform
IWCM'04 Proceedings of the 1st international conference on Complex motion
Modeling of Unbounded Long-Range Drift in Visual Odometry
PSIVT '10 Proceedings of the 2010 Fourth Pacific-Rim Symposium on Image and Video Technology
Visual odometry aided by a sun sensor and inclinometer
AERO '11 Proceedings of the 2011 IEEE Aerospace Conference
Path planning on a network of paths
AERO '11 Proceedings of the 2011 IEEE Aerospace Conference
Error propagation on the Euclidean group with applications to manipulator kinematics
IEEE Transactions on Robotics
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We examine how the estimation error grows with time when a mobile robot estimates its location from relative pose measurements without global position or orientation sensors. We show that, in both two-dimensional and three-dimensional space, both the bias and the variance of the position estimation error grows at most linearly with time asymptotically. Non-asymptotic bounds on the bias and variance are obtained, which provide insight into the mechanism of error growth. The bias is crucially dependent on the trajectory of the robot. Conclusions on the asymptotic growth rate of the bias continue to hold even with unbiased measurements or error-free translation measurements. Exact formulas for the bias and the variance of the position estimation error are provided for two specific two-dimensional trajectories-straight line and periodic. Experiments with a P3-DX wheeled robot and Monte Carlo simulations are provided to verify the theoretical predictions. A method to reduce the bias is proposed based on the lessons learned.