Some Useful Results for Closed-Form Propagation of Error in Vehicle Odometry

Alonzo Kelly
tech. report CMU-RI-TR-00-20, Robotics Institute, Carnegie Mellon University, December, 2000


Download
  • Adobe portable document format (pdf) (2MB)
Copyright notice: This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. These works may not be reposted without the explicit permission of the copyright holder.

Abstract
Odometry can be modelled as a nonlinear dynamical system. The linearized error propagation equations for both deterministic and random errors in the odometry process have time varying coefficients and therefore may not be easy to solve. However, the odometry process exibits a property here called "commutable dynamics" which makes the transition matrix easy to compute. As a result, an essentially closed form solution to both deterministic and random linearized error propagation is available. Examination of the general solution indicates that error expressions depend on a few simple path functionals which are analogous to the moments of mechanics and equal to the first two coefficients of the power and Fourier series of the path followed. The resulting intuitive understanding of error dynamics is a valuable tool for many problems of mobile robotics. Required sensor performance can be computed from tolerable error, trajectories can be designed to minimize error for operation or to maximize it for calibration and evaluation purposes. Optimal estimation algorithms can be implemented in nearly closed form for small footprint embedded applications, etc.

Notes

Text Reference
Alonzo Kelly, "Some Useful Results for Closed-Form Propagation of Error in Vehicle Odometry," tech. report CMU-RI-TR-00-20, Robotics Institute, Carnegie Mellon University, December, 2000

BibTeX Reference
@techreport{Kelly_2000_3610,
   author = "Alonzo Kelly",
   title = "Some Useful Results for Closed-Form Propagation of Error in Vehicle Odometry",
   booktitle = "",
   institution = "Robotics Institute",
   month = "December",
   year = "2000",
   number= "CMU-RI-TR-00-20",
   address= "Pittsburgh, PA",
}