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A Bayesian approach to empirical local linearizations for robotics


Conference Paper


Local linearizations are ubiquitous in the control of robotic systems. Analytical methods, if available, can be used to obtain the linearization, but in complex robotics systems where the the dynamics and kinematics are often not faithfully obtainable, empirical linearization may be preferable. In this case, it is important to only use data for the local linearization that lies within a ``reasonable'' linear regime of the system, which can be defined from the Hessian at the point of the linearization -- a quantity that is not available without an analytical model. We introduce a Bayesian approach to solve statistically what constitutes a ``reasonable'' local regime. We approach this problem in the context local linear regression. In contrast to previous locally linear methods, we avoid cross-validation or complex statistical hypothesis testing techniques to find the appropriate local regime. Instead, we treat the parameters of the local regime probabilistically and use approximate Bayesian inference for their estimation. This approach results in an analytical set of iterative update equations that are easily implemented on real robotics systems for real-time applications. As in other locally weighted regressions, our algorithm also lends itself to complete nonlinear function approximation for learning empirical internal models. We sketch the derivation of our Bayesian method and provide evaluations on synthetic data and actual robot data where the analytical linearization was known.

Author(s): Ting, J.-A. and D’Souza, A. and Vijayakumar, S. and Schaal, S.
Book Title: International Conference on Robotics and Automation (ICRA2008)
Year: 2008

Department(s): Autonomous Motion
Bibtex Type: Conference Paper (inproceedings)

Address: Pasadena, CA, USA, May 19-23, 2008
Cross Ref: p10265
Note: clmc
URL: http://www-clmc.usc.edu/publications/T/ting-ICRA2008.pdf


  title = {A Bayesian approach to empirical local linearizations for robotics},
  author = {Ting, J.-A. and D'Souza, A. and Vijayakumar, S. and Schaal, S.},
  booktitle = {International Conference on Robotics and Automation (ICRA2008)},
  address = {Pasadena, CA, USA, May 19-23, 2008},
  year = {2008},
  note = {clmc},
  crossref = {p10265},
  url = {http://www-clmc.usc.edu/publications/T/ting-ICRA2008.pdf}