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Latent force models encode the interaction between multiple related dynamical systems in the form of a kernel or covariance function. Each variable to be modeled is represented as the output of a differential equation and each differential equation is driven by a weighted sum of latent functions with uncertainty given by a Gaussian process prior. In this paper we consider employing the latent force model framework for the problem of determining robot motor primitives. To deal with discontinuities in the dynamical systems or the latent driving force we introduce an extension of the basic latent force model, that switches between different latent functions and potentially different dynamical systems. This creates a versatile representation for robot movements that can capture discrete changes and non-linearities in the dynamics. We give illustrative examples on both synthetic data and for striking movements recorded using a Barrett WAM robot as haptic input device. Our inspiration is robot motor primitives, but we expect our model to have wide application for dynamical systems including models for human motion capture data and systems biology.
Author Information
Mauricio A Alvarez (University of Manchester)
Jan Peters (TU Darmstadt & MPI Intelligent Systems)
Jan Peters is a full professor (W3) for Intelligent Autonomous Systems at the Computer Science Department of the Technische Universitaet Darmstadt and at the same time a senior research scientist and group leader at the Max-Planck Institute for Intelligent Systems, where he heads the interdepartmental Robot Learning Group. Jan Peters has received the Dick Volz Best 2007 US PhD Thesis Runner-Up Award, the Robotics: Science & Systems - Early Career Spotlight, the INNS Young Investigator Award, and the IEEE Robotics & Automation Society‘s Early Career Award as well as numerous best paper awards. In 2015, he was awarded an ERC Starting Grant. Jan Peters has studied Computer Science, Electrical, Mechanical and Control Engineering at TU Munich and FernUni Hagen in Germany, at the National University of Singapore (NUS) and the University of Southern California (USC). He has received four Master‘s degrees in these disciplines as well as a Computer Science PhD from USC.
Bernhard Schölkopf (MPI for Intelligent Systems, Tübingen)
Bernhard Scholkopf received degrees in mathematics (London) and physics (Tubingen), and a doctorate in computer science from the Technical University Berlin. He has researched at AT&T Bell Labs, at GMD FIRST, Berlin, at the Australian National University, Canberra, and at Microsoft Research Cambridge (UK). In 2001, he was appointed scientific member of the Max Planck Society and director at the MPI for Biological Cybernetics; in 2010 he founded the Max Planck Institute for Intelligent Systems. For further information, see www.kyb.tuebingen.mpg.de/~bs.
Neil D Lawrence (University of Cambridge)
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Gabriele B Schweikert · Christian Widmer · Bernhard Schölkopf · Gunnar Rätsch -
2008 Poster: Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes »
Ben Calderhead · Mark A Girolami · Neil D Lawrence -
2008 Poster: Diffeomorphic Dimensionality Reduction »
Christian Walder · Bernhard Schölkopf -
2007 Workshop: Robotics Challenges for Machine Learning »
Jan Peters · Marc Toussaint -
2007 Workshop: Approximate Bayesian Inference in Continuous/Hybrid Models »
Matthias Seeger · David Barber · Neil D Lawrence · Onno Zoeter -
2007 Spotlight: Kernel Measures of Conditional Dependence »
Kenji Fukumizu · Arthur Gretton · Xiaohai Sun · Bernhard Schölkopf -
2007 Poster: An Analysis of Inference with the Universum »
Fabian H Sinz · Olivier Chapelle · Alekh Agarwal · Bernhard Schölkopf -
2007 Poster: Kernel Measures of Conditional Dependence »
Kenji Fukumizu · Arthur Gretton · Xiaohai Sun · Bernhard Schölkopf -
2007 Spotlight: An Analysis of Inference with the Universum »
Fabian H Sinz · Olivier Chapelle · Alekh Agarwal · Bernhard Schölkopf -
2007 Spotlight: A Kernel Statistical Test of Independence »
Arthur Gretton · Kenji Fukumizu · Choon Hui Teo · Le Song · Bernhard Schölkopf · Alexander Smola -
2007 Poster: A Kernel Statistical Test of Independence »
Arthur Gretton · Kenji Fukumizu · Choon Hui Teo · Le Song · Bernhard Schölkopf · Alexander Smola -
2006 Workshop: Learning when test and training inputs have different distributions »
Joaquin Quiñonero-Candela · Masashi Sugiyama · Anton Schwaighofer · Neil D Lawrence -
2006 Workshop: Towards a New Reinforcement Learning? »
Jan Peters · Stefan Schaal · Drew Bagnell -
2006 Poster: Modelling transcriptional regulation using Gaussian Processes »
Neil D Lawrence · Guido Sanguinetti · Magnus Rattray -
2006 Poster: Implicit Surfaces with Globally Regularised and Compactly Supported Basis Functions »
Christian Walder · Bernhard Schölkopf · Olivier Chapelle -
2006 Poster: Learning Dense 3D Correspondence »
Florian Steinke · Bernhard Schölkopf · Volker Blanz -
2006 Poster: A Local Learning Approach for Clustering »
Mingrui Wu · Bernhard Schölkopf -
2006 Poster: A Kernel Method for the Two-Sample-Problem »
Arthur Gretton · Karsten Borgwardt · Malte J Rasch · Bernhard Schölkopf · Alexander Smola -
2006 Poster: Correcting Sample Selection Bias by Unlabeled Data »
Jiayuan Huang · Alexander Smola · Arthur Gretton · Karsten Borgwardt · Bernhard Schölkopf -
2006 Spotlight: Correcting Sample Selection Bias by Unlabeled Data »
Jiayuan Huang · Alexander Smola · Arthur Gretton · Karsten Borgwardt · Bernhard Schölkopf -
2006 Talk: A Kernel Method for the Two-Sample-Problem »
Arthur Gretton · Karsten Borgwardt · Malte J Rasch · Bernhard Schölkopf · Alexander Smola -
2006 Poster: A Nonparametric Approach to Bottom-Up Visual Saliency »
Wolf Kienzle · Felix A Wichmann · Bernhard Schölkopf · Matthias Franz -
2006 Poster: Learning with Hypergraphs: Clustering, Classification, and Embedding »
Denny Zhou · Jiayuan Huang · Bernhard Schölkopf