On Simulation and Trajectory Prediction with Gaussian Process Dynamics

Lukas Hewing, Elena Arcari, Lukas P. Fröhlich, Melanie N. Zeilinger
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:424-434, 2020.

Abstract

Established techniques for simulation and prediction with Gaussian process (GP) dynamics implicitly make use of an independence assumption on successive function evaluations of the dynamics model. This can result in significant error and underestimation of the prediction uncertainty, potentially leading to failures in safety-critical applications. This paper proposes methods that explicitly take the correlation of successive function evaluations into account. We first describe two sampling-based techniques; one approach provides samples of the true trajectory distribution, suitable for ‘ground truth’ simulations, while the other draws function samples from basis function approximations of the GP. Second, we present a linearization-based technique that directly provides approximations of the trajectory distribution, taking correlations explicitly into account. We demonstrate the procedures in simple numerical examples, contrasting the results with established methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v120-hewing20a, title = {On Simulation and Trajectory Prediction with Gaussian Process Dynamics}, author = {Hewing, Lukas and Arcari, Elena and Fr\"ohlich, Lukas P. and Zeilinger, Melanie N.}, booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control}, pages = {424--434}, year = {2020}, editor = {Bayen, Alexandre M. and Jadbabaie, Ali and Pappas, George and Parrilo, Pablo A. and Recht, Benjamin and Tomlin, Claire and Zeilinger, Melanie}, volume = {120}, series = {Proceedings of Machine Learning Research}, month = {10--11 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v120/hewing20a/hewing20a.pdf}, url = {https://proceedings.mlr.press/v120/hewing20a.html}, abstract = {Established techniques for simulation and prediction with Gaussian process (GP) dynamics implicitly make use of an independence assumption on successive function evaluations of the dynamics model. This can result in significant error and underestimation of the prediction uncertainty, potentially leading to failures in safety-critical applications. This paper proposes methods that explicitly take the correlation of successive function evaluations into account. We first describe two sampling-based techniques; one approach provides samples of the true trajectory distribution, suitable for ‘ground truth’ simulations, while the other draws function samples from basis function approximations of the GP. Second, we present a linearization-based technique that directly provides approximations of the trajectory distribution, taking correlations explicitly into account. We demonstrate the procedures in simple numerical examples, contrasting the results with established methods.} }
Endnote
%0 Conference Paper %T On Simulation and Trajectory Prediction with Gaussian Process Dynamics %A Lukas Hewing %A Elena Arcari %A Lukas P. Fröhlich %A Melanie N. Zeilinger %B Proceedings of the 2nd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2020 %E Alexandre M. Bayen %E Ali Jadbabaie %E George Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire Tomlin %E Melanie Zeilinger %F pmlr-v120-hewing20a %I PMLR %P 424--434 %U https://proceedings.mlr.press/v120/hewing20a.html %V 120 %X Established techniques for simulation and prediction with Gaussian process (GP) dynamics implicitly make use of an independence assumption on successive function evaluations of the dynamics model. This can result in significant error and underestimation of the prediction uncertainty, potentially leading to failures in safety-critical applications. This paper proposes methods that explicitly take the correlation of successive function evaluations into account. We first describe two sampling-based techniques; one approach provides samples of the true trajectory distribution, suitable for ‘ground truth’ simulations, while the other draws function samples from basis function approximations of the GP. Second, we present a linearization-based technique that directly provides approximations of the trajectory distribution, taking correlations explicitly into account. We demonstrate the procedures in simple numerical examples, contrasting the results with established methods.
APA
Hewing, L., Arcari, E., Fröhlich, L.P. & Zeilinger, M.N.. (2020). On Simulation and Trajectory Prediction with Gaussian Process Dynamics. Proceedings of the 2nd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 120:424-434 Available from https://proceedings.mlr.press/v120/hewing20a.html.

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