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2015


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Probabilistic Interpretation of Linear Solvers

Hennig, P.

SIAM Journal on Optimization, 25(1):234-260, 2015 (article)

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Web PDF link (url) DOI [BibTex]

2015


Web PDF link (url) DOI [BibTex]


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Exciting Engineered Passive Dynamics in a Bipedal Robot

Renjewski, D., Spröwitz, A., Peekema, A., Jones, M., Hurst, J.

{IEEE Transactions on Robotics and Automation}, 31(5):1244-1251, IEEE, New York, NY, 2015 (article)

Abstract
A common approach in designing legged robots is to build fully actuated machines and control the machine dynamics entirely in soft- ware, carefully avoiding impacts and expending a lot of energy. However, these machines are outperformed by their human and animal counterparts. Animals achieve their impressive agility, efficiency, and robustness through a close integration of passive dynamics, implemented through mechanical components, and neural control. Robots can benefit from this same integrated approach, but a strong theoretical framework is required to design the passive dynamics of a machine and exploit them for control. For this framework, we use a bipedal spring–mass model, which has been shown to approximate the dynamics of human locomotion. This paper reports the first implementation of spring–mass walking on a bipedal robot. We present the use of template dynamics as a control objective exploiting the engineered passive spring–mass dynamics of the ATRIAS robot. The results highlight the benefits of combining passive dynamics with dynamics-based control and open up a library of spring–mass model-based control strategies for dynamic gait control of robots.

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link (url) DOI Project Page [BibTex]

link (url) DOI Project Page [BibTex]


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Probabilistic numerics and uncertainty in computations

Hennig, P., Osborne, M. A., Girolami, M.

Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 471(2179), 2015 (article)

Abstract
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.

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PDF DOI [BibTex]

PDF DOI [BibTex]

2013


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Quasi-Newton Methods: A New Direction

Hennig, P., Kiefel, M.

Journal of Machine Learning Research, 14(1):843-865, March 2013 (article)

Abstract
Four decades after their invention, quasi-Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to the objective function. We show that many, including the most popular, quasi-Newton methods can be interpreted as approximations of Bayesian linear regression under varying prior assumptions. This new notion elucidates some shortcomings of classical algorithms, and lights the way to a novel nonparametric quasi-Newton method, which is able to make more efficient use of available information at computational cost similar to its predecessors.

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website+code pdf link (url) [BibTex]

2013


website+code pdf link (url) [BibTex]


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Analytical probabilistic modeling for radiation therapy treatment planning

Bangert, M., Hennig, P., Oelfke, U.

Physics in Medicine and Biology, 58(16):5401-5419, 2013 (article)

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PDF DOI [BibTex]

PDF DOI [BibTex]