Differential dynamic programming: Difference between revisions

Revision as of 12:20, 11 May 2020

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== Differential dynamic programming ==

DDP proceeds by iteratively performing a backward pass on the nominal trajectory to generate a new control sequence, and then a forward-pass to compute and evaluate a new nominal trajectory. We begin with the backward pass. If

:<math>\ell(\mathbf{x},\mathbf{u}) + V(\mathbf{f}(\mathbf{x},\mathbf{u}),i+1)</math>

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Sampled differential dynamic programming (SaDDP) is a Monte Carlo variant of differential dynamic programming.<ref>{{Cite document|title=Sampled differential dynamic programming - IEEE Conference Publication|language=en-US|doi=10.1109/IROS.2016.7759229}}</ref><ref>{{Cite web|url=https://ieeexplore.ieee.org/document/8430799|title=Regularizing Sampled Differential Dynamic Programming - IEEE Conference Publication|website=ieeexplore.ieee.org|language=en-US|access-date=2018-10-19}}</ref><ref>{{Cite book|last=Joose|first=Rajamäki|date=2018|title=Random Search Algorithms for Optimal Control|url=http://urn.fi/URN:ISBN:978-952-60-8156-4|language=en|issn=1799-4942|isbn=9789526081564|publisher=Aalto University}}</ref> It is based on treating the quadratic cost of differential dynamic programming as the energy of a [[Boltzmann distribution]]. This way the quantities of DDP can be matched to the statistics of a [[Multivariate normal distribution|multidimensional normal distribution]]. The statistics can be recomputed from sampled trajectories without differentiation.

Sampled differential dynamic programming has been extended to Path Integral Policy Improvement with Differential Dynamic Programming.<ref>{{Cite journal|last=Lefebvre|first=Tom|last2=Crevecoeur|first2=Guillaume|date=July 2019-07|title=Path Integral Policy Improvement with Differential Dynamic Programming|url=https://ieeexplore.ieee.org/abstract/document/8868359|journal=2019 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM)|pages=739–745|doi=10.1109/AIM.2019.8868359}}</ref>. This creates a link between differential dynamic programming and path integral control,<ref>{{Cite journal|last=Theodorou|first=Evangelos|last2=Buchli|first2=Jonas|last3=Schaal|first3=Stefan|date=May 2010-05|title=Reinforcement learning of motor skills in high dimensions: A path integral approach|url=https://ieeexplore.ieee.org/document/5509336|journal=2010 IEEE International Conference on Robotics and Automation|pages=2397–2403|doi=10.1109/ROBOT.2010.5509336}}</ref>, which is a framework of stochastic optimal control.

== See also ==

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<!--- Categories --->

[[Category:Dynamic programming]]