Klanke, S.

Mitrovic, D.

Vijayakumar, S.

Edinburgh Research Explorer

     Edinburgh Research Explorer                                      Learned system dynamics for adaptive optimal feedback controlCitation for published version:Mitrovic, D, Klanke, S & Vijayakumar, S 2007, Learned system dynamics for adaptive optimal feedbackcontrol. in Neural Information Processing Conference (NIPS 2007) : Workshop on Robotics Challenges forMachine Learning.Link:Link to publication record in Edinburgh Research ExplorerDocument Version:Peer reviewed versionPublished In:Neural Information Processing Conference (NIPS 2007) : Workshop on Robotics Challenges for MachineLearningGeneral rightsCopyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s)and / or other copyright owners and it is a condition of accessing these publications that users recognise andabide by the legal requirements associated with these rights.Take down policyThe University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorercontent complies with UK legislation. If you believe that the public display of this file breaches copyright pleasecontact openaccess@ed.ac.uk providing details, and we will remove access to the work immediately andinvestigate your claim.Download date: 28. Apr. 2017Learned system dynamics for adaptive optimal feedback controlDjordje Mitrovic, Stefan Klanke, and Sethu Vijayakumar{d.mitrovic, s.klanke, sethu.vijayakumar}@ed.ac.ukSchool of Informatics, University of Edinburgh, United KingdomOptimal feedback control (OFC) has been proposed as an attractive movement generationstrategy in goal reaching tasks for anthropomorphic manipulator systems. In contrast to classicopen loop optimizers that produce “just” a minimal-cost trajectory with implicit resolutionof kinematic and dynamic redundancies, the OFC framework additionally yields a feedbackcontrol law which corrects errors only if they adversely affect the task performance (minimumintervention principle).Locally, the optimal feedback control law for systems with non-linear dynamics and non-quadratic costs can be found by iterative methods, such as the recently introduced iterativeLinear Quadratic Gaussian (iLQG) algorithm [1]. So far this framework relied on an analyticform of the system dynamics, which may often be unknown, difficult to estimate for morerealistic control systems or may be subject to frequent systematic changes.We present a novel combination of learning a forward dynamics model within the iLQGframework, for which we employ Locally Weighted Projection Regression (LWPR) [2]. Utilisingsuch adaptive internal models can compensate for complex dynamic perturbations of the con-trolled system in an online fashion. Moreover, through the availability of analytic derivativesof the learned model, the adaptive iLQG–LD framework we introduce lends itself to a compu-tationally more efficient implementation of the iLQG optimization without sacrificing controlaccuracy, allowing the method to scale to large DoF systems.Up to now, we studied iLQG–LD on two different joint torque controlled manipulators assimulated by the Matlab Robotics Toolbox: i) a planar 2 DoF manipulator, which is idealfor performing extensive (quantitative) comparison studies and to test the manipulator undercontrolled perturbations and force fields during planar motion, and ii) a 6 DoF manipulatorwith realistic physical parameters. We successfully tested our iLQG–LD framework with bothstationary and non-stationary dynamics, simulating constant or velocity-dependent force fields.Our current work concentrates on implementing the iLQG–LD framework on the 7-DOFrobot arm hardware of the German Aerospace Centre (DLR), which raises challenges such asa very high-dimensional input space (7 commands + 14 motor states + 14 joint states) anda high sampling rate of 1kHz. In the future, we will aim for the biomorphic variable stiffnessbased highly redundant actuation system that is currently developed at DLR – this will not onlyexplore an alternative control paradigm, but will also provide the only viable and principledcontrol strategy for such a system.References[1] E. Todorov and W. Li. A generalized iterative LQG method for locally-optimal feedbackcontrol of constrained nonlinear stochastic systems. In Proc. of the American Control Con-ference, 2005.[2] S. Vijayakumar, A. D’Souza, and S. Schaal. Incremental online learning in high dimensions.Neural Computation, 17:2602–2634, 2005.

Learned system dynamics for adaptive optimal feedback control

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