@inproceedings{7fa2a36c9b3840cca601bf0a06a0982b,
title = "Feedback synthesis for controllable underactuated systems using sequential second order actions",
abstract = "This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions-the needle variations of optimal control-as the basis for choosing each control response to the current state. A second result of the paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Moreover, the simulated examples demonstrate superior convergence when compared to synthesis based on first-order needle variations. Lastly, the underactuated dynamic underwater vehicle model demonstrates the convergence even in the presence of a velocity field.",
author = "Giorgos Mamakoukas and MacIver, {Malcolm A.} and Murphey, {Todd D.}",
note = "Funding Information: ACKNOWLEDGMENTS This work was supported by the Office of Naval Research under grant ONR N00014-14-1-0594. Any opinions, findings, and conclusions or recommendations expressed here are those of the authors and do not necessarily reflect the views of the Office of Naval Research. Publisher Copyright: {\textcopyright} 2017 MIT Press Journals. All rights reserved.; 2017 Robotics: Science and Systems, RSS 2017 ; Conference date: 12-07-2017 Through 16-07-2017",
year = "2017",
language = "English (US)",
series = "Robotics: Science and Systems",
publisher = "MIT Press Journals",
editor = "Siddhartha Srinivasa and Nora Ayanian and Nancy Amato and Scott Kuindersma",
booktitle = "Robotics",
address = "United States",
}