Feedback synthesis for controllable underactuated systems using sequential second order actions

Giorgos Mamakoukas, Malcolm A. MacIver, Todd D. Murphey

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


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.

Original languageEnglish (US)
Title of host publicationRobotics
Subtitle of host publicationScience and Systems XIII, RSS 2017
EditorsSiddhartha Srinivasa, Nora Ayanian, Nancy Amato, Scott Kuindersma
PublisherMIT Press Journals
ISBN (Electronic)9780992374730
StatePublished - 2017
Event2017 Robotics: Science and Systems, RSS 2017 - Cambridge, United States
Duration: Jul 12 2017Jul 16 2017

Publication series

NameRobotics: Science and Systems
ISSN (Electronic)2330-765X


Other2017 Robotics: Science and Systems, RSS 2017
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Artificial Intelligence
  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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