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

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.

Original languageEnglish (US)
Title of host publicationRobotics
Subtitle of host publicationScience and Systems XIII, RSS 2017
PublisherMIT Press Journals
Volume13
ISBN (Electronic)9780992374730
StatePublished - Jan 1 2017
Event2017 Robotics: Science and Systems, RSS 2017 - Cambridge, United States
Duration: Jul 12 2017Jul 16 2017

Other

Other2017 Robotics: Science and Systems, RSS 2017
CountryUnited States
CityCambridge
Period7/12/177/16/17

Fingerprint

Feedback
Needles
Nonlinear feedback
Controllability
Feedback control
Dynamic models
Kinematics

ASJC Scopus subject areas

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

Cite this

Mamakoukas, G., MacIver, M. A., & Murphey, T. D. (2017). Feedback synthesis for controllable underactuated systems using sequential second order actions. In Robotics: Science and Systems XIII, RSS 2017 (Vol. 13). MIT Press Journals.
Mamakoukas, Giorgos ; MacIver, Malcolm A. ; Murphey, Todd D. / Feedback synthesis for controllable underactuated systems using sequential second order actions. Robotics: Science and Systems XIII, RSS 2017. Vol. 13 MIT Press Journals, 2017.
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Mamakoukas, G, MacIver, MA & Murphey, TD 2017, Feedback synthesis for controllable underactuated systems using sequential second order actions. in Robotics: Science and Systems XIII, RSS 2017. vol. 13, MIT Press Journals, 2017 Robotics: Science and Systems, RSS 2017, Cambridge, United States, 7/12/17.

Feedback synthesis for controllable underactuated systems using sequential second order actions. / Mamakoukas, Giorgos; MacIver, Malcolm A.; Murphey, Todd D.

Robotics: Science and Systems XIII, RSS 2017. Vol. 13 MIT Press Journals, 2017.

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

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Mamakoukas G, MacIver MA, Murphey TD. Feedback synthesis for controllable underactuated systems using sequential second order actions. In Robotics: Science and Systems XIII, RSS 2017. Vol. 13. MIT Press Journals. 2017