Online feedback control for input-saturated robotic systems on Lie groups

Taosha Fan, Todd Murphey

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

8 Scopus citations


In this paper, we propose an approach to designing online feedback controllers for input-saturated robotic systems evolving on Lie groups by extending the recently developed Sequential Action Control (SAC). In contrast to existing feedback controllers, our approach poses the nonconvex constrained nonlinear optimization problem as the tracking of a desired negative mode insertion gradient on the configuration space of a Lie group. This results in a closed-form feedback control law even with input saturation and thus is well suited for online application. In extending SAC to Lie groups, the associated mode insertion gradient is derived and the switching time optimization on Lie groups is studied. We demonstrate the efficacy and scalability of our approach in the 2D kinematic car on SE(2) and the 3D quadrotor on SE(3). We also implement iLQG on a quadrator model and compare to SAC, demonstrating that SAC is both faster to compute and has a larger basin of attraction.

Original languageEnglish (US)
Title of host publicationRobotics
Subtitle of host publicationScience and Systems XII, RSS 2016
EditorsDavid Hsu, Nancy Amato, Spring Berman, Sam Jacobs
PublisherMIT Press Journals
Number of pages10
ISBN (Electronic)9780992374723
StatePublished - Jan 1 2016
Event2016 Robotics: Science and Systems, RSS 2016 - Ann Arbor, United States
Duration: Jun 18 2016Jun 22 2016

Publication series

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


Other2016 Robotics: Science and Systems, RSS 2016
Country/TerritoryUnited States
CityAnn Arbor


  • Input saturation
  • Lie group
  • Online feedback control
  • Sequential action control

ASJC Scopus subject areas

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


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