Marginal stability in ℒ1 -adaptive control of manipulators

Kim Doang Nguyen, Harry Dankowicz, Naira Hovakimyan

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


This paper presents a preliminary analysis of the robustness of a recently-proposed adaptive controller for robot manipulators based on the ℒ1 control paradigm. Here, the use of a lowpass filter in the control input decouples the estimation loop from the control loop, thereby facilitating an arbitrary increase of estimation rates (limited only by hardware) without sacrificing robustness. Tuning of the filter also allows for shaping the nominal response and enhancing the system's robustness. The paper further demonstrates improvements in the critical time delay associated with a static reference input achieved through the introduction of time delay in the state-predictor formulation. Guided by results from the theory of single-input-single-output ℒ1 control systems, a linear, time-invariant system is proposed in order to derive a conservative lower bound on the system's actuator critical time delay for static reference input in the limit of large estimation gains, as an indicator of robustness. Finally, a numerical method is proposed for quantifying the robustness against time delay of the system's response to a given static reference input based on techniques of parameter continuation. This method computes the critical time delay at which local stability is lost in a Hopf bifurcation. The dependence of this critical time delay on control parameters, such as adaptive gains and filter bandwidth, is here obtained using advanced algorithms for computing approximate covers of implicitly defined manifolds.

Original languageEnglish (US)
Title of host publication9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
PublisherAmerican Society of Mechanical Engineers
ISBN (Print)9780791855966
StatePublished - 2013
EventASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013 - Portland, OR, United States
Duration: Aug 4 2013Aug 7 2013

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume7 A


OtherASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013
Country/TerritoryUnited States
CityPortland, OR

ASJC Scopus subject areas

  • Modeling and Simulation
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design


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