Stability analysis of controlled multiple-link robotic manipulator systems with time delays

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)53-74
Journal / PublicationMathematical and Computer Modelling
Issue number1
Publication statusPublished - Jan 1998
Externally publishedYes


Controlled robotic manipulator systems, normally operating in an acceptable manner, may become unstable, when time delays exist in the feedback loop. This instability may cause oscillations and thus deteriorate the system performance. In this paper we introduce a method to analyze the performance of robotic manipulators with small time delays in the feedback loop. Specifically, we may predict the limits of a stable system operation, i.e., the robustness and expected system error bounds, as a function of the time delay and system parameters. The analysis method uses nonlinear control theory concepts, such as Lyapunov's second method, and takes advantage of norms to establish operational bounds. Previous research of time-delay systems analysis is also reviewed, in general, and pertaining to robotic controls, in particular. The results of the analysis can be displayed graphically and may be used to adjust the controller gains and trajectories to ensure satisfactory operation. Predictably, the system response is slowed as the time delay increases. The validity of the analysis is demonstrated with a numerical example of a two-link manipulator using a computed-torque controller. The time responses of the example, run on a computer-generated model, supports the analysis results and predicted performance.

Research Area(s)

  • Control, Feedback delay, Robotic manipulator systems, Stability, Time delay