Abstract
A tool for the design of a periodic motion in underactuated systems via generating a self-excited oscillation of a desired amplitude and frequency driven by a variable structure control is reviewed. In this chapter, we overview the capabilities of the two-relay controller to induce oscillations in dynamical systems. In this chapter, we will focus on underactuated mechanical systems with degree of underactuation one, that is, n degrees-of-freedom and n – 1 actuators only. Threemethods to set the frequency and amplitude of oscillation and its application to one-degree of underactuation systems are reviewed: describing function method, Locus of the perturbed relay system design (LPRS), and Poincaré map based design. Theoretical and practical open problems are also discussed.KeywordsPeriodic MotionSlide Mode ControllerOrbital StabilizationBiped RobotVariable Structure SystemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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