Actuating Eigenmanifolds of Conservative Mechanical Systems Via Bounded or Impulsive Control Actions

C. Della Santina, Davide Calzolari, Alessandro Massimo Giordano, Alin Albu-Schaffer

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Eigenmanifolds are two-dimensional submanifolds of the state space, which generalize linear eigenspaces to nonlinear mechanical systems. Initializing a robot on an Eigenmanifold (or driving it there by control) yields hyper-efficient and regular oscillatory behaviors, called modal oscillations. This letter investigates the possibility of transitioning between two modal oscillations without ever leaving the Eigenmanifold. This is essential to generate control inputs that decrease or increase the amplitude of the nonlinear oscillations. First, we prove that this goal can be achieved using bounded inputs only for Eigenmanifolds with unidimensional projection in configuration space. Then, we show that by allowing for impulsive control actions, the problem can be solved for all Eigenmanifolds which self-intersect when projected in configuration space.

Original languageEnglish
Pages (from-to)2783-2790
JournalIEEE Robotics and Automation Letters
Volume6
Issue number2
DOIs
Publication statusPublished - 2021

Keywords

  • Compliant Joints and Mechanisms
  • Manifolds
  • Mechanical systems
  • Motion Control
  • Natural Machine Motion
  • Orbits
  • Oscillators
  • Robots
  • Space vehicles
  • Trajectory

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