Abstract

Continuum robot manipulators present challenges for controller design due to the complexity of their infinite-dimensional dynamics. This paper develops a practical dynamics-based approach to synthesizing state feedback controllers for a soft continuum robot arm composed of segments with local sensing, actuation, and control capabilities. Each segment communicates its states to its two adjacent neighboring segments, requiring a tridiagonal feedback matrix for decentralized controller implementation. A semi-discrete numerical approximation of the Euler-Bernoulli beam equation is used to represent the robot arm dynamics. Formulated in state space representation, this numerical approximation is used to define an H-{\infty} optimal control problem in terms of a Bilinear Matrix Inequality. We develop three iterative algorithms that solve this problem by computing the tridiagonal feedback matrix which minimizes the H-{\infty} norm of the map from disturbances to regulated outputs. We confirm through simulations that all three controllers successfully dampen the free vibrations of a cantilever beam that are induced by an initial sinusoidal displacement, and we compare the controllers' performance.

Original languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages7002-7009
Number of pages8
ISBN (Electronic)9781538613955
DOIs
StatePublished - Jan 18 2019
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December
ISSN (Print)0743-1546

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
CountryUnited States
CityMiami
Period12/17/1812/19/18

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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