Reduced dynamical equations for barycentric spherical robots

Barycentric spherical robots (BSRs) rely on a noncollocated center of mass and center of rotation for propulsion. Unique challenges inherent to BSRs include a nontrivial correlation between internal actuation, momentum, and net vehicle motion. A new method is presented for deriving reduced dynamical...

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Bibliographic Details
Published in2016 IEEE International Conference on Robotics and Automation (ICRA) pp. 2725 - 2732
Main Authors Burkhardt, Matt, Burdick, Joel W.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.05.2016
Subjects
Electron tubes
Gravity
Planning
Potential energy
Robots
Shape
Vehicles
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Summary:Barycentric spherical robots (BSRs) rely on a noncollocated center of mass and center of rotation for propulsion. Unique challenges inherent to BSRs include a nontrivial correlation between internal actuation, momentum, and net vehicle motion. A new method is presented for deriving reduced dynamical equations of motion (EOM) for a general class of BSRs which extends and synthesizes prior efforts in geometric mechanics. Our method is an extension of the BKMM approach [1], allowing Lagrangian reduction and reconstruction to be applied to dynamical systems with symmetry-breaking potential energies, such as those encountered by BSRs rolling on a surface. The resulting dynamical equations are of minimal dimension and vehicle motion due to actuation and momenta appear linearly in a simple first-order differential equation. The EOM of a BSR named Moball [2] [3] are derived to illustrate the approach's utility. A simple table summarizes our algorithm's application to popular BSRs in the literature, and the approach is extended to sloped terrains.
DOI:10.1109/ICRA.2016.7487434