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 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

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 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