2 citations · 2 across the 9 of their papers we have counts for
6 papers · 1 filter
Variational Lifting and Optimal Gauges on Riemannian Homogeneous Spaces
Jacob R. Goodman, Leonardo J. Colombo
Building on standard Euler-Poincaré reduction on Lie groups, we develop a variational lifting framework for mechanical systems on Riemannian homogeneous spaces . A mechanica…
Reduction of Necessary Conditions for the Variational Collision Avoidance Problem
Jacob R. Goodman, Leonardo J. Colombo
In this work, we study the reduction by a Lie group of symmetries of variational collision avoidance probelms of multiple agents evolving on a Riemannian manifold and derive necess…
Reduction of Sufficient Conditions in Variational Obstacle Avoidance Problems
Jacob R. Goodman, Leonardo J. Colombo
This paper studies sufficient conditions in a variational obstacle avoidance problem on complete Riemannian manifolds. That is, we minimize an action functional, among a set of adm…
Reduction by Symmetry in Obstacle Avoidance Problems on Riemannian Manifolds
Jacob R. Goodman, Leonardo J. Colombo
This paper studies the reduction by symmetry of a variational obstacle avoidance problem. We derive the reduced necessary conditions in the case of Lie groups endowed with a left-i…
Local Minimizers for Variational Obstacle Avoidance on Riemannian manifolds
Jacob R. Goodman
This paper studies a variational obstacle avoidance problem on complete Riemannian manifolds. That is, we minimize an action functional, among a set of admissible curves, which dep…
Geometric Control for Load Transportation with Quadrotor UAVs by Elastic Cables
Jacob R. Goodman, Juan S. Cely, Thomas Beckers +1
Groups of unmanned aerial vehicles (UAVs) are increasingly utilized in transportation task as the combined strength allows to increase the maximum payload. However, the resulting m…