2 citations · 2 across the 9 of their papers we have counts for
9 papers
Connection Towers and Sasaki Metrics on Higher-Order Tangent Bundles
Margarida Camarinha, Jacob R. Goodman
Higher-order tangent bundles possess a rich tower of fibrations, suggesting the existence of geometric structures compatible with their iterated bundle structure. In this paper, we…
Riemannian Metric Preconditioning for Trajectory Tracking
Jacob R. Goodman, Hajg Jasa
We introduce a rank-one Riemannian cometric update inducing a modification of the Riemannian metric that makes specific directions of motion cheaper to travel along. We establish b…
A Generalized Sasaki Metric on the Second-Order Tangent Bundle
Margarida Camarinha, Jacob R. Goodman
This paper constructs a connection map on the second-order tangent bundle induced by a linear connection on the base manifold and uses it to define a generalized Sasaki metric. The…
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…