36 citations · 210 across the 58 of their papers we have counts for
8 papers · 1 filter
On the Existence and Uniqueness of Poincaré Maps for Systems with Impulse Effects
Jacob Goodman, Leonardo Colombo
The Poincaré map is widely used to study the qualitative behavior of dynamical systems. For instance, it can be used to describe the existence of periodic solutions. The Poincaré m…
Dynamic interpolation for obstacle avoidance on Riemannian manifolds
Anthony Bloch, Margarida Camarinha, Leonardo Colombo
This work is devoted to studying dynamic interpolation for obstacle avoidance. This is a problem that consists of minimizing a suitable energy functional among a set of admissible…
Motion Feasibility Conditions for Multi-Agent Control Systems on Lie Groups
Leonardo J. Colombo, Dimos V. Dimarogonas
We study the problem of motion feasibility for multiagent control systems on Lie groups with collision avoidance constraints. We first consider the problem for kinematic left invar…
Variational collision avoidance problems on Riemannian manifolds
Mishal Assif, Ravi Banavar, Anthony Bloch +2
In this article we introduce a variational approach to collision avoidance of multiple agents evolving on a Riemannian manifold and derive necessary conditions for extremals. The p…
Lagrangian Lie subalgebroids generating dynamics for second-order mechanical systems on Lie algebroids
Ligia Abrunheiro, Leonardo Colombo
The study of mechanical systems on Lie algebroids permits an understanding of the dynamics described by a Lagrangian or Hamiltonian function for a wide range of mechanical systems…
Optimal Control of Left-Invariant Multi-Agent Systems with Asymmetric Formation Constraints
Leonardo Colombo, Dimos Dimarogonas
In this work, we study an optimal control problem for a multi-agent system modeled by an undirected formation graph with nodes describing the kinematics of each agent, given by a l…