2 citations · 4 across the 18 of their papers we have counts for
8 papers · 1 filter
Nonholonomic mechanics and virtual constraints on Riemannian homogeneous spaces
Efstratios Stratoglou, Alexandre Anahory Simoes, Anthony Bloch +1
Nonholonomic systems are, so to speak, mechanical systems with a prescribed restriction on the velocities. A virtual nonholonomic constraint is a controlled invariant distribution…
Geometric stabilization of virtual linear nonholonomic constraints
Alexandre Anahory Simoes, Anthony Bloch, Leonardo Colombo +1
In this paper, we give sufficient conditions for and deduce a control law under which a mechanical control system converges exponentially fast to a virtual linear nonholonomic cons…
Comparison of two numerical methods for Riemannian cubic polynomials on Stiefel manifolds
Alexandre Anahory Simoes, Leonardo Colombo, Fátima Silva Leite
In this paper we compare two numerical methods to integrate Riemannian cubic polynomials on the Stiefel manifold . The first one is the adjusted de Casteljau alg…
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…
Virtual Holonomic and Nonholonomic Constraints on Lie groups
A. Anahory Simoes, A. Bloch, L. Colombo +1
This paper develops a geometric framework for virtual constraints on Lie groups, with emphasis on mechanical systems modeled as affine connection systems. Virtual holonomic and vir…
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…
On the Geometry of Virtual Nonlinear Nonholonomic Constraints
Efstratios Stratoglou, Alexandre Anahory Simoes, Anthony Bloch +1
Virtual constraints are relations imposed on a control system that become invariant via feedback control, as opposed to physical constraints acting on the system. Nonholonomic syst…