4 research outputs found
Variational collision avoidance problems on Riemannian manifolds
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 problem consists of finding non-intersecting
trajectories of a given number of agents, among a set of admissible curves, to
reach a specified configuration, based on minimizing an energy functional that
depends on the velocity, covariant acceleration and an artificial potential
function used to prevent collision among the agents. The results are validated
through numerical experiments on the manifolds and
Variational collision and obstacle avoidance of multi-agent systems on Riemannian manifolds
In this paper we study a path planning problem from a variational approach to
collision and obstacle avoidance for multi-agent systems evolving on a
Riemannian manifold. The problem consists of finding non-intersecting
trajectories between the agent and prescribed obstacles on the workspace, among
a set of admissible curves, to reach a specified configuration, based on
minimizing an energy functional that depends on the velocity, covariant
acceleration and an artificial potential function used to prevent collision
with the obstacles and among the agents. We apply the results to examples of a
planar rigid body, and collision and obstacle avoidance for agents evolving on
a sphere.Comment: Submitted to European Control Conference 202
Symmetry Reduction in Optimal Control of Multiagent Systems on Lie Groups
We study the reduction of degrees of freedom for the equations that determine
necessary optimality conditions for extrema in an optimal control problem for a
multiagent system by exploiting the physical symmetries of agents, where the
kinematics of each agent is given by a left-invariant control system. Reduced
optimality conditions are obtained using techniques from variational calculus
and Lagrangian mechanics. A Hamiltonian formalism is also studied, where the
problem is explored through an application of Pontryagin's maximum principle
for left-invariant systems, and the optimality conditions are obtained as
integral curves of a reduced Hamiltonian vector field. We apply the results to
an energy-minimum control problem for multiple unicycles.Comment: IEEE Transactions on Automatic Control, Vol 65 (11), 4973-4980. arXiv
admin note: text overlap with arXiv:1802.0122
Variational Collision Avoidance on Riemannian Manifolds
This paper studies variational collision avoidance problems for multi-agents
systems on complete Riemannian manifolds. That is, we minimize an energy
functional, among a set of admissible curves, which depends on an artificial
potential function used to avoid collision between the agents. We show the
global existence of minimizers to the variational problem and we provide
conditions under which it is possible to ensure that agents will avoid
collision within some desired tolerance. We also study the problem where
trajectories are constrained to have uniform bounds on the derivatives, and
derive alternate safety conditions for collision avoidance in terms of these
bounds - even in the case where the artificial potential is not sufficiently
regular to ensure existence of global minimizers.Comment: 16 pages, 3 figure