Variational point-obstacle avoidance on Riemannian manifolds

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 ...

Stochastic variational principle on riemannian manifolds

Optimal Collision Avoidance and Formation Switching on Riemannian Manifolds

In this paper the problems of optimal collision avoidance and optimal formation switching for multiple agents moving on a Riemannian manifold are studied. It is assumed that the underlying manifold admits a group of isometries, with respect to which the Lagrangian function is invariant. Reduction method is used to derive optimality conditions for the solutions. Some examples are presented.

Existence of solutions for variational inequalities on Riemannian manifolds

We establish the existence and uniqueness results for variational inequality problems on Riemannian manifolds and solve completely the open problem proposed in [21]. Also the relationships between the constrained optimization problem and the variational inequality problems as well as the projections on Riemannian manifolds are studied. Keyword: Variational inequalities; Riemannian manifold; Mon...

Convergence of Variational Regularization Methods for Imaging on Riemannian Manifolds

We consider abstract operator equations Fu = y, where F is a compact linear operator between Hilbert spaces U and V , which are function spaces on closed, finite dimensional Riemannian manifolds, respectively. This setting is of interest in numerous applications such as Computer Vision and non-destructive evaluation. In this work, we study the approximation of the solution of the ill-posed oper...