We investigate higher-order geometric k-splines for template matching on Lie groups. This is
motivated by the need to apply diffeomorphic template matching to a series of images, eg, in …

This paper studies variational collision avoidance problems for multiagent systems on
complete Riemannian manifolds. That is, we minimize an energy functional, among a set of …

In this paper, we present a generalization of the classical least squares problem on
Euclidean spaces, introduced by Lagrange, to more general Riemannian manifolds. Using …

In this paper, we study variational point-obstacle avoidance problems on complete
Riemannian manifolds. The problem consists of minimizing an energy functional depending …

Motivated by applications in computational anatomy, we consider a second-order problem in
the calculus of variations on object manifolds that are acted upon by Lie groups of smooth …

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In this paper we investigate the existence and uniqueness of Riemannian cubics under
boundary conditions on position and velocity. We restrict the study to cubics close to …

We present a generally covariant formulation of human arm dynamics and optimization
principles in Riemannian configuration space. We extend the one-parameter family of mean …

We study variational obstacle avoidance problems on complete Riemannian manifolds and
apply the results to the construction of piecewise smooth curves interpolating a set of knot …

We provide an approach of elastic flow with dynamic conditions at the knot points to resolve
the path planning problem in the plane. The elastic flow is set up by a second-order …