Related papers: Variational dynamic interpolation for kinematic sy…
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 curves subject to some interpolation conditions. The given…
This paper investigates first-order variable metric backward forward dynamical systems associated with monotone inclusion and convex minimization problems in real Hilbert space. The operators are chosen so that the backward-forward…
Designing dynamically feasible trajectories for rigid bodies is a fundamental problem in robotics. Although direct trajectory optimization is widely applied to solve this problem, inappropriate parameterizations of rigid body dynamics often…
We construct noncommutative principal bundles deforming principal bundles with a Drinfeld twist (2-cocycle). If the twist is associated with the structure group then we have a deformation of the fibers. If the twist is associated with the…
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 points in systems with impulse effects. We derive the…
We propose a method for developing the flows of stochastic dynamical systems, posed as Ito's stochastic differential equations, on a Riemannian manifold identified through a suitably constructed metric. The framework used for the stochastic…
The problem of interpolating a rigid body motion is to find a spatial trajectory between a prescribed initial and terminal pose. Two variants of this interpolation problem are addressed. The first is to find a solution that satisfies…
Finding constrained saddle points on Riemannian manifolds is significant for analyzing energy landscapes arising in physics and chemistry. Existing works have been limited to special manifolds that admit global regular level-set…
We define a Chern--Simons invariant of connections on stably trivial vector bundles over smooth manifolds, taking values in $3$-forms modulo closed forms with integral cohomology class. We show an additivity property of this invariant for…
Optimal control problems for underactuated mechanical systems can be seen as a higher-order variational problem subject to higher-order constraints (that is, when the Lagrangian function and the constraints depend on higher-order…
A one-parameter family of variational problems is introduced that interpolates between torsional rigidity and the first Dirichlet eigenvalue of the Laplacian. The associated partial differential equation is derived, which is shown to have…
We propose to augment standard grid-based fluid solvers with pointwise divergence-free velocity interpolation, thereby ensuring exact incompressibility down to the sub-cell level. Our method takes as input a discretely divergence-free…
In this paper we introduce the Integration Problem for principal connections. Just as a principal connection on a principal bundle $\phi:Q\rightarrow M$ may be used to split $TQ$ into horizontal and vertical subbundles, a discrete…
Computing the cohomology of the tensor product of two vector bundles is central in the study of their moduli spaces and in applications to representation theory, combinatorics and physics. These computations play a fundamental role in the…
In this paper we propose a finite-dimensional and deterministic approach to the study of invariant sets of certain nonautonomous differential inclusions naturally arising in the context of random and control dynamical systems, as well as in…
Our main theorem is that the pullback of an associated noncommutative vector bundle induced by an equivariant map of quantum principal bundles is a noncommutative vector bundle associated via the same finite-dimensional representation of…
We consider the problem of estimating missing values in trajectories of linear parameter-varying (LPV) systems. We solve this interpolation problem for the class of shifted-affine LPV systems. Conditions for the existence and uniqueness of…
This paper develops a structure-preserving numerical integration scheme for a class of higher-order mechanical systems. The dynamics of these systems are governed by invariant variational principles defined on higher-order tangent bundles…
We introduce variational obstacle avoidance problems on Riemannian manifolds and derive necessary conditions for the existence of their normal extremals. The problem consists of minimizing an energy functional depending on the velocity and…
We consider a net of *-algebras, locally around any point of observation, equipped with a natural partial order related to the isotony property. Assuming the underlying manifold of the net to be a differentiable, this net shall be…