Related papers: Path Planning in a Riemannian Manifold using Optim…

For the sub-Riemannian problem on the group of motions of Euclidean space we present explicit formulas for extremal controls in a special case, when one of the initial momenta is fixed.

In this paper, we give a simple control on how an optimal shape can be characterized. The framework of Riemannian manifold of infinite dimension is essential. And the covariant derivative plays a key role in the computation and in the…

In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an…

This paper presents a novel on-line path planning method that enables aerial robots to interact with surfaces. We present a solution to the problem of finding trajectories that drive a robot towards a surface and move along it. Triangular…

This paper presents a new and straightforward procedure for solving bilinear quadratic optimal control problem. In this method, first the original optimal control problem is transformed into a nonlinear twopoint boundary value problem…

We consider nonsmooth optimal control problems subject to a linear elliptic partial differential equation with homogeneous Dirichlet boundary conditions. It is well-known that local solutions satisfy the celebrated Pontryagin maximum…

We formulate and analyse an optimal control problem for the coagulation-fragmentation equation, where a scalar, time-dependent control modulates the coagulation rate by multiplying the coagulation kernel. The objective functional consists…

In this paper, we derive first-order Pontryagin optimality conditions for risk-averse stochastic optimal control problems subject to final time inequality constraints, and whose costs are general, possibly non-smooth finite coherent risk…

We give curvature-dependant convergence rates for the optimization of weakly convex functions defined on a manifold of 1-bounded geometry via Riemannian gradient descent and via the dynamic trivialization algorithm. In order to do this, we…

The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…

To perform autonomous driving maneuvers, such as parallel or perpendicular parking, a vehicle requires continual speed and steering adjustments to follow a generated path. In consequence, the path's quality is a limiting factor of the…

Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization maps can be conveniently lifted to the…

Recently solutions to the aggregation equation on compact Riemannian Manifolds have been studied with different techniques. This work demonstrates the small time existence of measure-valued solutions for suitably regular intrinsic…

Computing optimal, collision-free trajectories for high-dimensional systems is a challenging problem. Sampling-based planners struggle with the dimensionality, whereas trajectory optimizers may get stuck in local minima due to inherent…

We analyze a novel class of rough stochastic control problems that allows for a convenient approach to solving pathwise stochastic control problems with both non-anticipative and anticipative controls. We first establish the well-posedness…

The paper addresses the problem of providing suitable reference trajectories in motion planning problems for autonomous vehicles. Among the various approaches to compute a reference trajectory, our aim is to find those trajectories which…

End-to-end learning for autonomous navigation has received substantial attention recently as a promising method for reducing modeling error. However, its data complexity, especially around generalization to unseen environments, is high. We…

We propose a novel second-order ODE as the continuous-time limit of a Riemannian accelerated gradient-based method on a manifold with curvature bounded from below. This ODE can be seen as a generalization of the ODE derived for Euclidean…

We provide an improvement of the maximum principle of Pontryagin of the Optimal Control problems. We establish differentiability properties of the value function of problems of Optimal Control with assumptions as low as possible. Notably,…

Accelerating controlled thermodynamic processes requires an auxiliary Hamiltonian to steer the system into instantaneous equilibrium states. An extra energy cost is inevitably needed in such finite-time operation. We recently develop a…