Related papers: Inexact trajectory planning and inverse problems i…
We revisit the dynamics of the post-Newtonian (PN) two-body problem for two inspiraling compact bodies. Starting from a matter-only reduced Hamiltonian, we present an adapted framework based on the Lie series approach, enabling the…
An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
Planning trajectories for automated vehicles in urban environments requires methods with high generality, long planning horizons, and fast update rates. Using a path-velocity decomposition, we contribute a novel planning framework, which…
A variational formulation of accelerated optimization on normed spaces was recently introduced by considering a specific family of time-dependent Bregman Lagrangian and Hamiltonian systems whose corresponding trajectories converge to the…
The trajectory optimization of the atmospheric entry of a reusable launch vehicle is studied. The objective is to maximize the crossrange of the vehicle subject to two control-inequality path constraints, two state-inequality path…
Motion path planning is an intrinsically geometric problem which is central for design of robot systems. Since the early years of AI, robotics together with computer vision have been the areas of computer science that drove its development.…
In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…
We study variational systems for space curves, for which the Lagrangian or action principle has a Euclidean symmetry, using the Rotation Minimising frame, also known as the Normal, Parallel or Bishop frame. Such systems have previously been…
We consider symmetries and perturbed symmetries of canonical Hamiltonian equations of motion. Specifically we consider the case in which the Hamiltonian equations exhibit a Lambda symmetry under some Lie point vector field. After a brief…
We consider piecewise-deterministic optimal control problems in which the environment randomly switches among several deterministic modes, and the goal is to optimize the expected cost up to the termination while taking the likelihood of…
The optimal visiting problem is the optimization of a trajectory that has to touch or pass as close as possible to a collection of target points. The problem does not verify the dynamic programming principle, and it needs a specific…
In this paper we consider an optimal control problem in large time horizon and solve it numerically. More precisely, we are interested in an aerial vehicle guidance problem: launched from a ground platform, the vehicle aims at reaching a…
This paper proposes an algorithmic technique for a class of optimal control problems where it is easy to compute a pointwise minimizer of the Hamiltonian associated with every applied control. The algorithm operates in the space of relaxed…
We introduce an iterative method to search for time-optimal Hamiltonians that drive a quantum system between two arbitrary, and in general mixed, quantum states. The method is based on the idea of progressively improving the efficiency of…
We apply the method of controlled Lagrangians by potential shaping to Euler--Poincar\'e mechanical systems with broken symmetry. We assume that the configuration space is a general semidirect product Lie group $\mathsf{G} \ltimes V$ with a…
We propose an algorithm using method of evolving junctions to solve the optimal path planning problems with piece-wise constant flow fields. In such flow fields with a convex Lagrangian in the objective function, we can prove that the…
This paper proposes an interior-point framework for constrained optimization problems whose decision variables evolve on matrix Lie groups. The proposed method, termed the Matrix Lie Group Interior-Point Method (MLG-IPM), operates directly…
Since they were introduced in the 1990s, Lie group integrators have become a method of choice in many application areas. These include multibody dynamics, shape analysis, data science, image registration and biophysical simulations. Two…
Controlling marine vehicles in challenging environments is a complex task due to the presence of nonlinear hydrodynamics and uncertain external disturbances. Despite nonlinear model predictive control (MPC) showing potential in addressing…