Related papers: Time-dependent Zermelo navigation with tacking
Some links between Lorentz and Finsler geometries have been developed in the last years, with applications even to the Riemannian case. Our purpose is to give a brief description of them, which may serve as an introduction to recent…
In this paper, we present a novel algorithm called the Hybrid Search algorithm that integrates the Zermelo's Navigation Initial Value Problem with the Ferraro-Mart\'in de Diego-Almagro algorithm to find the optimal route for a vessel to…
We propose an algorithm for solving the time-dependent shortest path problem in flow fields where the FIFO (first-in-first-out) assumption is violated. This problem variant is important for autonomous vehicles in the ocean, for example,…
A major limitation of online algorithms that track the optimizers of time-varying nonconvex optimization problems is that they focus on a specific local minimum trajectory, which may lead to poor spurious local solutions. In this paper, we…
We take J. S. Bell's commendation of ``frame-dependent'' perspectives to the limit here, and consider motion on a ``map'' of landmarks and clocks fixed with respect to a single arbitrary inertial-reference frame. The metric equation…
A geometric approach to kinematics in control theory is illustrated. A non-linear control system is derived for the problem and the Pontryagin maximum principle is used to find the time-optimal trajectories of the Parallel navigation. The…
In this article, based on two case studies, we discuss the role of abnormal geodesics in planar Zermelo navigation problems. Such curves are limit curves of the accessibility set, in the domain where the current is strong. The problem is…
This paper studies the time-optimal path tracking problem for a team of cooperating robotic manipulators carrying an object. Considering the problem for rigidly grasped objects, we show that it can be cast as a convex optimization problem…
In connection with the optimization problem $$\inf_{x\in argmin \Psi}\{\Phi(x)+\Theta(x)\},$$ where $\Phi$ is a proper, convex and lower semicontinuous function and $\Theta$ and $\Psi$ are convex and smooth functions defined on a real…
The problem Orienteering asks whether there exists a walk which visits a number of sites without exceeding some fuel budget. In the variant of the problem we consider, the cost of each edge in the walk is dependent on the time we depart one…
In this article, we provide a novel and broadly-applicable contraction-theoretic approach to continuous-time time-varying convex optimization. For any parameter-dependent contracting dynamics, we show that the tracking error is…
This paper addresses the problem of trajectory optimization for an unmanned surface vehicle while considering direction-dependent ocean currents and flexible refueling constraints. This work is motivated by the rising interest in developing…
The analysis of spatio-temporal data presents significant challenges due to the complexity and heterogeneity of movement patterns. This project proposes a data analytics tool that combines data visualization and statistical computation to…
We investigate the long time behavior of solutions to a shape and topology optimization problem with respect to the time-dependent Navier--Stokes equations. The sought topology is represented by a stationary phase-field that represents a…
A quantum navigation problem concerns the identification of a time-optimal Hamiltonian that realises a required quantum process or task, under the influence of a prevailing `background' Hamiltonian that cannot be manipulated. When the task…
We study swimming of small spherical particles who regulate fluid flow on their surface by applying tangential squirming strokes. We derive translational and rotational velocities for any given stroke which is not restricted by axial…
In this paper, we present a novel strategy to compute minimum-time trajectories for quadrotors in constrained environments. In particular, we consider the motion in a given flying region with obstacles and take into account the physical…
Many real-world problems require to optimise trajectories under constraints. Classical approaches are based on optimal control methods but require an exact knowledge of the underlying dynamics, which could be challenging or even out of…
Magneto-inductive navigation is an inexpensive and easily deployable solution to many of today's navigation problems. By utilizing very low frequency magnetic fields, magneto-inductive technology circumvents the problems with attenuation…
Navigating mobile robots through environments shared with humans is challenging. From the perspective of the robot, humans are dynamic obstacles that must be avoided. These obstacles make the collision-free space nonconvex, which leads to…