Related papers: A solution of the minimum-time velocity planning p…

This paper studies the lattice agreement problem and proposes a stronger form, $\varepsilon$-bounded lattice agreement, that enforces an additional tightness constraint on the outputs. To formalize the concept, we define a quasi-metric on…

Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable…

The current paper deals with the subject of shortest path routing in transportation networks (in terms of travelling time), where the speed in several of the network's roads is a function of the time interval. The main contribution of the…

This paper demonstrates a refined approach to solving dynamic optimization problems for underactuated marine surface vessels. To this end the differential flatness of a mathematical model assuming full actuation is exploited to derive an…

Osculating paths are sets of directed lattice paths which are not allowed to cross each other or have common edges, but are allowed to have common vertices. In this work we derive a constant term formula for the number of such lattice paths…

We develop a general framework for designing polynomial-time approximation schemes (PTASs) for various vehicle routing problems in trees. In these problems, the goal is to optimally route a fleet of vehicles, originating at a depot, to…

The Bhatia-Davis theorem provides a useful upper bound for the variance in mathematics, and in quantum mechanics, the variance of a Hamiltonian is naturally connected to the quantum speed limit due to the Mandelstam-Tamm bound. Inspired by…

Motion Sickness (MS) is an issue of most transportation systems. Several countermeasures for such problem in cars are proposed in the literature, but most of them are qualitative, behavioural or involving complex chassis systems. With the…

Shaping the reachable set of a dynamical system is a fundamental challenge in control design, with direct implications for both performance and safety. This paper considers the problem of selecting the optimal input matrix for a linear…

A remarkably simple result is found for the optimal protocol of drivings for a general two-level Hamiltonian which transports a given initial state to a given final state in minimal time. If one of the three possible drivings is…

Widespread development of driverless vehicles has led to the formation of autonomous racing, where technological development is accelerated by the high speeds and competitive environment of motorsport. A particular challenge for an…

A lattice is a set of all the integer linear combinations of certain linearly independent vectors. One of the most important concepts on lattice is the successive minima which is of vital importance from both theoretical and practical…

In this paper, we address a minimum-time steering problem for a drone modeled as point mass with bounded acceleration, across a set of desired waypoints in the presence of gravity. We first provide a method to solve for the minimum-time…

The effectiveness of a robot manipulation to a large extent is determined by the speed of making this or that movement needed for carrying out the task. Accordingly to this the problem of optimal robot control is often subdivided into two…

Motion planning is a difficult problem in robot control. The complexity of the problem is directly related to the dimension of the robot's configuration space. While in many theoretical calculations and practical applications the…

In this paper, we consider a dynamic equilibrium transportation problem. There is a fixed number of cars moving from origin to destination areas. Preferences for arrival times are expressed as a cost of arriving before or after the…

We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control problem in such a way that feasible controls are mappings…

The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…

This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory…

We proposed an algorithm for solving Hamilton-Jacobi equation associated to an optimal trajectory problem for a vehicle moving inside the pre-specified domain with the speed depending upon the direction of the motion and current position of…