Related papers: The Weighted Markov-Dubins Problem

In 1934, Reinhardt conjectured that the shape of the centrally symmetric convex body in the plane whose densest lattice packing has the smallest density is a smoothed octagon. This conjecture is still open. We formulate the Reinhardt…

In this paper, we investigate the problem of coordinated path following for fixed-wing UAVs with speed constraints in 2D plane. The objective is to steer a fleet of UAVs along the path(s) while achieving the desired sequenced inter-UAV arc…

We address a dynamic pricing problem for airlines aiming to maximize expected revenue from selling cargo space on a single-leg flight. The cargo shipments' weight and volume are uncertain and their precise values remain unavailable at the…

Many problems in robotics seek to simultaneously optimize several competing objectives under constraints. A conventional approach to solving such multi-objective optimization problems is to create a single cost function comprised of the…

Classic optimal transport theory is formulated through minimizing the expected transport cost between two given distributions. We propose the framework of distorted optimal transport by minimizing a distorted expected cost, which is the…

We consider a Beckmann formulation of an unbalanced optimal transport (UOT) problem. The $\Gamma$-convergence of this formulation of UOT to the corresponding optimal transport (OT) problem is established as the balancing parameter $\alpha$…

An analytical formulation for collision avoidance maneuvers involving a spacecraft and a space debris is presented, including solutions for the maximum deviation and minimum collision probability cases. Gauss' planetary equations and…

With an extensive increment of computation demands, the aerial multi-access edge computing (MEC), mainly based on unmanned aerial vehicles (UAVs) and high altitude platforms (HAPs), plays significant roles in future network scenarios. In…

A method is presented to solve a stochastic, nonlinear optimal control problem representative of spacecraft trajectory design under uncertainty. The problem is reformulated as a chance constrained nonlinear program, or what is known as a…

While many techniques have been developed for chance constrained stochastic optimal control with Gaussian disturbance processes, far less is known about computationally efficient methods to handle non-Gaussian processes. In this paper, we…

We consider the problem of controlling an unknown stochastic linear system with quadratic costs - called the adaptive LQ control problem. We re-examine an approach called ''Reward Biased Maximum Likelihood Estimate'' (RBMLE) that was…

The Orienteering Problem (OP) is a well-studied routing problem that has been extended to incorporate uncertainties, reflecting stochastic or dynamic travel costs, prize-collection costs, and prizes. Existing approaches may, however, be…

The problem of mixed static and dynamic obstacle avoidance is essential for path planning in highly dynamic environment. However, the paths formed by grid edges can be longer than the true shortest paths in the terrain since their headings…

This paper addresses the inverse optimal control problem of finding the state weighting function that leads to a quadratic value function when the cost on the input is fixed to be quadratic. The paper focuses on a class of infinite horizon…

This paper studies the formation mission design problem for commercial aircraft in the presence of uncertainties. Specifically, it considers uncertainties in the departure times of the aircraft and in the fuel burn savings for the trailing…

This study proposes a novel multi-objective integer programming model for a collision-free discrete drone path planning problem. Considering the possibility of bypassing obstacles or flying above them, this study aims to minimize the path…

In upcoming 6G networks, unmanned aerial vehicles (UAVs) are expected to play a fundamental role by acting as mobile base stations, particularly for demanding vehicle-to-everything (V2X) applications. In this scenario, one of the most…

The paper deals with finite-state Markov decision processes (MDPs) with integer weights assigned to each state-action pair. New algorithms are presented to classify end components according to their limiting behavior with respect to the…

A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation…

This paper proposes a novel mission planning algorithm for autonomous robots that selects an optimal waypoint sequence from a predefined set to maximize total reward while satisfying obstacle avoidance, state, input, derivative, mission…