Related papers: Optimal Target Intercept Paths for Vehicles with T…
We consider the Monge problem of optimal transport between a compactly supported source measure and a target probability measure with unbounded support. We consider the convergence of optimal maps and potential functions when the target…
This paper presents an optimal control problem to analyze the efficacy of counter-terrorism tactics. We present an algorithm that efficiently combines the Minimum Principle of Pontryagin, the shooting method and the cyclic descent of…
In this paper we investigated a model that describes the motion of a material point in a viscous medium under a force that is arbitrary in direction, but limited in magnitude. This model was named "the isotropic rocket" in the early work of…
We demonstrate an iterative scheme to approximate the optimal transportation problem with a discrete target measure under certain standard conditions on the cost function. Additionally, we give a finite upper bound on the number of…
We introduce a new route-finding problem which considers perception and travel costs simultaneously. Specifically, we consider the problem of finding the shortest tour such that all objects of interest can be detected successfully. To…
In this paper we study the problem of maximizing the distance to a given point $C_0$ over a polytope $\mathcal{P}$. Assuming that the polytope is circumscribed by a known ball we construct an intersection of balls which preserves the…
We study the regularity of solutions to an optimal transportation problem where the dimension of the source is larger than that of the target. We demonstrate that if the target is $c$-convex, then the source has a canonical foliation whose…
This paper addresses the problem of motion planning for differential drive micro-mobility platforms. This class of vehicle is designed to perform small-distance transportation of passengers and goods in structured environments. Our approach…
Homotopy methods are attractive due to their capability of solving difficult optimisation and optimal control problems. The underlying idea is to construct a homotopy, which may be considered as a continuous (zero) curve between the…
We propose a new proximal, path-following framework for a class of constrained convex problems. We consider settings where the nonlinear---and possibly non-smooth---objective part is endowed with a proximity operator, and the constraint set…
This work addresses the problem of constrained motion control of the uncrewed surface vessels. The constraints are imposed on states/inputs of the vehicles due to the physical limitations, mission requirements, and safety considerations. We…
We address the optimal dynamic formation problem in mobile leader-follower networks where an optimal formation is generated to maximize a given objective function while continuously preserving connectivity. We show that in a convex mission…
This paper addresses the challenging problem of robust path-following for fixed-wing unmanned aerial vehicles (UAVs) in complex environments with bounded external disturbances and non-smooth predefined paths. Due to the unique aerodynamic…
This paper presents a triple optimization algorithm of two-dimensional space, driving path and driving speed, and iterates in the time dimension to obtain the local optimal solution of path and speed in the optimal driving area. Design…
This article presents a three-dimensional nonlinear trajectory tracking control strategy for unmanned aerial vehicles (UAVs) in the presence of spatial constraints. As opposed to many existing control strategies, which do not consider…
We consider a new type of optimal stopping problems where the absorbing boundary moves as the state process X attains new maxima S. More specifically, we set the absorbing boundary as S-b where b is a certain constant. This problem is…
Driver distraction strongly contributes to crash-risk. Therefore, assistance systems that warn the driver if her distraction poses a hazard to road safety, promise a great safety benefit. Current approaches either seek to detect critical…
Robotic systems are frequently deployed in missions that are dull, dirty, and dangerous, where ensuring their safety is of paramount importance when designing stabilizing controllers to achieve their desired goals. This paper addresses the…
Path planning for autonomous vehicles in arbitrary environments requires a guarantee of safety, but this can be impractical to ensure in real-time when the vehicle is described with a high-fidelity model. To address this problem, this paper…
We present a unified approach for constraint displacement problems in which a robot finds a feasible path by displacing constraints or obstacles. To this end, we propose a two stage process that returns locally optimal obstacle…