Optimal Control with Budget Constraints and Resets

Takei, Ryo; Chen, Weiyan; Clawson, Zachary; Kirov, Slav; Vladimirsky, Alexander

doi:10.1137/110853182

Cited by 9 publications

(4 citation statements)

References 28 publications

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“…However, a straightforward linear scaling of coefficients has not been found in practice to thoroughly probe the space of solutions, without being exhaustive. Instead we turn to a multi-objective search method proposed for graphs over which costs are non-negative, but not strictly positive [29]. This approach entails the search of an expanded graph, which applies one of the competing resources to its edge weights, and the second resource is represented by expanding the original graph across many separate layers, representing different amounts of resource consumption.…”

Section: Computational Resultsmentioning

confidence: 99%

A Lexicographic Search Method for Multi-Objective Motion Planning

Shan¹,

Englot²

2019

Preprint

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We consider multi-objective motion planning problems in which two competing resources are penalized hierarchically. The highest-priority resource takes on non-negative values over robot paths, and is frequently zero-valued. This is intended to capture problems in which robots must manage a resource such as collision risk, exposure to threats, or access to valuable measurements, whose consideration is critical in some regions of the environment, and unimportant in others. This leaves freedom for tie-breaking with respect to a secondary resource, which we assume to be a strictly positive quantity consumed by the robot, such as distance traveled, energy expended or time elapsed. We leverage the paradigm of lexicographic optimization and apply it for the first time to graph search over roadmaps. Specifically, our "lexicographic search" is employed in concert with probabilistic roadmaps to solve motion planning problems under various nonnegative cost functions motivated by real-world applications.

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Section: Computational Resultsmentioning

confidence: 99%

A Lexicographic Search Method for Multi-Objective Motion Planning

Shan¹,

Englot²

2019

Preprint

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“…In [7,13,32], the authors propose optimal paths for an evader to reach a target destination, while minimizing exposure to an observer. In [13],…”

Section: Related Workmentioning

confidence: 99%

“…In [7], the observer moves according to a fixed trajectory. In [32], the evader can tolerate brief moments of exposure so long as the consecutive exposure time does not exceed a given threshold. In all three cases, the observer's controls are restricted to choosing from a known distribution of trajectories; they are not allowed to move freely.…”

Section: Related Workmentioning

confidence: 99%

Visibility Optimization for Surveillance-Evasion Games

Ly¹,

Tsai²

2020

Preprint

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We consider surveillance-evasion differential games, where a pursuer must try to constantly maintain visibility of a moving evader. The pursuer loses as soon as the evader becomes occluded. Optimal controls for game can be formulated as a Hamilton-Jacobi-Isaac equation.We use an upwind scheme to compute the feedback value function, corresponding to the end-game time of the differential game. Although the value function enables optimal controls, it is prohibitively expensive to compute, even for a single pursuer and single evader on a small grid. We consider a discrete variant of the surveillance-game. We propose two locally optimal strategies based on the static value function for the surveillance-evasion game with multiple pursuers and evaders.We show that Monte Carlo tree search and self-play reinforcement learning can train a deep neural network to generate reasonable strategies for on-line game play. Given enough computational resources and offline training time, the proposed model can continue to improve its policies and efficiently scale to higher resolutions.

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“…If the matter is moving as a wave, u represents the wavefront, and if it is a particle, u indicates the path length of the particle moving. 4 So, the eikonal equation is extremely widely used in the engineering field, for example, troposphere slant delay calculation in space geodesy, 5 radar wave ray path tracing in radar field, 6 optical rendering in computer art design, 7 ray tracing in acoustic positioning, 8 seismic travel time tomography simulation, 9 particle scattering characteristic asymptotic fits in quantum chromodynamics, 10 gravity model modeling in cosmology, 11 simulation analysis in ophthalmology, 12 geometrical hydromagnetics calculation, 13 optimal control, 14 and path planning 15 in optimization field.…”

Section: Introductionmentioning

confidence: 99%

A new method for solving the eikonal equation in the spherical computing domain

Feng

Huang

2020

Math Methods in App Sciences

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In order to overcome the problem of singularities and nonuniform grids arising when solving eikonal equation in spherical coordinate systems, a spherical Cartesian coordinate system is defined and the Hamiltonian form of the eikonal equation according to this coordinate system is given. A modified velocity function that can transform spherical coordinate system–based eikonal equation into ones based on a spherical Cartesian coordinate system is deduced by using a differential geometric method where a layered distribution of the velocity function is assumed. After comparing the results of using this approach with the traditional method of solving eikonal equation based on a spherical coordinate system, the viability of the transformation to a spherical Cartesian coordinate system based on a modified velocity function is proven. Despite the assumption of a layered distribution of the velocity function, it is also proven that the method will hold for a velocity function under any three‐dimensional distribution. The new method overcomes problems present in traditional approaches and opens up a new way of solving eikonal equation in a spherical computational domain.

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Optimal Control with Budget Constraints and Resets

Cited by 9 publications

References 28 publications

A Lexicographic Search Method for Multi-Objective Motion Planning

A Lexicographic Search Method for Multi-Objective Motion Planning

Visibility Optimization for Surveillance-Evasion Games

A new method for solving the eikonal equation in the spherical computing domain

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