Time-Optimal Collaborative Guidance Using the Generalized Hopf Formula

Presented is a new method for calculating the time-optimal guidance control for a multiple vehicle pursuit-evasion system. A joint differential game of k pursuing vehicles relative to the evader is constructed, and a Hamilton-Jacobi-Isaacs (HJI) equation that describes the evolution of the value fun...

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Bibliographic Details
Published in:arXiv.org 2017-12
Main Authors: Kirchner, Matthew R, Mar, Robert, Hewer, Gary, Darbon, Jérôme, Osher, Stanley, Chow, Y T
Format: Article
Language:English
Subjects:
Guidance systems
Optimal control
Pursuit-evasion games
Time optimal control
Vehicles
Online Access:Get full text
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Summary:Presented is a new method for calculating the time-optimal guidance control for a multiple vehicle pursuit-evasion system. A joint differential game of k pursuing vehicles relative to the evader is constructed, and a Hamilton-Jacobi-Isaacs (HJI) equation that describes the evolution of the value function is formulated. The value function is built such that the terminal cost is the squared distance from the boundary of the terminal surface. Additionally, all vehicles are assumed to have bounded controls. Typically, a joint state space constructed in this way would have too large a dimension to be solved with existing grid-based approaches. The value function is computed efficiently in high-dimensional space, without a discrete grid, using the generalized Hopf formula. The optimal time-to-reach is iteratively solved, and the optimal control is inferred from the gradient of the value function.
ISSN:2331-8422
DOI:10.48550/arxiv.1709.06590