Optimal Motion Planning for Searching for Uncertain Targets
Johannes Royset2014, IFAC Proceedings Volumes
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Abstract
This paper explores the potential for applying newly available numerical methods in optimal control to solve motion planning problems created by the search for targets with motion uncertainty characterized by constant but unknown parameters. These recent developments enable the efficient computation of numerical solutions for search problems with multiple searchers, nonlinear dynamics, and a broad class of objectives. We demonstrate the efficacy of these methods through implementing a multi-agent optimal search problem. We then derive an expansion of the optimal search modeling framework which facilitates the consideration of multi-agent searching problems with more general strategic objectives and utilize this expanded framework to implement an example combat defense scenario.
Figures (6)
![n order to construct a performance criterion for the opti- mal search problem, the probability of target detection must be modeled. In [Koopman (1956)] an exponential probability of detection model is derived which has since become ubiquitous in optimal search literature. The ex- ponential detection model follows from the assumption that the instantaneous rate of detection of a target can be effectively modeled. Given the position of a searcher at x(t) and a target at y(t), this instantaneous rate of detec- tion is a function r(x(t), y(t), t) such that the probability of detection in a sufficiently small interval [t,t + At] is independent from previous time intervals and given by the quantity r(a(t), y(t), t)At. The rate function r(a(t), y(t), t) is chosen to model the qualities of sensor equipment such as acoustic and sonar sensors, which have rapid enough sweep rates to be modeled as continuous processes. Fig. 1. Example detection rate function: Poisson Scan Model](https://figures.academia-assets.com/93775217/figure_001.jpg)
![feasible trajectories created with heuristic methods. These trajectories are illustrated in Figure [3]. The first com-](https://figures.academia-assets.com/93775217/figure_003.jpg)
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