Claire Walton

Optimal Motion Planning for Searching for Uncertain Targets

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.

Consistent approximation of a nonlinear optimal control problem with uncertain parameters

This paper focuses on a non-standard constrained nonlinear optimal control problem in which the objective functional involves an integration over a space of stochastic parameters as well as an integration over the time domain. The research is inspired by the problem of optimizing the trajectories of multiple searchers attempting to detect non-evading moving targets. In this paper, we propose a framework based on the approximation of the integral in the parameter space for the considered uncertain optimal control problem. The framework is proved to produce a zeroth-order consistent approximation in the sense that accumulation points of a sequence of optimal solutions to the approximate problem are optimal solutions of the original problem. In addition, we demonstrate the convergence of the corresponding adjoint variables. The accumulation points of a sequence of optimal state-adjoint pairs for the approximate problem satisfy a necessary condition of Pontryagin Minimum Principle type, which facilitates assessment of the optimality of numerical solutions.

Issues in multi-agent search: False positives and Bayesian map updates

This paper explores the incorporation of false positives and Bayesian updates into the framework of optimal search. Optimal search is an open-loop optimal control framework developed by the US Navy to optimize search and rescue path planning for rapid sweep sensors such as sonar. Although useful as a pre-planning tool, this framework lacks features necessary for online planning, such as quantification of the role of detection events and subsequent probability map updates. This paper discusses these limitations and provides tools for implementing these features.

Sensor-based motion planning for autonomous vehicle teams

This paper employs a computational optimal control framework to develop a mission planning tool for a team of heterogeneous unmanned vehicles conducting a nominal mine countermeasures (MCM) mission. We first describe our motivation for developing vehicle-specific sensor models for unmanned surface and underwater vehicles working collaboratively to detect mines. Next, we describe the sonar detection models used to evaluate the performance of a long-range, forward-looking detection sonar and a high-resolution sidescan sonar deployed from these unmanned vehicles. Results from multiple computer simulations which highlight the flexibility and utility of this solution framework are presented.