Multi-Objective Risk-Aware Path Planning in Uncertain Transient Currents: An Ensemble-Based Stochastic Optimization Approach

Abstract

A multi-objective, risk-aware framework is developed for optimal path planning of autonomous underwater vehicles operating in uncertain current fields. The uncertainty in the current is described in terms of a finite ensemble of flow realizations. The proposed approach is based on a nonlinear stochastic programming methodology that uses a risk-aware objective function, accounting for the full variability of the flow ensemble, and accommodating solutions that may not necessarily coincide with a deterministic solution corresponding to a specific member of the ensemble. We formulate stochastic problems that aim to minimize a risk measure of the travel time or energy consumption, using a flexible methodology that enables the user to seamlessly explore various objectives, ranging from risk-neutral to risk-averse. The former is defined by the expectation operator whereas the latter is based on the conditional value at risk. We illustrate the application of the proposed approach using synthetic 2D settings, including an uncertain steady current field, and a stochastic, transient, double-gyre flow. The applications are used to assess the results of the proposed framework, demonstrate the value of stochastic solutions over individual scenario solutions, and to guide the selection of suitable risk measures.