We obtain, solve, and verify fundamental differential equations for energy–time path
planning in dynamic flows. The equations govern the energy–time reachable sets, optimal …

We develop an accurate partial differential equation-based methodology that predicts the
time-optimal paths of autonomous vehicles navigating in any continuous, strong, and …

Autonomous underwater vehicles (AUVs) are a valuable resource in several oceanic
applications such as security, surveillance and data collection for ocean prediction. These …

A stochastic optimization methodology is formulated for computing energy-optimal paths
from among time-optimal paths of autonomous vehicles navigating in a dynamic flow field …

We present a novel stochastic optimization method to compute energy–optimal paths,
among all time–optimal paths, for vehicles traveling in dynamic unsteady currents. The …

For a vehicle operating across arbitrarily-contoured terrain, finding the most fuel-efficient
route between two points can be viewed as a high-level global path-planning problem with …

This work concerns a specific indirect method to solve an optimal control problem with state
constraints in which the dynamics are driven by an ordinary differential equation involving a …

We develop and illustrate an efficient but rigorous methodology that predicts the time-
optimal paths of ocean vehicles in continuous dynamic flows. The goal is to best utilize or …

Path-planning for dynamic systems is an important problem with applications in robotics,
aerospace and chemical engineering. Here, a state and input trajectory is to be computed to …

Autonomous surface and underwater vehicles (ASVs and AUVs) used for ocean monitoring
are typically deployed for long periods of time and must operate with limited energy budgets …