Route determination in dynamic and uncertain environments

1. A method for use in automatically determining an optimized route for a vehicle, the method comprising:

using at least one computer hardware processor to perform:

obtaining a target state, a fixed initial position of the vehicle, and uncertain dynamic environmental flow information;

determining an optimized route from the fixed initial position to the target state using the uncertain dynamic environmental flow information;

wherein the determining includes solving for stochastic time optimum paths and/or probabilistic reachability sets in a dynamically uncertain environment using dynamic stochastic order reduction including using a dynamically orthogonal (DO) decomposition of a stochastic time-optimal level set or value function to efficiently solve corresponding stochastic DO level-set equations; and

guiding the vehicle using the optimized route.

2. The method of claim 1 , wherein determining the optimized route comprises calculating a forward reachability set and front by numerically solving an unsteady Hamilton-Jacobi (HJ) equation.

3. The method of claim 1 , wherein determining the optimized route comprises using a predicted probabilistic environmental velocity field.

4. The method of claim 3 , wherein predicting the probabilistic velocity field comprises solving discrete stochastic dynamically orthogonal (DO) barotropic quasi-geostrophic equations.

5. The method of claim 3 , wherein predicting the probabilistic velocity field comprises solving discrete stochastic dynamically orthogonal (DO) primitive equations.

6. The method of claim 3 , wherein determining the optimized path further comprises performing stochastic optimized route planning by solving stochastic DO level-set equations and computing discrete time-optimal routes and headings using backtracking equations.

7. The method of claim 6 , wherein determining the optimized route further comprises performing risk evaluation and optimization.

8. The method of claim 7 , wherein performing risk evaluation and optimization comprises:

simulating trajectories using waypoint objective or heading objectives;

computing an error metric matrix for the simulated trajectories;

computing a cost matrix for the simulated trajectories based on the error metric matrix;

computing a risk for each of the simulated trajectories based on the cost matrix; and

determining the optimized route as the simulated trajectory associated with a lowest value of the computed risk.

9. At least one non-transitory computer-readable storage medium storing processor executable instructions that, when executed by at least one computer hardware processor, cause the at least one computer hardware processor to perform a method for use in automatically determining an optimized route for a vehicle, the method comprising:

obtaining a target state, a fixed initial position of the vehicle, and uncertain dynamic environmental flow information; and

determining an optimized route from the fixed initial position to the target state using the uncertain dynamic environmental flow information;

wherein the determining includes solving for stochastic time optimum paths and/or probabilistic reachability sets in a dynamically uncertain environment using dynamic stochastic order reduction including using a dynamically orthogonal (DO) decomposition of a stochastic time-optimal level set or value function to efficiently solve corresponding stochastic DO level-set equations; and

guiding the vehicle using the optimized route.

10. The at least one non-transitory computer-readable storage medium of claim 9 , wherein determining the optimized route further comprises:

performing stochastic optimized path planning by solving stochastic DO level-set equations and computing discrete time-optimal paths and headings using backtracking equations;

performing risk evaluation and optimization by:

simulating trajectories using waypoint objective or heading objectives;

computing an error metric matrix for the simulated trajectories;

computing a cost matrix for the simulated trajectories based on the error metric matrix; and

computing a risk for each of the simulated trajectories based on the cost matrix; and

determining the optimized route as the simulated trajectory associated with a lowest value of the computed risk.

11. A system, comprising:

at least one computer hardware processor; and

at least one non-transitory computer-readable storage medium storing processor executable instructions that, when executed by the at least one computer hardware processor, cause the at least one computer hardware processor to perform a method for use in automatically determining an optimized route for a vehicle, the method comprising:

obtaining a target state, a fixed initial position of the vehicle, and uncertain dynamic environmental flow information; and

determining an optimized route from the fixed initial position to the target state using the uncertain dynamic environmental flow information;

wherein the determining includes solving for stochastic time optimum paths and/or probabilistic reachability sets in a dynamically uncertain environment using dynamic stochastic order reduction including using a dynamically orthogonal (DO) decomposition of a stochastic time-optimal level set or value function to efficiently solve corresponding stochastic DO level-set equations; and

a device that guides the vehicle using the optimized route.

12. The system of claim 11 , wherein determining the optimized route comprises calculating a forward reachability front set by numerically solving an unsteady Hamilton-Jacobi (HJ) equation.

13. The system of claim 11 , wherein determining the optimized route further comprises:

performing stochastic optimized route planning by solving stochastic DO level-set equations and computing discrete time-optimal routes and headings using backtracking equations;

performing risk evaluation and optimization; and

determining the optimized route as the simulated trajectory associated with a lowest value of the computed risk.

14. The system of claim 11 , wherein performing risk evaluation and optimization comprises:

simulating trajectories using waypoint objective or heading objectives;

computing an error metric matrix for the simulated trajectories;

computing a cost matrix for the simulated trajectories based on the error metric matrix; and

computing a risk for each of the simulated trajectories based on the cost matrix.