Ben Gardiner, Travis Cooper, Matthew Haveard, Waseem Ahmad

Bringing MILP Online

Outline

Introduction

Visualization

Quick Review of MILP and prior Problems

Taking MILP Online Virtual Grid Versus Longitude and Latitude

Receding Horizons

Current Results

Conclusion

Visualization

Started with KMLCreator.cpp

Problem: KMLCreator saves the KML just onceSolution: Infinite Loop

Bug: Only one path segment per plane visible at a timeProblem: Queue of locations repeatedly emptied as part of the file writing process

Solution: Iterate through the queue, push things back on after working

Brave New World?

Server Side program

Control through webpage

Visualization integrated and updating in real time

Mixed Integer Linear Programming

Used to solve problems that can be formulated as systems of linear constraints

The programmer needs to properly set up the problem for a software (like Gurobi) to solve

Excellent for offline problems, like crop optimization.

When given enough time finds the best solution

Problems with MILP and UAVs

MILP itself is not dynamic, so cannot react to problems as they are detected

MILP does not solve routes for UAVs quickly enough

MILP uses a Cartesian coordinate system, which does not function with longitude and latitude

Easy Discretization

Geographic to Polar

(Latitude, Longitude) representing origin of grid

Latitude and Longitude representing UAV location

Find distance (d) between the two using the Haversine formula

Calculate bearing () from origin to plane:

Geographic to Polar

Calculate angle ():

Polar to Cartesian

Use the polar coordinates to get (x, y) pair:

Polar to Cartesian and Back

And Reverse It

Go back to polar coordinates: Distance (d) from Pythagorean theorem

Angle, ( )

Polar to Geographic

Use Distance and Angle in relation to Origin latitude and longitude

Receding Horizon/ Model Predictive Control

Process control methodTypically used in the process industries such as chemical plants and oil refineries

Model Predictive Control (MPC) is a multivariable control algorithm that uses: an internal dynamic model of the process

a history of past control moves and

an optimization cost function J over the receding prediction horizon

Receding Horizon

Receding Horizon

Receding Horizon

Receding Horizon

Receding Horizon

Receding Horizon

Receding Horizon

Receding Horizon

Receding Horizon

Receding Horizon

The End

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6/22/11

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6/22/11