PROGRESS REPORT

ANDREW KAIZER, THOMAS CRESCENZI, AND TYLER YOUNG

HOW FAR ARE WE?

Divide and Conquer

•  Andrew: (Sparse) A*

•  Thomas: Plane prediction, ROS integration

•  Tyler: Best cost/danger grids, X-Plane visualization

Refresher: Plane Prediction

l  Works by evaluating the chances that a plane will be in a specific grid

l  Takes into account time which allows for the plane to be seen as moving through time

l  Branches in the chance that a plane could equally be in two places at one time

New Additions

l  Now planes are predicted to their avoidance way point and from there to their goal

l  In addition planes are predicted a second past their goal

New Additions

Best Cost Estimates

If you find yourself in this square, the best path you can find is of cost ____.

A* Search

• Divided into three parts: – Sparse A* Setup – Dynamic-Sparse A* Search – Dynamic Collision Analysis

Sparse A* Setup: Steps 1-7

1.  Get Start Point, Waypoint Point 2.  Construct optimal grid forward path 3.  Construct optimal grid back path 4.  Fill in rest of optimal spaces 5.  Calculate Optimal Continuous Space

Path 6.  Determine if Optimal Path is Clear 7.  Clear ? Return goal : continue to step 8;

Dynamic-Sparse A* Search: Steps 8-13

8.  Look at current minimal (smallest) node 9.  Calculate bearing of current node 10. Calculate legal expansion 11. Create successors 12. Goal ? Go to Step 13 : Go to Step 8 13. Push every single point, in order of time,

onto the A_STAR queue

A* Collision Analysis: Step 14-17

14. Pop OPT and A_STAR points 15. Compare o.x, o.y and a.x, a.y 16. DIFFER ? go to step 17 : go to step 14 17. Return Collision Avoidance Point 18. If queues empty: OPT ≈ A_STAR

Step One: Start/End

Step Two: Optimal Forward

Step Three: Optimal Backwards

Step Four: Full Optimal

Step Five: Optimal Path

Step 6/7: Determine Path Clarity

For time t = {0…n} a)  Calculate expected values b)  Retrieve real values from Danger/Best Cost c)  if REAL > EXPECTED

a)  PATH is not clear; go to step 8

d)  t++ e)  Go back to step a

Step 8-13: (2,2,0)

Step 8-13: (3,3,1)

Step 8-13: (3,2,1)

Step 8-13: (4,1,2)

Or if you like Crudely Drawn GIFs

Steps 14-17 OPTIMAL PATH 1: (2,2,0) -- START 2: (3,2,1) 3: (4,2,2) 4: (5,2,3) -- GOAL 5: …

A STAR PATH 1: (2,2,0) 2: (3,2,1) 3: (4,1,2) – Collision Point 4: (5,2,3) -- GOAL 5: …

RETURN: Point (4, 1, 2)

Sparse-Dynamic A*

•  Sparse: Looks at a minimal area, instead of wasting time on dead ends

•  Sparse: Does not call A* if the path is clear

•  Dynamic: Makes educated guesses based on time steps into the future

•  Dynamic: Versatile, can respond to change quickly

ROS Integration

l  Two services are used l  requestwaypointinfo is used to get

the final goal of each plane for use with predicting paths

l  gotowaypoint is used to send the planes to the right waypoint

l  Telemetry updates are received through a message

Classes to Help with Integration

l  Plane class l  Represents a plane and contains all

of the information from telemetry, and a bit more

l  Position class l  Represents a position in both latitude

and longitude and x and y l  Used by the Plane class to aid in

storing information

Steps Done by ROS

l  Get telemetry data l  Update the plane object l  Get and set the plane’s goal with the

requestwaypointinfo service l  Build the best cost grid l  Run A* l  Tell plane to go to the point A* says with

the gotowaypoint service

Integrating with ROS

A* works brilliantly in our simulated world of dots, starts, and goals.

What happens, though, when we work with UAVs?

“Chicken”

Integrating with ROS

Playing nice with ROS—and doing so reliably—is proving more difficult.

Visualization in X-Plane

WHAT OBSTACLES HAVE WE OVERCOME?

A* Works Really Well

Andrew has graphs to show tomorrow!

BC Grids—Where Do We Stop?

BC Grids—Where Do We Stop?

BC Grids—Where Do We Start?

Giving Planes Breathing Room

Difficulties Predicting Planes

l  Very few due to excessive planning on paper

l  Swaths created when time was predicted incorrectly

l  Only predicting to final goal and ignoring intermediate way points

Difficulties with ROS

Troubleshooting l  No debugger l  No call stack listing l  No outputting (if you’re doing

it wrong!)

Difficulties with ROS

Troubleshooting l  No debugger l  No call stack listing l  No outputting (if you’re doing

it wrong!)

Solutions

l  assert(false) deeper and deeper into the stack

l  Turn outputting on and add tons of colors to the terminal

l  Add a good number of compiler directives to direct output

Learning to Troubleshoot… Again

Without a debugger, we end up asserting everything we can.

Insidious Planar Assumptions

• Accidentally modeled a flat earth •  Background in planar

(Euclidean) geometry makes our intuitions unreliable

Insidious Planar Assumptions

Distance between two points:

Compare to planar distance:

Insidious Planar Assumptions

Bearing between two points

Insidious Planar Assumptions

Ending point given distance and bearing:

Insidious Planar Assumptions

Ending point given distance and bearing:

Computation Time and Parallelism

•  Time complexity is linear with respect to the number of aircraft

•  Each aircraft’s path is plotted independently of others—can have one plane per CPU with no penalty

WHAT OBSTACLES DO WE STILL FACE?

Testing in the Air

• Autopilots are untested • No guarantee that behavior

observed in the simulator will carry over to the real world

Improving Our Methods

•  Plane prediction • Heuristic (best cost grid)

generation •  Parallelism

Troubleshooting the Little Things

We're done with the things we aimed to do—just need to bring them together.

•  E.g., plane 0 doesn't take more than 1 goal...

HOW WILL WE OVERCOME THESE?

We’ll see.

•  Troubleshooting has to take place as we encounter problems. – Same methods as ever: trace the problem to its roots.

We’ll see.

•  Research – Use known methods of optimizing

code, predicting planes – Use built-in methods for parallelizing in ROS