1. Robots for the Kid in All of Us
GS.com/Engineering
Fall, 2016
Nikhil Nanivadekar
Donald Raab

2. Introductions – JavaOne 2016
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3. Introductions – JavaOne 2016

4. Agenda Robot videos Java vs EV3 Programmer App
Dijkstra’s and A* Algorithm at a glance
Dijkstra’s Algorithm on EV3
JRE vs Compact Profiles
Demos

5. Robot Videos

6. Agenda Robot videos Java vs EV3 Programmer App
Dijkstra’s and A* Algorithm at a glance
Dijkstra’s Algorithm on EV3
JRE vs Compact Profiles
Demos

7. EV3 Programmer App EV3 Programmer App distributed by Legos
Visual and graphical programming interface
Available at Mindstorms website

8. Lejos Runs standard Java Virtual machine Does not run Lego software
Write code similar to a standard Java project
Better motor control, faster processing, open source

9. Robo4J Sits on top of Lejos
Framework focused on asynchronous events/tasks
More information at Robo4J website

10. Third Party Libraries Lejos is a Java Virtual Machine
Easy integration with third party libraries
Upload jars to EV3 and reference on classpath
Run similar to a standard Java project

11. Agenda Robot videos Java vs EV3 Programmer App
Dijkstra’s and A* Algorithm at a glance
Dijkstra’s Algorithm on EV3
JRE vs Compact Profiles
Demos

12. Dijkstra’s Algorithm Find the least cost path from source to all nodes
Each node has cost for traversal
Least cost path can be a longer path
Conceived by Edsger W. Dijkstra
Source: Wikipedia(Dijkstra’s Algorithm)

13. A* Algorithm Extension to Dijkstra’s Algorithm
Add a heuristic to guide the program towards the goal
Heuristic can be anything (distance, time, etc.)
Algorithm functions:
Dijkstra : f(n) = c(n) c: cost function
A* : f(n) = c(n) + h(n) h: heuristic function

14. Agenda Robot videos Java vs EV3 Programmer App
Dijkstra’s and A* Algorithm at a glance
Dijkstra’s Algorithm on EV3
JRE vs Compact Profiles
Demos

15. Problem Statement Solve the maze
Motion in x direction costs 1x the absolute distance
Motion in y direction costs 2x the absolute distance

16. Graph Use RGB data of maze Red: Traversable Blue: Obstacle
Forms an adjacency matrix of x, y co-ordinates
Use adjacency matrix, color data to get nodes

17. Graph Store node, color data in a MutableObjectIntMap
public class Point { private final int x;
private final int y;
public Point(int x, int y) { this.x = x; this.y = y; } }
MutableObjectIntMap<Point> GRAPH = new ObjectIntHashMap<>();
GRAPH.put(new Point(0, 0), 1);

18. Successors Find successors
public static SetIterable<Point> getSuccessors(Point point) { if(GRAPH.get(point) > 1) { MutableSet<Point> successors = Sets.mutable.withInitialCapacity(4); if (GRAPH.get(negativeX) > 1) { successors.add(negativeX); }
return successors; } return Sets.immutable.empty(); }

19. Cost Function
public static int getCost(Point point1, Point point2) { int xCost = Math.abs(point1.getX() – point2.getX());
int yCost = 2 * Math.abs(point1.getY() – point2.getY()); return xCost + yCost; }

20. Prioritization vertexCostMap: Map of node to cost to visit
public static Point getNodeToVisit(
Point point,
SetIterable<Point> verticesToSearch) { return verticesToSearch.minBy(each -> vertexCostMap.get(each)); }
vertexCostMap:
Map of node to cost to visit
Initialized with all node costs to be Integer.MAX_VALUE
Each time node is visited; update with least cost to visit

21. Path
MutableStack<Point> path = Stacks.mutable.empty(); boolean isPathComplete = false; while (!isPathComplete) { if (start.equals(path.peek())) { isPathComplete = true; } else { path.push(nodeBackpointerMap.get(path.peek())); } } return path;

22. Path: Dijkstra’s

23. Path: A*
Heuristic = |xendpoint – xpoint2| + |yendpoint – ypoint2|

24. Path: A*
Heuristic = |xendpoint – xpoint2| + |yendpoint – xpoint2|

25. Motion Uninterrupted Path comprised of 226 nodes
Robot moves node to node, pausing 225 times
How to make robot move smoothly?

26. Motion Uninterrupted Path comprised of 226 nodes
Robot moves node to node, pausing 225 times
How to make robot move smoothly?
Flatten the path during motion by peeking in the future
Check if the next next node has the same heading
Same heading: Mark it to be flattened
Different heading: Compute the angle the robot needs to turn
Hence, achieving motion uninterrupted

27. Agenda Robot videos Java vs EV3 Programmer App
Dijkstra’s and A* Algorithm at a glance
Dijkstra’s Algorithm on EV3
JRE vs Compact Profiles
Demos

28. JRE vs Compact Profiles
Stripped down version of JRE into subsets
Source: Compact Profiles Overview

29. Performance Comparison
Task
Compact2 (Time in s)
Full JRE (Time in s)
EV3 start-up 80
Program execution start-up 13 15
Graph initialization 22
Dijkstra’s algorithm
110
115
A* algorithm 49 54
Performed on a standard Lego EV3 Mindstorms running Lejos beta

30. Empirical Observations
Does it stop mid-execution?
Is the performance consistent?
What about the jar sizes?
What about the memory footprint?
Discuss these points live

31. Agenda Robot videos Java vs EV3 Programmer App
Dijkstra’s and A* Algorithm at a glance
Dijkstra’s Algorithm on EV3
JRE vs Compact Profiles
Demos

32. Learn more at GS.com/Engineering
© 2016 Goldman Sachs. This presentation should not be relied upon or considered investment advice. Goldman Sachs does not warrant or guarantee to anyone the accuracy, completeness or efficacy of this presentation, and recipients should not rely on it except at their own risk. This presentation may not be forwarded or disclosed except with this disclaimer intact.