Revisiting the Mars Surveyor Challenge

1. Revisiting the Mars Surveyor Challenge AY-REU Fall 2013 Students: Andrew Stubblebine, Tejas Deshpande Faculty Mentor: Dr. Elad Kivelevitch

2. The Challenge • Originally a MathWorks-sponsored contest using MATLAB, 1999 • Find optimal strategy to explore as much of a 50x50-space map as possible with 5 rovers • “Collaborative Contest” • All solutions submitted visible to all • Winning solutions built off each other • Top ranked solutions “hard-coded”

3. Time Schedule

4. Motivation • Implement single algorithm for any situation • Scalable to any number of vehicles, any map, any map area • Increase efficiency of autonomous cooperative search • Amazon Air 4

5. Objectives Test and simulate both algorithms vs. winning competition solution on given maps and randomly generated maps Based on FS13 results: present in the AIAA Dayton-Cincinnati conference Based on the whole year: write a paper and present research at the 2015 national AIAA Aerospace Science Meeting conference

6. Challenge Conditions • Set of 8 predesigned maps • Number of obstacles and their placement are known • 5 rovers • Limited number of total instructions for each rover (500) • Individual instructions limited 1: Rover moves forward one space 2: Rover turns 90° to the left 3: Rover turns 90° to the right

7. Sample Solution Sample Instruction Set • 1 1 1 1 1 • 1 1 1 1 1 • 3 1 1 2 1 • 2 1 3 1 1 • 1 1 1 1 1 • 1 1 1 1 1 • 1 2 1 1 3 • 1 1 1 1 1 • 1 1 2 1 1 • 1 1 1 1 1

8. Approaches Rule-Based Algorithm Genetic Algorithm Imitates Natural Selection Searches a large solution space Potential to reach perfect/near perfect solution • Uses a loose set of logic-based rules • Local area surrounding each rover used in decision making • Think of how humans would search an area

9. Different Approaches – Same Goal Rule based approach -> Looks at the local level GA approach -> Looks at a more global level

10. Rule-Based Algorithm Genetic Algorithm Pros: Works on any map Theoretically scalable Only rule is survival of the fittest Gets decent results on complex maps Cons: Computationally intensive Pros: • Simple concept • Easily scalable • Fast computation • Gets decent results Cons: • Limited visibility area • Only local decisions made • Can overwhelm rovers on complicated maps

11. Rule-Based Algorithm

12. Rules • Prioritize forward movement (if open in front of rover, go forward) • Dead end encountered (rover path or obstacle): • Look beyond 3 squares in each direction • If decision cannot be reached, expand area of visibility until a “more informed” decision can be made • Test for rover local areas and proximity to other rovers to keep spread out and cover map more efficiently

13. More on Rule-Based Algorithm • Similar to popular flocking technique as discovered through research • Uses rules to guide “flock” of vehicles through certain events • Cohesion • Alignments • Separation • Evasion • Migration • Uses local information • Makes decisions for each rover based on immediate surroundings • Builds set of instructions one instruction (and one decision) at a time

14. Genetic Algorithm

15. Initial Population Assume Population is set to 100, Instructions set to 500 and iterations set to 100 and ‘planning horizon’ at 100 Iterates in ‘planning horizons’ Variable probability for each member of population

16. Iteration in ‘Horizons’ Old Population New Population 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 3 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 • 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 2 1 1 1 1 1 1 1 3 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Best Fitness

17. Variable Probability Go straight: 0.9, Turn Left and Right: 0.05 Go straight: 0.8, Turn Left and Right: 0.1 Go straight: 0.7, Turn Left and Right: 0.15 Go straight: 0.6, Turn Left and Right: 0.2 Go straight: 0.5, Turn Left and Right: 0.25 Total Population

18. Selection Procedure Child Child Child Truncation Selection Computationally efficient

19. Crossover Procedure • 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 2 1 1 1 1 1 1 1 3 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 • 1 1 1 1 1 • 1 1 2 1 1 • 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 Three Point Crossover

20. Mutation Procedure Randomly Selects a member of the population Randomly selects a rover and an instruction Adds 1 to the number if 1 or 2, otherwise makes it 1.

21. Results

22. Rule-Based Algorithm Results • Maps cut into sections • Circle within section until completed • Find new open section • Circle until new section completed • Process continued until rovers out of instructions or map covered

23. Genetic Algorithm Performance

24. Genetic Algorithm Performance

25. Rule-Based Algorithm Results

26. Genetic Algorithm Results

27. Algorithms vs. Competition Solution

28. Evaluates the ability of the designed algorithm to find an efficient solution • Based on winning competition solution (considered best possible solution) • Solution strength is the difference between the algorithm solution and the most optimal solution as a percentage of the number of open spaces (lower % is better) • *Solution on Map 4 does not function properly, likely due to difference in MATLAB editions. Number approximated from next lowest Map 4 solution

30. Conclusions • Rovers behavior patterns very interesting • Especially when comparing algorithm solutions • The overall results were similar to expected results • Improvements can be made for each algorithm to improve solution strength

31. Future Work Explore computationally efficient guided mutation Explore fuzzy logic for the rule based algorithm Implement position history so rovers can back track if stuck

32. Acknowledgements • We would like to acknowledge the National Science Foundation for funding this project • NSF Type 1 Grant • DUE-075691 • We would also like to acknowledge Dr. Kivelevitch for all of his help and guidance for this research