Thesis Presentation : Cellular Automata for Control and Interactions of Large Formations of Robots

1. Thesis Presentation:Cellular Automata forControl and Interactions ofLarge Formations of Robots Ross Mead Committee: Dr. Jerry B. Weinberg Dr. Stephen Blythe Dr. Xudong Yu

2. Outline • Introduction and Significance • Comparison of Cellular Automata Approaches • 1-Dimensional Robot-Space Cellular Automata • Algorithm • Implementation • 2-Dimensional Robot-Space Cellular Automata • Algorithm Extension • Implementation • Conclusions • Future Work • Q&A 2

3. Motivation • Space Solar Power (SSP) • How can a massive collection of robots moving with no group organization coordinate to form a global structure? 3

4. Problem swarm formation 4

5. Approach • Utilize reactive robot control strategies • closely couple sensor input to actions • Treat the formation as a cellular automaton • lattice of computational units (cells) • each cell is in one of a given set of states • governed by a set of rules • complex emergent behavior from simplicity 5

6. Environment is represented topologically as a 2- or 3-dimensional grid of cells… robot between grid cells boundary surrounds the automaton automaton wraps along boundaries two robots collide trying to occupy same grid cell “World-Space” Cellular Automata 6

7. Each robot is represented as a cell ci in a 1-dimensional automaton… ci = {H, s, F, S} “Robot-Space” Cellular Automata 7

8. Each robot is represented as a cell ci in a 1-dimensional automaton… ci = {H, s, F, S} neighborhood Hi = {ci-1, ci, ci+1} ci-1← left neighbor ci+1← right neighbor cj← some neighbor j “Robot-Space” Cellular Automata • C← automaton: • C= H1UH2U … UHn • = {c1, c2, …,cn} 8

9. Each robot is represented as a cell ci in a 1-dimensional automaton… ci = {H, s, F, S} state si = {p, rdes, ract, Γ, Θ , t} ( ... described later ... ) “Robot-Space” Cellular Automata • C← automaton: • C= H1UH2U … UHn • = {c1, c2, …,cn} 9

10. Each robot is represented as a cell ci in a 1-dimensional automaton… ci = {H, s, F, S} state transition si = {p, rdes, ract, Γ, Θ , t} ( ... described later ... ) sit = S(si-1t-1, sit-1, si+1t-1) t← time step (counter) “Robot-Space” Cellular Automata • C← automaton: • C= H1UH2U … UHn • = {c1, c2, …,cn} 10

11. Each robot is represented as a cell ci in a 1-dimensional automaton… ci = {H, s, F, S} formation F = {f(x),R, Φ, pseed} f(x)← description R← robot separation Φ← relative heading pseed← start position “Robot-Space” Cellular Automata • C← automaton: • C= H1UH2U … UHn • = {c1, c2, …,cn} 11

12. Algorithm – Formation Definition • F is sent to some robot, designating it as the seedcell cseed... • cseed is not a leader, but rather an initiator of the coordination process • For purposes of calculating desired relationships, each cell ci considers itself to be at some formation-relative positionpi: pi = [ xif(xi) ]T • In the case of cseed, this position pseed is given… f(x) = a x2 cseed pseed 12

13. Algorithm – Desired Relationships • The desired relationship ri→j,des from ci to some neighbor cj is determined by calculating a vector v from pi to the intersection f(vx) and a circle centered at pi with radius R: R2 = (vx–pi,x)2 + (f(vx) –pi,y)2ri→j,des = [ vxf(vx) ]T • The relationship is rotated by –Φ to account for robot heading... f(x) = a x2 R –v +v desired relationship with left neighbor ci-1 desired relationship with right neighbor ci+1 ri→i-1,des ri→i+1,des pseed 13

14. Algorithm – Desired Relationships • F and ri→j,des are communicated locally within the neighborhood. • Each neighbor cj repeats the process, but considers itself to be at different formation-relative position pj… • determined by the desired relationship from the sending neighbor ci pj = pi + ri→j,des f(x) = a x2 Note: rj→i,des = –ri→j,des pi-1 pi+1 pseed 14

15. Algorithm – Desired Relationships • Propagate changes in neighborhoods in succession. • Calculated relationships generate a connected graph that yields the shape of the formation. f(x) = a x2 15

16. Algorithm – Actual Relationships • Using sensor readings, robots calculate an actual relationship ri→j,act with each neighbor cj. • State of Hi governs robot movement: • rotational errorΘi and translational errorΓi • relationships based on individual coordinate systems 16

17. Algorithm – Formation Manipulation 17

18. Algorithm – Formation Manipulation 18

19. Algorithm – Formation Manipulation 19

20. Algorithm – Formation Manipulation 20

21. Algorithm – Formation Manipulation 21

22. Algorithm – Formation Manipulation 22

23. Implementation– Robot Platform • ZigBee module • packet communication • share state information • within neighborhood • Color-coding system • visual identification • neighbor localization • (actual relationships) • Scooterbot II base • strong, but very light • differential steering system • XBCv2 microcontroller • Interactive C • back-EMF PID motor control • color camera 23

24. Implementation – Color-Coding System • Visual identification • the color of each robot is assigned based on ID: • orange for odd, green for even • Neighbor localization (actual relationships) • ri→j,act = [ di→jαi→j ]T 24

25. Implementation – State Diagram 25

26. Implementation – Results ... and because embedding Windows’ own media format is a too much for PowerPoint... [ Click Here ] 26

27. Extending the Formation Definition • Consider a set f' of M mathematical functions: f' = {f1(x),f2(x), ..., fM(x)} F = {f',R, Φ, pseed} • For desired relationships, each fm(x) is considered individually... • yielding its own 1-dimensional neighborhood mhi • resulting in M neighborhoods and a 2-dimensional cellular automaton (M > 1) Hi = 1hiU2hiU ... UMhi = {Mc1-1, …,2c1-1,1c1-1,c1,1c1+1,2c1+1, …,Mc1+1} f3(x) = –x √3 f2(x) = x √3 f1(x) = 0 R 1hi = 1{ci-1, ci, ci+1} 2hi = 2{ci-1, ci, ci+1} 3hi = 3{ci-1, ci, ci+1} 27

28. How can this be applied to SSP? • Reflector viewed as 2-dimensional lattice of robots and, thus, a 2-dimensional cellular automaton... 28

29. Multi-Function Formations 29

30. Multi-Function Formations • Desired relationship: ri→j,des = [ vxf(vx) ]T What happened? • Original:R2 = (vx–pi,x)2 + (f(vx) –pi,y)2 30

31. Multi-Function Formations • Desired relationship: ri→j,des = [ vxf(vx) ]T What happened? • Original:R2 = (vx–pi,x)2 + (f(vx) –pi,y)2 • Alternative:R2 = vx2 + f(vx)2 31

32. Multi-Function Formations • Desired relationship: ri→j,des = [ vxf(vx) ]T Similarly... • Original:R2 = (vx–pi,x)2 + (f(vx) –pi,y)2 32

33. Multi-Function Formations Similarly... • Alternative:R2 = vx2 + f(vx)2 33

34. Implementation– Robot Platform 34

35. Implementation – Robot “Faces” • Visual identification • each robot has a unique three-color column... • vertical locations of color bands correspond to ID • green on top for even, magenta on top for odd • 5 locations × 4 locations = 20 unique faces 35

36. Implementation – Robot “Faces” “All around me are familiar faces... ” 36

37. Implementation – Results [ Click Here ] 37

38. Conclusions – Algorithm • Designed and implemented a general distributed robot formations algorithm... • able to conform to a wide variety of formations • Robots represented as cells in multi-dimensional cellular automata... • simple rule sets produce complex group behavior • Distinguishes itself as leaderless algorithm... • only communication is to instigate coordination 38

39. Conclusions – Robot Platform Hardware  Software  Extensive and reusable collection of libraries. Greatest implementation hurdle—Interactive C... most time spent debugging workarounds—not fixes serial library deadlock bug list is... amusing... imposes harsh program size ... stay away! • 19 robots developed. • Accurate motion control. • Reasonable execution time. • Reliable communication. • Robot faces were excellent! 39

40. Conclusions – Formation Classification • Non-formation (swarm) • Explicit formation • Straight line formation • Function-based formation • Branching formation • Lattice formation 40

41. Future Work • Dynamic neighborhoods • Seed election • Formation repair • Obstacle avoidance • Global positioning • 3-dimensional formations • Disconnected formations • Formation classification • Analysis [ Click here ] • Formation management 42

42. Mead, R. & Weinberg, J.B. (2008). A Distributed Control Algorithm for Robots in Grid Formations. To appear in the Proceedings of the Robot Competition and Exhibition of The 23rd National Conference on Artificial Intelligence (AAAI-08), Chicago, Illinois. Mead, R. & Weinberg, J.B. (2008). 2-Dimensional Cellular Automata Approach for Robot Grid Formations. To appear in Student Abstracts and Poster Program of The 23rd National Conference on Artificial Intelligence (AAAI-08). Chicago, Illinois. Mead, R., Weinberg, J.B., & Croxell, J.R. (2007). A Demonstration of a Robot Formation Control Algorithm and Platform. To appear in the Proceedings of the Robot Competition and Exhibition of The 22nd National Conference on Artificial Intelligence (AAAI-07), Vancouver, British Columbia. Mead, R., Weinberg, J.B., & Croxell, J.R. (2007). An Implementation of Robot Formations using Local Interactions. In the Proceedings of The 22nd National Conference on Artificial Intelligence (AAAI-07), 1889-1890. Vancouver, British Columbia. Questions? For more information, please visithttp://roboti.cs.siue.edu/projects/formations/or see the following papers: 43