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Search Designing a solution The FRIT Algorithm Results Future work Reconnection with the Ideal Tree A New Approach to Real-Time Search Le on Illanes Department of Computer Science School of Engineering Pontificia Universidad Cat

  1. Search Designing a solution Agent-centered Search The FRIT Algorithm Issue: Heuristic Depressions Results Future work Heuristic learning (` a la LRTA*) 6 5 4 3 2 7 4 3 2 1 8 9 8 1 0 5 4 3 2 1 Path finding in an unknown environment (w/ free-space assumption) Le´ on Illanes Reconnection with the Ideal Tree

  2. Search Designing a solution Agent-centered Search The FRIT Algorithm Issue: Heuristic Depressions Results Future work Heuristic learning (` a la LRTA*) 6 5 4 3 2 7 4 3 2 1 8 9 1 0 10 5 4 3 2 1 Path finding in an unknown environment (w/ free-space assumption) Le´ on Illanes Reconnection with the Ideal Tree

  3. Search Designing a solution Agent-centered Search The FRIT Algorithm Issue: Heuristic Depressions Results Future work Heuristic learning (` a la LRTA*) 6 5 4 3 2 7 4 3 2 1 8 9 1 0 10 5 4 3 2 1 Path finding in an unknown environment (w/ free-space assumption) Le´ on Illanes Reconnection with the Ideal Tree

  4. Search Designing a solution Agent-centered Search The FRIT Algorithm Issue: Heuristic Depressions Results Future work How do we avoid erratic movements? More lookahead More learning Pruning states Le´ on Illanes Reconnection with the Ideal Tree

  5. Search Designing a solution Agent-centered Search The FRIT Algorithm Issue: Heuristic Depressions Results Future work How do we avoid erratic movements? More lookahead More learning Pruning states We asked ourselves: Anything simpler? Le´ on Illanes Reconnection with the Ideal Tree

  6. Search Designing a solution The FRIT Algorithm Design principles Results Future work Design principles 1 2 Le´ on Illanes Reconnection with the Ideal Tree

  7. Search Designing a solution The FRIT Algorithm Design principles Results Future work Design principles Avoid expensive computation 1 Sorting Learning 2 Le´ on Illanes Reconnection with the Ideal Tree

  8. Search Designing a solution The FRIT Algorithm Design principles Results Future work Design principles Avoid expensive computation 1 Sorting Learning Exploit the heuristic 2 Le´ on Illanes Reconnection with the Ideal Tree

  9. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work The FRIT Algorithm F ollow and R econnect with the I deal T ree Le´ on Illanes Reconnection with the Ideal Tree

  10. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work The Ideal Tree Definition (Ideal Tree) For a problem graph G with goal g and free-space assumption graph G M , we define an Ideal Tree to be any spanning tree for G M rooted at g . Le´ on Illanes Reconnection with the Ideal Tree

  11. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work The Ideal Tree Definition (Ideal Tree) For a problem graph G with goal g and free-space assumption graph G M , we define an Ideal Tree to be any spanning tree for G M rooted at g . In practice: parent ( s ) = argmin c ( s , u ) + h ( u ) u :( s , u ) ∈ E ( G M ) Le´ on Illanes Reconnection with the Ideal Tree

  12. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work The Ideal Tree Le´ on Illanes Reconnection with the Ideal Tree

  13. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work The Ideal Tree Le´ on Illanes Reconnection with the Ideal Tree

  14. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT Input : Given the free-space assumption graph G M , a goal g , and a starting node s 0 . s ← s 0 // Set the current state to s 0 while s � = g do Le´ on Illanes Reconnection with the Ideal Tree

  15. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT Input : Given the free-space assumption graph G M , a goal g , and a starting node s 0 . s ← s 0 // Set the current state to s 0 while s � = g do Observe the environment around s and remove non-existent arcs from G M . Le´ on Illanes Reconnection with the Ideal Tree

  16. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT Input : Given the free-space assumption graph G M , a goal g , and a starting node s 0 . s ← s 0 // Set the current state to s 0 while s � = g do Observe the environment around s and remove non-existent arcs from G M . if s has no parent node then Reconnect: Le´ on Illanes Reconnection with the Ideal Tree

  17. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT Input : Given the free-space assumption graph G M , a goal g , and a starting node s 0 . s ← s 0 // Set the current state to s 0 while s � = g do Observe the environment around s and remove non-existent arcs from G M . if s has no parent node then Reconnect: Follow: Le´ on Illanes Reconnection with the Ideal Tree

  18. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT Input : Given the free-space assumption graph G M , a goal g , and a starting node s 0 . s ← s 0 // Set the current state to s 0 while s � = g do Observe the environment around s and remove non-existent arcs from G M . if s has no parent node then Reconnect: Follow: s ← parent ( s ) // Move the agent to the parent of s Le´ on Illanes Reconnection with the Ideal Tree

  19. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT Input : Given the free-space assumption graph G M , a goal g , and a starting node s 0 . s ← s 0 // Set the current state to s 0 while s � = g do Observe the environment around s and remove non-existent arcs from G M . if s has no parent node then Reconnect: Locally search around s to find any state s ′ connected to g . Update the Ideal Tree to include the path from s to s ′ . Follow: s ← parent ( s ) // Move the agent to the parent of s Le´ on Illanes Reconnection with the Ideal Tree

  20. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT by example Observe Follow Reconnect Le´ on Illanes Reconnection with the Ideal Tree

  21. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT by example Follow Reconnect Observe Le´ on Illanes Reconnection with the Ideal Tree

  22. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT by example Observe Reconnect Follow Le´ on Illanes Reconnection with the Ideal Tree

  23. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT by example Follow Reconnect Observe Le´ on Illanes Reconnection with the Ideal Tree

  24. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT by example Observe Reconnect Follow Le´ on Illanes Reconnection with the Ideal Tree

  25. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT by example Follow Reconnect Observe Le´ on Illanes Reconnection with the Ideal Tree

  26. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT by example Observe Follow Reconnect Le´ on Illanes Reconnection with the Ideal Tree

  27. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT by example Observe Follow Reconnect Le´ on Illanes Reconnection with the Ideal Tree

  28. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT by example Observe Follow Reconnect Le´ on Illanes Reconnection with the Ideal Tree

  29. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT by example Observe Follow Reconnect Le´ on Illanes Reconnection with the Ideal Tree

  30. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT by example Observe Follow Reconnect Le´ on Illanes Reconnection with the Ideal Tree

  31. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT by example Observe Follow Reconnect Le´ on Illanes Reconnection with the Ideal Tree

  32. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work FRIT by example Observe Reconnect Follow Le´ on Illanes Reconnection with the Ideal Tree

  33. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work A better example Le´ on Illanes Reconnection with the Ideal Tree

  34. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work A better example Le´ on Illanes Reconnection with the Ideal Tree

  35. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work A better example Le´ on Illanes Reconnection with the Ideal Tree

  36. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work A better example Le´ on Illanes Reconnection with the Ideal Tree

  37. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work A better example Le´ on Illanes Reconnection with the Ideal Tree

  38. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work A better example Le´ on Illanes Reconnection with the Ideal Tree

  39. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work A better example Le´ on Illanes Reconnection with the Ideal Tree

  40. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work A better example Le´ on Illanes Reconnection with the Ideal Tree

  41. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work A better example Le´ on Illanes Reconnection with the Ideal Tree

  42. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work A better example Le´ on Illanes Reconnection with the Ideal Tree

  43. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work A better example Le´ on Illanes Reconnection with the Ideal Tree

  44. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work A better example Le´ on Illanes Reconnection with the Ideal Tree

  45. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work A better example Le´ on Illanes Reconnection with the Ideal Tree

  46. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work A better example Le´ on Illanes Reconnection with the Ideal Tree

  47. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work A better example Le´ on Illanes Reconnection with the Ideal Tree

  48. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work A better example Le´ on Illanes Reconnection with the Ideal Tree

  49. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work A better example Le´ on Illanes Reconnection with the Ideal Tree

  50. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work A better example Le´ on Illanes Reconnection with the Ideal Tree

  51. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work Video! Le´ on Illanes Reconnection with the Ideal Tree

  52. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work The Real-Time Property As described, FRIT is not a Real-Time Search Algorithm. We need a bound on the amount of states visited while reconnecting. Le´ on Illanes Reconnection with the Ideal Tree

  53. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work The Real-Time Property As described, FRIT is not a Real-Time Search Algorithm. We need a bound on the amount of states visited while reconnecting. What to do when the bound is surpassed? Le´ on Illanes Reconnection with the Ideal Tree

  54. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work Two approaches 1 2 Le´ on Illanes Reconnection with the Ideal Tree

  55. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work Two approaches Standard FRIT: Do nothing. . . [RIBH13, RIBH14] 1 2 Le´ on Illanes Reconnection with the Ideal Tree

  56. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work Two approaches Standard FRIT: Do nothing. . . [RIBH13, RIBH14] 1 FRIT RT : Use a Real-Time Search Algorithm for 2 Reconnection. [RIBH14] Le´ on Illanes Reconnection with the Ideal Tree

  57. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work Complexity Follow is O (1) Le´ on Illanes Reconnection with the Ideal Tree

  58. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work Complexity Follow is O (1) Reconnect can be O ( | V | ) Le´ on Illanes Reconnection with the Ideal Tree

  59. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work Complexity Follow is O (1) Reconnect can be O ( | V | ) Reconnect can be O ( | V | ). Using BFS as the local search algorithm, we check at most | V | nodes to see if they are connected to the goal. This check can be done as a recursive function with no side effects and can thus be memoized, ensuring that for each reconnection search we do at most | V | comparisons. Le´ on Illanes Reconnection with the Ideal Tree

  60. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work Complexity Follow is O (1) Reconnect can be O ( | V | ) Reconnect can be O ( | V | ). Using BFS as the local search algorithm, we check at most | V | nodes to see if they are connected to the goal. This check can be done as a recursive function with no side effects and can thus be memoized, ensuring that for each reconnection search we do at most | V | comparisons. Additionally, we prove correcteness and completeness for both FRIT and FRIT RT , while giving an explicit upper bound of ( | V | +1) 2 4 moves for FRIT and O ( | V | 3 ) moves for FRIT RT . Le´ on Illanes Reconnection with the Ideal Tree

  61. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work Convergence FRIT immediately converges to a suboptimal solution Le´ on Illanes Reconnection with the Ideal Tree

  62. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work Convergence FRIT immediately converges to a suboptimal solution Le´ on Illanes Reconnection with the Ideal Tree

  63. Search The Ideal Tree Designing a solution Follow and Reconnect The FRIT Algorithm FRIT and Real-Time Search Results Properties Future work Convergence FRIT immediately converges to a suboptimal solution Le´ on Illanes Reconnection with the Ideal Tree

  64. Search Designing a solution FRIT RT The FRIT Algorithm FRIT with BFS Results Comparison between approaches Future work Games: FRIT RT halves daRTAA*’s solutions 10000000 FRIT_rt(RTAA) FRIT_rt(daRTAA) Average Solution Cost (log-scale) RTAA 1000000 daRTAA 100000 10000 1000 0 20 40 60 80 100 120 140 Average time per planning episode (us) Le´ on Illanes Reconnection with the Ideal Tree

  65. Search Designing a solution FRIT RT The FRIT Algorithm FRIT with BFS Results Comparison between approaches Future work Mazes: Similar tendencies 10000000 FRIT_rt(RTAA) FRIT_rt(daRTAA) Average Solution Cost (log-scale) RTAA 1000000 daRTAA 100000 10000 1000 0 20 40 60 80 100 120 Average time per planning episode (us) Le´ on Illanes Reconnection with the Ideal Tree

  66. Search Designing a solution FRIT RT The FRIT Algorithm FRIT with BFS Results Comparison between approaches Future work Games: FRIT dominates for very small t 10000000 FRIT(BFS) Average Solution Length (log-scale) RA* AA* 1000000 100000 10000 1000 0 100 200 300 400 500 600 Average time per planning episode (us) Le´ on Illanes Reconnection with the Ideal Tree

  67. Search Designing a solution FRIT RT The FRIT Algorithm FRIT with BFS Results Comparison between approaches Future work Mazes: Again, similar tendencies 10000000 FRIT(BFS) Average Solution Length (log-scale) RA* AA* 1000000 100000 10000 1000 0 100 200 300 400 500 600 Average time per planning episode (us) Le´ on Illanes Reconnection with the Ideal Tree

  68. Search Designing a solution FRIT RT The FRIT Algorithm FRIT with BFS Results Comparison between approaches Future work FRIT(BFS) obtains better solutions 10000000 FRIT_rt(daRTAA) Average Solution Length (log-scale) FRIT(BFS) 1000000 100000 10000 1000 0 10 20 30 40 50 60 Average time per planning episode (us) Le´ on Illanes Reconnection with the Ideal Tree

  69. Search Designing a solution The FRIT Algorithm Results Future work Future work Other applications Optimizing for pathfinding in grids [RIB14] Moving-target search Dense graphs (e.g.: Airport networks) Le´ on Illanes Reconnection with the Ideal Tree

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