Artificial Intelligence

Transcription

1 rtificial Intelligence Robotics, a ase Study - overage Many applications: Floor cleaning, mowing, de-mining,. Many approaches: Off-line or On-line Heuristic or omplete Multi-robot, motivated by robustness and efficiency Lesson Static - to be able to guarantee completeness Inaccessible - greater impact on the on-line version Non-deterministic ontinuous Environment ssumptions Exact cellular decomposition pproximate cellular decomposition MST- Multi Robot Spanning Tree overage omplete - with approximate cellular decomposition Robust overage completed as long as one robot is alive The robustness mechanism is simple Off-line and On-line algorithms Off-line: o nalysis according to initial positions o Efficiency improvements On-line: o Implemented on simulation of real-robots

2 Off-line overage, asic ssumptions rea division n cells k homogenous robots Equal associated tool size Robots movement ST: Spanning Tree overage (Gabrieli and Rimon 2001) rea division Graph definition uilding the spanning tree Non-backtracking MST Initialization phase: uild ST, distribute to robots istributed execution: Each robot follows its section Low risk of collisions Robot is done! Guaranteed Robustness overage completed as long as one robot is alive Low communication, no need for re-allocation Robot is done! Robot is done!

3 nalysis: Non-backtracking MST Running time = max i k step(i) est case: n 1 k acktracking MST Similar initialization phase Robots backtrack to assist others No point is covered more than twice Worst case: n k Unfortunately, common case General non-backtracking worst case: n - 2(k-1) acktracking MST (cont.) acktracking MST nalysis Same robustness mechanism Same communication requirements Robot is done! Robot is done! est case: The same Worst case: k=2 k>2 n 1 k 2n 1 3 n 2 Robot is done!

4 Efficiency in Off-line overage Optimal MST- improves the average case Heterogeneous robots- flexibility Optimal MST Similar initialization phase Robots backtrack to assist others: ll the robots can backtrack acktracking on any number of steps No point is covered more than twice Optimal spanning tree- improves the worst case Same robustness mechanism Same communication requirements E Optimal MST (cont.) hoose a robot Search for the minimum valid solution Left search Right search omplexity: heck on all the robots: k Each search: O(n logn) Validity check: O(k) Total: O(k 2 n logn) 209 E ifferent speeds Heterogeneous Robots Non-backtracking MST acktracking MST Optimal MST ifferent fuel/battery time Non-backtracking MST acktracking MST Optimal MST 210 4

5 Optimal Spanning tree Improves the worst case with all 3 algorithms The construction is believed to be NP-Hard R1 R1 Generating a Good Spanning Tree (elieved to be NP-Hard) = 28 cells = 12 cells R2 R3 R2 R3 = 4 cells = 12 cells (a) (b) = 4 cells = 12 cells Heuristic Solution uild k subtrees on coarse grid Start building subtrees from initial locations dd cells to each subtree gradually Spread away from other robots (based on Manhattan dist) onnect subtrees Randomly pick connections between subtrees alculate x in resulting tree Repeat k^a times (a is a parameter) Report tree yielding minimal x Illustration Stage 1 Min{1,2} = 1 Min{3,4} = 3 Min{2,3} =

6 Example X = On-line MST Same basic assumptions: rea decomposition- n cells k homogenous robots Equal tool size and robot movements ll the robots know their absolute initial position Initialization phase 1. greed-upon grid construction 2. Self-localization 3. Locations update On-line MST (ont.) Guaranteed Robustness overage completed as long as one robot is alive No need for re-allocation

7 overage time overage time overage time From Theory to Practice Player/Stage with modeled RV-400 robots Localization solutions GPS Odometry with limited errors greed-upon grid options ig enough work-area ynamic work-area ollisions avoidance with bumps Random wait ommunication based Limited sensors solution 219 Off-line lgorithms Experiments (1) Work area: 30X20 cells, 2400 sub-cells Each point represents 100 trials Number of robots non-backtracking-random backtracking-random optimal-random best case Off-line lgorithms Experiments (2) Experimental Results Work area: 30X20 cells with 80 holes, 2080 sub-cells Each point represents 100 trials Number of robots non-backtracking-random backtracking-random optimal-random best case Number of robots 222 non-backtrackingrandom backtracking-random optimal-random non-backtracking- est ST optimal-est ST best case 7

8 Time Experimental Results - 27% Obstacles On-line lgorithm Run-time Example On-line lgorithm Experiments Random places Each point represents 10 trials 04:19:12 03:50:24 onclusion omplete and robust multi-robot algorithms Redundancy vs. efficiency with off-line algorithms 03:21:36 02:52:48 02:24:00 Optimal MST which handle heterogeneous robots 01:55:12 01:26:24 00:57:36 Implemented on-line MST with approximation techniques 00:28:48 00:00: Number of robots 225 Outdoor environment Indoor environment 226 8