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# October 19, Probabilistic Modeling III

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Multi-Robot Systems

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### October 19, Probabilistic Modeling III

1. 1. Mul\$‐Robot Systems  Probabilis\$c Modeling III  CSCI 7000‐006  Monday, October 19, 2009  Nikolaus Correll
2. 2. So far   •  Probabilis\$c models for reac\$ve and  delibera\$ve systems  •  Parameter calibra\$on using   –  Control parameters  –  Geometric proper\$es  •  System iden\$ﬁca\$on for reac\$ve swarms
3. 3. Today  •  Modeling of delibera\$ve systems with large  state space  –  Probabilis\$c models for sub‐systems  –  Discrete Event System simula\$on  •  Examples  –  Coverage  –  Task alloca\$on
4. 4. Review: Probabilis\$c Modeling  •  Enumerate all possible states of a system  •  Calculate all state transi\$on probabili\$es  •  Write down rate equa\$ons for the probability  of the system to be a in a certain state  •  Solve equa\$ons analy\$cally/numerically  •  Problem: What about systems with large state  spaces
5. 5. Modeling of large state spaces  •  Iden\$fy key sources of uncertainty in a system  –  Actua\$on  –  Sensing  –  Communica\$on  •  Measure/approximate probability density  func\$on  •  Sample from these distribu\$ons when  simula\$ng the algorithm  S. Ru\$shauser, N. Correll, and A. Mar\$noli. Collabora\$ve Coverage using a  Swarm of Networked Miniature Robots. Robo\$cs & Autonomous Systems,  57(5):517‐525, 2009.
6. 6. Example: coverage  •  Algorithm  –  Build a minimal  spanning‐tree on‐line  –  Move from blade to  blade reac\$vely  –  Localiza\$on by coun\$ng  blades  –  Start‐over when lost  •  Uncertainty  –  Naviga\$on
7. 7. Basic Naviga\$on Behaviors  9/20/2007  Nikolaus Correll  7
8. 8. Quan\$fying Sensor & Actuator  Noise  6000 experiments in Webots, 10% wheel‐slip  Time for covering one blade  Probability of no naviga\$on error  (geometric distribu\$on)
9. 9. Discrete Event System Simula\$on  Webots‐Generated   Event Time Data  Choose robot (closest  next event \$me), add  event \$me for robot  Determine next node n to visit  Algorithm  Naviga\$on  Failure  Success?  probabilites  Yes  No  Move Robot  Move Robot  No  to n  somewhere else  All Blades  inspected?  Yes
10. 10. DES vs. Webots: Naviga\$on  uncertainty  50% slip.  10% slip
11. 11. Discrete Event System Simula\$on  •  Simula\$ng the algorithm generates sample  trajectories in state space  •  Previous example: limited to naviga\$on  uncertainty  •  Simula\$on can model arbitrary level of detail,  including communica\$on
12. 12. DES vs. Webots: Communica\$on  No Comm.  Comm.  10% wheel slip
13. 13. Example: Distributed Robot Garden  •  Mo\$va\$on: Precision  Agriculture  •  Robots water and forage  tomato plants  •  Pots monitor humidity  level and coordinate  robo\$c system  •  Robots inventory each  plant and store it into its  pot’s database
14. 14. Sub‐tasks / Sources of uncertainty  •  Visual recogni\$on of ripe and green tomatoes  •  Visual servoing with monocular vision  •  Manipula\$on with 4‐DOF arm  •  Coordina\$on / task alloca\$on of  heterogeneous system over wireless network  •  Mul\$‐robot naviga\$on in \$ght environments
15. 15. Robo\$c Plaeorm  Localiza(on  Vision  Hagisonic Stargazer  Logitech QuickCam  Computa(on  Dell La\$tude D620  Manipula(on  Crustcrawler 4‐DOF  Watering System  Hargrave  Diﬀeren(al Wheels  iRobot Create  Ubuntu Linux, Willow Garage ROS, USB
16. 16. Plant  Humidity Sensor  Vegetronix  Wireless router  Temperature@lert  Infra‐red Beacon  iRobot Roomba base  OpenWRT Linux, Atheros chipsets
17. 17. Filter‐based object recogni\$on  •  Filter image  –  Sobel  –  Hough transform  –  Color  –  Spectral  highlights  –  Size and shape  Sobel  Hough  Color  Spectral  •  Weighted sum of  Highlights  ﬁlters highlights  object loca\$on
18. 18. Inventory  •  Challenges  –  Percep\$on  1  6  –  Not possible from single perspec\$ve  •  Algorithm  2  5  -  Fetch fruit inventory from pot (JSON)  -  Object recogni\$on from 6 non‐ 3  4  overlapping perspec\$ves  -  Merge observa\$on with inventory  •  Conﬁdence grows with every  measurement  •  Inventory dura\$on: 45s
19. 19. Visual Servoing/Grasping  •  Challenges  –  Percep\$on (fruits + stem)  2  –  Limited DOF / workspace  •  Algorithm  -  Select fruit with the  strongest conﬁdence  -  Servo to ini\$al posi\$on  -  Servo to fruit using image  Jacobian  -  Rely on radius es\$mate for  depth  F. Chaumele and S. Hutchinson, “Visual servo control  part i: Basic approaches,” Robo\$cs & Automa\$on  -  Close gripper / retract arm  Magazine, vol. 13, no. 4, pp. 82–90  when arrived
20. 20. Results: Visual Servoing/Grasping  •  Percep\$on  –  75% correctly  detected  •  Visual Servo  –  75% correct grasps  (10 trials)  –  28.3s +/‐ 10s per  grasp
21. 21. Task Alloca\$on  •  Challenges  –  Unreliable channel (ad‐ hoc wiﬁ)  –  Uncertainty in  naviga\$on and task  execu\$on  •  Robots reply with their  distance + length of task  queue (approx. \$me)  •  Plant selects “best”  robot  •  Alloca\$on repeated  periodically
22. 22. Naviga\$on  •  Challenges  –  Narrow passages  –  Deadlocks (mul\$‐robot)  –  Communica\$on  •  Localiza\$on  –  Sensor fusion: odometry + passive  infrared beacons  –  Broadcast posi\$on at 1Hz  •  Mo\$on planning  –  Grid‐map of the environment: sta\$c  obstacles + other robots  –  Wavefront algorithm (Latombe)  –  Reac\$ve behavior for avoiding  bumps  –  Reac\$ve behavior for docking
23. 23. Model the distributed garden  •  Measure average \$me and success rate of  –  Naviga\$on from A to B  –  Watering  –  Communica\$on  –  Harves\$ng  •  Compare  –  Diﬀerent task alloca\$on schemes  –  Distribu\$on of sensing, actua\$on, and computa\$on  (ex: humidity sensing on the plant vs. robot)
24. 24. Possible model  T1: Harvest  T2: Robot   x *   T3: Robot  request  receives task  73s +/‐ 15s  reaches plant  (p|Naviga\$on failure)x  28.3s+/‐10s  25%  Assump\$ons  ‐ No task alloca\$on (single robot)  T4: Robot  ‐ Inﬁnite number of grasping trial  grasps  Next step  ‐simulate task alloca\$on based on  communica\$on model  ‐ﬁnite number of fruits per plant
25. 25. Open research ques\$ons  •  What about rare events?  –  How oten do we have to try each sub‐system?  –  How oten do we need to simulate the en\$re  system?
26. 26. Summary  •  Complex delibera\$ve systems can be modeled  by studying sample trajectories through state  space  •  Open problems  –  Genera\$ng suﬃcient number of samples  –  Rare events