Multi-Robot Systems

1. Mul$‐Robot Systems
Probabilis$c Modeling III
CSCI 7000‐006
Monday, October 19, 2009
Nikolaus Correll

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. 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. 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. 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. 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. Basic Naviga$on Behaviors
9/20/2007 Nikolaus Correll 7

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. 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. DES vs. Webots: Naviga$on
uncertainty
50% slip.
10% slip

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. DES vs. Webots: Communica$on
No Comm.
Comm.
10% wheel slip

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. 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. 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. Plant
Humidity Sensor
Vegetronix
Wireless router
Temperature@lert
Infra‐red Beacon
iRobot Roomba base OpenWRT Linux, Atheros chipsets

18. 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

19. 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

20. 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

21. Results: Visual Servoing/Grasping
• Percep$on
– 75% correctly
detected
• Visual Servo
– 75% correct grasps
(10 trials)
– 28.3s +/‐ 10s per
grasp

22. 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

23. 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

24. 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)

25. 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

26. 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?

27. 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