Tutorial on Ant Robotics Sven Koenig University of Southern - - PowerPoint PPT Presentation

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Tutorial on Ant Robotics Sven Koenig University of Southern - - PowerPoint PPT Presentation

Aug 23, 2023 483 likes •1.49k views

Tutorial on Ant Robotics Sven Koenig University of Southern California skoenig@usc.edu joint work with Jonas Svennebring, Boleslaw Szymanski, Yaxin Liu, and Craig Tovey Overview Cheap robots Robomow Limited capabilities

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SLIDE 1

Tutorial on Ant Robotics

Sven Koenig University of Southern California skoenig@usc.edu

joint work with Jonas Svennebring, Boleslaw Szymanski, Yaxin Liu, and Craig Tovey

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SLIDE 2

Overview

  • Cheap robots

– Limited capabilities

  • Computation capability
  • Sensing capability
  • Actuation capability

– Groups of robots

  • Fault tolerance
  • Parallelism

Robomow Cye Roomba

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SLIDE 3

Overview

  • Ant robots

– Robots with limited capabilities – Robots that leave information in the terrain

  • Ant robots cannot use conventional

planning methods. Rather, their behavior is driven by local interactions. This can result in very robust navigation.

Recommended special journal issue for further reading: AMAI special issue on Ant Robotics edited by Wagner and Bruckstein

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SLIDE 4

Overview

  • Our motivating task is the one-time or

repeated coverage of known or unknown terrain with single robots or teams of robots

– Mine sweeping – Surveillance – Search-and-rescue – Guarding – Surface inspection

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SLIDE 5

Overview

  • This topic is a bit far out. However, …
  • We will touch on different areas of AI and CS

– Agent coordination (swarms) – Robotics (robot architectures, ant robots, sensor networks) – Search (real-time search) – Complexity analysis of graph algorithms

  • We will see several good dissertation topics.
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SLIDE 6

Structure

  • Motivation
  • Real-time search
  • Results on real-time search
  • Application to ant robots and results
  • Serious application: smart markers
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SLIDE 7

Motivating Toy Task

  • Guarding a museum at night

– Robots

  • Computation is slow
  • Sensing is noisy
  • Actuation is noisy
  • Robots can fail

– Terrain

  • Terrain might be unknown initially
  • Terrain can change over time
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SLIDE 8

First Approach

  • Good location estimates - e.g. probabilities
  • Path planning – e.g. POMDPs
  • Explicit coordination – e.g. auctions
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SLIDE 9

First Approach

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SLIDE 10

First Approach

goal location mapping from poses to directives (“policy”) directive selection policy generation POMDP motion generation desired directive motor commands raw sonar data raw odometer data

  • ccupancy grid [Elfes]

sensor sensor report motion report pose estimation current pose distribution topological map prior actuator model prior sensor model prior distance model POMDP

Path Following Obstacle Avoidance Real-Time Control

path planning

Path Planning

path model learning interpretation compilation using GROW-BW (based on Baum-Welch)

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SLIDE 11

First Approach

  • Example: Xavier [Simmons and Koenig]

Xavier is a mobile robot at Carnegie Mellon University that received navigation requests from users worldwide via the World Wide Web and used POMDP-based navigation to travel more than 230 kilometers – an early used of POMP-based navigation which is now in wide-spread use.

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SLIDE 12

First (Standard) Approach

  • Good location estimates - e.g. probabilities
  • Path planning – e.g. POMDPs
  • Explicit coordination – e.g. auctions
  • The standard approach
  • Complex hardware and software

Recommended book for further reading: Probabilistic Robotics, Thrun, Burgard and Fox, MIT Press

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SLIDE 13

Second Approach

  • No location estimates
  • No planning
  • No explicit coordination
  • Not a standard approach at all
  • Simpler hardware and software
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SLIDE 14

Second Approach

  • No location estimates
  • No planning
  • No explicit coordination
  • Random walk
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SLIDE 15

Second Approach

  • No location estimates
  • No planning
  • No explicit coordination
  • Leaving trails in the terrain

– Short-lived trails

  • Heat [Russell]
  • Odor [Russell et al.]
  • Alcohol [Sharpe et al.]
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SLIDE 16

Second Approach

  • Chemical sensing is a relatively new area
  • f robotics with many interesting

challenges and important applications.

Recommended book for further reading: Odour Sensing for Mobile Robots, Russell, World Scientific

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SLIDE 17

Second Approach

  • Andrew Rusell’s RAT robot lays a

camphor trail and then follows it back to its starting point.

Recommended book for further reading: Odour Sensing for Mobile Robots, Russell, World Scientific

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SLIDE 18

Second Approach

  • Andrew Rusell’s RAT robot lays a

camphor trail and then follows it back to its starting point.

Recommended book for further reading: Odour Sensing for Mobile Robots, Russell, World Scientific

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SLIDE 19

Second Approach

  • Andrew Rusell’s RAT robot lays a

camphor trail and then follows it back to its starting point.

Recommended book for further reading: Odour Sensing for Mobile Robots, Russell, World Scientific

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SLIDE 20

Second Approach

  • Andrew Rusell’s hexapod robot follows a

camphor trail.

Recommended book for further reading: Odour Sensing for Mobile Robots, Russell, World Scientific

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SLIDE 21

Second Approach

  • Andrew Rusell’s hexapod robot follows a

camphor trail.

Recommended book for further reading: Odour Sensing for Mobile Robots, Russell, World Scientific

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SLIDE 22

Second Approach

  • No location estimates
  • No planning
  • No explicit coordination
  • Leaving trails in the terrain

– Short-lived trails

  • Heat [Russell]
  • Odor [Russell et al.]
  • Alcohol [Sharpe et al.]
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SLIDE 23

Second Approach

  • No location estimates
  • No planning
  • No explicit coordination
  • Leaving trails in the terrain

– Long-lived trails [Svennebring and Koenig]

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SLIDE 24

Structure

  • Motivation
  • Real-time search

– Analytical evaluation – Experimental evaluation

  • Results on real-time search
  • Application to ant robots and results
  • Serious application: smart markers
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SLIDE 25

Real-Time Search

  • Real-time search methods provide an interesting

means for coordinating single ant robots or teams of ant robots that cover known or unknown terrain once or repeatedly.

  • They leave markings in the terrain, similar to

what some ants do.

  • The ant robots robustly cover terrain even if the

robots are moved without realizing this, some robots fail, and some markings get destroyed. The robots do not even need to be localized.

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SLIDE 26

Node Counting

Initially, the u-values u(s) are zero for all cells s. 1. s := start cell 2. s’ := a cell adjacent to cell s with a minimal u-value 3. u(s) := 1 + u(s) 4. move the ant robot to cell s’ 5. go to 2

3 1 1 2 2 2 1 2 2 1 1

What do the u-values mean? Where would you move?

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SLIDE 27

Coverage: Node Counting

3 3 1 2 3 1 2 2 1 3 1 2 2 1 1 2 3 1 1 2 2 1 1 2 2 3 1 1 2 2 2 1 2 2 1 1 3 1 2 2 2 2 1 2 2 1 1 1 1 time step 0 time step 1 time step 2 time step 3 time step 4 time step 5 time step 6 time step 7 3 1 2 2 2 2 1 2 2 1 1 1 1

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SLIDE 28

Coverage: Node Counting

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Coverage: Node Counting

  • The u-values coordinate ant robots.

10 20 30 40 50 60 70 80 90 100 1000 2000 3000 4000 5000 6000 Coverage Number Cover Time (steps) Node Counting Random Walk

coverage number cover time random walk Node Counting

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SLIDE 30

Coverage: Node Counting

  • Sharing the u-values coordinates ant robots.

number of ant robots cover time Node Counting with joint u-values Node Counting with individual u-values

5 10 15 200 400 600 800 1000 1200 1400 Node Counting: Shared Markings Node Counting: Individual Markings Time (steps) Number of Robots

1 1 1

1

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SLIDE 31

Real-Time Search Methods

Initially, the u-values u(s) are zero for all cells s. 1. s := start cell 2. s’ := a cell adjacent to cell s with a minimal u-value 3. u(s) := 1 + u(s)

  • r u(s) := 1 + u(s’)
  • r if u(s) ≤ u(s’) then u(s) := 1 + u(s)
  • r u(s) := max(1+u(s), 1+u(s’))

4. move the ant robot to cell s’ 5. go to 2 Node Counting Korf’s LRTA* Wagner’s Rule Thrun’s Rule

3 1 1 2 2 2 1 2 2 1 1

What do the u-values mean? Where would you move?

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SLIDE 32

Structure

  • Motivation
  • Real-time search

– Analytical evaluation – Experimental evaluation

  • Results on real-time search
  • Application to ant robots and results
  • Serious application: smart markers
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SLIDE 33

Real-Time Search Methods

  • From grids to directed graphs

3 1 2 2 3 1 2 2

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SLIDE 34

Real-Time Search Methods

Theorem: Teams of ant robots that all use the same real-time search method cover all strongly connected graphs Proof: repeatedly. QED

The graphs need to be strongly connected:

start

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SLIDE 35

Real-Time Search Methods

  • How fast is the coverage (= cover time) in

the worst case, that is, if an adversary can choose the graph topology, the start vertex and the tie-breaking rule?

– Node Counting: exponential – Korf’s LRTA*: polynomial – Wagner’s Rule: polynomial – Thrun’s Rule: polynomial

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SLIDE 36

number of vertices

cover time (log scale)

Korf’s LRTA* Node Counting 2#vertices/2+1/2-2 cover time guaranteed to be no worse than O(#vertices diameter)

  • n any strongly connected graph

10 100 1000 10000 100000 1e+06 1e+07 1e+08 1e+09 1e+10 1e+11 1e+12 50 100 150 200 250 300 350 400 number of vertices (n)

start

[Koenig and Simmons, 1992] [Koenig and Simmons, 1992]

Real-Time Search Methods

  • strongly connected

directed graphs Node Counting is exponential

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SLIDE 37

Real-Time Search Methods

start

1 we break ties by going “up”

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SLIDE 38

Real-Time Search Methods

start

1 1

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SLIDE 39

Real-Time Search Methods

start

1 1 1

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SLIDE 40

Real-Time Search Methods

start

1 1 2

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SLIDE 41

Real-Time Search Methods

start

1 2 2

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SLIDE 42

Real-Time Search Methods

start

1 1 2 2

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SLIDE 43

Real-Time Search Methods

start

1 1 1 2 2

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SLIDE 44

Real-Time Search Methods

start

1 1 1 2 3

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SLIDE 45

Real-Time Search Methods

start

1 1 1 3 3

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SLIDE 46

Real-Time Search Methods

start

1 1 2 3 3

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SLIDE 47

Real-Time Search Methods

start

1 1 2 3 4

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SLIDE 48

Real-Time Search Methods

start

1 1 2 4 4

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SLIDE 49

Real-Time Search Methods

start

1 2 2 4 4

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SLIDE 50

Real-Time Search Methods

start

1 1 2 2 4 4

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SLIDE 51

Real-Time Search Methods

and so on …

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SLIDE 52

Real-Time Search Methods

start

4 2 8 16 1 4 8 16 1 2 1 4 8 16 1 2

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SLIDE 53

number of vertices cover time (log scale) Node Counting ≥ #verticessqrt((1/6-epsilon)#vertices)

10 100 1000 10000 100000 1e+06 1e+07 1e+08 1e+09 1e+10 1e+11 50 100 150 200 250 300 350 400 number of vertices (n) simulation formula

start Korf’s LRTA* cover time guaranteed to be no worse than O(#vertices diameter)

  • n any strongly connected graph

[Koenig and Simmons, 1992] [Koenig and Szymanski, 1999]

Real-Time Search Methods

  • connected

undirected graphs Node Counting is exponential

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SLIDE 54

Real-Time Search Methods

  • connected

undirected graphs with bounded degree Is is unknown whether Node Counting is polynomial Node Counting Korf’s LRTA* cover time guaranteed to be no worse than O(#vertices diameter)

  • n any strongly connected graph

[Koenig and Simmons, 1992]

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SLIDE 55

Real-Time Search Methods

  • connected

undirected grids Is is unknown whether Node Counting is polynomial Node Counting Korf’s LRTA* cover time guaranteed to be no worse than O(#vertices diameter)

  • n any strongly connected graph

[Koenig and Simmons, 1992]

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SLIDE 56

Structure

  • Motivation
  • Real-time search

– Analytical evaluation – Experimental evaluation

  • Results on real-time search
  • Application to ant robots and results
  • Serious application: smart markers
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SLIDE 57

Real-Time Search Methods

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SLIDE 58

Real-Time Search Methods

  • How fast is the coverage on average?

number of ant robots cover time

Node Counting Korf’s LRTA* Wagner’s Rule Thrun’s Rule

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SLIDE 59

Real-Time Search Methods

  • How even is the coverage on average?

Node Counting Korf’s LRTA* Wagner’s Rule Thrun’s Rule

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SLIDE 60

Structure

  • Motivation
  • Real-time search
  • Results on real-time search

– Analytical evaluation – Experimental evaluation

  • Application to ant robots and results
  • Serious application: smart markers
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SLIDE 61

Real Robots and Simulations

  • Ant robots that use Node Counting are

easy to implement.

trail generation

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SLIDE 62

Real Robots and Simulations

  • Ant robots that use Node Counting are

easy to implement.

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SLIDE 63

Real Robots and Simulations

  • Ant robots that use Node Counting are

easy to implement.

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SLIDE 64

Real Robots and Simulations

  • Ant robots that use Node Counting are

easy to implement.

4 4 4 4 4 7 2

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SLIDE 65

Real Robots and Simulations

  • Ant robots that use Node Counting are

easy to implement.

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SLIDE 66

Real Robots and Simulations

  • Ant robots that use Node Counting are

easy to implement.

4 4 4 4 4 4 7 2

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SLIDE 67

Real Robots and Simulations

  • Ant robot hardware: Pebbles III

A: trail sensor, B: trail sensor, C: pen, D: micro-controller, E: RS232 interface

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SLIDE 68

Real Robots and Simulations

  • Ant robot software: schema-based navigation
  • bstacle-avoidance behavior; trail-avoidance behavior
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SLIDE 69

Real Robots and Simulations

  • Ant robot software: importance of time delays
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SLIDE 70

Real Robots and Simulations

  • Empirical results
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SLIDE 71

Real Robots and Simulations

  • Empirical results
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SLIDE 72

Real Robots and Simulations

  • Our ant robots cover closed terrain even if

– they don’t know the terrain in advance; – some ant robots fail; – some ant robots are moved without realizing this; – some trails are destroyed.

destroyed area of trails low-intensity trails

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SLIDE 73

Real Robots and Simulations

  • The terrain gets saturated with trails over

time.

end of first coverage end of third coverage

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SLIDE 74

Real Robots and Simulations

Initially, the u-values u(s) are zero for all cells s. 1. s := start cell 2. s’ := a cell adjacent to cell s with a minimal u-value 3. u(s) := 1 + u(s) 4. move the ant robot to cell s’ 5. go to 2 4 4 4 4 4 7 2

drop a drop of ink into a randomly chosen small cell in this large cell increase the u-value of this large cell by one with probability (16-0)/16

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SLIDE 75

Real Robots and Simulations

Initially, the u-values u(s) are zero for all cells s. 1. s := start cell 2. s’ := a cell adjacent to cell s with a minimal u-value 3. with probability (170-u(s))/170 do: u(s) := 1 + u(s) 4. move the ant robot to cell s’ 5. go to 2 4 4 4 4 4 7 2

drop a drop of ink into a randomly chosen small cell in this large cell increase the u-value of this large cell by one with probability (16-0)/16

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SLIDE 76

Real Robots and Simulations

10 20 30 40 50 60 70 80 90 100 500 1000 1500 2000 2500 3000 Coverage Number Cover Time (minutes) Modified Node Counting TeamBots Simulation of Pebbles TeamBots Simualtion of Random Walk 1 TeamBots Simualtion of Random Walk 2 Cover Time (steps) 20000 16666 13333 10000 3333 6666

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SLIDE 77

Real Robots and Simulations

10 20 30 40 50 60 70 80 90 100 500 1000 1500 2000 2500 3000 Coverage Number Cover Time (minutes) Modified Node Counting TeamBots Simulation of Pebbles TeamBots Simualtion of Random Walk 1 TeamBots Simualtion of Random Walk 2 Cover Time (steps) 20000 16666 13333 10000 3333 6666

random walk modified Node Counting coverage number cover time There is a really interesting suggested explanation for the peak.

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SLIDE 78

Real Robots and Simulations

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SLIDE 79

Real Robots and Simulations

  • The terrain gets saturated with trails over
  • time. We can avoid this by

– letting the trails evaporate

  • but the evaporation rate depends on the terrain size

– removing the trails (via cleaning)

  • but we need to avoid odd behaviors

– e.g. one robot repeatedly turning around forever – e.g. one robot following another robot forever

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SLIDE 80

Real Robots and Simulation

trail generation trail removal trail removal

  • We chose to remove the trails.
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SLIDE 81

Real Robots and Simulators

10 ant robots in a 25 by 25 meter terrain

  • 85 hours without any ant robot getting

stuck in a realistic robot simulator

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SLIDE 82

Real Robots and Simulators

  • 85 hours without any ant robot getting

stuck in a realistic robot simulator

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SLIDE 83

Real Robots and Simulators

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SLIDE 84

Real Robots and Simulations

10 20 30 40 50 60 70 80 90 100 500 1000 1500 2000 2500 3000 Coverage Number Cover Time (minutes) Modified Node Counting TeamBots Simulation of Pebbles TeamBots Simualtion of Random Walk 1 TeamBots Simualtion of Random Walk 2 Cover Time (steps) 20000 16666 13333 10000 3333 6666

coverage number cover time

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SLIDE 85

Real Robots and Simulations

10 20 30 40 50 60 70 80 90 100 50 100 150 200 250 300 350 400 450 500 Cover Time (minutes) Coverage Number TeamBots Simulation of Pebbles with Cleaning TeamBots Simulation of Pebbles without Cleaning

coverage number cover time without trail removal with trail removal

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SLIDE 86

Real Robots and Simulations

500 1000 1500 2000 2500 3000 3500 4000 200 400 600 800 1000 1200 1400 1600 1800 Terrain Size (m

2)

Cover Time (minutes)

cover time terrain size

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SLIDE 87

Real Robots and Simulations

cover time number of ant robots

5 10 15 10 20 30 40 50 60 70 80 90 Number of Ant Robots Cover Time (minutes)

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SLIDE 88

Structure

  • Motivation
  • Real-time search
  • Results on real-time search
  • Application to ant robots and results

– Analytical evaluation – Experimental evaluation

  • Serious application: smart markers
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SLIDE 89

Motivating Toy Task

  • Guarding a museum at night?

– Why contaminate the terrain with trails?

  • People might slip.
  • The trails might be toxic.
  • The trail substance might be expensive.

– Why not simply use a system of cameras?

  • See whether you can come up with a good

application in the following. We use search and rescue after an earthquake.

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SLIDE 90

Smart Markers

small infrared transceivers (eventually about 1 dollar each) Robots are now localized with respect to the closest transceiver. We don’t avoid the localization problem, we solve it!

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SLIDE 91

Isolated Smart Markers

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SLIDE 92

Isolated Smart Markers

  • A robot always moves in the direction in

which the closest smart marker has been left the smallest number of times (= Edge Counting = Edge Ant Walk).

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SLIDE 93

Edge Counting

4 5 4 5 5 5

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SLIDE 94

Edge Counting

  • The worst-case cover time of Edge Counting is

exponential on strongly connected graphs. (The example is similar to the one for Node Counting.) It is at most #edges × diameter movements on undirected or Eulerian graphs, including grids. [Koenig]

start

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SLIDE 95

Networks of Smart Markers

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Networks of Smart Markers

  • A robot always moves in the direction in

which there is no smart marker yet (= Greedy Mapping).

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SLIDE 97

Greedy Mapping

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SLIDE 98

Greedy Mapping

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SLIDE 99

Greedy Mapping

  • The worst-case cover time of Greedy Mapping is Ω((log

#vertices / log log #vertices) #vertices) and O(#vertices log #vertices) movements on undirected connected vertex-blocked graphs, even on grids. [Tovey et. al.]

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SLIDE 100

Further Information

  • This was a short version of the tutorial on

ant robotics. Additional information about my own research on ant robotics can be found at:

idm-lab.org/project-b.html.

  • Thank you!