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1. Collective Transport in Autonomous Multi-Robot Systems
ALGORITHMS, ANALYSIS &APPLICATIONS GANESH P KUMAR Advisor:
Prof. Spring Berman 1
2. Motivation Pheeno Robots Search & Rescue Construction
Robot team transports heavy payload No GPS or prior information
about environment Robots sense and communicate within limited range
2
3. Novel Contributions Modelled collective transport in A.
cockerelli as a Stochastic Hybrid System (SHS) Designed a
stochastic controller for multi-robot boundary coverage Robust to
environmental variations May be made to mimic A. cockerelli
behaviour Computed statistical properties of multi-robot
configurations around single boundary Devised fast algorithm for
sampling saturated configurations 3
4. Outline Model collective transport in Desert Ant A.
Cockerelli Design stochastic controller to allocate robots around
boundaries Analyze properties of stochastic multi-robot
configurations around single boundary Future Work 4
5. Modelling Collective Transport in A. cockerelli HSCC 2013
5
6. pSHS : Behavioural Model FrontBack Detached F BD , , , State
vector = , , , , Behavioural states S = , , = population in state
Dynamical variables , Flow Equation = 0 0 0 6 reactions : in
Chemical Reaction Network 6
7. pSHS : Dynamical Model Front and back ants lift with net
force Net normal force = Front ants pull with proportional velocity
regulation = ( ) LOAD Fup = + Load Dynamics = = 7
10. Achieve target allocation of robots around disks at steady
state Robots: Perform correlated random walks Local sensing and
communication Can identify whether another robot is bound or
unbound Disks: Randomly distributed throughout environment Each
type requires a different target robot group size Example: 3 robots
per type-1 disk 1 robot per type-2 disk Problem Statement 10
12. Macroscopic Model Equilibrium Allocation ODEs 12
13. Statistical Analysis of Stochastic Boundary Coverage ICRA
2014 IEEE-Trans. On Robotics (Submitted) 2015 0 = 0 +1 = 1 2
13
14. Saturation dist Boundary of length identified with I 0,
robots each of radius attach randomly to boundary Configuration is
saturated iff all distances above are bounded above by = 0 =
14
15. ProblemStatement dist Given Quadruple = (, , , ) Define
random configuration. Compute probability of saturation . Compute
pdfs of robot positions and inter-robot distances for random
configurations. for random saturated configurations. = 0 = 15
16. SaturationforPointrobots 0 = 0 +1 = 1 2 Point robots have =
0 Random configuration: robots attach to boundary uniformly
randomly and independently Sort robot positions fixing two
artificial robots at end- points, creating = t1, , and 0:+1 16
17. PositionSimplex 0 = 0 3 = 1 2 samples from the th order
statistic of a uniform parent pdf can be considered a point in
Valid configurations form the position simplex { : :+} = = 0 T =
17
18. ConceptofSlack 18 1 2 Define th slack as 1 Collect all
slacks in slack vector 1 +1 T For any configuration, the sum of
slacks equals : = 3
19. Simplex-Hypercube Intersection 19 Valid slack vectors form
a slack simplex +1 { : = } Saturated slack vectors form a hypercube
+1 { : } Define favourable region by 1 2 2 1 2 2 2: 0 1, 2 1 + 2 =
1 (, 0) (0, ) ( , ) (, )
20. Computing We have Using Inclusion Exclusion Principle, we
have Here = is the maximum number of -separated robots that can
attach to boundary Positions and slacks have scaled Beta pdfs:
20
21. Small andLarge cases 1 = 2 = 2 = We need to determine PDFs
of robot positions and slacks under saturation Define 3 parameters
for (, , = 0, ): : = = max number of -separated robots = last slack
in such a configuration , if 0 + 1, if = 0 = remaining number of
robots +1 = more robots need to be placed 21
22. Small andLarge cases If = 0, then no more robots need to be
placed There are just enough robots to saturate This is the small
case (: 1, : 2, : 0, : 0.4) with = 2, = 0.2, = 0 If > 0, we have
the large case (: 1, : 2, : 0, : 0.6) with = 1, = 0.4, = 1 22
23. Saturationforsmall forms a regular simplex, with vertices
along the columns of: +1 (, : 0.2, : 0, : 2) 23
24. Large case Now we have = + robots to place Now is a convex
polytope with cospherical vertices Unlike in small case, no
analytic expression for pdfs of saturated slacks and positions
24
25. Shape of Vertices are permutations of Pyramids are formed
by adjoining centroid to facets Vertices of Base facets have zeros
at identical locations Vertices of Connecting facets do not (: 1, :
0.6, : 0, : 2) 25
26. GEOMSAMP Given , , = , , sample a random saturated slack
vector Use QuickHull to partition into pyramids Compute = /( ) for
each pyramid Choose a random pyramid with prob. Sample a point from
26
27. REPSAMP: SamplingusingRepresentatives Address large case
using results from small case Choose a saturated configuration of +
1 representatives This represents a sample from Corresponds to the
+ 1 nonzero elements in every vertex Choose intermediates randomly
Saturation condition remains invariant! 1 2 +1 1 2 +1 Hollow
circles are intermediates 0 27
28. Future Work 28
29. Pheeno Robot Developed as component of collective transport
testbed Differentially driven base, with R-P-R manipulator arm and
1 DOF gripper RPi Model B+ directing an Arduino Micro Pro RPi
camera, IR Sensors, Wi-fi Adapter, LEDs 29 Total cost ~ $400
30. Timeline 30 Complete internship at Mayfield Robotics by
15th Aug Implementing and serializing random attachment algorithm
using Pheenos (by 30th Sep) Submit journal paper by 31st Oct Visual
servoing for manipulation (Late fall) Dissertation Writing (from
1st Nov) Final Defence (by late January 2016)