MAE 598: Multi-Robot Systems Fall 2016 ! Instructor: Spring Berman - PowerPoint PPT Presentation

MAE 598: Multi-Robot Systems Fall 2016 ! Instructor: Spring Berman spring.berman@asu.edu Assistant Professor, Mechanical and Aerospace Engineering Autonomous Collective Systems Laboratory http://faculty.engineering.asu.edu/acs/ Lecture 5

Microscopic Model: Task Switching k ij = f ( c ij ) c ij = Prob( a"par%cular"combina%on"of"reactants"in"the"reac%on" associated"with" k ij will react ) per timestep Δ t 3 Spontaneous Interac-on.dependent task i task j k ij enc ⋅ c ij react Tunable ! c ij Tunable ! c ij = c ij Robot"executes"transi%on"with" Robot"encounters"poten%al"reactant" probability""""""""""""""at"each" Δ t " c ij Δ t in"next" Δ t with"probability" """"","executes"transi%on"with" enc Δ t c ij react probability"" c ij """""" ASU MAE 598 Multi-Robot Systems Berman 2 "

Modeling Approach Species populations (integers) Chemical Master Equation Time-evolution equation for Mesoscopic model c ij dt [Gillespie, Annu. Rev. Phys. Chem. ’07] Microscopic model N elements, Directed"graph" S species Adjacent"complexes:

Modeling Approach Species populations (integers) Numerical realizations of N ( t ) using a Stochastic Simulation Algorithm [Gillespie, J. Comp. Phys. 1976] Macroscopic model [Gillespie, Annu. Rev. c ij dt Phys. Chem. ’07] Microscopic model N elements, Directed"graph" S species Adjacent"complexes:

Modeling Approach Species"concentra%ons;"" ! E ( N ( t )/ V ) Linear3model3 3 3 3 3 3Mul-.affine3model ! T x = c i , i = 1,.., S − rank ( S ) c i only ! ="Vector"of"complexes ! Macroscopic model Thermodynamic"limit ! N i →∞ , V →∞ , N i / V finite Mesoscopic model

Top-Down Controller Synthesis ! Analysis :"establish" ! Controller synthesis : theore%cal"guarantees"on" """" Design"rate"constants" k ij performance" Macro- scopic model Broadcast k ij Decentralized robot control policies based on c ij that produce desired collective behavior Microscopic model

Analysis of Macroscopic Model Equilibria3characteriza-on3 Equilibrium ! 333 Model"must"have"a"unique,"posi%ve," asympto%cally"stable"equilibrium" (="final"swarm"popula%on"distribu%on)"" !!! ! ! Chemical Reaction Network Theory • General network topology, mass action kinetics: M. Feinberg, F. Horn, R. Jackson (1970’s, 1980’s) • More restricted topology, monotone kinetics: E. Sontag, D. Angeli, P. de Leenheer (2000’s) ! Algebraic Graph Theory ! Lyapunov Stability Theory ASU MAE 598 Multi-Robot Systems Berman 7

Hybrid System Macroscopic Models • 3Reachability3analysis3 333 Algorithms"for"systems"with"mul%Jaffine"dynamics" """ [Berman, Halász, Kumar HSCC’07] ˙ x = M 1 K 1 y ( x ) unstable x = M 2 K 2 y ( x ) ˙ 8 U ! stable ASU MAE 598 Multi-Robot Systems Berman 8

Reallocation of a Swarm among Multiple Sites [Berman, Halász, Hsieh, Kumar, IEEE Trans. on Robotics 2009] Develop a strategy for redistributing a swarm of robots among multiple sites in specified population fractions to perform tasks at each site Applications: - surveillance of multiple buildings - search-and-rescue - reconnaissance - environmental monitoring - construction ASU MAE 598 Multi-Robot Systems Berman 9

Required Robot Controller Properties Synthesize robot controllers that: - can be computed a priori by an external supervisor - are based on a set of parameters that are independent of swarm size - do not require inter-robot communication - have provable guarantees on performance - can be optimized for fast convergence to the desired allocation among sites, with a constraint on robot traffic between sites - require minimal adjustments when task demands change ASU MAE 598 Multi-Robot Systems Berman 10

Objective • Develop a strategy for redistributing a swarm of robots among multiple sites in specified fractions ASU MAE 598 Multi-Robot Systems Berman 11

Objective • Develop a strategy for redistributing a swarm of robots among multiple sites in specified fractions 0.08 0.08 0.08 0.36 0.08 0.08 0.08 0.08 0.08 ASU MAE 598 Multi-Robot Systems Berman 12

Objective • Develop a strategy for redistributing a swarm of robots among multiple sites in specified fractions ASU MAE 598 Multi-Robot Systems Berman 13

Approach Challenges: Difficult to use centralized control, communication across sites may be risky or impossible " Decentralized decision-making, no communication for control - Promotes scalability , robustness to changes in swarm size - In contrast to coalition-formation algorithms such as market-based approaches Dias et al. , “Market-based Multirobot Coordination: A Survey and Analysis” Proc. IEEE , 2006 # Robots redistribute themselves autonomously by switching stochastically between sites Inspired by social insect behavior, particularly ant house-hunting (select a new nest and move the colony there) Franks et al. , “Information flow, opinion polling and collective intelligence in house-hunting social insects,” Phil. Trans. of the Royal Society B , 2002 Simple rules based on local sensing, physical contact ASU MAE 598 Multi-Robot Systems Berman 14

“House-Hunting” in Temnothorax albipennis Occupy"1" New" Recruit"to"1" site"1" Damaged"nest" Assess"1" Search"" Assess"2" New" Occupy"old"nest" site"2" Recruit"to"2" Occupy"2" (beOer)" Tandem3run3 Transport3 15 Courtesy of Prof. Stephen Pratt, ASU

“House-Hunting” in Temnothorax albipennis Occupy"1" New" 33Site3pop. < q Recruit"to"1" site"1" Damaged"nest" Assess"1" Search"" Assess"2" New" Occupy"old"nest" site"2" Recruit"to"2" 33Site3pop. Occupy"2" ≥ q (beOer)" Tandem3run3 Transport3 16 Courtesy of Prof. Stephen Pratt, ASU

“House-Hunting” in Temnothorax albipennis Occupy"1" New" < q Rates"of"switching" Recruit"to"1" site"1" between"tasks" Damaged"nest" Assess"1" determine"final" alloca%on" Search"" " Assess"2" New" Occupy"old"nest" site"2" Recruit"to"2" Occupy"2" ≥ q k ij = f (site pop ., q ) (beOer)" Tandem3run3 Transport3 33Site3pop. < q 33Site3pop. ≥ q ASU MAE 598 Multi-Robot Systems Berman 17

Microscopic Model Unimolecular3(spontaneous) task i task j k ij Decisions modeled as chemical reactions X i ~3 chemical3species 3 i Rate3constant3 k ij Task i Task j Controllers Y r Y r Y r Y r ⊂ R n ASU MAE 598 Multi-Robot 18 Systems Berman

Macroscopic Model [Franks 2002] Site 0 (home) is destroyed; Site 2 is better than Site 1 Active Ants pN Passive Ants (1 – p ) N θ ( X ) = 1 when X > 0, 0 otherwise ASU MAE 598 Multi-Robot Systems Berman 19

Macroscopic Model: Active Ants Naive Recruiters Assessors 2 µ i = rate of discovery of site i 0 1 ASU MAE 598 Multi-Robot Systems Berman 20

Macroscopic Model: Active Ants Naive Recruiters Assessors 2 k i = rate at which assessors of site i 0 become recruiters to i 1 ASU MAE 598 Multi-Robot Systems Berman 21

Macroscopic Model: Active Ants Naive Recruiters Assessors λ i = rate at which 2 recruiters lead tandem runs to site i 0 [Franks 2002] 1 T = Quorum ASU MAE 598 Multi-Robot Systems Berman 22

Macroscopic Model: Active Ants Naive Recruiters Assessors 2 ρ ij = rate of switching allegiance from site i to 0 site j 1 ASU MAE 598 Multi-Robot Systems Berman 23

Macroscopic Model: Passive Ants φ i = rate at which recruiters perform 2 transports to site i 0 [Franks 2002] 1 T = Quorum ASU MAE 598 Multi-Robot Systems Berman 24

Agreement between macroscopic , mesoscopic, and microscopic models (modified ant house-hunting model) 208 ants Macroscopic Mesoscopic Microscopic Spring Berman, Adam Halasz, Vijay Kumar, and Stephen Pratt, “Bio-Inspired Group Behaviors for the Deployment of a Swarm of Robots to Multiple Destinations” ICRA 2007.

Mesoscopic Model Fluctuations in Recruiter Populations • Effect of population size on steady-state Y 1 , Y 2 : N = 52, 208, 832 Dashed lines are macroscopic steady-state values N = 208: Std dev is < 9% of mean ASU MAE 598 Multi-Robot Systems Berman 26