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Adaptive Distribution of a Swarm of Heterogeneous Robots Amanda Prorok, M. Ani Hsieh, Vijay Kumar Workshop on On-line decision-making in multi-robot coordination IROS 2015 Penn Engineering GRASP Laboratory General Robotics,Automation, Sensing & Perception Lab

Introduction How do we design heterogeneous multi-robot systems to maximize performance? Diversity Metric Design Paradigm * * Image credits: M. Egerstedt, Georgia Tech

Examples One robot type cannot cater to all aspects of a task Collaborative Perception Collaborative Manipulation an ell Idea: A task needs certain capabilities

Approach Robot community Tasks • Species • Need traits • Binary traits • Switching trait abundance trait distribution tasks

Problem Formulation How do we redistribute a heterogeneous team of robots? initial target Redistribution of traits (capabilities) among tasks

System Y ( t ) = X ( t ) · Q trait robot species-traits distribution distribution matrix traits species

Method d x ( s ) — for a large number of robots, = K ( s ) x ( s ) model system as ODE d t K ( s ) — transition rates for each species Y ( t ) = X ( t ) · Q — system S e K ( s ) ⋆ t x ( s ) � · q ( s ) — solution to the ODE Y ( t ) = 0 s =1

Method S E = Y ⋆ − e K ( s ) ⋆ τ x ( s ) � · q ( s ) — error in trait distribution 0 s =1 J (1) = ∥ E ∥ 2 minimize — basic optimization problem 1. F J (2) = J (1) + ατ 2 minimize — explicit opt. of convergence time 2. 2 � � � e K ( s ) τ x ( s ) − e K ( s ) ( τ + ν ) x ( s ) 3. minimize J (3) = J (2) + β P S � � 0 0 s =1 � 2 — reinforcing steady-state

Example 3 2 4 1 5 8 6 7 initial target trait 1 trait 2 trait 3 trait 4 8 Distrib. of trait 4 Distrib. of trait 1 Distrib. of trait 3 Distrib. of trait 2 3 7 6 5 2 1 4

Experiment initial target * Work submitted to ICRA 2016

Movie submitted to ICRA 2016

⎨ Continuous Optimization K ( s ) ⋆ , τ ⋆ = argmin J (3) Fixed K: K ( s ) , τ ˜ K ( s ) ⋆ ( t ) , τ ⋆ ( t ) J (3) ( X ( t p )) Adaptive K: = argmin K ( s ) , τ ( X ( t p ))

Results Mic. Fixed-NC Macroscopic Ratio of misplaced traits Mic. Adapt.-NC Adaptive Micro. Mac. Fixed-NC Fixed Micro. µ ( Y ) Time [s]

Approach How hard is it to redistribute the robot community as a function of its diversity ? initial target

Effects of Diversity If rank( Q ) = S , o If rank( Q ) < S , t All species are independent There are dependent species

Effects of Diversity If rank( Q ) = S , o If rank( Q ) < S , t Time to convergence [s] Fixed-C Fixed-NC Adapt.-NC e e k k d d v v r r e e a i a i t t x p x m p m i i F a F a h h d d c c A A n n e e B B

Conclusions • Model for heterogeneous robot system • Efficient optimization algorithm • Formulation for adaptive control • Real robot experiments • Effects of diversity Further work: • Automatic generation of task requirements • Continuous trait instantiations • Foundations of diversity

Thank you for your attention. prorok@seas.upenn.edu Penn Engineering GRASP Laboratory General Robotics,Automation, Sensing & Perception Lab