Penn Engineering GRASP Laboratory General Robotics,Automation, - - PowerPoint PPT Presentation

Adaptive Distribution of a Swarm

• f 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

Collaborative Perception

One robot type cannot cater to all aspects of a task

an

ell

Collaborative Manipulation

Idea: A task needs certain capabilities

Approach

Robot community

• Species
• Binary traits

tasks trait abundance trait distribution Tasks

• Need traits
• Switching

Problem Formulation

Redistribution of traits (capabilities) among tasks

initial target

How do we redistribute a heterogeneous team of robots?

System

traits species

Y(t) = X(t) · Q

trait distribution robot distribution species-traits matrix

Method

dx(s) dt = K(s)x(s)

— for a large number of robots, model system as ODE

K(s)

— transition rates for each species

Y(t) =

S

• s=1

eK(s)⋆tx(s) · q(s)

— solution to the ODE

Y(t) = X(t) · Q

— system

Method

E = Y⋆ −

S

• s=1

eK(s)⋆τx(s) · q(s)

minimize J (1) = ∥ E ∥2

F

— error in trait distribution — basic optimization problem

minimize J (2) = J (1) + ατ 2

— explicit opt. of convergence time — reinforcing steady-state

1. 2.

• 3. minimize J (3) = J (2) + β PS

s=1

• eK(s)τx(s)

− eK(s)(τ+ν)x(s)

• 2

2

Example

1 2 3 4 5 6 7 8

initial target

• Distrib. of trait 2
• Distrib. of trait 4
• Distrib. of trait 3
• Distrib. of trait 1

trait 1 trait 2 trait 3 trait 4

Experiment

initial target

* Work submitted to ICRA 2016

Movie

submitted to ICRA 2016

Continuous Optimization

K(s)⋆, τ⋆ = argmin

K(s),τ

J (3) K(s)⋆(t), τ⋆(t) = argmin

K(s),τ

˜ J (3)(X(tp))

(X(tp))

⎨

Fixed K: Adaptive K:

Results

µ(Y)

• Mic. Fixed-NC
• Mic. Adapt.-NC
• Mac. Fixed-NC

Ratio of misplaced traits Time [s] Macroscopic Adaptive Micro. Fixed Micro.

Approach

initial target

How hard is it to redistribute the robot community as a function

• f its diversity?

Effects of Diversity

If rank(Q) < S, t

If rank(Q) = S, o

All species are independent There are dependent species

Effects of Diversity

Fixed-C Fixed-NC Adapt.-NC

If rank(Q) < S, t

If rank(Q) = S, o

Time to convergence [s] B e n c h m a r k F i x e d A d a p t i v e B e n c h m a r k F i x e d A d a p t i v e

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