Distributed Iterative Learning Control for a Team of Quadrotors - - PowerPoint PPT Presentation

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Distributed Iterative Learning Control for a Team of Quadrotors - - PowerPoint PPT Presentation

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Distributed Iterative Learning Control for a Team of Quadrotors Andreas Hock, Angela P. Schoellig 13 December 2016 Motivation dis isturbances! tim ime delays! Source: www.itsinternational.com model Source: www.kuka.com mis ismatches!

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SLIDE 1

Distributed Iterative Learning Control for a Team of Quadrotors

Andreas Hock, Angela P. Schoellig

13 December 2016

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SLIDE 2

Motivation

2 Andreas Hock

Le Learnin ing can make mult lti-robot coordin inatio ion more accurate or faster, , and en enable le it it to adapt to ch changin ing tasks or en envir ironment!

Source: www.itsinternational.com Source: www.kuka.com

model mis ismatches! tim ime delays! dis isturbances!

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SLIDE 3

Dis istributed IL ILC fo for r a Team of f Quadrotors

Dis istr tributed Control:

3 Andreas Hock

  • No central control unit
  • Autonomous agents
  • Communication only between certain neighbors

Ite Iterative Le Learning Control (IL (ILC):

  • Machine Learning technique
  • Learning by repetition
  • Updating the feedforward input based on past

measurements Team of f Quadrotors:

  • Goal: synchronous formation flying
  • Homogeneous LTI dynamics
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SLIDE 4

theoretic ical l develo lopment of advanced IL ILC alg lgori rithms for r mult lti-agent systems (M (MAS) S) & exp xperim imental l im imple lementatio ion

Pro roble lem Form rmulation

4 Andreas Hock

Rela lated Work rk Open Proble lems There exist several studies on…

  • ILC for a sin

single le agent:

  • theoretic survey [Bristow, 2006]
  • quadrotor vehicle [Schoellig, 2012]
  • mult

lti-agent ILC: [Ahn, 2009; Meng, 2012; Yang, 2012]

  • previous stability proofs for multi-agent ILC restricted to

D-type learning functions => cannot compensate for position offsets

  • pure feedforward control

=> cannot compensate for non-repetitive errors

  • no experimental validation so far
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SLIDE 5

Andreas Hock 5

Dis istributed IL ILC fo for r MAS – Algorithm

[Arimoto, 1984] [Ahn, 2009]

so so far r inp input update for r mult lti-agent IL ILC C only ly based on err rror r deriv rivativ ive

restrictive, limited design parameters position offsets can not be compensated where L can be an arbitrary linear mapping in discrete time!

New Input = = Old ld Input + + Corr rrecting Actio ion, depending on error in last trial Id Idea of f ILC ILC :

Use se er error inf informatio ion to to im improve fe feedforward inp input fo for su subsequent ite iteratio ions! Goal: l: synchronous reference tr trackin ing

agent i iteration k

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SLIDE 6

Andreas Hock 6

Dis istributed IL ILC fo for r MAS – Proof of Stability

Li Lifted System Representation

[Bri [Bristow, 2006] ]

  • IL

ILC stabili ility an anal alysis in in dis iscrete tim time

  • tim

time sam sample les => => fu full ll tr trajectory ry vectors

Graph Theoretic ical Definitions

[Y [Yang, 2012]

  • Con
  • ncept of
  • f graph Lap

Laplacia ian LG

  • Reference as

as vir irtu tual l le lead ader nod

  • de =>

=> B

  • Single agents’ states => full MAS state

Theorem 1: 1:

The multi-agent ILC is as asymptotic icall lly stable le if and only if . For causal learning, this holds iff . Graph Information with eigenvalues System Dynamics , Learning Function , w/ diagonal entries crucial design parameter

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SLIDE 7

Pure IL ILC IL ILC C with ith Feedback

COMPARISON Feedback Con

  • ntrol

(Co (Consensus) IL ILC IL ILC + + Con

  • nsensus

s Feedback learn from tr trac ackin ing erro errors compensate for non non- rep repetitiv ive erro errors incorporate rep repetitiv ive di disturb rbances

Andreas Hock 7

Dis istributed IL ILC fo for r MAS – Combination with Consensus Feedback Control

COMPARISON Feedback Con

  • ntrol

(Co (Consensus) IL ILC learn from tr trac ackin ing erro errors rs compensate for non non- rep repetitiv ive erro errors incorporate rep repetitiv ive di disturb rbances

Theorem 2: 2:

A time domain feedback term with linear mapping C

C ,does not affect

stability of the proposed ILC system! NE NEW!

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SLIDE 8

Andreas Hock 8

Experimental Result lts

Link to Video

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SLIDE 9

Andreas Hock 9

Experimental Result lts - Trajectories in x over time

v2 v1 xd

fee eedback reaction dela layed an and attenuated IL ILC compensates dela lays an and corrects err rrors alm lmost perfect tr trackin ing can an be ach achieved

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SLIDE 10

Andreas Hock 10

Experimental Result lts - Error Convergence Comparison

lower formati tion err error in in the the fir first it iter erati tions s can an help lp avoid id col

  • llis

lisions accountin ing for non

  • n-repetitive

dis isturbances im improves performance aft fter le lear arnin ing

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SLIDE 11

Andreas Hock 11

Conclu lusion

Generali lized stabil ilit ity proof demonstrated that the multi-agent ILC algorithm converges if l0 is chosen properly => many tuning options for input-update rule We proved that including a consensus feedback controll ller r does not affect stability but improves performance as it compensates for non-repeating disturbances Multi-agent ILC was successfully implemented on a real l exp xperim iment for the first time

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SLIDE 12

Andreas Hock 12

Experimental Result lts – Experiment with four quadrotors

Link to Video

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SLIDE 13

Andreas Hock 13

Conclu lusion

Generali lized stabil ilit ity proof demonstrated that the multi-agent ILC algorithm converges if l0 is chosen properly => many tuning options for input-update rule We proved that including a consensus feedback controll ller r does not affect stability but improves performance as it compensates for non-repeating disturbances Multi-agent ILC was successfully implemented on a real l exp xperim iment for the first time

andreas.hock@robotics.utias.utoronto.ca

Andreas Hock

www.DynSysLab.org Thank you!