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On the control of a multirobot system for an elastic hose Zelmar - - PowerPoint PPT Presentation

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On the control of a multirobot system for an elastic hose Zelmar Echegoyen, Alicia dAnjou, Manuel Graa Computational Intelligence Group, Universidad del Pais Vasco www.ehu.es/ccwintco ICONIP 2008, Auckland New Zealand, november 26, 2008

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ICONIP 2008, Auckland New Zealand, november 26, 2008

On the control of a multirobot system for an elastic hose

Zelmar Echegoyen, Alicia d’Anjou, Manuel Graña Computational Intelligence Group, Universidad del Pais Vasco www.ehu.es/ccwintco

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ICONIP 2008, Auckland New Zealand, november 26, 2008

Contents

  • Motivation
  • Hose model
  • Basic multirobot centralized control

problem

  • Introducing the internal dynamics
  • Further and on-going work
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ICONIP 2008, Auckland New Zealand, november 26, 2008

Motivation

  • Hoses are quite common in construction sites:

– Shipyards – Building sites

  • They transport

– Water – Power – Air – Fluids of other kind

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ICONIP 2008, Auckland New Zealand, november 26, 2008

Motivation

  • Problem statement

– Design of a control strategy for a multirobot system composed of a collection of cooperative robots manipulating the hose

  • Desired features

– Distributed: the local decisions are based on local knowledge – Self-sensing: able to determine its actual configuration – Adaptive: able to perform under uncertain and new environmental conditions

  • Able to sense the environment
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ICONIP 2008, Auckland New Zealand, november 26, 2008

Motivation

  • Long term research plan

– Assuming global perfect knowledge

  • Model hose dynamics
  • Derive adaptive control rules

– Assuming perfect local knowledge

  • Model local hose dynamics
  • Local control rules

– Incorporate communication noise – Incorporate local sensing

  • Integrate local models from uncertain local and remote sensing

information

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ICONIP 2008, Auckland New Zealand, november 26, 2008

Motivation

  • Scope of the paper

– Introducing the geometrical model of the hose – Giving an adaptive rule for configuration modification

  • Based on global knowledge
  • Without taking into account internal dynamics

– Giving some hints about the introduction of the internal dynamics in the system model

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ICONIP 2008, Auckland New Zealand, november 26, 2008

Contents

  • Motivation
  • Hose model
  • Basic multirobot centralized control

problem

  • Introducing the internal dynamics
  • Further and on-going work
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ICONIP 2008, Auckland New Zealand, november 26, 2008

Hose geometrical modeling

  • Splines

– Give a continuous description along the unidimensional object – Geometrically Exact Dynamic Splines (GEDS)

  • Accounts for the rotation of the hose at each point
  • Exhaustive and rigorous mechanical analysis exist

for this kind of systems.

– Def: piecewise polynomial functions

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ICONIP 2008, Auckland New Zealand, november 26, 2008

Hose geometrical modeling

  • Splines: a set of

control points are parameters of the curve

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ICONIP 2008, Auckland New Zealand, november 26, 2008

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ICONIP 2008, Auckland New Zealand, november 26, 2008

Hose geometrical modeling

  • We assume

– Constant section diameter – Transversal sections not deformed – No internal dynamics in the initial model

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ICONIP 2008, Auckland New Zealand, november 26, 2008

  • GEDS model

– The hose is described by a collection of traversal sections

  • centers
  • orientations
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ICONIP 2008, Auckland New Zealand, november 26, 2008

Hose geometrical modeling

  • The spline model
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ICONIP 2008, Auckland New Zealand, november 26, 2008

Contents

  • Motivation
  • Hose model
  • Basic multirobot centralized control

problem

  • Introducing the internal dynamics
  • Further and on-going work
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ICONIP 2008, Auckland New Zealand, november 26, 2008

Basic control

  • Goal: to give an adaptive rule for the

transition between hose configurations

  • No internal dynamics
  • Spline model
  • Robots placed at regular intervals along the

hose

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ICONIP 2008, Auckland New Zealand, november 26, 2008

Basic control

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ICONIP 2008, Auckland New Zealand, november 26, 2008

Basic control

  • Derivative of hose points relative to control

points

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ICONIP 2008, Auckland New Zealand, november 26, 2008

Basic control

  • Dynamic dependence of individual robot

speed on the variation of the spline control points

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ICONIP 2008, Auckland New Zealand, november 26, 2008

Basic control

  • Objective function: distance between actual

and desired control point positions

  • Minimized by gradient descent
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ICONIP 2008, Auckland New Zealand, november 26, 2008

Basic control

  • Let it be u(t) the position of the spline

control point

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ICONIP 2008, Auckland New Zealand, november 26, 2008

Basic control

  • The multi robot dynamics that move the

hose to the desired configuration is given by

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ICONIP 2008, Auckland New Zealand, november 26, 2008

Contents

  • Motivation
  • Hose model
  • Basic multirobot centralized control

problem

  • Introducing the internal dynamics
  • Further and on-going work
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ICONIP 2008, Auckland New Zealand, november 26, 2008

Internal dynamics

  • The relationship between the external and

the internal forces is given by eq.

  • F : external forces
  • U: hose potential energy
  • T: kinetic energy
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ICONIP 2008, Auckland New Zealand, november 26, 2008

Internal dynamics

  • External forces

– Fs streching force – FT tension torque – FB curve torque

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ICONIP 2008, Auckland New Zealand, november 26, 2008

Internal dynamics

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ICONIP 2008, Auckland New Zealand, november 26, 2008

Internal dynamics

  • Potential energy
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ICONIP 2008, Auckland New Zealand, november 26, 2008

Internal dynamics

  • Kinetic energy

Inertial matrix

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ICONIP 2008, Auckland New Zealand, november 26, 2008

Internal dynamics

  • We arrive to a matrix expression of the external

forces needed to reach the desired configuration

where

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ICONIP 2008, Auckland New Zealand, november 26, 2008

Contents

  • Motivation
  • Hose model
  • Basic multirobot centralized control

problem

  • Introducing the internal dynamics
  • Further and on-going work
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ICONIP 2008, Auckland New Zealand, november 26, 2008

On going work

  • Integrate the internal dynamics into the

basic multirobot control

  • Development of simulation models
  • Design of physical realizations

– Gripping – Sensing: the hose and the environment – Communication

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ICONIP 2008, Auckland New Zealand, november 26, 2008

Further work

  • Design of the decentralized control system
  • Design cooperative sensing strategies
  • Design of experimental settings and tasks
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ICONIP 2008, Auckland New Zealand, november 26, 2008

  • Thanks for your attention