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Master Project Design and simulation of locomotion of - - PowerPoint PPT Presentation

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Master Project Design and simulation of locomotion of self-organising modular robots for adaptive furniture Rafael Arco Arredondo < rafael.arcoarredondo@epfl.ch > Supervisor: Prof. Auke Jan Ijspeert Biologically Inspired Robotics Group

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SLIDE 1

Master Project Design and simulation of locomotion of self-organising modular robots for adaptive furniture

Rafael Arco Arredondo <rafael.arcoarredondo@epfl.ch> Supervisor: Prof. Auke Jan Ijspeert

Biologically Inspired Robotics Group (BIRG) Swiss Federal Institute of Technology Lausanne (EPFL)

19th July 2006

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 1 / 28

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SLIDE 2

The Roombots project

Development of modular robots for adaptive and self-organising furniture for the new Learning Centre at the EPFL: Design of the prototypes of the modules Control of locomotion Self-reconfiguration User interface (LASA)

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 2 / 28

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SLIDE 3

Overview

Design of the modules (with

  • S. Cevey)

Design of some multi-unit robots (with S. Cevey) Simulation of locomotion

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 3 / 28

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SLIDE 4

Overview

Adaptation to the terrain using reflexes Online optimisation of locomotion

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 3 / 28

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SLIDE 5

Outline

1

Background

2

Design of the modules

3

Control of locomotion

4

Conclusions and future work

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 4 / 28

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SLIDE 6

Outline

1

Background

2

Design of the modules

3

Control of locomotion

4

Conclusions and future work

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 5 / 28

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SLIDE 7

Modular Robotics

Design of complex robots out of simple building blocks (modules): Simplicity Homogeneity Flexibility Reliability Adaptability Low cost Origins in Karl Sims’ creatures (1994)

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 6 / 28

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SLIDE 8

Modular Robotics: examples

M-TRAN (AIST): Conro (USC): Polybot (PARC): YaMoR (BIRG):

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 7 / 28

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SLIDE 9

Control of locomotion with CPGs

Central Pattern Generators are responsible of locomotion in chordates (Grillner, 70’s) Neural networks in the spinal cord which produce the necessary rhythms for locomotion Modulation with simple signals (gait transition, control of amplitude and frequency, adaptation) Successfully applied to Modular Robotics (M-TRAN)

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 8 / 28

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SLIDE 10

Outline

1

Background

2

Design of the modules

3

Control of locomotion

4

Conclusions and future work

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 9 / 28

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SLIDE 11

Characterisation of the modules: requirements and decisions

Requisites the robots must fulfill: Simple control Locomotion Reconfiguration Self-organisation, adaptation Use as real furniture Main design constraints adopted: Homogeneous modules Two orthogonal DOFs Strong attachment mechanisms (no magnets), with 4 orientations (0◦, 90◦, 180◦ and 270◦) Dimensions suitable for furniture Static pieces (e.g. the top of a table) Webots+ODE to model the robots

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 10 / 28

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SLIDE 12

The universal joint module

Two identical boxes linked by a universal joint (two perpendicular DOFs) Each DOF can rotate in [−90◦, +90◦] In principle, 10 attachment points Dimensions: ∼ 24 × 8 × 8 cm (12 × 8 × 8 cm each box)

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 11 / 28

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SLIDE 13

The wheeled module

One big box and one smaller one that has a wheel (inscribed or circumscribed) on one of the faces Two DOFs: one rotates the small box+wheel group on the vertical plane, the other rotates the wheel

  • n the horizontal plane

The small box+wheel can rotate in [−112.5◦, +112.5◦], the wheel rotates freely with no limits 14 attachment points Dimensions: 24 × 8 × 8 cm (16 × 8 × 8 cm the big box, 6 × 8 × 8 cm the small one)

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 12 / 28

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SLIDE 14

Attachments

Hermaphrodite: Male/female: Should:

◮ Be mechanical ◮ Be strong enough to hold the weight of

the structure and a person

◮ Need energy just at the moment of

attaching/detaching, not to be maintained

◮ Ideally be hermaphrodite, although

male/female connectors still offer high flexibility

Use of docking stations To be studied in further work Simulations done with hermaphrodite connectors abstracting mechanical details

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 13 / 28

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SLIDE 15

Multi-unit robots

Pre-defined pieces of furniture: Transient configurations (e.g. during reconfiguration): Fast creation in Webots with the library robot-positioning

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 14 / 28

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SLIDE 16

Multi-unit robots

Pre-defined pieces of furniture:

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 14 / 28

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SLIDE 17

Multi-unit robots

iture:

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 14 / 28

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SLIDE 18

Multi-unit robots

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 14 / 28

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SLIDE 19

Multi-unit robots

configurations (e.g. during

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 14 / 28

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SLIDE 20

Multi-unit robots

during reconfiguration):

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 14 / 28

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SLIDE 21

Outline

1

Background

2

Design of the modules

3

Control of locomotion

4

Conclusions and future work

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 15 / 28

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SLIDE 22

The Matsuoka oscillator

τ ˙ u{e,f } = u0 − u{e,f } + wfey{f ,e} − βv{e,f } τ′ ˙ v{e,f } = y{e,f } − v{e,f } y{e,f } = max(u{e,f }, 0) yosc = yf − ye

connection excitatory vf uf ve ue τ ye = max(ue, 0) wfe u0 u0 yf = max(uf , 0) Extensor neuron Flexor neuron − + yosc β β connection inhibitory τ τ′ τ′

For u0 = 2.05, β = 2.5, τ = 0.13, τ′ = 0.26, wfe = −2.0

1 2 3 4 5 6 7 8 9 10 −1 −0.8 −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8 1 time [s]
  • utput
−1.5 −1 −0.5 0.5 1 1.5 −0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 uf vf

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 16 / 28

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SLIDE 23

Couplings between oscillators

τ ˙ ui,{e,f } = u0 − ui,{e,f } + wfeyi,{f ,e} − βvi,{e,f } +

  • j

wijyj,{e,f } Phase difference between two

  • scillators:

wij i j wji

−1 −0.8 −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8 1 −1 −0.8 −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8 1 w12 w21 1 2 3 4 5 6

Structure of the CPG for the pieces of furniture:

hfl kfr kfl hfr hhr khr hhl khl Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 17 / 28

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SLIDE 24

Exploration of different locomotion gaits

u0 = 2.05, β = 3.0, wfe = −2.0, τ = 0.1, τ′ = 0.3

Gait θfl θhl θfr θhr Walk π 3π/2 π/2 Trot π π Bound π π Pace π π Jump π/2 π/2 Pronk

Trot:

  • 0.4
  • 0.8

fl fr hr hl

  • 0.5

+0.4

  • 0.4
  • 0.8
  • 0.4

+0.4

  • 0.4
  • 0.5

k

  • 0.3
5 10 15 −1 −0.8 −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8 1 time [s]
  • utput
flh hlh flk

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 18 / 28

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SLIDE 25

Exploration of different locomotion gaits

u0 = 2.05, β = 3.0, wfe = −2.0, τ = 0.1, τ′ = 0.3

Gait θfl θhl θfr θhr Walk π 3π/2 π/2 Trot π π Bound π π Pace π π Jump π/2 π/2 Pronk

Walk:

fl fr hr hl k

  • 0.5

+0.5 +0.5

  • 0.5
  • 0.4

+0.8

  • 0.4

+0.8

  • 0.2

+0.2

5 10 15 −1 −0.8 −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8 1 time [s]
  • utput
flh hlh frh hrh

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 18 / 28

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SLIDE 26

Exploration of different locomotion gaits

u0 = 2.05, β = 3.0, wfe = −2.0, τ = 0.1, τ′ = 0.3

Gait θfl θhl θfr θhr Walk π 3π/2 π/2 Trot π π Bound π π Pace π π Jump π/2 π/2 Pronk

Bound:

fl fr hr hl k

  • 0.3

+0.1 +0.1

  • 0.5

+0.5

  • 0.5

+0.5

  • 0.5
5 10 15 −1 −0.8 −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8 1 time [s]
  • utput
flh hlh

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 18 / 28

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SLIDE 27

Exploration of different locomotion gaits

Gait transitions: Trot to bound:

20 22 24 26 28 30 32 34 36 38 40 −1 −0.8 −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8 1 time [s]
  • utput
flh frh

Trot to walk:

15 20 25 30 35 −1 −0.8 −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8 1 time [s]
  • utput
flh frh hrh

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 18 / 28

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SLIDE 28

Increasing the speed of locomotion

Amplitude and frequency are the main factors that determine the locomotion speed Amplitude is directly related to u0, while frequency is proportional to (τ · τ′)−1

u0 τ(τ′ = 3τ)

  • Lin. speed (cm/s)

2.05 0.1 1.05 2.50 0.02 8.27 3.00 0.01 4.39 3.00 0.02 17.81 3.00 0.06 12.03 3.00 0.12 3.38 3.20 0.02 15.61 3.50 0.02 0.42 4.00 0.01 0.34 4.00 0.02 3.51 4.00 0.12 5.27

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 19 / 28

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SLIDE 29

Control of direction

Useful for: navigation, obstacle avoidance... Two approaches: modulation of amplitude (u0) and rotation of the legs (slide 17) Modulation of amplitude: Rotation of the legs: More regular behaviour when rotating the legs

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 20 / 28

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SLIDE 30

Walking on irregular surfaces

Floor of the Learning Centre not completely flat: adaptation to irregular surfaces is required Sensory feedback is included into the CPG to adapt the locomotion gait to the terrain:

◮ Occurrence of an obstacle (e.g. a step) or not (touch sensor in

the lower part of every leg)

◮ Inclination of the robot (to modulate the gait depending on the

inclination of the terrain): roll and pitch angle (Fukuoka et al. 2003)

The objective is to:

◮ Lift a leg when it hits an obstacle (and overcome it) ◮ Flex (extend) a leg when the height of the terrain is larger

(smaller) than the average height of the robot

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 21 / 28

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SLIDE 31

Sensory feedback in the CPG

Incorporation into the CPG:

τ ˙ ui,{e,f } = u0 − ui,{e,f } + wfeyi,{f ,e} − βvi,{e,f } +

  • j

wijyj,{e,f } + fbi,{e,f } fbi,f = −fbi,e fbi,e = fbi,obs + fbi,roll + fbi,pitch

fbi,obs =

  • −gobs

if obst. found in [t − tobs, t]

  • therwise

fbi,roll =      −groll · α if α > 0 and i ∈ {FL, HL} groll · α if α < 0 and i ∈ {FR, HR}

  • therwise

fbi,pitch =      −gpitch · β if β > 0 and i ∈ {FL, FR} gpitch · β if β < 0 and i ∈ {HL, HR}

  • therwise

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 22 / 28

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SLIDE 32

Examples of locomotion on irregular surfaces

Best parameters found after experiments: tobs = 50 ms, gobs = 15.0, groll = 2.0, gpitch = 5.0 Without feedback: With feedback:

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 23 / 28

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SLIDE 33

Examples of locomotion on irregular surfaces

Best parameters found after experiments: tobs = 50 ms, gobs = 15.0, groll = 2.0, gpitch = 5.0 Without feedback: With feedback:

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 23 / 28

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SLIDE 34

Online optimisation of locomotion

The users of Roombots will define new, not-predefined pieces

  • f furniture

Intermediate, simple multi-unit structures required in reconfiguration processes All these robots are supposed to have locomotion abilities Online optimisation of locomotion allows the new robots to dynamically learn efficient gaits adapted to their internal structure and the external conditions Successfully applied in MR (Marbach and Ijspeert, 2005) Downhill simplex method in multidimensions to perform the

  • ptimisation

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 24 / 28

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SLIDE 35

Description of the optimisation method

Robot with a tree structure. CPG imitating the mechanical structure. 1 Matsuoka oscillator per DOF (2 per module) Identical parameters of the Matsuoka

  • scillator for all the DOFs: u0 = 2.05,

β = 3.0, wfe = −2.0, τ = 0.13, τ′ = 0.26 Optimisation of the linear speed by changing the weight of the couplings between the oscillators Bidirectional couplings in [−1, 1] chosen by the algorithm For a n-module robot, 4n − 2 parameters to optimise 4n − 1 random vectors of parameters (i.e. of 4n − 2 values) and evaluates them. Readjustment of one or several vectors in each iteration (reflection, reflection and expansion, contraction, multiple contraction) End at a local maximum (may require reinitialisation).

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 25 / 28

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SLIDE 36

Examples of online optimisation

20 seconds per evaluation, registering the average linear speed Salamander-like robot:

◮ 26 parameters to optimise, good results in less than 1 h

50 100 150 200 250 300 350 400 450 5 10 15 20 25 30 35 40 evaluation lin speed [cm/s]

Worm-like robot:

50 100 150 200 250 300 350 400 450 500 2 4 6 8 10 12 14 evaluation
  • lin. speed [cm/s]

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 26 / 28

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SLIDE 37

Outline

1

Background

2

Design of the modules

3

Control of locomotion

4

Conclusions and future work

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 27 / 28

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SLIDE 38

Conclusions and future work

Simple modules with proper interactions as the ones proposed here are effective to form furniture structures The multi-unit robots are able to move in several different ways and their gaits can be modulated with simple mechanisms Online optimisation of locomotion with the simplex algorithm provides a robust method to automatically find good gaits The design of the modules has to be characterised with more detail (exact shape and dimensions, mechanical properties, attachment mechanisms...) Adaptation to the terrain should be further explored Reconfiguration must be better explored in simulation, which might lead to redesign the modules Study of self-repairing mechanisms Realisation of the modules!

Rafael Arco Arredondo (BIRG, EPFL) Roombots, MR for adaptive furniture 19th July 2006 28 / 28