bio-inspired robotic touch

ArtificialTouch

L. Ascari

Introduction

The tactilesystem

Modelling

Validation

Conclusionsand FutureOptions

References

Artificial TouchTowards a new approach in prosthetics?

L. Ascari

HENESIS S.R.L.

Parma - February 22nd, 2012—

All the activity described in the presentation has beencarried on while post-doc at

Scuola Superiore Sant’Anna, Pisa (I)

ArtificialTouch

L. Ascari

Introduction

The tactilesystem

Modelling

Validation


References

Outline

1 IntroductionTouch in RoboticsTouch in Prosthetics - Commercial SoAApproachThe pick and lift taskBioinspiration

2 The tactile systemHardwareSoftware

3 Modelling

4 Validation

5 Conclusions and Future Options

ArtificialTouch

L. Ascari

IntroductionTouch in Robotics

Prosthetics SoA

Approach

The pick and lift task

Bioinspiration

The tactilesystem

Modelling

Validation


References

Outline



3 Modelling

4 Validation


ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Touch in Robotics I

Robots are now very complex and sophisticated systems.Higher computational requirements.

Automation robots: very high performing and reliablemachines.Outside the factory floor: limited interaction with humans,specially in terms of autonomous behavior and of friendlyHMIs1,despite a huge market is expected to develop rapidly2.

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Touch in Robotics II

Tactile sensing can provide information about mechanicalproperties such as compliance, friction, and mass.Knowledge of these parameters is essential if robots are toreliably handle unknown objects in unstructuredenvironments. For interaction, localization of the stimulusis essential3.

1J. Ayers et al. Neurotechnology for biomimetic robots. MIT Press,2002.

2WorldRobotics. World Robotics 2006. International Federation ofRobotics, Statistical Department, 2006. url:http://www.worldrobotics-online.org/.

3R. D. Howe. “Tactile sensing and control of robotic manipulation”. In:Journal of Advanced Robotics 8 (1994), pp. 245–261.

http://www.worldrobotics-online.org/

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

For what?

Interaction

Autonomy

Locomotion

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

SOA in robotic skins?

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Open Issues

wiringrobustnessstretchabilitybandwidthprocessing

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Touch in Prosthetics - Commercial SoA

More advanced: myoelectric controlI-Limb Ultra from Touch BionicsUltra from BeBionics

Often refused by patients!

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Touch in Prosthetics - Commercial SoA

Classical prosthesis, cable actuatedOtto bock grippers

Not sensorized. Higher user acceptance. Why?

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Contemporary prosthetics: directions and openissues4

Directionsautonomous control of low level taskshigher spatial resolution of the sensing systemneural control (prototypes exist)feedback to the patient (preliminary results)

Open issuesconnection with tactile nervesdexteritysensitivityCONTROL (myo-electrical vs neural)feedback to the patient

4R.G.E. Clement et al. “Bionic prosthetic hands: A review of presenttechnology and future aspirations”. In: The Surgeon 9.6 (12/2011),pp. 336–340. issn: 1479-666X. doi: 10.1016/j.surge.2011.06.001.url: http://www.sciencedirect.com/science/article/pii/S1479666X11000904.

http://dx.doi.org/10.1016/j.surge.2011.06.001

http://www.sciencedirect.com/science/article/pii/S1479666X11000904


ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Basic questions

Some fundamental questionsWhat is the main issue with advanced prosthesis?

ObjectSlippage and Grasp force control

Is feedback to the user essential for this?

No!

“Solved” Issueslow level control with many signals (here)parallel but portable processing (here)mechanics (single fingers, underactuation, . . . )

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Basic questions

Some fundamental questionsWhat is the main issue with advanced prosthesis? ObjectSlippage and Grasp force controlIs feedback to the user essential for this?

No!


ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Basic questions

Some fundamental questionsWhat is the main issue with advanced prosthesis? ObjectSlippage and Grasp force controlIs feedback to the user essential for this? No!


ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Bio-inspired approach

Why and to what extent?

ManUltimate model: man

Technological, wiring, processing limitations

Lower complexity sensory systemsInnovative approach

•Technology

•Processing

•Scalability

Star-nosed mole

Model and Principle validation

Infinite Complexity: sensors and processing

Simplification

Larger dimensions, higher densities

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Bio-inspired approach

Why and to what extent?




•Technology

•Processing

•Scalability

Star-nosed mole



Simplification


Touch sense

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

The human hand: tactile structure

Human hand touch3 major groups of afferent(tactile afferents, jointmechanoreceptors, spindles)The glabrous skin has 17.000tactile units4 main types ofmechanoreceptors (Ruffini,Pacini, Merkel, Meissner) forintensity, pressure, accelerationstimuli

Structure of the skin

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

The human hand: tactile structure

Human hand touch3 major groups of afferent(tactile afferents, jointmechanoreceptors, spindles)The glabrous skin has 17.000tactile units4 main types ofmechanoreceptors (Ruffini,Pacini, Merkel, Meissner) forintensity, pressure, accelerationstimuli

Structure of the skin

from Johansson and Westling (“Roles of glabrous skin receptors andsensorimotor memory in automatic control of precision grip whenlifting rougher or more slippery objects”)

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Sensors performance...

... in engineering terms

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References


Two aspects are crucial for a stable grasp:the ability of the HW/SW system to avoid object slipto control in real-time the grasping force.

Human physiology of the task

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

On the need for feedback

EvidenceJohansson measured50-60ms of reactiontimeincompatible withpropagation time to themotor cortexevidence of circuitclosed at subcorticallevel (olivo-cerebellarsystem and thalamus).

Where?

from Johansson and Westling (“Roles of glabrous skin receptors andsensorimotor memory in automatic control of precision grip whenlifting rougher or more slippery objects”)

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Biological vs Robotic worlds

Do we have these limitations (signaling speed) in robots?

3

Man

Brain LimbsNerves

Robot

ArtificialBrain

Artificiallimbs

Electric wires

Biological models for the design of biomimetic robots

• Robots as physical platforms for validating biological models

Interfacing Bio and Robotics

No, but other constraints exist. Ex: computational power

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References






•Technology

•Processing

•Scalability

Star-nosed mole



Simplification


Touch sense


ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References



Ultimate model: man


•Technological

•Processing

•ScalabilityStar-nosed mole

Touch sense

Man


ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Multidisciplinarity — The animal model (touch)

Condylura Cristata12 mobile appendagescovered with more than25.000 tactile receptors(Eimer organs)Structure of the Eimerorgan: a sort of pillar with3 nervous terminations(for constant pressures,vibrations, fine surfacedetails);foveated tactile vision.

A nose to see / Eimer

from Catania and Kaas (“Somatosensory Fovea in the Star-NosedMole: Behavioral Use of the Star in Relation to Innervation Patternsand Cortical Representation”)

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Multidisciplinarity — The animal model (vision)

HoneybeeNon-mobile compoundeyes (ommatidia);3000-4000 facets each eye( = 64x64 pixel array);spatial resolution = 1/60of the human eye;No distance informationfrom stereo vision;Center facets larger thanthe peripheral sensors.yet: high performance

Fixed yet good eye

optical flow balancemotion detection(Flicker effect)

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Multidisciplinarity — The computational model

Cellular non linear networksCNN is a massive parallelcomputing paradigm definedin discrete N-dimensionalspaces.A CNN is an N-dimensionalregular array of elements(cells);Cells are multiple input-singleoutput analog processors, alldescribed by one or just somefew parametric functionals.

Parallel topologicalarchitecture

from Chua and Roska (Cellular Neural Networks and VisualComputing: Foundations and Applications)

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

CNN characteristics I

Locality of the connections between the units: in fact themain difference between CNN and other Neural Networksparadigms is the fact that information are directlyexchanged just between neighbouring units. Of course thischaracteristic allows also to obtain global parallelprocessing.A cell is characterized by an internal state variable,sometimes not directly observable from outside the cellitself;More than one connection network can be present;

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

CNN characteristics II

A CNN dynamical system can operate both in continuous(CT-CNN) or discrete time (DT-CNN), with analogicalsignals from different sources;CNN data and parameters are typically real values;CNN operate typically with more than one iteration, i.e.they are recurrent networks; It is a Universal Machine(CNN-UM);It offers Stored programmability;a Hardware implementation exists.

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

CNN core: the template

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Template meaning

in

State-out

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Features of the ACE4K (16K) chip — 3TOps

System Desktop PC, PC-104 industrial PC, Windows NT, 2000

Bus PCI, 33 MHz, 32 bit data width;

Visual Microprocessor type ACE4k, 64x64 processor array

Grayscale image download (64x64) 2688 frame/sec 372 !s

Grayscale image readback (64x64) 3536 frame/sec (compensated through look-up table); 283!s

Binary image download (64x64) 44014 frame/sec; 22.72 !s

Binary image readback (64x64) 23937frame/sec; 41.78 !s

Array operation (64x64) 9 !s + N*100ns

Logical operation (64x64) 3.8 !s

DSP type Texas TMS320C6202; 250MHz, 1600 MIPS operation

Memory 16MB, SDRAM 125 MHz; 2Mbyte FLASH (bootable)

Serial Ports 3

Other features Watch Dog, Timer

Programmability C language, native languages

Image processing library Several image processing functions optimized for CVM

Application Program Interface (API) Integrate the Aladdin systerm into different environments

ArtificialTouch

L. Ascari


Prosthetics SoA

Approach


Bioinspiration

The tactilesystem

Modelling

Validation


References

Recall

Tactile system HW

TASK CONTROLLER

COMPUTATIONAL PLATFORMFINAL GOAL

TASK, PHYSIOLOGICAL

STRATEGY

ROBOTIC PLATFORM

Tactile system SW

ArtificialTouch

L. Ascari

Introduction

The tactilesystemHardware

Software

Modelling

Validation


References

Outline



3 Modelling

4 Validation


ArtificialTouch

L. Ascari

Introduction


Software

Modelling

Validation


References

The MEMS mechanoreceptor

V13 V24

Vc

0

RpuRpu

R2R2

R4R4

R1R1

R3R3

ArtificialTouch

L. Ascari

Introduction


Software

Modelling

Validation


References

The array — Fabrication steps

ArtificialTouch

L. Ascari

Introduction


Software

Modelling

Validation


References

The whole system — HW

From L Ascari et al. “A miniaturized and flexible optoelectronicsensing system for tactile skin”. In: Journal of Micromechanicsand Microengineering 17.11 (11/2007), pp. 2288–2298. issn:0960-1317. doi: 10.1088/0960-1317/17/11/016. url:http://ejournals.ebsco.com/direct.asp?ArticleID=4A9A98E0B7D16F0C429C

http://dx.doi.org/10.1088/0960-1317/17/11/016

http://ejournals.ebsco.com/direct.asp?ArticleID=4A9A98E0B7D16F0C429C


ArtificialTouch

L. Ascari

Introduction


Software

Modelling

Validation


References

The whole system — from HW to SW

From L. Ascari et al. “Bio-inspired grasp control in a robotichand with massive sensorial input”. In: Biological Cybernetics100.2 (2009), p. 109. doi: 10.1007/s00422-008-0279-0

http://dx.doi.org/10.1007/s00422-008-0279-0

ArtificialTouch

L. Ascari

Introduction


Software

Modelling

Validation


References

Recap

We have an array of analog multidirectional tactile signalsThe load cell were NOT calibrated: qualitative and onlyloose orthogonalitywe can load and process analog tactile images on the CNNchip at 400 Hz54 sensors wrapped around the thumb and index fingers ofa robotic underactuated handrobotic arm controlled by DSP

Where is information? What kind of spatial and temporalpatterns? How to recognize and prevent slippage?We need to learn the tactile “alphabet”

ArtificialTouch

L. Ascari

Introduction


Software

Modelling

Validation


References

Recap


Where is information? What kind of spatial and temporalpatterns? How to recognize and prevent slippage?

We need to learn the tactile “alphabet”

ArtificialTouch

L. Ascari

Introduction


Software

Modelling

Validation


References

Recap


Where is information? What kind of spatial and temporalpatterns? How to recognize and prevent slippage?We need to learn the tactile “alphabet”

ArtificialTouch

L. Ascari

Introduction


Software

Modelling

Validation


References

The task controller — FSM

ArtificialTouch

L. Ascari

Introduction


Software

Modelling

Validation


References

The task controller — Features

ArtificialTouch

L. Ascari

Introduction

The tactilesystem

Modelling

Validation


References

Outline



3 Modelling

4 Validation


ArtificialTouch

L. Ascari

Introduction

The tactilesystem

Modelling

Validation


References

The slip effect in robotic grasp

Slip as vibrations. “Catch and snap” effect on the rubber(60Hz stable + initial 10Hz component). Recall FAII humanmechanoreceptors.

Holweg et al., “Slip detection by tactile sensors: algorithms andexperimental results”

ArtificialTouch

L. Ascari

Introduction

The tactilesystem

Modelling

Validation


References

Definition of Tactile Events of interest

Variations, oscillations, vibrationsTime is divided in periods ofduration T ∗s

Variation change in signallarger than σ insame period

Oscillation seq. of 2 subsequentvariations of oppositesign in same T ∗.(m,n)

Vibration seq. of 2 oscillationsin 2 adjacent periods σ = 2% dynamic range

ArtificialTouch

L. Ascari

Introduction

The tactilesystem

Modelling

Validation


References

Assumptions - Naming conventions

Bandwidth = 200 Hz ⇒ st = 2.5msAnalysis period where to look for events:T ∗ = 8 ∗ st = 20ms ≡ 50Hz ≡ period = 8 ∗ L;σ = 2%dynamicrange ≡ 5gray levels(m, n) ≡ [(±m,±n) | (±n,±m)]. Optimal choice(empirically): (3,1)Both amplitude and frequency of catch and snap backoscillations may vary (mechanical properties of skin,material, weight, roughness of object) ⇒ flexible,parametrizable, robust approach.

ArtificialTouch

L. Ascari

Introduction

The tactilesystem

Modelling

Validation


References

Some definitions

y(t) = a sin(2πνt + ϕ) (1)

with amplitude a, frequencyν Hz and phaseϕ rad ∈ [−π, π] uniformlydistributed.

This modeling is consistent with the non constancy of the meanvalue of the vibration, being the analysis limited to one period

ArtificialTouch

L. Ascari

Introduction

The tactilesystem

Modelling

Validation


References

Phase and frequency

Biol Cybern

0 T*/2 T*t°

fM

=f0+!

f0

fM

!3!

st (L!1)"st

Fig. 15 A possible configuration of the input tactile signal: (+1,!3)

length of the period, consisting of L consecutive frames; thephase ! " [!","] is supposed to be uniformly distributed.

A.1 Phase and frequency

One oscillation implies the presence of a peak (modeled asa null-derivative point) in t# "

!0, T $", thus originating the

equation:

2"#t# + ! = "/2 + K · " (2)

where K " Z. Therefore:

t# = 12"#

·#"

2+ K · " ! !

$(3)

Figure 15 contains a possible situation, the case in whichthe signal increases by at least 1 · $ and then decreases by atleast 3 · $ (situation indicated by the notation (+1,!3)).

Two cases can be identified: t# "!0, T $/2

!or t# "!

T $/2, T $", depending on the position of the peak, in thefirst or in the second half of the period.

Case A. By inserting Eq. 3 into the condition 0 < t# % T $/2we obtain:

"/2 + K" ! "#T $ % ! < "/2 + K" (4)

The range of variation of ! (! " [!","[) imposes that,in order for Eq. 4 to have at least one solution, two boundaryconditions are satisfied, precisely:%

"/2 + K" ! "#T $ < "

"/2 + K" > !"(5)

which, solved, originates:%K > !3/2 & K ' !1

#T $ > K ! 1/2(6)

The product #T $ is worth a more detailed analysis. In theframework of this modeling lower frequencies are more inter-esting than higher ones, which are more easily detected bythe filter. We limit our analysis to the range # " ]0, 80] Hz (inother words, #max = 80 Hz). The latency of the filter equalsL · st and, in our implementation, st = 2.5 ms: latencieshigher that 25 ms would cause too slow reactions of the handto unexpected tactile stimuli, therefore an upper bound to L isfixed: Lmax = 10. Therefore, T $

max = Lmax $ st = 10/400 s.These boundaries bring to #T $ < #maxT $

max = 2. In all thefollowing analysis we consider the boundary

#T $ % 2 (7)

Equation 6 then becomes:%K ' !1

K % 2(8)

Only four values of K need then to be considered: K =!1, 0, 1, 2 (for instance, K = 3 ( #T $ > 5/2).

Case B. By inserting Eq. 3 into the condition T $/2 < t# <

T $ we obtain:

"/2 + K" ! 2"#T $ <!<"/2 + K"!"#T $

(9)

By imposing the conditions for the existence of at leastone ! " [!","[ solution of Eq. 9, we obtain:%

"/2 + K" ! "#T $ > !"

"/2 + K" ! 2"#T $ < "(10)

which, solved, originates:

! 1/4 + K/2 < #T $ < 3/2 + K (11)

The variability range #T $ " [0, 2] applied to Eq. 11 toassure the existence of a solution, originates:%

3/2 + K > 0

!1/2 + K/2 < 2(12)

From Eq. 12, we obtain the 6 values that K can acquire inthis second case: K " [!1, 4].

In conclusion, two sets of equations must be solved: thefirst for 0 < t# % T $/2 and the second for T $/2 < t# < T $:

Case A :

&'(')"/2 + K" ! "#T $ %! < "/2+K"

#T $ > K ! 1/2K " [!1, 2]

(13)

Case B :

&''('')"/2+K"!2"#T $ <!<"/2 + K" ! "#T $

!1/4 + K/2<#T $ <3/2+K

K " [!1, 4](14)

123

Biol Cybern

0 T*/2 T*t°

fM

=f0+!

f0

fM

!3!

st (L!1)"st






equation:

2"#t# + ! = "/2 + K · " (2)


t# = 12"#

·#"

2+ K · " ! !

$(3)



!or t# "!



"/2 + K" ! "#T $ % ! < "/2 + K" (4)


"/2 + K" ! "#T $ < "

"/2 + K" > !"(5)


#T $ > K ! 1/2(6)




#T $ % 2 (7)


K % 2(8)



T $ we obtain:

"/2 + K" ! 2"#T $ <!<"/2 + K"!"#T $

(9)


"/2 + K" ! "#T $ > !"

"/2 + K" ! 2"#T $ < "(10)


! 1/4 + K/2 < #T $ < 3/2 + K (11)


3/2 + K > 0

!1/2 + K/2 < 2(12)



Case A :

&'(')"/2 + K" ! "#T $ %! < "/2+K"

#T $ > K ! 1/2K " [!1, 2]

(13)

Case B :

&''('')"/2+K"!2"#T $ <!<"/2 + K" ! "#T $

!1/4 + K/2<#T $ <3/2+K

K " [!1, 4](14)

123

Biol Cybern

0 T*/2 T*t°

fM

=f0+!

f0

fM

!3!

st (L!1)"st






equation:

2"#t# + ! = "/2 + K · " (2)


t# = 12"#

·#"

2+ K · " ! !

$(3)



!or t# "!



"/2 + K" ! "#T $ % ! < "/2 + K" (4)


"/2 + K" ! "#T $ < "

"/2 + K" > !"(5)


#T $ > K ! 1/2(6)




#T $ % 2 (7)


K % 2(8)



T $ we obtain:

"/2 + K" ! 2"#T $ <!<"/2 + K"!"#T $

(9)


"/2 + K" ! "#T $ > !"

"/2 + K" ! 2"#T $ < "(10)


! 1/4 + K/2 < #T $ < 3/2 + K (11)


3/2 + K > 0

!1/2 + K/2 < 2(12)



Case A :

&'(')"/2 + K" ! "#T $ %! < "/2+K"

#T $ > K ! 1/2K " [!1, 2]

(13)

Case B :

&''('')"/2+K"!2"#T $ <!<"/2 + K" ! "#T $

!1/4 + K/2<#T $ <3/2+K

K " [!1, 4](14)

123

ArtificialTouch

L. Ascari

Introduction

The tactilesystem

Modelling

Validation


References

Phase and frequency

Biol Cybern

0 T*/2 T*t°

fM

=f0+!

f0

fM

!3!

st (L!1)"st






equation:

2"#t# + ! = "/2 + K · " (2)


t# = 12"#

·#"

2+ K · " ! !

$(3)



!or t# "!



"/2 + K" ! "#T $ % ! < "/2 + K" (4)


"/2 + K" ! "#T $ < "

"/2 + K" > !"(5)


#T $ > K ! 1/2(6)




#T $ % 2 (7)


K % 2(8)



T $ we obtain:

"/2 + K" ! 2"#T $ <!<"/2 + K"!"#T $

(9)


"/2 + K" ! "#T $ > !"

"/2 + K" ! 2"#T $ < "(10)


! 1/4 + K/2 < #T $ < 3/2 + K (11)


3/2 + K > 0

!1/2 + K/2 < 2(12)



Case A :

&'(')"/2 + K" ! "#T $ %! < "/2+K"

#T $ > K ! 1/2K " [!1, 2]

(13)

Case B :

&''('')"/2+K"!2"#T $ <!<"/2 + K" ! "#T $

!1/4 + K/2<#T $ <3/2+K

K " [!1, 4](14)

123

Biol Cybern

Table 2 Resume of all the possibilities for a signal of given phase !and frequency " to be recognized as oscillation by the filter

K = !1

!"T " > 0

!#/2 ! #"T " # ! < !#/2+ $1

K = 0

!"T " > 0

#/2 ! #"T " # ! < #/2+ %1

K = 1

!"T " > 1/2

3/2# ! #"T " # ! < #+ $1

K = 2

!"T " > 3/2

5/2# ! #"T " # ! < #+ %1

K = !1

!0 < "T " < 1/2

!#/2 ! 2#"T " # ! < !#/2 ! #"T " + $2

K = 0

!0 < "T " < 3/2

#/2 ! 2#"T " # ! < #/2 ! #"T " + %2

K = 1

!1/4 < "T " < 5/2

3/2# ! 2#"T " # ! < 3/2# ! #"T " + $2

K = 2

!3/4 < "T " < 7/2

5/2# ! 2#"T " # ! < 5/2# ! #"T " + %2

K = 3

!5/4 < "T " < 9/2

7/2# ! 2#"T " # ! < 7/2# ! #"T " + $2

K = 4

!7/4 < "T " < 11/2

9/2# ! 2#"T " # ! < 9/2# ! #"T " + %2

The double line separator splits Case A from Case B

Table 3 Equations on the amplitude of the input signal

%1

!f (t&) ! f (0) > $

f (t&) ! f (T ") > 3$

!sin(!) < !y

sin(%) < !x

$1"

f (0) ! f (t&) > $f (T ") ! f (t&) > 3$

!sin(!) > y

sin(%) > x

%2!

f (t&) ! f (0) > 3$

f (t&) ! f (T ") > $

!sin(!) < !x

sin(%) < !y

$2

!f (0) ! f (t&) > 3$

f (T ") ! f (t&) > $

!sin(!) > x

sin(%) > y

For all cases, the minimum amplitude of the signal to be detected isa = 3/2$

Table 2 lists the 10 systems obtained inserting the corres-ponding values of K into Eqs. 13 (4 values) and 14(6 values). From simple geometrical considerations (seeEq. 2), even and odd values of K are associated with a maxi-

Table 4 Final set of equations

K = !1

#$$$$$%$$$$$&

"T " > 0

!#/2 ! #"T " # ! < !#/2

sin(!) > y

sin(2#"T ") > x

K = 0

#$$$$$%$$$$$&

"T " > 0

#/2 ! #"T " # ! < #/2

sin(!) < !y

sin(2#"T ") < !x

K = 1

#$$$$$%$$$$$&

"T " > 1/2

3/2# ! #"T " # ! < #

sin(!) > y

sin(2#"T ") > x

K = 2

#$$$$$%$$$$$&

"T " > 3/2

5/2# ! #"T " # ! < #

sin(!) < !y

sin(2#"T ") < !x

K = !1

#$$$$$%$$$$$&

0 < "T " < 1/2

!#/2 ! 2#"T " # ! < !#/2 ! #"T "

sin(!) > x

sin(2#"T ") > y

K = 0

#$$$$$%$$$$$&

0 < "T " < 3/2

#/2 ! 2#"T " # ! < #/2 ! #"T "

sin(!) < !x

sin(2#"T ") < !y

K = 1

#$$$$$%$$$$$&

1/4 < "T " < 5/2

3/2# ! 2#"T " # ! < 3/2# ! #"T "

sin(!) > x

sin(2#"T ") > y

K = 2

#$$$$$%$$$$$&

3/4 < "T " < 7/2

5/2# ! 2#"T " # ! < 5/2# ! #"T "

sin(!) < !x

sin(2#"T ") < !y

K = 3

#$$$$$%$$$$$&

5/4 < "T " < 9/2

7/2# ! 2#"T " # ! < 7/2# ! #"T "

sin(!) > x

sin(2#"T ") > y

K = 4

#$$$$$%$$$$$&

7/4 < "T " < 11/2

9/2# ! 2#"T " # ! < 9/2# ! #"T "

sin(!) < !x

sin(2#"T ") < !y

mum and a minimum in t&, respectively: symbols $1,2 and%1,2 are used to indicate a minimum and maximum conditionsassociated with each case, the number stands for the first orsecond half-period of occurrence.

123

ArtificialTouch

L. Ascari

Introduction

The tactilesystem

Modelling

Validation


References

Phase and frequency

Biol Cybern


K = !1

!"T " > 0

!#/2 ! #"T " # ! < !#/2+ $1

K = 0

!"T " > 0

#/2 ! #"T " # ! < #/2+ %1

K = 1

!"T " > 1/2

3/2# ! #"T " # ! < #+ $1

K = 2

!"T " > 3/2

5/2# ! #"T " # ! < #+ %1

K = !1

!0 < "T " < 1/2

!#/2 ! 2#"T " # ! < !#/2 ! #"T " + $2

K = 0

!0 < "T " < 3/2

#/2 ! 2#"T " # ! < #/2 ! #"T " + %2

K = 1

!1/4 < "T " < 5/2

3/2# ! 2#"T " # ! < 3/2# ! #"T " + $2

K = 2

!3/4 < "T " < 7/2

5/2# ! 2#"T " # ! < 5/2# ! #"T " + %2

K = 3

!5/4 < "T " < 9/2

7/2# ! 2#"T " # ! < 7/2# ! #"T " + $2

K = 4

!7/4 < "T " < 11/2

9/2# ! 2#"T " # ! < 9/2# ! #"T " + %2



%1

!f (t&) ! f (0) > $

f (t&) ! f (T ") > 3$

!sin(!) < !y

sin(%) < !x

$1"

f (0) ! f (t&) > $f (T ") ! f (t&) > 3$

!sin(!) > y

sin(%) > x

%2!

f (t&) ! f (0) > 3$

f (t&) ! f (T ") > $

!sin(!) < !x

sin(%) < !y

$2

!f (0) ! f (t&) > 3$

f (T ") ! f (t&) > $

!sin(!) > x

sin(%) > y




K = !1

#$$$$$%$$$$$&

"T " > 0

!#/2 ! #"T " # ! < !#/2

sin(!) > y

sin(2#"T ") > x

K = 0

#$$$$$%$$$$$&

"T " > 0

#/2 ! #"T " # ! < #/2

sin(!) < !y

sin(2#"T ") < !x

K = 1

#$$$$$%$$$$$&

"T " > 1/2

3/2# ! #"T " # ! < #

sin(!) > y

sin(2#"T ") > x

K = 2

#$$$$$%$$$$$&

"T " > 3/2

5/2# ! #"T " # ! < #

sin(!) < !y

sin(2#"T ") < !x

K = !1

#$$$$$%$$$$$&

0 < "T " < 1/2

!#/2 ! 2#"T " # ! < !#/2 ! #"T "

sin(!) > x

sin(2#"T ") > y

K = 0

#$$$$$%$$$$$&

0 < "T " < 3/2

#/2 ! 2#"T " # ! < #/2 ! #"T "

sin(!) < !x

sin(2#"T ") < !y

K = 1

#$$$$$%$$$$$&

1/4 < "T " < 5/2

3/2# ! 2#"T " # ! < 3/2# ! #"T "

sin(!) > x

sin(2#"T ") > y

K = 2

#$$$$$%$$$$$&

3/4 < "T " < 7/2

5/2# ! 2#"T " # ! < 5/2# ! #"T "

sin(!) < !x

sin(2#"T ") < !y

K = 3

#$$$$$%$$$$$&

5/4 < "T " < 9/2

7/2# ! 2#"T " # ! < 7/2# ! #"T "

sin(!) > x

sin(2#"T ") > y

K = 4

#$$$$$%$$$$$&

7/4 < "T " < 11/2

9/2# ! 2#"T " # ! < 9/2# ! #"T "

sin(!) < !x

sin(2#"T ") < !y


123

Biol Cybern


K = !1

!"T " > 0

!#/2 ! #"T " # ! < !#/2+ $1

K = 0

!"T " > 0

#/2 ! #"T " # ! < #/2+ %1

K = 1

!"T " > 1/2

3/2# ! #"T " # ! < #+ $1

K = 2

!"T " > 3/2

5/2# ! #"T " # ! < #+ %1

K = !1

!0 < "T " < 1/2

!#/2 ! 2#"T " # ! < !#/2 ! #"T " + $2

K = 0

!0 < "T " < 3/2

#/2 ! 2#"T " # ! < #/2 ! #"T " + %2

K = 1

!1/4 < "T " < 5/2

3/2# ! 2#"T " # ! < 3/2# ! #"T " + $2

K = 2

!3/4 < "T " < 7/2

5/2# ! 2#"T " # ! < 5/2# ! #"T " + %2

K = 3

!5/4 < "T " < 9/2

7/2# ! 2#"T " # ! < 7/2# ! #"T " + $2

K = 4

!7/4 < "T " < 11/2

9/2# ! 2#"T " # ! < 9/2# ! #"T " + %2



%1

!f (t&) ! f (0) > $

f (t&) ! f (T ") > 3$

!sin(!) < !y

sin(%) < !x

$1"

f (0) ! f (t&) > $f (T ") ! f (t&) > 3$

!sin(!) > y

sin(%) > x

%2!

f (t&) ! f (0) > 3$

f (t&) ! f (T ") > $

!sin(!) < !x

sin(%) < !y

$2

!f (0) ! f (t&) > 3$

f (T ") ! f (t&) > $

!sin(!) > x

sin(%) > y




K = !1

#$$$$$%$$$$$&

"T " > 0

!#/2 ! #"T " # ! < !#/2

sin(!) > y

sin(2#"T ") > x

K = 0

#$$$$$%$$$$$&

"T " > 0

#/2 ! #"T " # ! < #/2

sin(!) < !y

sin(2#"T ") < !x

K = 1

#$$$$$%$$$$$&

"T " > 1/2

3/2# ! #"T " # ! < #

sin(!) > y

sin(2#"T ") > x

K = 2

#$$$$$%$$$$$&

"T " > 3/2

5/2# ! #"T " # ! < #

sin(!) < !y

sin(2#"T ") < !x

K = !1

#$$$$$%$$$$$&

0 < "T " < 1/2

!#/2 ! 2#"T " # ! < !#/2 ! #"T "

sin(!) > x

sin(2#"T ") > y

K = 0

#$$$$$%$$$$$&

0 < "T " < 3/2

#/2 ! 2#"T " # ! < #/2 ! #"T "

sin(!) < !x

sin(2#"T ") < !y

K = 1

#$$$$$%$$$$$&

1/4 < "T " < 5/2

3/2# ! 2#"T " # ! < 3/2# ! #"T "

sin(!) > x

sin(2#"T ") > y

K = 2

#$$$$$%$$$$$&

3/4 < "T " < 7/2

5/2# ! 2#"T " # ! < 5/2# ! #"T "

sin(!) < !x

sin(2#"T ") < !y

K = 3

#$$$$$%$$$$$&

5/4 < "T " < 9/2

7/2# ! 2#"T " # ! < 7/2# ! #"T "

sin(!) > x

sin(2#"T ") > y

K = 4

#$$$$$%$$$$$&

7/4 < "T " < 11/2

9/2# ! 2#"T " # ! < 9/2# ! #"T "

sin(!) < !x

sin(2#"T ") < !y


123

Biol Cybern


K = !1

!"T " > 0

!#/2 ! #"T " # ! < !#/2+ $1

K = 0

!"T " > 0

#/2 ! #"T " # ! < #/2+ %1

K = 1

!"T " > 1/2

3/2# ! #"T " # ! < #+ $1

K = 2

!"T " > 3/2

5/2# ! #"T " # ! < #+ %1

K = !1

!0 < "T " < 1/2

!#/2 ! 2#"T " # ! < !#/2 ! #"T " + $2

K = 0

!0 < "T " < 3/2

#/2 ! 2#"T " # ! < #/2 ! #"T " + %2

K = 1

!1/4 < "T " < 5/2

3/2# ! 2#"T " # ! < 3/2# ! #"T " + $2

K = 2

!3/4 < "T " < 7/2

5/2# ! 2#"T " # ! < 5/2# ! #"T " + %2

K = 3

!5/4 < "T " < 9/2

7/2# ! 2#"T " # ! < 7/2# ! #"T " + $2

K = 4

!7/4 < "T " < 11/2

9/2# ! 2#"T " # ! < 9/2# ! #"T " + %2



%1

!f (t&) ! f (0) > $

f (t&) ! f (T ") > 3$

!sin(!) < !y

sin(%) < !x

$1"

f (0) ! f (t&) > $f (T ") ! f (t&) > 3$

!sin(!) > y

sin(%) > x

%2!

f (t&) ! f (0) > 3$

f (t&) ! f (T ") > $

!sin(!) < !x

sin(%) < !y

$2

!f (0) ! f (t&) > 3$

f (T ") ! f (t&) > $

!sin(!) > x

sin(%) > y




K = !1

#$$$$$%$$$$$&

"T " > 0

!#/2 ! #"T " # ! < !#/2

sin(!) > y

sin(2#"T ") > x

K = 0

#$$$$$%$$$$$&

"T " > 0

#/2 ! #"T " # ! < #/2

sin(!) < !y

sin(2#"T ") < !x

K = 1

#$$$$$%$$$$$&

"T " > 1/2

3/2# ! #"T " # ! < #

sin(!) > y

sin(2#"T ") > x

K = 2

#$$$$$%$$$$$&

"T " > 3/2

5/2# ! #"T " # ! < #

sin(!) < !y

sin(2#"T ") < !x

K = !1

#$$$$$%$$$$$&

0 < "T " < 1/2

!#/2 ! 2#"T " # ! < !#/2 ! #"T "

sin(!) > x

sin(2#"T ") > y

K = 0

#$$$$$%$$$$$&

0 < "T " < 3/2

#/2 ! 2#"T " # ! < #/2 ! #"T "

sin(!) < !x

sin(2#"T ") < !y

K = 1

#$$$$$%$$$$$&

1/4 < "T " < 5/2

3/2# ! 2#"T " # ! < 3/2# ! #"T "

sin(!) > x

sin(2#"T ") > y

K = 2

#$$$$$%$$$$$&

3/4 < "T " < 7/2

5/2# ! 2#"T " # ! < 5/2# ! #"T "

sin(!) < !x

sin(2#"T ") < !y

K = 3

#$$$$$%$$$$$&

5/4 < "T " < 9/2

7/2# ! 2#"T " # ! < 7/2# ! #"T "

sin(!) > x

sin(2#"T ") > y

K = 4

#$$$$$%$$$$$&

7/4 < "T " < 11/2

9/2# ! 2#"T " # ! < 9/2# ! #"T "

sin(!) < !x

sin(2#"T ") < !y


123

Biol Cybern


K = !1

!"T " > 0

!#/2 ! #"T " # ! < !#/2+ $1

K = 0

!"T " > 0

#/2 ! #"T " # ! < #/2+ %1

K = 1

!"T " > 1/2

3/2# ! #"T " # ! < #+ $1

K = 2

!"T " > 3/2

5/2# ! #"T " # ! < #+ %1

K = !1

!0 < "T " < 1/2

!#/2 ! 2#"T " # ! < !#/2 ! #"T " + $2

K = 0

!0 < "T " < 3/2

#/2 ! 2#"T " # ! < #/2 ! #"T " + %2

K = 1

!1/4 < "T " < 5/2

3/2# ! 2#"T " # ! < 3/2# ! #"T " + $2

K = 2

!3/4 < "T " < 7/2

5/2# ! 2#"T " # ! < 5/2# ! #"T " + %2

K = 3

!5/4 < "T " < 9/2

7/2# ! 2#"T " # ! < 7/2# ! #"T " + $2

K = 4

!7/4 < "T " < 11/2

9/2# ! 2#"T " # ! < 9/2# ! #"T " + %2



%1

!f (t&) ! f (0) > $

f (t&) ! f (T ") > 3$

!sin(!) < !y

sin(%) < !x

$1"

f (0) ! f (t&) > $f (T ") ! f (t&) > 3$

!sin(!) > y

sin(%) > x

%2!

f (t&) ! f (0) > 3$

f (t&) ! f (T ") > $

!sin(!) < !x

sin(%) < !y

$2

!f (0) ! f (t&) > 3$

f (T ") ! f (t&) > $

!sin(!) > x

sin(%) > y




K = !1

#$$$$$%$$$$$&

"T " > 0

!#/2 ! #"T " # ! < !#/2

sin(!) > y

sin(2#"T ") > x

K = 0

#$$$$$%$$$$$&

"T " > 0

#/2 ! #"T " # ! < #/2

sin(!) < !y

sin(2#"T ") < !x

K = 1

#$$$$$%$$$$$&

"T " > 1/2

3/2# ! #"T " # ! < #

sin(!) > y

sin(2#"T ") > x

K = 2

#$$$$$%$$$$$&

"T " > 3/2

5/2# ! #"T " # ! < #

sin(!) < !y

sin(2#"T ") < !x

K = !1

#$$$$$%$$$$$&

0 < "T " < 1/2

!#/2 ! 2#"T " # ! < !#/2 ! #"T "

sin(!) > x

sin(2#"T ") > y

K = 0

#$$$$$%$$$$$&

0 < "T " < 3/2

#/2 ! 2#"T " # ! < #/2 ! #"T "

sin(!) < !x

sin(2#"T ") < !y

K = 1

#$$$$$%$$$$$&

1/4 < "T " < 5/2

3/2# ! 2#"T " # ! < 3/2# ! #"T "

sin(!) > x

sin(2#"T ") > y

K = 2

#$$$$$%$$$$$&

3/4 < "T " < 7/2

5/2# ! 2#"T " # ! < 5/2# ! #"T "

sin(!) < !x

sin(2#"T ") < !y

K = 3

#$$$$$%$$$$$&

5/4 < "T " < 9/2

7/2# ! 2#"T " # ! < 7/2# ! #"T "

sin(!) > x

sin(2#"T ") > y

K = 4

#$$$$$%$$$$$&

7/4 < "T " < 11/2

9/2# ! 2#"T " # ! < 9/2# ! #"T "

sin(!) < !x

sin(2#"T ") < !y


123

Biol Cybern


K = !1

!"T " > 0

!#/2 ! #"T " # ! < !#/2+ $1

K = 0

!"T " > 0

#/2 ! #"T " # ! < #/2+ %1

K = 1

!"T " > 1/2

3/2# ! #"T " # ! < #+ $1

K = 2

!"T " > 3/2

5/2# ! #"T " # ! < #+ %1

K = !1

!0 < "T " < 1/2

!#/2 ! 2#"T " # ! < !#/2 ! #"T " + $2

K = 0

!0 < "T " < 3/2

#/2 ! 2#"T " # ! < #/2 ! #"T " + %2

K = 1

!1/4 < "T " < 5/2

3/2# ! 2#"T " # ! < 3/2# ! #"T " + $2

K = 2

!3/4 < "T " < 7/2

5/2# ! 2#"T " # ! < 5/2# ! #"T " + %2

K = 3

!5/4 < "T " < 9/2

7/2# ! 2#"T " # ! < 7/2# ! #"T " + $2

K = 4

!7/4 < "T " < 11/2

9/2# ! 2#"T " # ! < 9/2# ! #"T " + %2



%1

!f (t&) ! f (0) > $

f (t&) ! f (T ") > 3$

!sin(!) < !y

sin(%) < !x

$1"

f (0) ! f (t&) > $f (T ") ! f (t&) > 3$

!sin(!) > y

sin(%) > x

%2!

f (t&) ! f (0) > 3$

f (t&) ! f (T ") > $

!sin(!) < !x

sin(%) < !y

$2

!f (0) ! f (t&) > 3$

f (T ") ! f (t&) > $

!sin(!) > x

sin(%) > y




K = !1

#$$$$$%$$$$$&

"T " > 0

!#/2 ! #"T " # ! < !#/2

sin(!) > y

sin(2#"T ") > x

K = 0

#$$$$$%$$$$$&

"T " > 0

#/2 ! #"T " # ! < #/2

sin(!) < !y

sin(2#"T ") < !x

K = 1

#$$$$$%$$$$$&

"T " > 1/2

3/2# ! #"T " # ! < #

sin(!) > y

sin(2#"T ") > x

K = 2

#$$$$$%$$$$$&

"T " > 3/2

5/2# ! #"T " # ! < #

sin(!) < !y

sin(2#"T ") < !x

K = !1

#$$$$$%$$$$$&

0 < "T " < 1/2

!#/2 ! 2#"T " # ! < !#/2 ! #"T "

sin(!) > x

sin(2#"T ") > y

K = 0

#$$$$$%$$$$$&

0 < "T " < 3/2

#/2 ! 2#"T " # ! < #/2 ! #"T "

sin(!) < !x

sin(2#"T ") < !y

K = 1

#$$$$$%$$$$$&

1/4 < "T " < 5/2

3/2# ! 2#"T " # ! < 3/2# ! #"T "

sin(!) > x

sin(2#"T ") > y

K = 2

#$$$$$%$$$$$&

3/4 < "T " < 7/2

5/2# ! 2#"T " # ! < 5/2# ! #"T "

sin(!) < !x

sin(2#"T ") < !y

K = 3

#$$$$$%$$$$$&

5/4 < "T " < 9/2

7/2# ! 2#"T " # ! < 7/2# ! #"T "

sin(!) > x

sin(2#"T ") > y

K = 4

#$$$$$%$$$$$&

7/4 < "T " < 11/2

9/2# ! 2#"T " # ! < 9/2# ! #"T "

sin(!) < !x

sin(2#"T ") < !y


123

ArtificialTouch

L. Ascari

Introduction

The tactilesystem

Modelling

Validation


References

Phase and frequency

Biol Cybern

Fig. 16 White color indicatessolutions of the equation systemof Table 4. A sinusoid withamplitude a = 10! (roughlycorresponding to 0.2 in the yaxis of the pictures, given thecurrent choice of ! = 5/255) isrecognized as oscillation in 50%of the cases if L = 8 (a), in 81%if L = 10 (b), depending on itsphase "

!=20 Hz , L=8 . " coverage at a=10#: 50%

Phase " (rads)

Sign

al A

mpl

itude

a ($

51

#)

!3 !2 !1 0 1 2 3

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

!=28 Hz , L=8 . " coverage at a=10#: 81%

Phase " (rads)

Sign

al A

mpl

itude

a ($

51

#)

!3 !2 !1 0 1 2 3

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

a b

0 0.005 0.01 0.015 0.02!0.2

!0.15

!0.1

!0.05

0

0.05

0.1

0.15

0.2

time (s)

ampl

itude

($51

#)

Sinusoid Amplitude:10#.

Fig. 17 Comparison between to sinusoidal inputs having the same fre-quency but different phase. The dashed signal does not match the requi-rements to be considered an oscillation

Up to this point, only phase and frequency of the inputsignal have been considered in the model. Symbols !1, "1,!2, "2 contain additional relations linking amplitude a andthe ! parameter to ", # and T #, as it will be shownnow.

A.2 Amplitude

The possibility for the peak of being located in the first or inthe second half of the period, and of being a maximum or aminimum, originates four cases: for the sake of brevity, wedescribe completely one of them, namely the case in whichthe input tactile signal has the shape shown in Fig. 15, i.e. amaximum in 0 < t$ < T #/2.

From the definition given in Sect. 5.1 an oscillation iscontained in the period if:!

f (t$) % f (0) > !

f (t$) % f (T #) > 3!(15)

After direct substitution of Eq. 1 into Eq. 15 we obtain:!a % a sin(") > !

a % a sin(2$#T # + ") > 3!(16)

and then!sin(") < a%!

a

sin(2$#T # + ") < a%3!a

(17)

Defining y = !%aa , x = 3!%a

a , % = 2$#T #, the finalequation for case 1 is obtained:!

sin(") < %y

sin(%) < %x(18)

In order for Eq. 18 to have at least one solution, the condi-tions:!

%y > %1 & y < 1

%x > %1 & x < 1(19)

must be satisfied: the condition on signal amplitude thatdirectly follows is a > 3/2! . Equation 18 models the case"1. Analogous equations can be derived with the same pas-sages for the other three cases, as summarized in Table 3:in the central column the descriptive equation of the signal(analogous to Eq. 15) is indicated, while in the right column,the final equations (analogous to Eq. 18) are reported.

A.3 Solution of the joint equations

The set of equations to be solved is the combination of theequations in Table 2 with the corresponding ones in Table 3,as summarized in Table 4.

Visualizing results requires some attention, as solutionsare in a multidimensional space: a, ! , ", #, duration of theperiod T #, expressed by L , the number of considered frames.To better understand the role of each parameter, let us analyzea simplified case, by considering two pure sinusoids at # =20 Hz and # = 28 Hz, and a period of L = 8 frames sampled

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Fig. 18 Detection Probabilityfunctions for L = 6 (a) andL = 10 (b). Darker regionsmean lower detectionprobability. Values in thecolorbar are in percentage

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100Detection/Frequency plot for a=10 !.

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Fig. 19 Detection probability plot for a = 10! and several values ofL . Higher values of L cause lower cut-off frequency of the filer andlonger latency

at 400 Hz (st = 2.5 ms). Figure 16 shows a projection of thesolution space in the two cases on the [", a] plane: signalswith phase and amplitude corresponding to a white area arerecognized as oscillations by the filter, whilst black areasindicate waves non classified as oscillations.

Figure 17 exemplifies the concept showing two sinusoids(solid and dashed lines) with equal frequency and differentinitial phase: "solid = 0.5 rad, "dashed = 2 rad over a period.In the first one an oscillation is recognized, while the dashedline (" = 2rad) is correctly discarded, no matter how largeits amplitude is.

With reference to Fig. 16, as the phase " was supposed tobe a uniformly distributed random variable, the cumulativelength of a horizontal white segment (corresponding to acertain amplitude a) over the whole phase interval 2# can beregarded as the probability of a signal having that amplitudea to be recognized as containing an oscillation in the currentperiod. On the base of this observation, plots like the ones in

Fig. 18 can be obtained, in which the gray level indicates theprobability that in a signal of given amplitude a and frequency$, an oscillation is recognized in the current period of Lsamples acquired every st seconds. If L = 6, the filter candetect with a probability of 100% all oscillations in signalshaving minimum amplitude (a = 3/2! ) and $ > 50 Hz. IfL = 10, the cut-off frequency at minimum amplitude lowersto 30 Hz. For higher amplitudes the cut-off frequency slightlylowers.

To better clarify the importance of the correct choice ofL , Fig. 19 contains a section of the detection probabilityfunction for a = 10! as a function of the signal frequencyfor several values of L. The latency lat = L · st ranges from10 ms when L = 4 to 25 ms when L = 10 if st = 2.5 ms,corresponding to sampling frequency of 400 Hz as in ourcase.

Acknowledgments The authors express their gratitude to Mr. LuigiManfredi, for the precious help in setting up the biomechatronic handand the fruitful discussions. The work described in this paper was carriedon in the framework of the BIOMETH (Biomimetic Touch and Sight)project, supported by Toyota Motor Corporation. A special thank goes toMr. Hiromichi Yanagihara and Mr. Jonas Ambeck-Madsen from ToyotaMotor Europe for the many fruitful discussions and the continuoussupport. The authors are finally grateful to the anonymous reviewers,for their helpful comments.

References

Ascari L, Ziegenmeyer M, Corradi P, Gaßmann B, Zoellner M, DillmannR, Dario P (2006) Can statistics help walking robots in assessingterrain roughness? platform description and preliminary conside-rations. In: Prooceedings of the 9th ESA Workshop on AdvancedSpace Technologies for Robotics and Automation ASTRA2006,ESTEC, Noordwijk, The Netherlands

Ascari L, Corradi P, Beccai L, Laschi C (2007) A miniaturizedand flexible optoelectronic sensing system for tactile skin.J Micromech Microeng 17(11):2288–2298. doi:10.1088/0960-1317/17/11/016, http://ejournals.ebsco.com/direct.asp?ArticleID=4A9A98E0B7D16F0C429C

Asuni G, Teti G, Laschi C, Guglielmelli E, Dario P (2005) A bio-inspired sensory-motor neural model for a neuro-robotic manipu-

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Latency lat at samplingfrequency of 400Hz asin our case.

lat = L · st = 10mswhen L = 4lat = L · st = 25mswhen L = 10

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Outline



3 Modelling

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1240 1260 1280 1300 1320 13400

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Tactile input and oscillation detected (row:21, col:24).

StimulusEvent

Fig. 11 Dashed line tactile stimulus, as provided by the experimenterfinger pushing oscillatory on the sensor array (intensity plot over timeas recorded by the CNN chip), in correspondence of the pixel in row21 and column 24 (see Fig. 10); solid line filter output (correspondingpixel brightness on the output image)

500 600 700 800 900

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Fig. 12 Dashed line intensity plot over time of the pixel in row 21and column 7 (see Fig. 10); solid line filter output highlights detectedoscillations. Frames before 560 are called “segment 1”, while framesbetween 820 and 900 belong to “segment 2”

frames 540 and 560 (let us call these frames segment 1), thefilter seems to fail between frames 820 and 900 (segment 2).

The power spectral density estimate of the two signal seg-ments (shown in Fig. 13) reveals the reasons behind that:segment 1 has a much stronger component at “higher” fre-quency (around 1.3 Hz ) than segment 2, whose main contri-bution is at 0.5Hz. In other words, segment 2 is below thecut-off frequency of the filter (see Appendix A and Fig. 19for further details).

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Fig. 13 Power spectral densities estimate of “segment 1” and“segment 2” sections (with reference to Fig. 12)

6.2 MEMS sensors: grasp task

This experiment, differently form the previous one, involveda real time task, such as grasping and lifting several objects,thus requiring much higher frame rates. Given the bandwidthlimitations of the current HW system in image transfer illus-trated above, all images were acquired and processed insidethe Bi-I camera, and thus non visible outside; this limitingfactor, besides making the tuning of the filters’ parameters forreal time tasks more difficult, should be removed in the nextreleases of the HW platform. Results of the experiments canbe evaluated only in terms of success or failure of the task.

The pick and lift experiments were performed using therobotic arm, the biomechatronic hand and the tactile sensorysystem described in Sect. 3, and consisted in picking andlifting three different objects using a standard pinched grasp:a plastic bottle, a soft sponge sphere, and a piece of Japanesesoft tofu.

These objects were chosen to make the proposed approachfacing with different tactile situations: the plastic bottle hasa smooth surface, a little deformable; the sponge sphereis much softer and deformable, and has a rugged surface;the Japanese tofu is extremely slippery, soft, and smooth.Moreover, its fragility is extremely pronounced, as an off-line preliminary experiment showed: one of the fingers ofthe antropomorphic robotic hand was instrumented with asix-components load cell (ATI NANO 17 F/T, Apex, NC,USA), covered with a protective layer identical to that cove-ring the sensors, and a piece of tofu was grasped at severallevels of grasping force; an increase in the grasping force ofless than 0.5 N was sufficient to pass from complete slip todestruction of the sample.

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Fig. 9 Aluminum-made finger mock-up covered with a flexible arrayof QTC sensors

Comb electrodes were patterned on a flexible substrate ofLF9150R Pyralux (DuPont, USA) material consisting of a127-mm thick Kapton sheet with a 35mm layer of copper,by means of a lithographic process. QTC sensors were fixedto the surface by means of UV curable adhesive Electro-LiteELC-4481 on the perimeter. A protective rubber layer waswrapped around the sensors; Fig. 9 shows the array structureand the aluminum finger mock-up. Each sensor edge is 3-mmlong.

The sensors were polarized so as to generate voltagesignals proportional to the pressure applied; the nine signalswere fed into the electro-optical converter presented in Ascariet al. (2007), so that tactile images were produced and pro-jected onto the ACE16K processor.

The acquisition rate on the ACE16K processor, limited bytransmission delay of the images over the network, was setaround 10 Hz and a modification of the definition of oscil-lation was introduced, to restrict the sensitivity of the filteronly to macroscopic changes in the stimuli (for visualizationpurposes): an oscillation is defined here as the sequence oftwo opposite variations having minimum amplitudes of 3!

and 4! or vice versa (in contrast with the sequence 3! -! orvice versa adopted in Sect. 5.1). ! was set to 9 gray levels(out of 255 coding the whole input dynamics of the ACE16Kprocessor).

Tactile stimuli were provided by the experimenter fin-ger, pressing on the array in various ways: continuously,slowly and rapidly oscillatory. This solution was preferred toa controlled mechanical stimulation because it offered morerealistic situations.

A tactile image sequence of 4 frames is shown in Fig. 10.The area on the ACE16K processor interested by these signalsis a square whose edge is 29 pixel long. On the left side are thestimuli, while the right side of each picture contains the cor-responding output of the CNN when searching for the eventoscillation: non black areas in the third and fourth framesindicate detected oscillations; it is worth noting that the fourcentral pixels (corresponding to the central sensor) remainsaturated along the sequence, indicating that the finger didnot leave the array completely, nevertheless events are detec-

Fig. 10 Sequence of four tactile input frames (on the left half ), withthe corresponding output image generated by the ACE16K processorwhen looking for oscillations, on the right

ted on the periphery of the central area, indicating that theintensity of the light emitted from the sensor was decreasing.

A close look to a single pixel helps in understanding thebehaviour of the filter: Fig. 11 contains a plot of the lightintensity on one pixel, together with the time instants at whichoscillations were detected. Oscillations around frames 1280are correctly not recognized by the filter, given the morestringent requirements in terms of minimum amplitude set-up for this experiment (see above).

The filter is intrinsically stochastic (see Appendix A for acomplete description), as shown by the following example.The amplitude of the oscillation around frame 1320 should,at a first sight, be detected by the filter: in this case, the couple(amplitude, phase) of the signal corresponds to a detectionprobability less than 100% (see Fig. 18). A longer periodwould have been necessary in this case, although introducinglatency, virtually absent in this example.

Instead, the next example focuses on the filter frequencyselectivity: Fig. 12 shows the intensity plot on a differentlocation of the array. Whilst oscillations are detected between

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Fig. 9 Aluminum-made finger mock-up covered with a flexible arrayof QTC sensors

Comb electrodes were patterned on a flexible substrate ofLF9150R Pyralux (DuPont, USA) material consisting of a127-mm thick Kapton sheet with a 35mm layer of copper,by means of a lithographic process. QTC sensors were fixedto the surface by means of UV curable adhesive Electro-LiteELC-4481 on the perimeter. A protective rubber layer waswrapped around the sensors; Fig. 9 shows the array structureand the aluminum finger mock-up. Each sensor edge is 3-mmlong.

The sensors were polarized so as to generate voltagesignals proportional to the pressure applied; the nine signalswere fed into the electro-optical converter presented in Ascariet al. (2007), so that tactile images were produced and pro-jected onto the ACE16K processor.

The acquisition rate on the ACE16K processor, limited bytransmission delay of the images over the network, was setaround 10 Hz and a modification of the definition of oscil-lation was introduced, to restrict the sensitivity of the filteronly to macroscopic changes in the stimuli (for visualizationpurposes): an oscillation is defined here as the sequence oftwo opposite variations having minimum amplitudes of 3!

and 4! or vice versa (in contrast with the sequence 3! -! orvice versa adopted in Sect. 5.1). ! was set to 9 gray levels(out of 255 coding the whole input dynamics of the ACE16Kprocessor).

Tactile stimuli were provided by the experimenter fin-ger, pressing on the array in various ways: continuously,slowly and rapidly oscillatory. This solution was preferred toa controlled mechanical stimulation because it offered morerealistic situations.

A tactile image sequence of 4 frames is shown in Fig. 10.The area on the ACE16K processor interested by these signalsis a square whose edge is 29 pixel long. On the left side are thestimuli, while the right side of each picture contains the cor-responding output of the CNN when searching for the eventoscillation: non black areas in the third and fourth framesindicate detected oscillations; it is worth noting that the fourcentral pixels (corresponding to the central sensor) remainsaturated along the sequence, indicating that the finger didnot leave the array completely, nevertheless events are detec-

Fig. 10 Sequence of four tactile input frames (on the left half ), withthe corresponding output image generated by the ACE16K processorwhen looking for oscillations, on the right

ted on the periphery of the central area, indicating that theintensity of the light emitted from the sensor was decreasing.

A close look to a single pixel helps in understanding thebehaviour of the filter: Fig. 11 contains a plot of the lightintensity on one pixel, together with the time instants at whichoscillations were detected. Oscillations around frames 1280are correctly not recognized by the filter, given the morestringent requirements in terms of minimum amplitude set-up for this experiment (see above).

The filter is intrinsically stochastic (see Appendix A for acomplete description), as shown by the following example.The amplitude of the oscillation around frame 1320 should,at a first sight, be detected by the filter: in this case, the couple(amplitude, phase) of the signal corresponds to a detectionprobability less than 100% (see Fig. 18). A longer periodwould have been necessary in this case, although introducinglatency, virtually absent in this example.

Instead, the next example focuses on the filter frequencyselectivity: Fig. 12 shows the intensity plot on a differentlocation of the array. Whilst oscillations are detected between

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1240 1260 1280 1300 1320 13400

50

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150

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250

Tactile input and oscillation detected (row:21, col:24).

StimulusEvent

Fig. 11 Dashed line tactile stimulus, as provided by the experimenterfinger pushing oscillatory on the sensor array (intensity plot over timeas recorded by the CNN chip), in correspondence of the pixel in row21 and column 24 (see Fig. 10); solid line filter output (correspondingpixel brightness on the output image)

500 600 700 800 900

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Fig. 12 Dashed line intensity plot over time of the pixel in row 21and column 7 (see Fig. 10); solid line filter output highlights detectedoscillations. Frames before 560 are called “segment 1”, while framesbetween 820 and 900 belong to “segment 2”

frames 540 and 560 (let us call these frames segment 1), thefilter seems to fail between frames 820 and 900 (segment 2).

The power spectral density estimate of the two signal seg-ments (shown in Fig. 13) reveals the reasons behind that:segment 1 has a much stronger component at “higher” fre-quency (around 1.3 Hz ) than segment 2, whose main contri-bution is at 0.5Hz. In other words, segment 2 is below thecut-off frequency of the filter (see Appendix A and Fig. 19for further details).

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Fig. 13 Power spectral densities estimate of “segment 1” and“segment 2” sections (with reference to Fig. 12)

6.2 MEMS sensors: grasp task

This experiment, differently form the previous one, involveda real time task, such as grasping and lifting several objects,thus requiring much higher frame rates. Given the bandwidthlimitations of the current HW system in image transfer illus-trated above, all images were acquired and processed insidethe Bi-I camera, and thus non visible outside; this limitingfactor, besides making the tuning of the filters’ parameters forreal time tasks more difficult, should be removed in the nextreleases of the HW platform. Results of the experiments canbe evaluated only in terms of success or failure of the task.

The pick and lift experiments were performed using therobotic arm, the biomechatronic hand and the tactile sensorysystem described in Sect. 3, and consisted in picking andlifting three different objects using a standard pinched grasp:a plastic bottle, a soft sponge sphere, and a piece of Japanesesoft tofu.

These objects were chosen to make the proposed approachfacing with different tactile situations: the plastic bottle hasa smooth surface, a little deformable; the sponge sphereis much softer and deformable, and has a rugged surface;the Japanese tofu is extremely slippery, soft, and smooth.Moreover, its fragility is extremely pronounced, as an off-line preliminary experiment showed: one of the fingers ofthe antropomorphic robotic hand was instrumented with asix-components load cell (ATI NANO 17 F/T, Apex, NC,USA), covered with a protective layer identical to that cove-ring the sensors, and a piece of tofu was grasped at severallevels of grasping force; an increase in the grasping force ofless than 0.5 N was sufficient to pass from complete slip todestruction of the sample.

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Fig. 14 Pictures taken from the grasping experiments with a plasticbottle (a), a piece of soft Japanese tofu (b), and a soft sponge ball (c).In the third picture the tactile modules can be seen around the distalphalanges of the index and thumb fingers, as well as the optical fibrescarrying the optically coded signals to the ACE16K CNN processor

During the grasp experiment, the task controller hosted inthe Bi-I camera evaluated at first the quality of contact, rea-ching a state of stable grasp with the lowest grasping force;then lifted the arm, reacting to tactile events such oscillationsor vibrations, caused by object slip and/or external stimuli,by sudden small closures of one or both fingers, dependingon the involved sensors. The parameters of the event detec-tion filter were set as follows: sampling rate was fixed to400 Hz, ! = 5 gray levels, frame buffer length L = 8 (seeAppendix A). Figure 14 shows three moments of the experi-ments.

Results of this experiment are manifold and can be sum-marized as follows:

Bottle. The assessment of a stable grasp proved to be quitestraightforward, based on spatial and temporal features; thecontrol of stability during the lift and hold phases based onthe recognition of oscillations and vibrations proved to beessential to maintain the grasp with minimum force.

Sphere. The requirements of the spatial stability check couldin this case be much relaxed: thanks to the soft consistency

and adaptability of the object and the rougher surface, thetime-based stability condition even on a small portion of thefingers area proved to be enough to start lifting; reactiontime from stimulus application to motor command, alwaysless than 20ms, allowed the system to successfully opposeto essays to pull the ball from the closed hand, producing avery “natural-feeling” behaviour.

Tofu. With this object, space-based stability check before lif-ting proved to be much more effective than the time-basedmechanisms. The extremely slippery and smooth surfacemade the recognition of oscillations and vibrations extre-mely difficult (successful grasping of tofu is a very challen-ging task also for a human hand, as preliminary experimentstaught us).

7 Conclusion

The use of cellular nonlinear networks (CNN) in real-timerobotic grasp control with massive sensory input has beenpresented for the first time, to the authors’ knowledge; whileemployed to model the visual sensory system (Roska et al.1993), their use in the tactile domain is just beginning, asreported in a very recent work (Kis et al. 2006) where shearand torque information is extracted from 2 ! 2 array ofsilicon-made sensors.

We presented a complete system for reactive real-timesafe grasp of unknown objects, based on the detection ofspatial–temporal events, the core of the software platformbeing a topological analog filter, designed and implementedin a CNN processor. The proposed filter can be completelyparametrized: its sensitivity, latency, robustness to noise, canbe easily tuned to adapt to several sensors, covering materials,and thicknesses.

The approach could appear oversized, given the limitedamount of sensors (54) exploited in this work; our aim wasindeed to present and validate an architecture conceived within mind:

– a couple of specific scenarios , i.e. (1) a mechatronic pros-thetic hand covered with a dense tactile skin and takingcare of the low and middle level mechanisms to assure asafe grasp, while leaving to the user only the high levelintentional control of the task; and (2) a humanoid robotfully covered with a tactile skin consisting of several thou-sands of sensors;

– some desired features, namely: the ability to process allthe signals in real time, to localize the stimulus, with abandwidth large enough to capture also the sudden forcechanges (which proved to be so important in the humancontrol mechanisms), the robustness to broken sensors,the low computational requirements (the core of the resul-

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Sampling rate of 400HzMax number of sensors:16384Parallel processing:semantic featuresextractionIncipient slip detection:successful.Final DEMO: soft tofugrasping (movie)Working with 30% ofsensors

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Introduction

The tactilesystem

Modelling

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References

Outline



3 Modelling

4 Validation


ArtificialTouch

L. Ascari

Introduction

The tactilesystem

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References

Biological vs artificial tactile system

Biol Cybern

Table 1 Parallelism between the biological and artificial tactile systems at sensorimotor, tactile features, and sensors levels

Human system Artificial system

Sensorimotor scheme Event-based strategy; Event-based strategy;

parallel coordination mechanism; stability check;

Tactile features RF-based; sudden force RF-based; detection of

change detection; oscillations and vibrations

Sensors Four kinds of mechanoreceptors with One kind of sensors and CNN-based computation to mimic the main

different spatial and temporal characteristics; spatial and temporal responses of the mechanoreceptors

ting tactile system, housing data collection from the per-ipheral modules, as well as the computational HW andSW units, was hosted in a box with external dimensionsof 20 ! 10 ! 6 cm and showed a power absorption of afew Ws).

Taking the anatomy and physiology of the human tactilesystem as a reference and guiding model in the design of thisartificial system has helped to approach the scenarios andsatisfy these requirements. In particular, Table 1 summarizesthe main aspects we took inspiration from in the biologicaltactile system and how they were implemented in the propo-sed approach, at various levels.

The performed experiments showed that all the computedfeatures are important for the task to be completed, but withdifferent weights, depending on the particular object beinggrasped: this could be seen as an indirect evidence of thedemonstrated coexistence of both bottom-up and top-downcontrol strategies in biological grasp control; secondarily,this puts into evidence a limitation of our current implemen-tation, i.e. the static use of the tactile features, whose relativeimportance is now manually selected: if an average setting issuitable for the majority of objects, particularly challengingones such Japanese tofu require some parameters tuning tobe successfully grasped. By adding other perceptive modali-ties to the system (for instance, vision, allowing pre-shapingstrategies) from one side and, from the other, by siding CNNswith learning architectures such as artificial neural networks,or optimization methods such as genetic algorithms, auto-matic relative weighting of the features extracted from thetactile system could be achieved; this would result in a betterand automatic adaptation of the system to a wider class ofobjects.

Other key features of the proposed solution, that make ita potential candidate for being the signal processing core indense and diffused sensitive skins, are the recognition andautomatic exclusion of broken sensors and the high band-width, virtually independent from the number of sensorsembedded in the skin (the only limit is the number of inputpixels of the CNN chip); these are features that biologicalnervous systems offer, and that could be more efficiently

investigated and implemented in robotic systems using a bio-mimetic computing platform such as CNNs.

In addition, the presented hardware/software platformcould be considered as a biorobotic tool allowing both toinvestigate on strategies for solving complex sensory-motortasks, and to validate neuroscientific models requiring thepresence of many sensors and biomimetic processing, likethe one, for instance, recently proposed by Johansson andBirznieks (2004), hypothesizing that the very first spike inensambles of human skin afferents may encode complexmechanical events such as the direction of force on the fin-gertip or the local shape at the fingertip-object interface.

In conclusion, it is our opinion that this approach couldhelp to fill the gap between tactile sensing and tactile per-ception, that is recognized to be still a bottleneck to the nextchallenges for robot manipulation in human environments(Kemp et al. (2007)).

Appendix A: Mathematical modeling of tactile events

This section is devoted to the formal model of a generic tactileevent isolated by the filter presented in Sect. 5.6: the objectiveof the filter is to recognize oscillations and vibrations (asdefined in section 5.1) generated by the catch and snap backeffect during, for instance, object slip.

The generic tactile signal can therefore be modeled as asinusoid wave:

y(t) = a sin(2!"t + #) (1)

having amplitude a, frequency " Hz and phase # rad. Thismodeling is consistent with the non constancy of the meanvalue of the vibration, being the analysis limited to one period(see below).

A number of parameters tunes the behaviour of the fil-ter, in terms of lower cut-off frequency, sensitivity, latency.The model highlights the cross-dependencies among all ofthem, searching for the lowest frequency a signal of a certainamplitude and phase must have to contain an oscillation inthe current period. In particular, st is the time interval bet-ween two subsequent samples (frames), T " = L · st is the

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Main achievementsadaptive minimum force event based grasp controllerparallel analog processingRobustUniversal

ArtificialTouch

L. Ascari

Introduction

The tactilesystem

Modelling

Validation


ReferencesThank you for your attention!

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ArtificialTouch

L. Ascari

Introduction

The tactilesystem

Modelling

Validation


References

References I

[1] L Ascari et al. “A miniaturized and flexible optoelectronicsensing system for tactile skin”. In: Journal ofMicromechanics and Microengineering 17.11 (11/2007),pp. 2288–2298. issn: 0960-1317. doi:10.1088/0960-1317/17/11/016. url:http://ejournals.ebsco.com/direct.asp?ArticleID=4A9A98E0B7D16F0C429C.

[2] L. Ascari et al. “Bio-inspired grasp control in a robotichand with massive sensorial input”. In: BiologicalCybernetics 100.2 (2009), p. 109. doi:10.1007/s00422-008-0279-0.

[3] J. Ayers et al. Neurotechnology for biomimetic robots.MIT Press, 2002.

http://dx.doi.org/10.1088/0960-1317/17/11/016



http://dx.doi.org/10.1007/s00422-008-0279-0

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References

References II

[4] K.C. Catania and J.H. Kaas. “Somatosensory Fovea inthe Star-Nosed Mole: Behavioral Use of the Star inRelation to Innervation Patterns and CorticalRepresentation”. In: THE JOURNAL OFCOMPARATIVE NEUROLOGY 387 (1997),pp. 215–233.

[5] L.O. Chua and T. Roska. Cellular Neural Networks andVisual Computing: Foundations and Applications.Cambridge University Press, 2002.

[6] R.G.E. Clement et al. “Bionic prosthetic hands: A reviewof present technology and future aspirations”. In: TheSurgeon 9.6 (12/2011), pp. 336–340. issn: 1479-666X.doi: 10.1016/j.surge.2011.06.001. url:http://www.sciencedirect.com/science/article/pii/S1479666X11000904.

http://dx.doi.org/10.1016/j.surge.2011.06.001



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References III

[7] E.G.M. Holweg et al. “Slip detection by tactile sensors:algorithms and experimental results”. In: Robotics andAutomation, 1996. Proceedings., 1996 IEEE InternationalConference on. Vol. 4. 1996, 3234–3239 vol.4.

[8] R. D. Howe. “Tactile sensing and control of roboticmanipulation”. In: Journal of Advanced Robotics 8(1994), pp. 245–261.

[9] RS Johansson and G. Westling. “Roles of glabrous skinreceptors and sensorimotor memory in automatic controlof precision grip when lifting rougher or more slipperyobjects”. In: Experimental Brain Research 56.3 (1984),pp. 550–564.

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Modelling

Validation


References

References IV

[10] WorldRobotics. World Robotics 2006. InternationalFederation of Robotics, Statistical Department, 2006.url: http://www.worldrobotics-online.org/.

http://www.worldrobotics-online.org/

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