WHEN A MECHANICAL CONTINUUM REQUIRES A DISCRETE WHEN A MECHANICAL CONTINUUM REQUIRES A DISCRETE...

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  • INTRODUCTIONINTRODUCTION

    WHEN A MECHANICAL CONTINUUM REQUIRES A DISCRETE CONTROL Olivier White 1,2, Thierry Pozzo 1,2,3,4 , Charalambos Papaxanthis 1,2

    1. Université de Bourgogne, Dijon, Campus Universitaire, Unité de Formation et de Recherche en Sciences et Techniques des Activités Physiques et Sportives, France. 2. Institut National de la Santé et de la Recherche Médicale (INSERM), Unité 887, Motricité-Plasticité, Dijon, France.

    3. Robotics, Brain and Cognitive Sciences Department, Italian Institute of Technology, Genoa, Italy. 4. Institut Universitaire de France, UFR STAPS, Université de Bourgogne, Dijon, France.

    CONCLUSION

    TYPICAL TRIALS

    METHODS Materials

    Experimental procedure

    B1 B2 B3 B4 B5 Ascending

    B6 B7 B8 B9 B10 Descending

    Position [mm]

    F or

    ce [N

    ]

    0 30 60 90 120 150 0

    1

    2

    3

    4

    Trials

    F or

    ce o

    ns et

    [m m

    ]

    1 10 20 30 40 45 30

    60

    90

    120

    150 normal catch

    0

    100

    200

    -1000

    0

    1000

    -1

    0

    1 × 104

    0

    2

    4

    0

    4

    8

    -50

    0

    50

    0

    100

    200

    -1000

    0

    1000

    -1

    0

    1 × 104

    0

    2

    4

    0

    4

    8

    -50

    0

    50

    0 200 400 600 800 0 200 400 600 800

    High stiffness (133N/m, force onset at 120mm)

    Low stiffness (40N/m, force onset at 50mm)

    30 60 90 120 150

    0

    1

    2

    3

    4

    30 60 90 120 150

    2

    3

    4

    5

    6

    30 60 90 120 150

    -30

    -20

    -10

    0

    10

    20

    30

    40

    0 200 400 600 800

    -30

    -20

    -10

    0

    10

    20

    30

    40

    4

    6

    8

    10

    12

    14

    4

    6

    8

    10

    12

    14

    REFERENCES AND ACKNOWLEDGMENTS

    A robot equipped with a grip force transducer was controlled in real time to generate elastic force fields. Feedback position was given as a green sphere on an LCD screen.

    Force onsets linearly increased from starting position in ascending blocks and decreased in descending blocks, leading to a modulation of stiffness. Catch trials in 13% of trials.

    P os

    iti on

    [m m

    ] Ve

    lo ci

    ty [m

    m /s

    ] A

    cc el

    er at

    io n

    [m m

    /s 2]

    Fo rc

    e [N

    ] G

    rip fo

    rc e

    [N ]

    G rip

    fo rc

    e ra

    te [N

    /s ]

    Time [ms] Time [ms]

    Position increased up to target (150 mm) and decreased to baseline

    Velocity was double-peaked (to and from target).

    Acceleration showed max after hand/target onsets and min when force was largest.

    Force increased linearly with position up to max 4N, slowly or quickly. Exact time-course depended on velocity.

    Grip force raised in anticipation of the force and reached a max slightly before (low stiffness) or after (high stiffness) the peak force.

    Grip force rates at 80ms and at expected force onset were used to assess the degree of pre- programming.

    Grip force leads by 4ms Grip force lags

    by 30ms

    GFrate @ 80ms

    GFrate @ exp. force onset

    GLOBAL REGULATION OF IMPEDANCE

    G rip

    fo rc

    e ba

    se lin

    e [N

    ]

    G rip

    fo rc

    e pe

    ak [N

    ]

    Trials

    F or

    ce o

    ns et

    [m m

    ]

    1 10 20 30 40 45 30

    60

    90

    120

    150

    As ce

    nd ing

    Descending

    Grip force regulates hand impedance.

    GF baseline decreases in ascending blocks reducing impedance for larger stiffness.

    GF peaks are larger in ascending blocks but stabilize after 15 trials.

    Grip force regulates hand impedance at two levels. High level: Baseline and peak grip forces are adjusted asymmetrically in ascending (decrease and plateau) and descending blocks (constant level of grip force). Low level: Impedance is regulated by modulating the occurrence of grip force max in function of expected force onset, and therefore stiffness. This modulation occurs up to a certain threshold which marks a discrete transition contrasting with the underlying mechanical continuum. A compromize is found between dissipation of energy through moderate impedance and controlability through larger impedance.

    FINE REGULATION OF IMPEDANCE

    G rip

    fo rc

    e la

    te nc

    y [m

    s]

    Force onset [mm] Stiffness [N/m]

    Force onset varies linearly with trials. Stiffness varies non-linearly with trials.

    1 5 10 15 20 25 30 35 40 45

    40

    60

    80

    100

    120

    140

    Fo rc

    e on

    se t [

    m m

    ]

    Trials

    87.5mm

    1 5 10 15 20 25 30 35 40 45 0

    200

    400

    600

    800

    S tif

    fn es

    s [N

    /m ]

    Trials

    64N/m

    Grip force peaks lead the maximum elastic force peaks in soft trials but lag these events in stiff trials. Latencies co-vary with force onsets up to some value (87.5mm) leading to a threshold of stiffness (64N/m). Impedance is regulated by modulating the occurrence of GF max in function of expected force onset.

    G rip

    fo rc

    e la

    te nc

    y [m

    s]

    Grip force latency = time of grip force peak - time of maximum elastic force

    OPTIMIZATION OF IMPEDANCE

    G rip

    fo rc

    e ra

    te a

    t 8 0

    m s

    [N /s

    ]

    G rip

    fo rc

    e ra

    te a

    t e xp

    ec te

    d fo

    rc e

    on se

    t [ N

    /s ]

    Hand onset

    Hand onset

    30-45 45-60 60-75 75-90 90-105 105-120 120-135 135-150

    Force onset [mm] 30-45 45-60 60-75 75-90 90-105 105-120 120-135 135-150

    Force onset [mm]

    Catch: no force generated Normal

    Grip force rate decreases with expected stiffness in normal and catch trials. Earliest force onsets were found at 100ms after movement start.

    Grip force rates at expected force onset times decrease 50% down to a minimum reached for stiffness corresponding to ~85N/m, then increase again. No difference between catch and normal trials.

    Optimize energy dissipation

    Optimize return movement

    White O, Thonnard JL, Wing A, Bracewell M, Diedrichsen J, Lefevre P. Grip force regulates hand impedance to optimize object stability in high impact loads. Neuroscience. 189C:269-276. 2011. Delevoye-Turrell Y, N Li F-X, Wing AM. Efficiency of grip force adjustments for impulsive loading during imposed and actively produced collisions. The Quarterly journal of experimental psychology. 56:1113-28. 2003

    The authors are grateful to Dr M. Bracewell, Prof. A. Wing and Dr. J. Diedrichsen for discussions and providing access to the equipment and to Dr. F. Danion for discussions. This research is supported by Université de Bourgogne and INSERM.

    Participants anticipate the effects of an elastic force field on the fingertips. Mechanically, this dynamics is only parameterized by its stiffness, ranging continuously from smooth forces to very high impact-like profiles.

    Recently, we showed that the CNS does not attempt to predict the exact time course of the force profile after impact but instead, it applies a default strategy consisting in gripping harder about 60ms after impact. This strategy optimizes object stability by regulating mechanical parameters including stiffness and damping through grip force. Interestingly, grip force control in extreme elastic forces (smooth vs. impact) exhibits structurally different mechanisms which contrasts with the underlying continuous dynamics.

    We designed an experiment to show that participants switch from one control to another upon a threshold stiffness value.

    Force onset [mm] Force onset [mm]

    Six participants produced back-and-forth tapping movements to a visual target (red bar). Velocity to the target was normalized to

    814.09