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19
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The ground reaction forces are modeled for all simulations using a spring and damper model.
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Figure 2.7 illustrates the model for a 2D system.
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Ground forces are applied to specific, pre-
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defined monitor pointson the model.
has penetrated the ground surface are:
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The ground forces exerted on a monitor point, M, which
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F=kp[!](P-M)-k·
d[!]M
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where Fis the ground reaction force, Mis the position of the monitor point, M · is its velocity, P
is the initial point of contact with the ground, and kpand kdare proportional and derivative
constants defining the stiffness and damping properties of the ground (see Figure 2.7).
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The ground reaction forces are bounded such that the vertical component is always positive, thus
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never allowing the damping term to impede the lifting of the foot.
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Monitor point slippage is
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implemented using a Coulomb friction model, which is used to limit the tangent of the ground
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reaction force.
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Slippage is allowed when the ratio of the vertical and tangent forces exceeds a
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specified limit as illustrated in Figure 2.8 for the 2D case.
point of initial contact, P, to be directly above monitor point.
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Slippage is simulated by moving the
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![[CONVERTED BY MYRMIDON]](Imgs/convBy.GIF)