,
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Jacobian eigenvalues
-1
-0.5
0
0.5
1
Real(ev1)
Imag(ev1)
Real(ev2)
Imag(ev2)
Real(ev3)
Imag(ev3)
Figure 13: Real and imaginary parts of the Jacobian eigen-
values, as a function of α, for the bouncing map with active
phase control (λ = 0.09, σ = 0.05, φ
∗
= 0.5).
about the equilibrium point.
Notwithstanding the stability of the task with ac-
tive amplitude and frequency control assessed in the
present paper, participants are shown to hit the ball
in the passive stability regime (Sternad et al., 2001).
The present papers analyzed two alternatives justiﬁ-
cations: the impact phase is either actively controlled
by participants or unconsciously driven by the passive
dynamics of the task. The study showed that the ac-
tive impact phase control does not increase stability
that would otherwise justify a voluntary control. It
is also shown that if at one moment of the trial the
active frequency control is switched off, then the pad-
dle acceleration is driven by the passive dynamics of
the task and goes back to the passive stability regime.
This second hypothesis thus seems more likely to ex-
plain the observed human behavior.
Finally, the efﬁcient prediction of the human con-
trol strategies stability was achieved without simulat-
ing the whole continuous and discrete dynamics of the
system. For robotic applications, with the objective
of identifying the control paradigm that gives humans
such a dexterity to achieve tasks in interaction with
the environment, the present study proposes a method
to discard unnecessary control hypotheses while fa-
cilitating the controller adaptation coefﬁcients setting.
The method can be extended to other tasks involving
repeated robot-environment interactions and reduces
the computation time of the robustness tests by avoid-
ing simulation of the task continuous dynamics.
ACKNOWLEDGEMENTS
This work was supported by the Foundation for Sci-
entiﬁc Cooperation (FSC) Paris-Saclay Campus.
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