Static Modeling of Pneumatic Artificial Muscle Actuator

Artificial pneumatic muscles, derived from the so-called McKibben muscle, are particularly popular for actuating robot joints with hybrid position/stiffness or torque/stiffness control. To be effective, such control modes require an accurate static model of the actuator. While historical studies about the McKibben artificial muscle privileged a physical approach of static force
$F(P,\epsilon)$
analysis versus both control pressure
$P$
and muscle length or contraction ratio
$\epsilon$
, the recent marketing of Festo air muscle led to purely mathematical modeling approaches, especially in the form:
$F(P,\epsilon)=f(\epsilon)P-g(\epsilon)$
with
$f$
,
$g$
positive and
$g(\epsilon=0)=0$
. Such a form is particularly useful for static modeling of the actuator made of two antagonist artificial muscles. We provide a justification of this mathematical model based on a physical approach combining the classic theory of McKibben muscle, applied to a thick-walled inner tube, with a Neo-Hookean model of rubber elasticity. We developed a four parameter static model, that we applied to the popular Festo DMSP-20-400 air muscle, and to a hand-made McKibben muscle. According to this model, the
$f$
-component would derive from McKibben muscle theory, while the g-component could be interpreted as a purely resistive elastic force. Because this model uses a so-called
$C_{1}$
-coefficient determined empirically, we propose to call our approach: hybrid physical-empirical.