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Peng et al. Soft Sci. 2025, 5, 38 https://dx.doi.org/10.20517/ss.2025.31 Page 5 of 19
Figure 3. (A) Theoretical scheme based on the Cosserat model; (B) SMA actuation method based on inverse kinematics; (C)
Continuous Robot Parameter Recognition Experiment; (D) Simulation of Continuous Robot Parameter Recognition. SMA: Shape memory
alloy.
The variables v(s) represent the linear rates of change of the rod’s position with respect to s in the local
l
frame, defined by v(s) = dp/ds, in the global frame,
l
l
(1)
where the dot · denotes a derivative with respect to s. In a similar manner, the angular rates of change in the
rod’s orientation with respect to s in the global frame are given by
(2)
where ^ indicates the conversion of the angular variables u(s) into a skew-symmetric matrix.
l
The distributed external forces and moments applied to the arbitrary section of the rod are specified by f
and l, respectively, and the internal or point forces and the moments in the global frame coordinates are
denoted by n and m, respectively. In addition, ξ is the position variable in the local frame ranging from
position s to a. Therefore, the force and torque equations of static equilibrium can be expressed as
