Multibody Syst Dyn
DOI 10.1007/s11044-016-9529-4
A window moving inverse dynamics optimization
for biomechanics of motion
C. Quental
1
· J. Folgado
1
· J. Ambrósio
1
Received: 24 September 2015 / Accepted: 6 June 2016
© Springer Science+Business Media Dordrecht 2016
Abstract The application of musculoskeletal models to estimate muscle and joint reaction
forces usually requires optimization strategies, regardless of using inverse or forward dy-
namics approaches. Most studies combined inverse dynamics and Static Optimization (SO)
to solve the redundant muscle force distribution problem. However, the SO does not allow
the simulation of time-dependent physiological criteria or of the time-dependent physiolog-
ical nature of muscles. The Extended Inverse Dynamics (EID), which solves all instants of
time simultaneously, was proposed to overcome these limitations of the SO, but the feasi-
bility of this procedure is limited by the size of the optimization problem that can be real-
istically considered. This work proposes a new method that overcomes the aforementioned
limitations of the SO and EID, i.e., that is able to handle time-dependent physiological crite-
ria and has no limitations on the size of the problem to be solved. The proposed procedure,
named here Window Moving Inverse Dynamics Optimization (WMIDO), consists in con-
sidering a moving window with the size of k instants of time in which the muscle force
distribution problem is solved. The window moves iteratively across all instants of time un-
til the muscle force distribution problem has been solved. The SO, EID, and WMIDO are
applied to solve an upper limb abduction in the frontal plane, for which results are widely
available in the literature, to demonstrate that similar optimal solutions are obtained for a
time-independent physiological criterion if the redundant problem is not too large. Although
the WMIDO is not as efficient as the SO for the type of problem tested, it is significantly
faster than the EID. Moreover, the WMIDO is able to solve the motion under analysis regard-
less of the discretization level considered, whereas the EID fails due to memory limitations.
Overall, the results show the WMIDO as a viable alternative to the current optimization
procedures based on inverse dynamics.
B C. Quental
cquental@dem.ist.utl.pt
J. Folgado
jfolgado@dem.ist.utl.pt
J. Ambrósio
jorge@dem.ist.utl.pt
1
IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1,
1049-001 Lisbon, Portugal