ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

The vertical force bump observed during time-interval [0-0.3s] was only reproduced
using our dynamic optimization approach. During this interval, ankle and hip
accelerations reached a local positive maximum while those computed by the classical
method decreased and showed negative values.
Fig. 3: Joint accelerations (left) and joint torques (right) computed using classical top-bottom inverse dynamics
and optimal inverse dynamics approaches.
Joint torques values computed by the classical method were over-estimated (see Fig. 3).
Due to the top-bottom iterations, ankle torque values were particularly disordered. At
time t = 0.6s, the observed deviation was larger than 50N.m (see Fig. 3). Its amplitude
decreased by about 50% while using our optimization approach (see Tab. 1). Moreover,
joint torque showed opposite values with respect to the approach used for the
computational process. As an example, opposite signs were observed for both ankle and
hip torque values at time t = 0.42s.
5. DISCUSSION
Our study proposed an optimal dynamic approach to adjust joint accelerations to
external force measurement. Then, our method prevents using double finite
differentiation well-known to amplify noise of measurement data.
To date, few researchers (Kuo, 1998; Cahoüet et al., 2002) have addressed this problem.
Nonetheless, they used a least-square approximation which did not completely cancel
the additional residual force. Our method differed by showing a perfect adjustment with
force plate measurements. This result was the consequence of solving of a dynamic
optimization problem. This problem has been recasted in a parametric problem with
piecewise quartic spline handling in order to the unknown vectors aggregate only joint
accelerations. A major interest was to keep an unconstrained nonlinear optimization
problem. Indeed, the joint coordinates, inherent to marker coordinates data, were
involved into spline connections. As a result, our method was less time consuming than
a classical dynamic optimization (Kuo, 1998).
An application on a measured knee flexion movement demonstrated both feasibility and
efficiency of our method. The acceleration adjustment method led to superposition of
the measured and adjusted reaction forces. Our results showed that the optimized joint
torques patterns were smoother combined with a strict respect of the equations of