Biomedical Engineering Reference
In-Depth Information
Lagrangian multipliers are added to this equation in order to express that body
segment displacement should correspond to motion capture data (see [ 8 ] for details).
The model must be associated with a robust representation of contact forces with
the ground to deliver realistic results. When simulating the system with a dynamic
solver, Lagrangian multipliers will naturally compute forces and torques that are
necessary to ensure that the resulting simulation is compatible with the imposed
motion (generally motion capture data).
A famous solution consists in modelling the joint torques as proportional-
derivative (PD) controllers which merely consists in associating damped springs
to each joint:
k p
θ i
d
i
k d θ i
τ i
=
θ
d
where
i stands for the desired joint angle for joint i, k p and k d are the proportionnal
and derivative gains of the controller. If we consider that the desired joint angles
correspond to those measured by the motion capture system, and if the gains are
correctly tuned, it is thus possible to compute the joint torques that are required
to perform the measured motion [ 42 ]. Torques obtained with the PD controller
is applied to a physical model of the human body. This physical model can be
obtained thanks to commercial software or opensource packages, such as OpenDy-
namicEngine ( http://www.ode.org ) . This type of software provides us with a sim-
ulator of a physical model which inputs are internal and external forces applied to
the system. In our case, external forces are obtained either by direct measurements
with gauges or by using the above inverse dynamic method applied to the global
whole-body system (human body is modelled by its center of mass). Internal forces
and torques are computed using the PD controllers.
This approach is very difficult to tune, especially the values of the PD gains.
However for well-known motions such as walking, many researchers have proposed
semi-automatic methods to estimate these gains.
θ
8.6 Conclusion About Inverse Dynamic Approaches
Joint torques and forces are mainly used in biomechanics and computer animation. In
biomechanics it enables to distinguish different motor strategies that kinematic data
fail to differentiate. In computer animation, it is mainly used to check if the square of
joint torques of a given simulated motion is minimized, assuming that it corresponds
to natural motions. When walking in VR, it could also help to evaluate gait effi-
ciency as human walking is supposed to be associated with low energy consumption
(see Chap. 3 ) . For example, it has been used as a relevant criterion to distinguish
overground and treadmill walking, as explained above [ 31 ]. Moreover animating the
user's avatar walking on uneven terrain implies to adapt the joint trajectories per-
formed by the user who is walking on a treadmill or a flat ground. Hence this motion
adaptation is necessary to compensate differences between the constraints imposed
 
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