Predicting the Biomechanics of Walking - Human Motion Simulation: Predictive Dynamics - page 149

It is noted that the material for this chapter is derived from several papers pub-
lished by the authors and the contributing author to this chapter ( Xiang, 2008;
Xiang et al., 2009a,b, 2010a,b,c ).
7.2 Joints as degrees of freedom (DOF)
To simulate walking, the lower part of the body is most important. The foot,
ankle, knee, and hip joints are most critical for simulation and prediction of walk-
ing motion. However, including the spine and arms is also important because the
inertia and dynamics associated with the upper torso and arms are significant to
the balance and dynamics of the motion.
We shall use a 55-DOF human skeleton as presented in Chapter 2. There are 6
DOF for global translation and rotation, and 49 DOF representing the kinematics
of the body. Each DOF corresponds to relative rotation of two body segments
connected by a revolute joint.
We shall also use the Denavit Hartenberg (DH) method as presented in
Chapter 2. The objective is to calculate the motion of each of those DOF for each
joint. Indeed, we also seek to calculate the torques required at each joint, denoted
by torque profiles. While both joint and torque profiles are smooth curves that
must be calculated for each joint, these curves will be represented with B-spline
interpolations. As such, it is only the control points of each curve that must be
calculated.
For dynamics and in order to represent the equations of motion, we shall use
the recursive Lagrangian formulation which is known for its computational
efficiency.
7.3 Muscle versus joint space
In the past, the emphasis in predicting motion has been on the local forces gener-
ated by muscle activation. As a result, there has been a significant amount of
research on trying to understand muscles, recruitment, and activation. We have
determined that a more direct approach is to deal with the joint space, i.e., the tor-
que generated by these muscles on the joint (regardless of which muscle is active
and which is recruited). Thus, our focus is the resultant action of these muscles
on the joint. Because we use the DH parameterization method at each individual
DOF, this approach lends itself well to our goals of estimating and predicting
how the body is set in motion.
To set up the optimization problem, we will also need the gradients for all
objective functions and constraints. Working in the joint space provides a direct
and feasible method for accomplishing an effective optimization problem
formulation.