Predictive Dynamics - Human Motion Simulation: Predictive Dynamics - page 100

2. Since GRF are directly obtained from the system equilibrium conditions, the
equilibrium is satisfied while evaluating GRF using equations of motion
( Xiang et al., 2007 ). This two-step algorithm is called GRF equilibrium
inclusion formulation.

5.4 Performance measures
In Chapter 3, we have presented some basic cost functions used to predict pos-
ture. We remind the reader that these human performance measures were used as
cost functions to drive the behavior of the system, which means the behavior of
the human's motion. However, these cost functions in Chapter 3 did not take into
consideration any dynamic or inertial quantities. They simply did not take the
dynamics of the motion into effect. In practice, the performance measures include
many different kinematics and dynamics criteria such as time minimization, tor-
que optimization, energy minimization, jerk minimization, and others.
In this chapter, we add a few more that are far more effective in the dynamics
simulation for human motion.

1. Dynamic effort

ð T
0 τ τ

f

5 dt (5.7)

which is defined as the integration of squares of all joint torques over
time. The value of this integration is a torque square summation, which is
very closely related to the energy of the system.
2. Mechanical energy

ð T
0 jτ q jdt

f (5.8)

5

which measures the mechanical energy for the mechanical system.
3. Metabolic energy

ð T
0 Edt

f (5.9)

5

E is the rate of total metabolic energy.

where

4. Jerk

ð T
0 τ τ

f dt (5.10)

5

which is defined as the integration of squares of all joint torque derivatives.
An alternative form of jerk is to evaluate the derivative of acceleration instead
of joint torque. Minimization of jerk gives a smoother motion.