Predictive Dynamics - Human Motion Simulation: Predictive Dynamics - page 104

an appropriate performance measure to simulate the applied force and response
histories for the biosystem, as follows:

min
q; τ

Jð q ; τ ; t Þ

s : t : :

τ 2 f ð q ; q ; q ; t Þ 5 0
g ðϒ minimal Þ # 0
q

(5.20)

L U

# q # q

L U

τ #τ#τ

The minimal constraint set depends on the complexity of the biosystem and
the motion to be simulated. For a simple motion, boundary conditions alone might
be enough to reveal the entire motion; in this case, the minimal constraint set
includes only boundary conditions. In contrast, for a complex motion some state
responses between the boundaries need to be known to simulate the real motion.
Therefore, these state responses have to be included in the minimal constraint set.

5.7 Types of constraints
5.7.1 Time-dependent constraints
5.7.1.1 Joint limits
To avoid hyperextension, the joint limits are taken into account in the formula-
tion. The joint limits representing the physical range of motion are:

L U

q

# q ðtÞ # q

; 0

# t # T

(5.21)

L are the lower joint limits and q U the upper limits. Limits on major

where q

joints are presented in Table 5.1 .
Joint limit constraint is also used to “freeze” a DOF by setting its lower bound
and upper bound to the neutral angle (the natural angle at rest) instead of elimi-
nating this DOF from the skeleton model. Changing lower or upper joint limit
constraints in conjunction with strength constraints at a single joint can simulate a
disability and will cause the model to respond differently.

5.7.1.2 Torque limits
Each joint torque is also bounded by its physical limits (strength), which are
obtained from several references ( Cahalan et al., 1989; Gill et al., 2002; Kaminski
et al., 1999; Kumar, 1996 ):

L U

τ #τ ðtÞ #τ ; 0 # t # T (5.22)

L are the lower torque limits and U the upper limits.

where

τ τ