Predicting the Biomechanics of Walking - Human Motion Simulation: Predictive Dynamics - page 158

Table 7.2

Foot Contacting Conditions: Four Modes in a Step

Double support Single support Double support

Rear-foot Fore-foot

Right toe Left heel Left ball Left toe

Left heel Left ball Left toe Right heel

Retrieve GRF from global equilibrium
M GRF , F GRF , o r GRF

Start

Input
q, q, q and GRF = 0

Calculate τ from EOM again

Calculate τ from EOM

Obtain real joint torques
Global Force: 0

Obtain the resultant active
forces : τ 1 , τ 2 , τ 3

End

FIGURE 7.6
Flow chart of the two-step algorithm to obtain GRF and real joint torques.

active forces, to recover the real joint torques. This two-step algorithm is depicted
in Figure 7.6 and explained as follows:

Step 1 q , external loads and gravity, the

joint torques are calculated using the inverse recursive Lagrangian dynamics
without the GRF. This is illustrated in Figure 7.6 . The global forces

: Given current state variables q , q , and _ €

τ 1 , τ 2 , τ 3

and moments τ 6 in the virtual branch are not zero at this stage due to

exclusion of GRF. These forces are in fact the resultants of the active forces at
the end of the virtual branch, i.e., the pelvis. After that, the ZMP is calculated
using these forces, as explained in the following subsection.
Step 2

τ 4 , τ 5 ,

: This step is illustrated in Figure 7.6 . Considering the global equilibrium
between the resultant active forces and the GRF at ZMP, the resultant GRF are
obtained and then treated as external forces applied at ZMP for the human
model, such as the forces f and h in Equations (7.5 7.9) .Giventhestate