Recursive Dynamics - Human Motion Simulation: Predictive Dynamics - page 90

3

2

q 1

q 2

1

0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Time (Normalized)

-1

-2

-3

FIGURE 4.7
Joint angle profile with external load.

Note that the objective here is to predict the motion, which means predicting
values for the joints as time progresses, also called joint profiles. The joint pro-
files are shown as the continuous and the dotted lines in the graph in Figure 4.7 .
Because of the recursive dynamics approach with optimization, it is also possi-
ble to predict the torques as a function of time (also called torque profiles as
shown in Figure 4.8 ), for the entire lifting motion.
In this example, we have used a numerical optimization solver called SNOPT.
The optimality and feasibility tolerances are both set to the default value

10 2 6
in SNOPT and the optimal solutions were obtained in 2.44 CPU seconds on a
1.40-GHz PC. Optimal

ε 5

travel time for the mixed optimization problem is

T 5 520 s. To verify the optimal solution, the problem was also solved using

commercial multi-body dynamics software called ADAMS

0 :

. The optimized joint
torques as shown in Figure 4.9 were treated as inputs and the equations of motion
were automatically generated and integrated to obtain the response. The two
motion trajectories matched quite well. Sensitivity results with the recursive algo-
rithm and the closed-form formulation at the optimal design are compared in
Figure 4.9 and Figure 4.10 . The sensitivity obtained from the two algorithms
match quite closely.

t

4.9 Concluding remarks
Dynamics of human limbs are best modeled using the DH parameters and the
Lagrangian formulation. This methodology is often chosen because it presents an
elegant and systematic method for representing the motion including all aspects
of dynamics, particularly for a multi-body serial system such as the human body.
It is also readily suitable for computer implementation.