Biomedical Engineering Reference
In-Depth Information
7.11
Example: predicting the gait
The examples presented below will demonstrate predictive dynamics as a method
for predicting normal walking, cause and effect, and symmetric and asymmetric
gaits.
We have chosen to use a sequential quadratic programming (SQP) algorithm
as implemented in SNOPT (
Gill et al., 2002
) to solve the optimization problem.
To use the algorithm, cost and constraint functions and their gradients need to be
calculated. The foregoing recursive kinematics and dynamics procedures provide
accurate gradients to improve the computational efficiency of the optimization
algorithm. Appropriate normal walking parameters (velocity and step length) are
obtained from Inman et al. (1981). In addition to normal walking, the current
work also considers situations where people walk and carry backpacks with vari-
ous weights (20 lbs, 40 lbs, and 80 lbs).
7.11.1
Normal walking
Walking speeds in humans vary greatly depending on factors such as anthropome-
try, weight, age, terrain, surface, load, culture, effort, and fitness. The average
human walking speed is about 5.0 km/h, or 1.4 m/s, about 3.1 mph. Walking
research has found pedestrian walking speeds ranging from 4.51 km/h to 4.75 km/h
for older individuals and 5.32 km/h to 5.43 km/h for younger individuals, although a
brisk walking speed can be around 6.5 km/h and champion race walkers can average
more than 14 km/h over a distance of 20 km.
For the problem defined herein, we shall assume a normal gait motion, where
the user inputs normal walking velocity
V
0.6 m.
There are 330 design variables (55 DOFs, each with 6 control points) and 1036
nonlinear constraints. First the optimization problem is solved to obtain a feasible
solution for the walking problem. Here q
1.2 m/s and step length
L
5
5
0 is used as the starting point with
5
Fð
q
Þ
5
constant
as the objective function and all constraints imposed. This is a
new procedure for obtaining feasible solutions for a nonlinear programming prob-
lem that has proved to be very effective in testing feasibility of the predictive
dynamics formulation.
Once a feasible solution has been obtained, it is used as the starting point for
the optimization problem with dynamic effort as the objective function. There are
two advantages of obtaining a feasible solution first: one is to test the feasibility
of the problem formulation; and the second is to obtain a good starting point for
the original optimization problem. The optimality and feasibility tolerances are
both set to
10
2
3
for SNOPT and the optimal solution is obtained in 512 CPU
seconds on a Pentium(R) 4, 3.46-GHz computer. There are 158 active constraints
at the optimal solution.
Figure 7.16
shows the resulting stick diagram of a 3D human walking on level
ground and includes the motion in the single support phase and the double sup-
port phase. As expected, correct knee bending occurs to avoid collision with the
ε
5
Search WWH ::
Custom Search