Predicting the Biomechanics of Walking - Human Motion Simulation: Predictive Dynamics - page 148

One well-established approach is the ZMP-based trajectory generation method,
which has received a great deal of attention. In this method, the walking motion
can be generated in real time for smaller-sized models to follow the desired ZMP
trajectory using an optimal control approach ( Kajita et al., 2003; Yamaguchi
et al., 1999 ). The ZMP concept can also be incorporated in an optimization for-
mulation to synthesize walking pattern by maximizing the stability, subject to
physical constraints ( Huang et al., 2001; Mu and Wu, 2003 ). The key point of
this approach is that the dynamics equations are used only to formulate the stabil-
ity condition rather than to generate the entire motion trajectory directly, thus
many dynamics details are not considered.
Optimization-based trajectory generation presents a viable method for addres-
sing the prediction of walking. This method has exhibited the possibility for pre-
dicting realistic and natural human motion. Furthermore, the method can easily
handle large DOF models, and can optimize many human-related performance
measures simultaneously and satisfy all the constraints ( Anderson and Pandy,
2001; Chevallereau and Aoustin, 2001; Fregly et al., 2007; Lo et al., 2002; Ren
et al., 2007; Saidouni and Bessonnet, 2003 ).
Chevallereau and Aoustin (2001) planned robotic walking and running
motions using optimization to determine the coefficients of a polynomial approxi-
mation for profiles of the pelvis translations and joint angle rotations. Saidouni
and Bessonnet (2003) used optimization to solve for cyclic, symmetric gait
motion of a 9-DOF model that moves in the sagittal plane; the control points for
the B-spline curves along with the time durations for the gait stages were opti-
mized to minimize the actuating torque energy. Anderson and Pandy (2001)
developed a musculoskeletal model with 23 DOFs and 54 muscles for normal
symmetric walking on level ground. Muscle forces were treated as design vari-
ables and metabolic energy expenditure per unit distance was minimized.
Lo et al. (2002) determined human motion that minimized the summation of the
squares of all actuating torques. The design variables were the control points for
the cubic B-spline approximation of joint angle profiles. Sensitivity of joint tor-
que with respect to control points were analytically obtained by using the recur-
sive Newton Euler formulation.
Our team ( Kim et al., 2005 ) has developed an optimization-based approach
for predicting 3D human gait motions on level and inclined planes. By mini-
mizing the deviation of the trunk from the upright posture, joint profiles were
calculated, subjected to some physical constraints. Time durations for various
gait phases were also optimized. The joint torques and ground reaction forces
were not calculated; therefore constraints on the joint strength could not be
imposed. In this chapter, recursive Lagrangian formulation is used for dynam-
ics; joint torques and GRFs are calculated using equations of motion; a more
realistic skeletal model is used; the optimization formulation is physics-based
where an energy-related objective function is minimized; and constraints on the
joint torques are imposed. As a result, a more realistic human walking motion
is obtained.