Posture Prediction and Optimization - Human Motion Simulation: Predictive Dynamics - page 57

primarily with gross movement; the nuances of skin deflection are not
addressed. Generally, minimizing delta potential energy results in increased
torso rotation about the vertical axis. This is because rotation about the y-axis
does not alter the potential energy of any part of the body. Using delta potential
energy also results in more bending of the elbow. As one can see from the
results with the front right target, delta potential energy should not necessarily
be used in place of joint displacement; it should not be used alone. This sug-
gests that human posture is not governed primarily by potential energy,butas
we show, potential energy does play a role. This finding is counterintuitive and
consequently significant.
3.7.6 Numerical solutions to optimization problems
The subject of this topic is the introduction of a new method called predictive
dynamics. The method uses numerical optimization at its core. Optimization is
a well-developed field, and many numerical methods and strategies have been
researched to obtain solutions since the 1960s. The intent here is not to
describe the details of numerical methods for solving optimization problems,
but only to give a brief introduction to how such problems can be solved.
Based on extensive research on numerical optimization methods, a few prom-
ising methods for solution of practical problems have emerged: the sequential
quadratic programming (SQP) method, the interior point (IP) methods, the exte-
rior penalty methods, the augmented Lagrangian methods, and the generalized
reduced gradient (GRG) methods. Some of these methods have been implemented
into widely used software environments, such as MATLAB and Excel. However,
these programs are cumbersome to use for digital human modeling applications.
Several other commercial codes are available, and some of these are listed below.
This is by no means a comprehensive list.
1. SNOPT: SNOPT stands for Sparse Nonlinear OPTimizer. It implements a
sparse SQP algorithm that is suitable for large sparse optimization problems
( Gill et al., 2002 ). It also has an algorithm to solve dense optimization problems.
2. KNITRO: KNITRO has three algorithms for solving nonlinear optimization
problems: interior-point direct, interior-point conjugate gradient, and active
set algorithms ( Byrd et al., 2006 ).
3. CONOPT: CONOPT implements a large-scale GRG algorithm ( Drud, 1992 ).
4. LANCELOT: LANCELOT implements an augmented Lagrangian method
( Conn et al., 1992 ).
Real-time optimization requires more sophisticated optimization formulation
and implementation. While we have been able to implement a real-time posture
prediction method into Santos s , including physics makes the problem difficult.
This topic will be briefly discussed in later chapters.