Posture Prediction and Optimization - Human Motion Simulation: Predictive Dynamics - page 41

CHAPTER
3

Posture Prediction and
Optimization

The concept is interesting and well-formed, but in order to earn better
than a 'C', the idea must be feasible.
A Yale University management professor in response to student Fred Smith's paper
proposing reliable overnight delivery service (Smith went on to found Federal
Express Corp.)

3.1 What is optimization?
Mathematical optimization is a branch of computational mathematics that seeks
to answer the question: “What is the best solution given a set of constraints?”
This type of optimization is well suited to problems for which the quality of
any answer can be expressed as a numerical value. Such problems arise in many
fields, particularly in business, engineering, structures, architecture, economics,
management, and just about every smart appliance on the market today. Equally
wide in scope is the range of methods used to solve such problems. An excellent
reference on the subject, including solution methods, is a text written by the sec-
ond author ( Arora, 2012 ).
This chapter presents the basic ideas of mathematical optimization and pro-
vides a rigorous understanding of the three ingredients: design variables, cost
functions, and constraints. The chapter does not, however, cover numerical meth-
ods or numerical solvers of optimization as this is quite a mature field and there
are many existing computational codes that can be used to solve a well-
formulated optimization problem. It is believed that optimal solutions are readily
obtained if the problem is well formulated.

3.2 What is posture prediction?
Posture prediction refers to the estimation of joint variables that will allow the
human body to assume a posture towards achieving an objective. For example,
prediction of upper extremity variables (joint angles) to achieve the grasping of
an object is a posture prediction problem. Note that grasping means the position-
ing of the hand (called the end-effector of a serial kinematic chain in the field of
robotics), often referred as inverse kinematics or

IK for short. Similarly,