Technical Report No. VSR-04.02
End-of-Year
Technical Report
For
Project
HUMAN PERFORMANCE MEASURES
By
Joo H. KIM
The Virtual Soldier Research (VSR) Program
Center
for Computer-Aided Design
College of Engineering
The
University of Iowa
116
Engineering Research Facility
Iowa
City, IA 52242-1000
Dated: October 25, 2004
CONTRACT/PR NO. DAAE07-03-D-L003/0001
ABSTRACT
This
paper presents an efficient optimization-based algorithm for predicting dynamic
motion of a virtual soldier called “SANTOSTM” and determines the
energy consumption level. SANTOSTM,
an avatar developed at The University of Iowa, exhibits extensive modeling and
simulation capabilities with 49 degrees of freedom. SANTOSTM is a part of a virtual environment for conducting
human factors analysis consisting of posture prediction, motion prediction, and
ergonomics studies. This paper presents
part of the functionality in the SANTOSTM virtual environment.
Mathematical cost functions that evaluate human
performance are essential to any effort that would evaluate and compare various
ergonomic designs. It is widely
accepted that the ergonomic design process is actually an optimization problem
with many design variables. We propose
using the concepts of design variables, cost functions, and constraints to
formulate the optimization problem for motion/posture prediction. This
effort is basically a task-based approach that believes humans assume different
postures and exert different forces to accomplish different tasks. Muscle energy consumption is one of the human performance
measures, where total muscle energy is decomposed as mechanical work and
heat. Muscle mechanical work equals the
sum of work done against applied forces, change of kinetic energy, change of
gravitational potential energy, and change of muscle strain energy. Heat dissipation is the sum of muscle
maintenance heat, muscle shortening heat, and basal metabolic energy. This
energy formulation serves as a basic human performance measure and the power
(energy rate) serves as a cost function for realistic human motion/posture
prediction. The energy consumption
throughout the task duration serves as the fundamental basis for fatigue
prediction.
The principle of generalized coordinates and
generalized torques is utilized to create an equivalent model with least number
of independent variables. The inverse
dynamics problem is then solved for the joint torque profiles during the motion
prediction process.
The proposed formulation for the joint torque
prediction should be useful in future studies of muscle stress/strain
prediction during a given task. An
illustrative example task using a human upper extremity model demonstrates this
method.
An optimization-based method for layout design is
also presented. The layout problem is
defined by the method whereby positions of target points are specified in the
environment surrounding a human. Visual
discomfort as well as energy consumption is considered as a cost function to be
minimized. It is indeed shown that this
method yields the most comfortable regions in space for a particular
anthropometric model and for one or more cost function(s).
Keywords: power, energy,
optimization, mechanical work, inverse dynamics, human performance measures,
generalized coordinates and generalized torques, Layout design, vision, muscle
Chapter 1. Introduction
1.1.
Objectives
Digital prototyping is an important aspect of the design cycle. Digital human models are used to simulate certain tasks and performance of a human in virtual world. Some examples of tasks can be pulling a lever, lifting an object, turning a steering wheel, turning a knob, moving tools, pushing a button, and so on. Within the past decade, digital design and prototyping leading to a digital mockup has allowed extensive analysis and simulation to be carried in the digital world rather on an expensive mockup. A success story has been the continued accomplishment achieved by finite element analysis where it has saved industries considerable prototyping and testing. In analogy, the field of digital human modeling has not yet achieved great success, at least not with many industries. The goal is to create methods and tools that allow for human analysis, design, and evaluation without actually having a physical mockup of the environment.
This paper addresses one such tool that would
allow a designer to predict the realistic human motion during various tasks and
the performance level of the tasks. It
also allows predicting the most suitable location of controls to be located in
the immediate reach envelope of a person.
To that end, we propose a general approach to a mathematical-based
motion, joint torque, and muscle power prediction. We assume that the human naturally moves in such a way as to
minimize certain cost functions. In the
case of human behavior, we call the cost functions the human performance
measures. Therefore, we propose the
implementation of an optimization-based approach whereby human performance
measures are developed and utilized to predict the realistic motion and
posture. The problem is of interest to
ergonomists, automobile packaging engineers, and vehicle designers.
1.2.
Literature review
Some theoretical approaches were used to
predict human motion or posture. Hase et
al. (Hase and Yamazaki 1997) have simulated walking and rowing motions using
rigorous muscle energy consumption formulas and human model. They have used the Newton-Euler method to
calculate the joint torques. However,
computing the muscle energy consumption directly from the element muscle fiber
model takes lots of computing efforts, and thus this method may not be suitable
for real-time simulation. Chaffin
(1997) has developed two- and three- dimensional computerized human models for
simulation of static strength during work.
The program can also predict some critical values of low back, such as
back compression loads and disc shear loads.
Umberger et al. (2003) formulated rather
simplified, but quite exact muscle energy expenditure, based on Hill-type
muscle model and coefficients. Some
simple examples as isolated muscle actions, single joint motion, and locomotion
are simulated and the computed energy values were compared with experimental
results. Another approach for obtaining
energy cost has been used by Alexander (1997).
Alexander’s energy formula is very simple and experiment-based. That energy cost was minimized to solve for
realistic human arm trajectories.
Significant research has been done on muscle energy
analysis, joint torque, and muscle control by Khang et al. (1989a,
b). They have simulated paraplegic
human anterior-posterior postural control in sagittal plane by simplifying the
links of the ankle, knee, hip, and trunk in two dimensions. Simple muscle model was used to formulate
muscle activation and contraction dynamics.
The muscle energy as a function of muscle active state and muscle force,
was minimized within the feedback control loop.
These works have shown acceptable results on the
human motion simulation. However, since
these researches are based on muscle activation states and the details of
muscle functioning mechanisms, the computational effort is too high and thus
not suitable for real-time dynamic simulation.
There have been
many studies on quantifying human discomfort.
The majority of these studies are experimental, that delimit ‘comfort’
and ‘convenient’ reach zones where objects may be placed for operators, to
reduce effort and minimize potential injuries (Lim and Hoffmann 1997; Das and
Sengupta 1996). Implementing a systematic
optimization scheme in ergonomics has been, to a certain extent, addressed by
some researchers (Fisher 1993, Pham and Onder 1992). Wiker et al (Wiker, Chaffin, and Langolf 1990) studied on
experimental relationship between discomfort/fatigue and arm postures in manual
performance to test the effect of strength capacity in the shoulder-complex on
the task environment.
Also,
there have been some studies where discomfort function is formulated based on
statistical data from experiments that reflexes the psychophysical
factors. This discomfort function is
then used to predict the posture of a 7 degrees-of-freedom model for given
target endpoints (Jung
and Choe 1996). Delleman et al
(Delleman and Dul 2002) measured each subject’s perceptions during operation to
formulate some guidelines for a comfortable work environment at the traditional
sewing machine workstation.
1.3.
Overview of the report
Our
approach is from rather macroscopic point of view using the principle of
generalized coordinates and generalized torques. We first introduce the kinematic modeling of human joints and
links using the method typically used in robotics. Based on this kinematic human model, we derive the muscle energy
consumption formula as a human performance measure. Muscle models are discussed for dynamics formulation. We then derive a general equation of motion
and muscle power cost function. Using
these equations, an optimization formulation is developed for simulation of the
natural human motion. An example of
joint torque and muscle power prediction is illustrated. Also, a formulation of optimum layout design
is developed using energy consumption and vision discomfort as multiobjective
cost functions. Conclusions and future
works are addressed. The ultimate goal
is to provide more intelligent human factors of soldiers within virtual
environment.
Chapter 2.
Kinematic human modeling
2.1.
SANTOSTM model
Whereas the anatomy of limbs and their joints are indeed very complex (as evidenced by the debate in the literature on the correct method for modeling joint motion), we will employ a kinematic pair (or combination thereof) as used in the field of robotics (which indicates a constrained kinematics joint). For example, if the resultant motion is rotational, the joint will be modeled as a revolute joint. The effect of a spherical joint is modeled as three revolute joints whose axes intersect at the center of the sphere. Indeed, all anatomical joints can be modeled using basic kinematic pairs.
A
digital human model called SANTOSTM, developed by The University of
Iowa, has 49 degree-of-freedom (DOF) where all the joints are modeled as
revolute joints (figure 1). It is an
anatomically realistic human model developed mainly for overall motion and
posture prediction.
Figure 1. SantosTM with 49
degree-of-freedom
2.2.
DH Parameters and Transformation Matrices
Using only
four parameters to describe
one coordinate system with respect to another, the position and orientation of
each axis determine the four DH parameters 
, and hence, determine the resulting 
transformation
matrix. To establish this matrix, it is
possible to observe that a vector 
resolved in the ith coordinate system may
be expressed in the (i-1)th
coordinate system (
) by performing four successive transformations as follows.
(a) A rotation about the 
axis by an angle of 
to align the 
axis with the 
axis (as shown in Figure 2, 
and pointing in the
same direction).
(b) A translation along the 
by a distance of 
units to make 
and 
aligned.
(c) A translation along the 
axis by a distance of
units to make the two
origins of the 
and 
systems coincide (the
and the 
will also be
aligned).
(d) A rotation about the 
axis by an angle 
to coincide the two
coordinate systems.
Figure
2. Establishing coordinate systems and the four D-H parameters
In order to obtain a systematic representation of
any serial kinematic chain, we define 
as the vector of n-generalized coordinates defining the
motion of a limb with respect to another, where 
is the individual DOF
variable. The position vector function (shown in Figure 3) generated by a point
of interest (typically on one of the fingers) is written as
where 
can be obtained from
the multiplication of the 4x4 homogeneous transformation matrices 
defined by the DH
method (Denavit and Hartenberg,
1955, Paul 1981, and Fu et al. 1987) such that
where 
is the joint angle
from 
axis to the 
axis for a revolute
joint, 
is the shortest
distance between 
and 
axes, 
is the offset
distance between 
and 
axes, and 
is the offset angle
from 
and 
axes.
The
4x4 transformation matrix 
used to represent ith
joint coordinate system with respect to the global base coordinate system (0th)
is
We
use the augmented 4x1 vector 
and 
to express the
Cartesian coordinate of the point fixed in the ith local frame in
terms of global and local coordinate system, respectively:
, 
where, 
is the fixed point at
the link i and expressed with respect to the ith coordinate system.
Using these relationships, 
can be written as
Figure
3. Definition of the position vector function 
Chapter 3. Human
performance measures and Energy consumption
3.1. Basic assumptions and optimization
Finding the natural human motion where human body system has redundant degrees-of-freedom, is a problem of finding the best solution among many feasible solutions. Our first assumption on the human motion/posture is that different tasks lead to different postures and different forces. Our second assumption on the natural human motion/posture is that human moves in such a way to minimize certain cost functions. These cost functions are called human performance measures. Indeed, the word “minimize” give rise to exploring the use of optimization as it addresses how to determine “the minimum” value from certain feasible domain. Thus, predicting human motion can be formulated as an optimization problem, where our purpose is to find the design variables that minimizes human performance measures subject to several physical and physiological constraints.
3.2. Human performance measures and energy consumption
Several human performance measures have been investigated and shown to produce various natural motions and postures (Yang et al. 2004; Kim et al. 2004; Khang and Zajac 1989a, 1989b). Some examples of human performance measures are, energy, muscle force/torque, discomfort, muscle fatigue, instability, effort, cardiovascular fatigue (heart ratio), biomechanical stress, vision discomfort, and so on.
The energy consumption is one of the most widely used cost functions in human simulation studies. This makes sense because the energy consumption (or, power at each time) measures how much ‘effort’ is consumed for any given motion. Food and oxygen are the main source of human energy. The Calories to fuel the muscle activation are supplied (via the intestinal tract) from food eaten just before or on the activation, or from the body's internal energy reserves (fat, glycogen) in the liver, fatty tissue, or in the muscle itself.
In fact, it is well known that energy consumption and muscle fatigue have positive correlation (Sahlin et al. 1998, Khang and Zajac 1989a). Therefore, minimum energy consumption indicates less muscle fatigue. We will use the minimum muscle power criteria for general motion/posture prediction in Chapter 5.
3.3. Muscle models and formulation of muscle elasticity
Several muscle models were proposed in the
literature, for example, Hill’s model (Hill, 1938) and Zajac’s Muscle model
(Zajac, 1989). Most of the proposed
muscle models have two main components - contractile components and
series/parallel elastic components (Figure 5).
Figure 5. Typical Muscle
Model
The muscle contractile elements generate tension
force by contracting themselves and act as actuators. The elastic elements of muscles contribute to the corresponding
single degree-of-freedom joint motion in complex ways due to the variable and
nonlinear muscle configuration during motion.
Considering only the effective elastic behavior at the joint, we can
regard the whole muscle elasticity mapped to the joint space as a nonlinear
rotational spring attached to each joint.
Then there exists resultant rotational spring constant for each joint,
which has the same effect as actual muscle elasticity. Thus, any change of the joint angle from
neutral position will result in restoring torque 
, which can be linear-approximated as:
where ks is appropriate equivalent
rotational spring constant for each generalized joint spring, and 
is the neutral joint
variable corresponding to sth joint angle 
. The variable
coefficient ks is assumed to be given as a specified weight value
for each 
. In vector-matrix
form, this equation is rewritten as below.
