IEEE Robotics & Automation Magazine - September 2017 - 38

the humanoid robot Romeo, and the whole movement is
reproduced by the robot. One of the main differences
between Romeo's movements and human movements from
the Kinetography Laban perspective (i.e., in terms of symbols
and signs in the Kinetography Laban score) is the arc with the
capital letter "I" to the side of each direction symbol inside the
arm columns (see Figure 7 and [6] for details about other differences). This new symbol indicates a description of the path
that the free end of the arm is now executing, i.e., a straight
line. In the context of the Kinetography Laban system, the
addition of this sign to the side of each direction symbol constrains the movements of the free end of the part of the body
to which the symbol refers along a straight line. Without that
sign, the movement adheres to the implicit rules of the
Kinetography Laban system that, after several years of analysis, reflect the natural way of moving.
The direction symbols state only information concerning
the element of direction. Once they are placed in the appropriate column of the vertical staff, it is possible to determine which
part of the body has to move. Moreover, depending on the current configuration of the body, information about the path that

Figure 7. A sequence of snapshots for the movement at step 6
in the Kinetography Laban score of Figure 6(a). The free end of
the right arm moves along a straight line between the starting
position and the desired one. This gives rise to other undesired
and unnatural movements. In this case, the elbow (red point)
does not remain at a fixed position in space.

First

Second

Third

Fourth
Figure 8. The degree of distance between direction symbols.
According to this distance, the free end of the arm has to
generate a peripheral movement, a transversal movement, or a
central movement.

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IEEE ROBOTICS & AUTOMATION MAGAZINE

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the free end of the body part to which the symbol refers can
also be obtained, giving rise to so-called implicit rules.
The information about the movement execution is
achieved from the concept of degree-distance between
direction symbols. Each symbol indicates a point to be
reached around the point of attachment of the body part
(e.g., the shoulder for the arm). Symbols that correspond
to adjacent points in space are at a first-degree distance
from one another (see Figure 8). For example, if the arm
moves from forward-middle to the adjacent right-front
diagonal point, this is a first-degree distance. In this case,
the free end of the arm, i.e., the hand, describes an arc-ofcircle on the surface of the sphere whose center is the
shoulder. This is called a peripheral movement in the
Kinetography Laban system. All movements between firstdegree distance points produce this type of path. If the arm
moves from forward-middle to side (right or left)-middle,
then the starting and ending points are at a second-degree
distance (see Figure 8), and the hand describes a quarter
of circle with respect to the shoulder. In this case, we also
obtain a peripheral movement. All movements between
second-degree points are performed without any special
flexion of the arm unless otherwise specified with the
addition of particular signs.
If two points are at a third-degree distance, the hand
moves along a trajectory close to the body. This movement is
not a peripheral path. Indeed, the arm is slightly bent, and the
free end of the arm takes a path between periphery and center
(in place). This is called an intermediate situation or a transversal movement.
Finally, diametrically opposite points are at a fourthdegree distance. This is the case when the arm moves from
forward-middle to the extreme opposite direction, i.e., backward-middle. The arm moves back into place, and then it
extends outward again. These types of movements are called
central movements in the Kinetography Laban system.
The control laws used to move Romeo's arms do not
generate all of these various movements. Instead, the control laws implemented in Romeo simply reduce the distance between the current configuration of the free end of
a body part and the desired position. The resulting path
for the free end of a body part is a straight line with a
noticeable loss in naturalness. To generate a straight-line
path, other undesirable and unnatural body movements
are necessary. To avoid such unnatural movement, an ad
hoc control law that moves the free end of a body part
along peripheral, central, or transversal movement might
be determined. The implicit rules of the notation come
from several years of observations, and they are based on
the naturalness of human movements and the mechanical
structure of the body. As is often conjectured in robotics,
an optimality principle might be inherent in human movements [5]. Thus, it would be interesting to understand this
principle, to express it in a suitable mathematic manner,
and then to use it to determine suitable control laws for
humanoid robots.
Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - September 2017
