IEEE Robotics & Automation Magazine - September 2011 - 88

human beings where movement style facilitates communication [9] and where instructions are given at a high level.
A number of human motions have been successfully
encoded using dynamic motion primitives [4] and labeled
with tasks, such as reaching, drawing, and arguably walking.
These primitives or movemes [2] are designed to produce
rich and complex human-like motions through systematic,
temporal composition. Traditionally, these primitives are
obtained from empirical data, e.g., collected using motion
capturing devices, that is segmented (often by hand [1] but
with progress toward automatic segmentation [6]) into
appropriate chunks and stored in a motion library [16]. But
full-fledged behaviors do not follow predictable, continuous
trajectories as humans constantly make discrete decisions
and may abruptly change behavioral modes, and there is no
clear method for stitching these chunks of stereotyped trajectories together [20]. Hence, a drawback of this representation
is that it cannot interpret long sequences of movement.
Furthermore, dance scholars have also attacked this problem. Notably, labanotation, created by Rudolf Laban [10],
[14], is a method for keeping track of a high degree-offreedom system. However, it has not integrated with the mainstream dance and is not amenable to robotics as it is nonintuitive and qualitative. Analogously, while many methods can
specify robotic control, the framework in this article uniquely
aims to bridge this gap and answer this exact dearth of engineering tools for movement analysis and generation and void
in our understanding of stylized movement sequences.
In this article, we draw inspiration from the formal principals of movement organization in basic classical ballet. The
execution of a few distilled rules produces highly sophisticated and complex motions; hence, this is an excellent candidate movement genre. Using the ability to produce movement
sequences as an initial metric for successful representation, we develop machinery to generate coherent movement phrases-in the style of classical ballet.
We extract static poses that are key to the experience of
classical ballet and dub them the states of a transition system.

*
Table 1. Basic movements from
the barre exercises.
Movement

Transition Label

Plie

plie

Releve

rele

Battement Tendu

Degaje

dega

tend

Coupe

Frappe

coup
frap

Grand Battement

Passe

pass

Battement
veloppe

deve

IEEE ROBOTICS & AUTOMATION MAGAZINE

gran
batt

SEPTEMBER 2011

Transitions between these states model the movements
between poses. This is the subject of [13]. Still, how do we
select among these many available pose sequences for one(s)
that is both physically feasible and aesthetically meaningful?
This problem requires discrete, non physical control methods
that can interpret high-level style specifications. Implementing
this full framework, we enumerate fundamental rules (hard
specifications) and secondary principles (soft specifications)
that govern this instantiation of stylized human behavior. In
the most basic sense, we are applying system verification and
model-checking techniques to a novel system. Our system's
unique properties require the full expressiveness afforded by
temporal logic statements. But more generally, the framework
in this article is sensitive to the void in our understanding of
the structure of movement sequences and dearth of tools for
movement analysis and generation for robotic systems.
This article extends the work detailed in [13] and [12]. By
creating more complex cases studies, we highlight the twofold goal of this work: On the one hand, we now require the
full expressiveness afforded by LTL to implement our stylistic task, and on the other hand, we produce an instantiation
of this basic classical ballet movement style.
A Discrete Model
A concept central to ballet's doctrine is that the barre trains
and safely warms the muscle groups critical to the correct
execution of the freestanding, full-fledged movements that
comprise the second portion of class and performances.
Hence, these canonical exercises contain the poses and
allowable trajectories through them that construct the
remaining vocabulary of ballet that is more rich and expressive. The term barre refers to the physical hand railing or
bar that dancers hold on to balance during the warm-up.
Exercises typically focus on one side of the body, the leg
dubbed the working leg, and are repeated twice to work both
sides of the body. As such, using the notion of a working leg,
we define ten states that correspond to poses in the body's
coronal plane (In classical ballet, this restriction still leaves
quite a rich vocabulary of movements to describe as many
balletic movements make extensive use of this plane.) that
are constructed from a triplet of joint angles: the hip, leg,
and ankle, as seen in Figure 1. These poses represent shapes
critical to the experience of ballet. They are chosen from
goal positions at the barre and, as such, are highly recognizable snapshots from the full vocabulary of ballet.
Table 1 lists basic movements from the barre exercises that
stitch together series of these goal poses (as demonstrated for
developpe in Figure 2. The event finishes in an upright standing position after the dancer closes her working leg next to
the standing leg.). It follows then that in our model, these
movements should correspond to transitions between states,
which are also listed in the table. Additionally, we distinguish
two transitions for each listed label using a subscript to indicate an in and out variant. The variants stem from the fact
that during a movement sequence, a dancer is either on the
way out to the goal pose or way back in to a previous one.

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - September 2011