IEEE Robotics & Automation Magazine - December 2013 - 77

103

1 /w $w $w $w $s,
2 i =1 l k j i i

(1)

where s i is the score given to each
mobility, maneuverability, or transition leaf; w i is the weight for that
individual score; w j is the subdomain weight; w k is the mobility or
maneuverability weight; and w l is
the domain weight. There are a total
of 103 components that make up
versatility, and the overall score is
normalized to one.
Complexity
For this article, we focus solely on
mechanical complexity. We postulate
that mechanical complexity is related
to the number of actuators and the
order of the system's kinematic
chains. Thus, of two systems with the
same kinematics, the one with fewer
actuators would be less complex.
Similarly, of two systems with the
same number of actuators, the one
with the higher order kinematic
chain would be more complex. Based
on this, the following metric is proposed for complexity, C:
C = N A $ N J,

Obstacle
Mobility
M1

M7
Convex

Subaquatic

M1
M7

Surface

Aerial

Aquatic

Inverted

Terrestrial
Deformable

Smooth

Flat

Scansorial
Versatility

Transitions

Rough

M1
M7

Domains

Rough

Subdomains

T1
T7

M7
Obstacle
Mobility

Mobilities

Figure 3. The versatility tree. Mobilities M1-M7 correspond to x, y, z, roll, pitch, yaw, and
hover. Transitions T1-T7 correspond to transitions among terrestrial, scansorial, aerial, and
aquatic domains. For a description of the obstacle mobility, see Figure 2(b).

(2)

where NA is the number of actuators and NJ is the number of
joints. For example, RHex [52] has a complexity value of 36
(6 DoF # six actuators). Again, this metric for complexity is
sufficient because the goal of the study is simply to understand the relationship among robots. Thus, it is not critical to
use a highly intricate and potentially convoluted metric.
Results and Discussion
This section presents the results of an in-depth study into the
current state of mobile robot design with consideration of the
above-defined metrics of versatility and complexity. It includes
a study of 85 systems that represent either basic configurations
(e.g., a standard tank) or unique locomotion designs.
The goal is to understand the relationship between versatility and complexity and identify any technologies or strategies
that yield a highly versatile system without requiring a high
level of complexity (Figure 4). We examined wheeled, tracked,
legged, modular/reconfigurable, aquatic, and aerial systems.
However, we focus on terrestrial and scansorial systems
because of an abundance of variety in their designs.
Grading for versatility is done by multiple people, and the
scores are compared in an effort to ensure consistency. However, because of the subjective nature of the grading, one
should view these results as a way to observe trends in mobile

robot design and not as definitive proof that one robot may be
superior to another.
We hypothesized that there would be a positive correlation
between versatility and complexity, but Figure 4 shows that no
such correlation exists. However, this is not unexpected as, in
many cases, designers are not attempting to create versatile
robots. For example, scansorial robot designs are not mature
enough for designers to consider additional functionality. In
other cases, there is a clear disconnect between the theoretical
possibilities of the system and the available technology. This is
evident in the modular systems, which may be capable of
rudimentary locomotion on a wide variety of surfaces, but do
not have the performance capabilities of their counterparts
that use dedicated wheels, tracks, or legs for locomotion.
To better understand the versatility/complexity relationship, consider only the systems that exhibit the best versatility for a given complexity (Figure 5). In other words, a robot
is removed if another robot with less complexity has a higher
versatility score. In this analysis, the correlation between
complexity and versatility is 0.97 for wheeled robots, 0.74 for
tracked robots, 0.93 for legged robots, and 0.92 for modular
robots. Several other points regarding mobile robot design
can be gathered from Figure 5, and each is discussed in the
next section.
DECEMBER 2013

IEEE ROBOTICS & AUTOMATION MAGAZINE

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - December 2013