Proceedings of the ASME 2011 International Design Engineering Technical Conferences &
Computers and Information in Engineering Conference
IDETC/CIE 2011
August 28-31, 2011, Washington, DC, USA
DETC2011-47746
DESIGN OF A FOUR-DOF MODULAR SELF-RECONFIGURABLE ROBOT WITH
NOVEL GAITS
Khoa D. Chu, S. G. M. Hossain and Carl A. Nelson
University of Nebraska-Lincoln
Dept. of Mechanical Engineering
N104 SEC
Lincoln, NE 68588
USA
Keywords: modular robots; reconfigurable robots; unstructured environments; robot gaits
ABSTRACT
Throughout the modern age, exploration of the unknown has
been an attractive pursuit to seekers of knowledge. One of the
primary frontiers for exploration today involves planetary and
lunar environments. Exploration in these environments can
involve many different types of tasks in a broad range of
environmental conditions. Modular Self-Reconfigurable Robots
(MSRs) would be beneficial for completing these tasks in
unstructured environments, while having the ability to complete
multiple assigned functions. Since payload is a critical concern,
a lighter and more dexterous MSR is preferable. This research
focuses on the design of a robot that has these qualities. A
chain-type modular robot with four degrees of freedom per
module has been designed with the goal of reducing weight and
size while increasing range of motion. Forward kinematic
transformations were derived to analyze the available
workspace provided by the MSR. Radio communication and
proximity sensing ability were provided in the individual MSR
modules to locate each other. The modules are designed to
maneuver independently using their individual navigation
capability as well as connect to each other by means of a
docking mechanism. Locomotion gaits for such multi-module
robot chains are also described.
1. INTRODUCTION
Many mobile robots are designed for specific tasks and are
optimized for those tasks. Though this approach provides
predictability and robustness under known operating conditions,
these robots are not well suited for uncontrolled environments
in which the tasks are unknown, such as space exploration [1].
During the last two decades, space exploration has increased
tremendously with the launch of the Hubble Space Telescope,
International Space Station, and current and past Mars landings.
Though these space missions were successful, there were times
when various equipment launched in space had to be repaired.
To enable the next wave of space exploration, robots would
need to be able to thrive in uncontrolled environments and be
able to self-reconfigure or adapt to complete these various
tasks.
We introduce a modular robot that can self-reconfigure to
complete diverse tasks in uncontrolled environments. Modular
self-reconfigurable robots (MSRs) are a type of robot that
consists of many identical programmable modules; these
modules can self-reconfigure, self-repair to adapt to different
environments, and complete multiple tasks without direct
outside intervention.
Types of Modular Self-Reconfigurable Robots
There are three main types of MSRs: chain, lattice, and
hybrid. These differ in design and their way of operation during
motion and self-reconfiguration.
 Chain Reconfiguration: Chain MSRs use continuousmotion kinematic joints. They are capable of attaching
and detaching their modules to other modules within
the system, thus making it easier for movement and
completion of different desirable tasks [2].
 Lattice Reconfiguration: Lattice MSRs use binary
kinematic states. The lattice type robots change their
overall shape by moving each module within a network
of bordering modules. For example, a block of cubic
unit cells changes its shape with the shifting of each
cubic cell within a grid [2].
 Hybrid: Hybrid MSRs can change shape using both
the chain and lattice reconfiguration features [3].
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Copyright © 2011 by ASME
In this research, the main focus is on chain- and hybridtype MSRs. Examples of these chain-type MSRs include
PolyBot [2], Polypod [3], CONRO [4], MTRAN III [5], and
SuperBot [6]. Though these robots are well developed, a goal of
this research is to create a robot for space applications (or other
unstructured environments) with greater kinematic abilities and
more dexterity [7]. Therefore, we are specifically interested in
3-D MSRs (not constrained to planar motion) with a high
number of degrees of freedom (DOF). From the list presented in
Table 1, several robots including Polypod, CONRO, MTRAN
III, and SuperBot are all identified as having qualities beneficial
to applications of MSRs in space exploration [7].
Table 1. Characteristics of certain MSRs.
System
YaMor
[8]
Tetrobot [13]
PolyBot
[2]
Molecube [11]
CONRO [4]
Polypod [3]
MTRAN III [5]
Superbot [6]
Class
chain
chain
chain
chain
chain
chain
hybrid
hybrid
DOF
1
1
1
1
2
2
2
3
Motion Space
2-D
3-D
3-D
3-D
3-D
3-D
3-D
3-D
The new MSR has features similar to these robots but
exceeds their dexterity. SuperBot was built with three DOF and
currently has the highest number of DOF for a hybrid type.
SuperBot’s three joints enable it to rotate on both ends of its
module and to rotate at the center of its body [9]. The new MSR
includes four DOF – three rotational (revolute) joints and one
translational (prismatic) joint – as shown in Figure 1. This
change in design will improve the ability of MSRs to perform
multitasking needed in future space exploration applications.
Another important design aspect for MSRs is the docking
mechanism, which needs to be robust, simple, low in power
consumption, fast-acting and accurate. In examples of docking
in previous research, EM-Cube [14] used permanent magnets
and electromagnets, Tetrahedral Walker [15] used threaded
connectors, and S-Bot [16] used gripper based connectors,
whereas Polybot [2] and CONRO [4] used SMA controlled
mechanisms for docking. More recent designs such as MTRAN
III [5] used mechanical interfacing using hooks which allowed
for better correction of alignment. Many of these robots
including the recently developed Cuboctahedron [17] modules
used classic peg-hole mechanisms coupled with electrically
controlled latching. Therefore, the MSR modules described in
this paper take influence from these works but also use some
novel design aspects such as using square-shaped components
for better interfacing and latching solenoids instead of SMA to
enable faster response and good power efficiency.
Improvement of Modular Self-Reconfigurable Robots
To generate an improved MSR design and to build from
previously designed robots, the following questions are of
interest:
 Can the number of actuated degrees of freedom (and
hence the dexterity) be increased while maintaining
low weight and low volume?
 Can improvements in dexterity be shown to lead to
improvements in the ability of the system to selfreconfigure and/or to achieve various forms of
locomotion?
 What are the optimal geometric parameters to maintain
both high dexterity and low weight/size?
 What is the minimum size/weight of actuators and
power sources that can be used while still providing
adequate driving forces/torques for the environment in
which the system will be used?
The analysis presented in this paper represents a step
towards answering some of these questions. In particular, we
focus in this paper on dexterity improvements, the associated
kinematic analysis, and resulting achievable gaits.
2. 4-DOF MSR DESIGN
Figure 1. A simple model of the MSR showing the four
(RRPR) degrees of freedom.
Figure 1 shows a simple 3-D model for visualizing the
robot module’s layout. The MSR module has five main
components: two end-brackets where modules can interconnect
and three central box-shaped sections housing motors,
transmissions, circuit components and power supply. The two
end brackets can rotate ±90°. The interface between the two
central parts (twisting box and central box) incorporates a
sliding DOF along their common axis of symmetry. A rotational
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Copyright © 2011 by ASME
DOF about that same axis is provided in the interface between
the central box and the sliding box (the box at the bottom as in
Figure 1).
The MSR modules were designed to minimize mechanical
complexity to help increase overall robustness, which is a key
factor in space applications. The first prototype of the MSR was
designed with two motors and binary actuators (solenoids) to
provide four degrees of freedom. This contained chain-sprocket
transmission and clutching mechanisms but had the limitation of
not all DOFs being independent. The second prototype was
implemented with all 4 DOF independently actuated, and it was
found through a simple torque analysis that the number of
actuators and the overall weight and volume of the modules
could be maintained while achieving the required dexterity. For
weight consideration, the modules were fabricated out of
aluminum sheet metal. Each module of this MSR has four
motors (three stepper gear-motors and one stepper linear
actuator). In one module, the combined weight of the actuators
is just above half of the overall weight of the module. The
translational DOF is achieved by means of a linear actuator,
which provides high force while remaining light-weight. Figure
2 shows the motors and docking mechanisms where this
comparison can be visualized.
Figure 2. Scaled 3D CAD model of a single MSR
module showing four motors for the four DOFs and
docking mechanisms with two solenoids. Each
module weighs approximately 6.5 lbs.
The improvement in dexterity achieved could be reflected
by the independent use of the DOFs, which could offer
possibilities of increased ability to self-reconfigure and perform
locomotion or manipulation tasks. The length of the MSR
module was minimized by accommodating the motors and
transmissions for rotating the end-brackets in a plane
perpendicular to the length of the module. For the central box
motor, this design feature was not applied to avoid complex
mechanisms which could affect the weight and robustness. The
docking mechanism is controlled by binary actuators
(solenoids) that can latch one end bracket into another using a
slim and simple crank-latch, which engages into a symmetric
arrangement of docking pins. Using this low-profile mechanism,
the ratio of overall length of the module to extension range
(prismatic DOF) was minimized; this improves workspace
characteristics. Furthermore, decreasing the length offers
reduced torque and weight requirements for the rotary motors
and thus may further reduce the overall weight for the MSR.
Figure 3 shows more details of the latching mechanism for
docking two modules. The pegs enter through the square holes
and the latch plate locks the pegs by means of the solenoid
actuation. Pegs were designed as pyramid-shaped to provide
self-alignment. The holes were made square-shaped to achieve
better gripping while latching. The pyramid peg-square hole
combination provides a ±0.25 inch tolerance for the alignment,
which is an advantage in the case of non-idealized docking.
Experimentation to validate docking was completed by
interfacing the manufactured docking brackets together.
Figure 3. Docking of two end brackets driven by a
solenoid operated latching mechanism to enable
multi-module configurations.
The electronic components can be classified in three main
groups – sensors, controls and power supply. Infrared proximity
sensors (range: 4cm – 30cm) are provided to detect other
modules or obstacles. Compass and tilt sensors are provided for
navigation. XBee radio is provided for the modules to
communicate among themselves (range: 120m). The motors are
controlled by an Arduino microcontroller via stepper motor
driver circuits. The sensors and binary actuators were also
controlled through the Arduino. 3.7 volt Li-Po (Lithium
polymer) batteries are used to power the circuits and actuators.
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Copyright © 2011 by ASME
The mechanical design of the MSR modules allowed enough
space for all these electronic components so that the modules
could operate independently and without being tethered.
Figure 4. Two MSR modules manufactured primarily
from aluminum sheet metal. The standard CD (4.7
inch diameter) is provided for size comparison.
3. KINEMATIC ANALYSIS
The transformation matrix for a combination of two MSR
modules was derived using the technique of coordinate
transformations. Denavit-Hartenberg (DH) parameters were
used to define these coordinate transformations in 3-D space
[10]. The DH general equation for coordinate transformation
based on Figure 5 is:
 si
0
ai 1 
 ci
 s c
c

c


s


s
 i 1di 
i
i 1
i
i 1
i 1
i 1

T

i
 si s i 1 ci s i 1 c i 1
c i 1di 


0
0
1 
 0
(1)
Figure 5. Kinematic reference frames for the MSR. A
two-module docked configuration is shown.
Eight matrix transformations were derived based on the DH
method to represent the coordinate frames shown in Figure 5.
These were then used to identify a global transform for forward
kinematics in the joint variables as follows.
T  01T 21T 23T ... N N1 T
0
N
(2)
Table 2. DH parameters for a two module MSR.
i
1
2
3
4
5
6
7
8
αi-1
0
0
θ2
0
0
0
θ5
0
ai-1
0
l1+d1
0
l2
l3
l4+d2
0
l5
di
0
0
0
0
0
0
0
0
θi
θ1
0
0
θ3
θ4
0
0
θ6
Using the result of the forward kinematics simulation for
one and two MSR modules (N = 4 and 8 respectively) and the
ranges of joint motions, approximate workspaces were plotted
(see Figure 6) to visualize the range of motion that the robot
could potentially achieve. With a single module as in Figure
6(a), the workspace is approximated by a half-toroid. Adding
one more module as depicted in Figure 6(b) offers a much
larger workspace with a near-spherical volume (excluding a
small area near the fixed docking bracket). This indicates that
dexterity and the potential for a variety of configurations
increases quite rapidly with increasing numbers of modules; this
constitutes one of the main advantages of this design compared
to other MSRs.
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Copyright © 2011 by ASME
Figure 8. The MSR using an inchworm locomotion.
(a) Single module workspace (N = 4).
(b) Double module workspace (N = 8)
Figure 6. The (a) single and (b) double module
configurations are pictured in green for a visual frame
of reference, and the position workspace (one end
fixed with the opposite end considered the end
effector) is in gray. This is based on the range of
motion of the joints (brackets’ rotation ±90°, axial
twist unlimited in both directions, translation 0”-2”)
The translation DOF increases the workspace volume
substantially (e.g., increasing the thickness of the
half-toroid in (a)).
4. LOCOMOTION GAITS
Figure 7. Multiple modules of the MSR linking
together to reach and climb over unstructured
obstacles.
Figures 7 and 8 illustrate the MSR’s motion capabilities.
Figure 7 shows how the fourth (prismatic) DOF can be used as
an advantage to reach across long obstacles. Figure 8 shows the
single-module inchworm locomotion step that the MSR would
be able to accomplish using the fourth DOF; this is believed to
be unique among existing chain-type unit-modular robot
systems.
To maneuver across unstructured terrain, the 4-DOF MSR
offers unique locomotion. In Figure 9, the schematic shows five
different possible MSR locomotion gaits. The first gait involves
only one MSR module and uses the translational DOF to
generate an inchworm-type locomotion. The second gait is also
an inchworm motion, but it uses two MSR modules linked
together such that no part of the robot is dragged along the
ground. The final three gaits listed are somewhat more unique
and describe a pair of MSR modules rolling sideways, steering
while moving forward in the inchworm mode, and steering
while rolling. To the authors’ knowledge, these gaits are not
achievable in 2-module configurations of other existing MSRs.
Even though the two-module configuration is enough to
demonstrate simple locomotion, with the addition of three or
more modules the locomotion can become more complex and
difficult to visualize; therefore in the context of this paper we
limit ourselves to demonstrating 2-module configurations. The
X-Y reference axis for each individual gait diagram is placed at
the far left of the module(s). The gait illustrations show the
beginning position of the MSR modules, followed by several
subdivided steps, and ending with the reference position to
finish the cycle.
For simplicity in representing the gaits, a triangle is placed
at the end of each module, representing the end’s rotational
DOF. A vertical line in the center of each module represents the
contraction of the translational DOF. Two parallel lines
represent the extension of the translational DOF. The third
rotational DOF of the MSR is located between the translational
and right-most rotational DOF. To further describe the
illustration, a set of numbers are used to represent the position
states of these DOF. The value of +1 represents
open/up/clockwise/extend,
while
-1
represents
closed/down/counterclockwise/contract, and 0 is the neutral
state. The different gaits with their DOF values are outlined in
Figure 9.
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Copyright © 2011 by ASME
(d) Two-Module Inchworm and Steering
(a) One-Module Inchworm
Module 1
Module 1
Module 2
Degree of Freedom
R
T
R
R
R
T
R
R
Degree of Freedom
R
T
R
R
Step 1
0
-1
0
0
0
-1
0
0
Step 1
0
-1
0
0
Step 2
-1
-1
0
0
0
1
0
-1
Step 2
-1
-1
0
1
Step 3
-1
-1
0
0
0
1
1
-1
Step 3
-1
1
0
1
Step 4
-1
-1
0
1
1
-1
0
1
Step 4
1
-1
0
-1
Step 5
-1
-1
0
-1
-1
-1
0
-1
Step 5
0
-1
0
0
Step 6
1
1
0
1
1
-1
0
-1
Step 7
-1
1
0
0
0
-1
0
-1
Step 8
0
-1
0
0
0
-1
0
0
(b) Two-Module Inchworm
Module 1
Module 2
Degree of Freedom
R
T
R
R
R
T
R
R
Step 1
0
-1
0
0
0
-1
0
0
Step 2
-1
-1
0
0
0
1
0
-1
Step 3
-1
-1
0
1
1
1
0
1
Step 4
-1
-1
0
-1
-1
-1
0
-1
Degree of Freedom
R
T
R
R
R
T
R
R
Step 5
1
1
0
1
1
-1
0
-1
Step 1
0
-1
0
0
0
-1
0
0
Step 6
-1
1
0
0
0
-1
0
-1
Step 2
1
-1
0
0
0
-1
0
-1
Step 7
0
-1
0
0
0
-1
0
0
Step 3
1
-1
1
0
0
-1
0
-1
Step 4
-1
-1
0
0
0
-1
1
1
Step 5
-1
-1
0
0
0
-1
0
1
Step 6
0
-1
0
0
0
-1
0
0
(e) Two-Module Rolling and Steering
Module 1
Module 2
(c) Two-Module Rolling Sideways
Module 1
Module 2
Degree of Freedom
R
T
R
R
R
T
R
R
Step 1
0
-1
0
0
0
-1
0
0
Step 2
-1
-1
0
1
1
-1
0
-1
Step 3
-1
-1
1
1
1
-1
1
-1
Step 4
-1
-1
0
1
1
-1
0
-1
Step 5
0
-1
0
0
0
-1
0
0
Figure 9. Five different MSR gaits explained using
step by step actuations of the four DOFs.
We can obtain information about the complexity involved in
each gait by comparing the numbers of actuations involved.
From the gait tables, we find that for the five gaits, this number
is 11, 30, 24, 35 and 22 respectively. For comparison, several
other published gaits on simple modular robot platforms include
11 (standing-wave crawling [18]), 16 (double-stride inchworm
[19]), and 13-31 (standing-wave inchworm [19]) actuations.
5. DISCUSSION AND CONCLUSIONS
In the design presented here, the approach was to offer
dexterity to the robot by means of increasing the per-module
degrees of freedom as compared to other MSRs. This allows the
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Copyright © 2011 by ASME
MSR to remain compact and robust but achieve significantly
larger per-module workspace and a variety of gaits using a
small number of modules. Unlike herd or swarm robotic
systems, these robot modules were designed to work in lower
numbers while performing relatively dexterous tasks and
achieving flexible gaits in unstructured environments. However,
this requires a balance between the size or torque requirement
of the actuators and the overall module weight and size.
It seems apparent that the increase in dexterity (particularly
the collocated prismatic and rotational DOFs in the center of the
module) will facilitate reaching configurations previously not
attainable. This should enable enhanced functionality and task
adaptability, which is one of the prime objectives of MSRs.
The weight/power tradeoff in the MSR design is closely
tied to motor selection. This in turn is dependent on the
environment in which the robot will be used (e.g., lunar,
Martian) as well as the tasks that may be considered typical. In
the current embodiment, the MSR module has been designed
for general tasks typical of those which would be required in
lunar colonization. The authors recognize that the laboratory
environment where the robot was developed did not offer such a
reduced-gravity environment. For space applications using this
MSR, the weight and torque specifications would be altered to
match the operating conditions.
MSRs can thrive in unstructured environments, selfreconfigure, and complete multiple tasks. This research focused
on designing a more dexterous chain-type MSR. The primary
design goal was to increase the number of DOF to four and
allow each DOF to be actuated independently in order to
facilitate reconfiguration for general and various tasks in
unstructured environments. Kinematic analysis and weight
considerations were used to measure progress toward this goal.
Additional important findings that are pertinent to practical
use of such a robot include gait planning. Here several simple
gaits have been presented, illustrating the relative advantage of
the new MSR compared to other less dexterous MSR designs.
This added dexterity allows the MSR to achieve greater task
adaptability.
To this point, the MSR design was validated by computeraided simulation using the Webots simulation platform, in
which it was possible to generate the gaits discussed in this
paper [20]. In addition, using at least four modules, it was
possible to achieve circular rolling and twisting gaits similar to
those demonstrated using other MSR designs in the past. Figure
10 illustrates the generation of the circular rolling configuration.
Figure 10. Circular rolling motion with four modules.
Future work includes further experimental validation of the
prototype system for achieving various possible gaits.
Experiments using at least two modules to show robustness of
docking capabilities, range of motion, locomotion, and selfreconfiguration are also anticipated. This is expected to lead
toward future applications of MSRs for space exploration.
ACKNOWLEDGMENTS
This research was made possible in part by the University
of Nebraska-Lincoln Undergraduate Creative Activities and
Research Experience program, the UNL McNair Scholars
program, and NASA Nebraska Space Grant, and with
collaboration from Dr. P. Dasgupta at the University of
Nebraska at Omaha.
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