A Novel Strut-type Modular Robotic Structure using Rigid Node

Weibing Li, Robert C. Richardson and Jongrae Kim

School of Mechanical Engineering, University of Leeds, LS2 9JT, Leeds, U.K.

Keywords:

Modular Robots, Rigid Nodes, Central Pattern Generators, Distributed Control, Physics-based Simulation.

Abstract:

This paper proposes a novel way of constructing strut-type modular robotic structures to avoid some difﬁ-

culties of designing and implementing ideal compliant nodes. Rigid nodes are employed to replace the ideal

compliant nodes and to reduce the structural complexity while the feasibility of hardware implementation

is dramatically improved. To release some kinematic constraints caused by the rigid nodes, we introduce

robotic struts that consist of two prismatic actuators linked by a passive revolute joint. Physics-based robot

models are constructed using a robot simulator. A scalable distributed control method is implemented using

coupled central pattern generators. And, for comparison, the same control method is applied to conventional

and the proposed strut-type modular robotic structures. Simulation results show that the proposed strut-type

structures have several advantages over the conventional ones including less number of passive joints and

shape-maintenance property.

1 INTRODUCTION

A modular robotic structure (MRS) consists of sep-

arate identical or different modules that can attach

to or detach from each other to make the whole

robot achieve manual or self-adaptive reconﬁguration

(Yim et al., 2007). One outstanding characteristic of

MRSs is their shape-changing capability. In modular

robotics, the following two shape-changing methods

have been widely studied:

• Reconﬁguration: an MRS can change its conﬁgu-

ration (i.e., connectivity) by attaching and detach-

ing robotic modules manually or self-adaptively.

• Deformation: an MRS with a speciﬁc conﬁgura-

tion can change its shape without changing the

connectivity of robotic modules.

Reconﬁguration endows an MRS with a wide range

of robotic structures which can emulate conventional

monolithic robots and are suitable for different tasks

under different working environments. Being differ-

ent from reconﬁguration, deformation can be used to

adjust the MRS shape to internal and external forces

exerted on the robotic structure.

To utilize the beneﬁts generated from reconﬁgu-

ration and deformation, numerous MRSs have been

designed and developed. Most of the existing MRSs

have block-like modules ﬁtted with only revolute ac-

tuators (Zhang et al., 2003; Kurokawa et al., 2006;

Østergaard et al., 2006; Salemi et al., 2006; Yim

et al., 2007; Spr¨owitz et al., 2014), which are suit-

able for reconﬁguration. Relatively less attention is

given on strut-type MRSs using prismatic actuators

(Curtis et al., 2007; Lyder, 2010; Yu, 2010; Zagal

et al., 2012), which are adept at deformation. A de-

sign case of using both prismatic and revolute actu-

ators can be found in (Baca et al., 2014). Usually, a

revolute actuator can only rotate around its axis, while

a prismatic actuator can elongate its body to reach

some positions in the workspace directly. Prismatic

actuators can form parallel truss-based structures that

provides inherent stability. Hence, prismatic actuators

may be more suitable for industrial activities such as

load transportation than revolute actuators (Ramchurn

et al., 2006).

In recent years, researchers have designed differ-

ent strut-type MRSs using prismatic actuators for in-

vestigating their deformation and locomotion capa-

bilities. Ideally, a strut-type MRS should have an

ideal node connector mechanism which can connect

numerous robotic struts. More importantly, robotic

struts can rotate around the node center with some

passive three degrees-of-freedom spherical joints and

robotic struts connected by a same node should have a

common center of rotation. In most simulations of the

existing literature, robotic struts are jointed by point-

like ideal nodes. Such point-likeideal nodes is helpful

to reducing the complexity of kinematics (Hamlin and

Sanderson, 1998) and providing compliant capability

for strut-type MRSs, however, physical implementa-

Li, W., Richardson, R. and Kim, J.

A Novel Strut-type Modular Robotic Structure using Rigid Node.

DOI: 10.5220/0006004502610268

In Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2016) - Volume 1, pages 261-268

ISBN: 978-989-758-198-4

261

tion of such ideal nodes is highly difﬁcult and even

impossible (Lyder, 2010).

A lot of efforts have been made to design and

implement an ideal compliant node. In the Tetrobot

project (Hamlin and Sanderson, 1998), a centric

multilink spherical (CMS) joint mechanism was de-

signed, which can let the extended lines of its con-

nected struts intersect at a same point. Such a CMS

joint design can not only make a homogeneousdesign

of Tetrobot possible but also simplify the kinematics

of structures. However, CMS joint cannot be used to

form chain-type structures. Additionally, CMS joints

tend to become too weak to sustain a massive robotic

structure. Moreover, the Tetrobot is hard to reconﬁg-

ure as adding or removing struts usually need to dis-

assemble the whole robotic structure (Lyder, 2010).

A workaround for constructing strut-type MRSs

is to use struts that have their own center of rotation

on the node surface. In such a solution, ball-and-

socket joints and universal joints are commonly em-

ployed. In (Yu, 2010; Lyder, 2010), passive ball-and-

socket joint based designs were adopted to provide

compliant movements. Another well-known connec-

tor mechanism is the one designed by NASA for a

12-tetrahedron (12-TET) robot (Curtis et al., 2007).

Speciﬁcally, NASA researchers developed two types

of connectors, one is a wheel-shaped node for loco-

motion and the other one is a special payload node.

The nodes endow itself with compliant ﬂexibility by

using passive universal joints. It is worth pointing out

that the above non-ideal compliant nodes do simplify

the physical implementation but make the kinematic

analysis more complex (Lyder, 2010). This may be

the reason why prototypes (e.g., Odin and 12-TET

modular robots) using such compliant nodes are difﬁ-

cult to control and can only complete simple locomo-

tion and/or deformation tasks.

Apart from the node design, another challenge

in modular robotics is to construct a uniﬁed control

framework that is both suitable to different modu-

lar robotic systems and scalable to robot size. Due

to the modularity of modular robots, distributed con-

trol methods are intrinsically more scalable than cen-

tralized control methods. The scalability of a phase-

automata based distributed control method developed

for chain-type PolyBot modular robots has been val-

idated by using a physical snake robot with 55 mod-

ules (Zhang et al., 2003). In (Yu, 2010), a scalable

control framework for realizing coordinating locomo-

tion of amorphous MRSs was established, analyzed

and veriﬁed. Such a scalable control framework is

based on a central pattern generator (CPG) based dis-

tributed control method.

Based on the above understanding, we focus on

using rigid nodes for constructing strut-type MRSs

to avoid the difﬁculty of implementing ideal com-

pliant nodes. Unlike passive compliant nodes, struts

connected using rigid nodes can not rotate passively

around the nodes. Rather, by connecting struts rigidly

using rigid nodes, the extended lines of struts intersect

at a same point, which simpliﬁes the kinematics com-

plexity. To release some kinematic constraints caused

by using rigid nodes, we use robotic struts that are

comprised of two prismatic actuators linked by a pas-

sive revolute joint. For validating the proposed way of

constructing strut-type MRSs, a scalable distributed

control method is developed inspired by (Yu, 2010).

This paper is organized as follows: ﬁrstly, a novel

strut-type modular robotic structure is presented; sec-

ondly, a control method using central pattern gen-

erator is designed based on a moving principle of

which the performance is demonstrated by a proto-

type; thirdly, locomotion and deformation capabilities

are veriﬁed by simulations; and ﬁnally, conclusions

are presented.

2 ROBOTIC STRUCTURE &

CONTROL

In this section, a novel strut-type MRS is to be intro-

duced and details about the robot modeling and con-

troller development environments including a CPG

control method are to be presented.

2.1 Strut-type MRSs

Two strut-type MRSs are illustrated: one is conven-

tional MRSs using ideal nodes and the other one is

the proposed MRSs using rigid nodes. Figure 1(a)

shows a conventional square-shaped MRS of which

each strut has two prismatic actuators. The four

robotic struts are connected using ideal compliant

nodes equipped with passive revolute joints. Hence,

the struts jointed by the same node can rotate around

a common center of rotation. Each revolute joint has

a rotation range of 80 degrees (Yu, 2010). As men-

tioned before, such ideal nodes are very difﬁcult to

design and implement. To avoid this implementation

difﬁculty and reduce the kinematics complexity, rigid

nodes are proposed for connecting robotic struts as

shown in Figure 1(b).

Besides, differing from conventional struts that

only have prismatic actuators, each strut is comprised

of two prismatic actuators and one revolute actua-

tor. To release the kinematic constraints introduced

by rigid nodes, we let the revolute actuator be passive

to add compliance for MRSs. To the authors’ best

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

262

(a) A square robot with ideal compliant nodes.

(b) A square robot with rigid nodes.

Figure 1: Square robots with compliant and rigid nodes.

knowledge, such a hybrid strut design has never been

investigated and reported in the literature. Consider-

ing the type of actuators and joints used within each

strut of the square robots, for convenience, hereafter,

we term the robots shown in Figure 1(a) and (b) as

RPPR (with R and P separately representing revolute

and prismatic actuators) and PRP square robots, re-

spectively. For constructing more complex structures,

we consider each square robot as a meta-module,

then arbitrary robotic structures can be constructed by

rigidly connecting such square meta-modules.

To obtain movements of a robotic strut, one can let

the two connected nodes work alternatively as a ﬁxed

anchor resorting to a friction-changing mechanism on

the node bottom (Cheng et al., 2010). In this paper,

to prevent from designing a friction-changing mech-

anism, we use the following moving steps to achieve

a worm-like locomotion of a robotic strut with two

prismatic actuators (Yu, 2010):

• Step 1: extend one of the prismatic actuators and

keep the other one still;

• Step 2: retract the fully extended prismatic actua-

tor and extend the other one simultaneously;

• Step 3: retract the fully extended prismatic actua-

tor and keep the other one still.

For better understanding, we have tested such a mov-

ing principle using a physical strut controlled by an

Arduino Uno board. Figure 2 shows the experimental

test results. Initially, the prismatic actuators are fully

retracted. Then, following the abovemoving steps pe-

riodically, the robotic strut can obtain a worm-like lo-

comotion due to the change of its mass center during

the task execution process.

Remarks. As illustrated in Figure 3, initially, the

robotic strut keeps still and the normal forces N

and N

as well as the gravity force G should satisfy

+ N

= G and N

= N

= G/2. During Step 1,

when actuating the left prismatic actuator, at the ﬁrst

few seconds, friction forces f

= µN

(with µ denot-

ing the friction coefﬁcient) and f

= µN

would less

than the actuation force F. Hence, Node 2 would

move rightward for a short time while Node 1 will

move leftward. Since the mass center of the whole

strut moves leftward and N

+ N

= G together with

G × l

= N

× l

, N

and f

increases while N

and

decreases. Therefore, Node 2 would keep still and

Node 1 keeps moving leftward. During Step 2, due

to the collective work of actuation forces F

and F

the horizontal resultant force exerted on the two nodes

would be around 0 (we assume F

= F

). Since such

a force is less than the maximum static friction forces

of the two nodes, the two nodes would not move. For

the outer casing, owing to its resultant force F

, it

will move leftward. The motion analysis of Step 3 is

similar to Step 1, during Step 3, Node 2 would keep

moving leftward while Node 1 would ﬁrst keep still

and then move rightward for a few seconds.

2.2 CPG Control Method

Inspired by (Yu, 2010) and (Sato et al., 2011), a CPG

based distributed control method is implemented for

comparing and investigating the conventional and

proposed strut-type MRSs. Each square meta-module

runs the developed identical controller. Initially, each

CPG oscillator for each square robot has its own

phase ϕ(0). To achieve a coordinating movement of

a whole structure comprised of several square meta-

modules, the following control law is used to update

the oscillator phase:

(k+ 1) = ϕ

(k) + γ

∑

j∈N

(ϕ

(k) − ϕ

∗

), (1)

A Novel Strut-type Modular Robotic Structure using Rigid Node

263

Figure 2: Experimental test of the employed moving principle within one cycle.

′

Node 1

Node 2

′

+ F

Step 1

Step 2

Figure 3: Force analysis of the employed moving principle.

where ϕ

(k) represents a part of the ith oscillator’s

phase at the kth time step, parameter γ is related to

the convergence speed of (1), and N

denotes a set

containing square meta-module i’s neighboring mod-

ules. Constant ϕ

∗

is the desired phase offset between

square meta-modules i and j. With respect to a mov-

ing direction, we have

∗











π, if j is in front of i

−π, if j is at back of i

0, if j is in parallel with i

then, by considering intrinsic frequency of the CPG

oscillator, we can have

(k) = ωk + ϕ

(k), (2)

where ω and θ

(k) denote the oscillator frequency and

oscillator phase, respectively.

For a square meta-module shown in Figure 1, we

can have four cardinal traveling directions, i.e., a

square robot can move along the positive and nega-

tive directions of X- or Z-axis. We use index 1, 2,

3, 4 for representing the traveling direction, which is

listed in Table 1. Let d and d

′

denote the traveling and

opposite directions, respectively. Set Ω represents the

struts that can enable the square robot move along the

traveling direction once they are actuated. By using

the index schemes shown in Figure 1 and Table 1, for

all i ∈ Ω, we do the following computation:

i,d

(k) = mod(θ

(k),

3π

), (3)

i,d

′

(k) = mod(θ

(k) −

3π

). (4)

In this way, the oscillator phase θ

(k) is forced to

become cyclic signals φ

i,d

(k) and φ

i,d

′

(k) with a pe-

riod of 3π/2. Finally, the following activation func-

tion (AF) is exploited to obtain the corresponding set

points x

i,d

(k) and x

i,d

′

(k):

f(φ) =

(

Lsin

(

sin

(

φ/P)), if 0 < φ < π

0, otherwise

(5)

where L indicates the fully extended length of a pris-

matic actuator and P is a constant parameter related to

the period of the output signal. With respect to time,

Figure 4 shows proﬁles of the designed AF (5) (i.e.,

AF I) and the AF presented in (Yu, 2010) (i.e., AF II).

Note that the proﬁle of (5) is smoother than that of

AF II. Actually, AF II is not continuous, which may

damage the physical motor as the motor velocity has

to change abruptly at time 0s, 2.5s, 5s,10s,12.5s and

15s. Such a case can be avoided using the continuous

function (5). One can easy to prove that the nth (with

n = 1,2,3. . .) order derivative of (5) would be 0 when

φ = 0 or φ = P. Hence, the AF (5) is more suitable

than AF II for motion planning in robotics. Besides,

Table 1: Index scheme for traveling directions.

Direction Index

+X 1

-X 2

-Z 3

+Z 4

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

264

0 2.5 5 7.5 10 12.5 15

100

150

200

250

300

350

Time (s)

Length (mm)

AF I

AF II

Figure 4: Two different activation functions.

AF (5) has a period of 7.5s (5s for actuation and 2.5

for keeping still) while AF II has a period of 10s (5s

for actuation and 5s for keeping still). This is because

we ﬁnd it can speed up the locomotion process by de-

creasing the time for keeping still.

3 SIMULATIONS

To validate the performance of the proposed way of

constructing strut type MRSs, simulations are con-

ducted comparatively. Speciﬁcally, MSRs with one

and two square meta-modules are investigated ﬁrst.

Then, we study the locomotion of an MSRs with six

PRP square meta-modules. After that, a tentative de-

formation test is ﬁnally performed using an MSR with

37 PRP struts.

Inspired by some successful work (Spr¨owitz et al.,

2014), Webots is used as the robot simulator. We-

bots is a physics-based simulator developed by Cy-

berbotics. By using a scene hierarchical tree, a robot

model in Webots directly describes the geometric,

kinematic and dynamic relationships of the robotic

components as well as between the robotic system

and its working environment.

3.1 Locomotion

This subsection investigates the locomotion capabil-

ity of strut-type MRSs. We ﬁrst study a single square

meta-module, then MRSs with two and six square

meta-modules are studied. Note that, for the compar-

ative simulations, same initial phase values are em-

ployed for a relatively fair comparison.

3.1.1 Single Square Module

Figures 5 and 6 show an RPPR and a PRP square

robots moving rightward (i.e., along the +X direc-

tion) using the mentioned moving principle. The con-

ventional RPPR square robot can move faster than

(a) Initial State (b) Step 1

Figure 5: Conventional square robot obtain a worm-like lo-

comotion within one cycle.

(a) Initial State (b) Step 1

Figure 6: Proposed square robot obtain a worm-like loco-

motion within one cycle.

the proposed one, since the PRP square robot expe-

riences deformations as shown in Figure 6(b) and (c).

Such a fact can be seen in Figure 7 from which we

can observe that, after actuating the square robots for

32s, the RPPR and PRP square robots move rightward

around 1.0m and 0.7m, respectively.

3.1.2 Two Square Modules

In this part, we let MRSs with two square meta-

modules move forward (i.e., along the -Z direction).

A Novel Strut-type Modular Robotic Structure using Rigid Node

265

0 4 8 12 16 20 24 28 32

−0.4

−0.2

0.2

0.4

0.6

0.8

Time (s)

Node 1 Position (m)

(a) Position proﬁles of the RPPR square robot

0 4 8 12 16 20 24 28 32

−0.5

−0.4

−0.3

−0.2

−0.1

0.1

0.2

0.3

0.4

0.5

Time (s)

Node 1 Position (m)

(b) Position proﬁles of the PRP square robot

Figure 7: Position proﬁles synthesized using CPG neural

network based control method.

The corresponding results are shown in Figures 8 and

9. As seen from Figure 8(a)–(d) and Figure 9(a)–(d),

initially, both the two kinds of MRSs can not move

efﬁciently. After coordinating the phases between the

two square meta-modules, a worm-like locomotion

can be obtained as shown in Figure 8(e)–(h) and Fig-

ure 9(e)–(h). Even though the conventional MRS can

still move slightly faster than the proposed MRS, it

keeps an unstructured shape when achieving a coordi-

nated locomotion. Unlike the conventional MRS, af-

ter some initial deformations, the proposed PRP MSR

can restore and maintain its structured shape. This

is important, as collisions between modules are more

common when moving with an unstructured shape.

3.1.3 Six Square Modules

For further validation, we established MRSs with six

square meta-modules. The corresponding simulation

results are presented in Figure 10. From the ﬁgure, we

can see that the MRSs can obtain a coordinating loco-

motion using the CPG control method. Speciﬁcally,

oscillator phases are updated with desired phase off-

sets achieved and actuators’ actual proﬁles ﬁnally co-

incide with their desired counterparts. Note that, dur-

ing the task execution, square meta-module 0’s pris-

matic actuators x

2,3

and x

2,4

are locked. Therefore,

(a) Structure labels (b) Snapshot 1

(e) Snapshot 4 (f) Snapshot 5

(g) Snapshot 6 (h) Snapshot 7

Figure 8: Locomotion of conventional MSR with two

square meta-modules.

desired values for x

2,3

and x

2,4

are 0. For readability,

we only show the ﬁrst 60s proﬁles of actuated actu-

ators x

4,1

and x

4,2

of square meta-module 0. The de-

viation in the x

4,1

proﬁle may result from unexpected

kinematic singularities. In future work, we will de-

vote time to coping with this phenomenon.

3.2 Deformation

A simulation is performed to show the deformation

capability of the proposed strut-type MRSs. Specif-

ically, we construct an MRS with 37 PRP struts as

shown in Figure 11(a). By actuating PRP struts

placed along the top and bottom segments of the

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

266

(a) Structure labels (b) Snapshot 1

(e) Snapshot 4 (f) Snapshot 5

(g) Snapshot 6 (h) Snapshot 7

Figure 9: Locomotion of proposed MSR with two square

meta-modules.

perimeter using (2)–(5) (with L = 50mm and ϕ

(k) =

0rad) and letting other struts be passive, we obtain the

deformation result shown in Figure 11(b). Such a de-

formation can be used for physical display.

4 CONCLUSIONS

This paper presents a novel way of constructing

strut-type MRSs using rigid nodes and robotic struts

equipped with two prismatic and one revolute actua-

tors. For testing such conceptual structures, Webots

is used to construct the physics-based robot models.

(a) Structure labels

0 20 40 60 80 100 120 140 160 180 200 220 240

100

150

200

250

300

350

400

Time (s)

Phase (deg)

(b) Phase proﬁle

0 20 40 60 80 100 120 140 160 180 200 220 240

−0.08

−0.06

−0.04

−0.02

0.02

0.04

0.06

0.08

0.1

Time (s)

Length (mm)

Actual x

2,3

Actual x

2,4

2,3

and x

2,4

proﬁles of square module 0 (with desired values

being 0)

0 10 20 30 40 50 60

−100

−50

100

150

200

250

300

350

Time (s)

Length (mm)

Actual x

4,2

Desired x

4,2

Actual x

4,1

Desired x

4,1

(d) x

4,2

and x

4,1

proﬁles of square module 0

Figure 10: Synthesized simulation results of an MSR with

six square meta-modules.

A Novel Strut-type Modular Robotic Structure using Rigid Node

267

(a) Original shape

(b) Deformation shape

Figure 11: Deformation test of an MRS with 37 PRP struts.

Then, a CPG based control method is implemented

for verifying the performance of the proposed MRSs.

Comparative simulation results demonstrate the efﬁ-

cacy of the control method and the proposed MRSs

as compared with conventional MRSs. Note that, by

using rigid nodes, the difﬁculty of implementing ideal

compliant nodes has been avoided, thus simplifying

the mechanical design process. Future work will fo-

cus on investigating useful deformation of the MRSs,

designing and building the proposed MRSs, and veri-

fying the control method using physical MRSs.

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