A Compliant Actuation Dynamics Gazebo-ROS Plugin for Effective

Simulation of Soft Robotics Systems: Application to CENTAURO Robot

Małgorzata Kameduła, Navvab Kashiri, Darwin G. Caldwell and Nikos G. Tsagarakis

Department of Advanced Robotics, Istituto Italiano di Technologia, Via Morego 30, 16163 Genoa, Italy

Keywords:

Gazebo-ROS Simulators, Legged Robots, Flexible Joint Robots, Series Elastic Actuators, Quadrupeds,

Humanoids, Simulation.

Abstract:

Despite the important role of simulation in the development and control of robotics systems, the majority of

open source simulation tools has however paid no attention to the progress and paradigm change on the robot

design in the past 15 years with the consideration of soft actuation technologies as a mean to power new robotic

systems. More speciﬁcally, the integration of series elastic actuators (SEAs) into robots modiﬁes signiﬁcantly

the dynamics characteristics of the system while the incorporation of the passive compliance into the actuators

is not applied in conventional simulators. This paper introduces a scheme for the implementation of the

SEA dynamics on a Gazebo-ROS framework exploited for the simulation of a new centaur-like robot. This

approach is based on designing a custom control plugin embodying the passive compliance dynamics so that

the controller associated with each joint receives both collocated and non-collocated feedback. A simulation

comparison with Matlab validating the performance of the designed control plugin is demonstrated. In the

end, a whole-body simulation of the centaur robot driven/controlled by the proposed plugin is presented.

1 INTRODUCTION

Simulators, as a necessary mean for the development

of dynamical systems permit the risk-free evaluation

and tuning of new control methods before

implementation on real systems. The increasing

attention paid to robotics during the past four decades

motivated the development of a large number of

simulation tools for this class of dynamic systems.

Furthermore, the communication of a higher-level

architecture with a robot and/or simulator requires

an operating platform capable of incorporating

different control architectures while interacting

with various devices. Hence, numerous middleware

software have being developed amongst which

one may report Robotic Operating System (ROS)

discussed in (Quigley et al., 2009), Yet Another

Robot Platform (YARP) studied in (Metta et al.,

2006), Player introduced in (Kranz et al., 2006), and

Open Robot Control Software (OROCOS) outlined

in (Bruyninckx, 2001). Evaluation of such tools in

terms of performance and practical features such as

supported programming languages is explored in

(Einhorn et al., 2012; Elkady and Sobh, 2012).

According to (Ivaldi et al., 2015), ROS and

YARP are the most commonly employed middleware

software solutions in humanoid robotics. ROS-based

open-source simulators are currently available for the

NAO robots (Forero et al., 2013) and the NimbRO

Open Platform(OP) (Allgeuer et al., 2013). As for the

HUBO (Alunni et al., 2013), a ROS interface with

a real-time control system is exploited to illustrate

the ROS capabilities of providing a communication

layer for the robot. The software architecture of

the iCub robot is developed in YARP. Besides, the

WALK-MAN (Negrello et al., 2016) and COMAN

(Tsagarakis et al., 2013) robots are utilising also a

YARP-based architecture.

Dynamic simulators are mainly classiﬁed in

two categories: physics engines and simulating

environments. The former includes light and efﬁcient

libraries solving the system dynamic equations, while

the latter comprises computer programs typically

possessing a graphical user interface, visualisation

features, and various toolboxes. An attempt to

compare different physics engines in an objective

manner was presented in (Erez et al., 2015). In this

group, one can refer to Open Dynamic Engine (ODE),

Open Robotics Automation Virtual Environment

(OpenRAVE), Simbody, Multi-Joint dynamics with

Contact (MuJoCo), and Bullet.

As for the simulating environments, for robotics

one can mention Gazebo, Urban Search And Rescue

simulation (USARSim) described in (Carpin et al.,

Kameduła, M., Kashiri, N., Caldwell, D. and Tsagarakis, N.

A Compliant Actuation Dynamics Gazebo-ROS Plugin for Effective Simulation of Soft Robotics Systems: Application to CENTAURO Robot.

DOI: 10.5220/0006001404850491

In Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2016) - Volume 2, pages 485-491

ISBN: 978-989-758-198-4

485

2007), Robot Control Simulator (ROCOS) explained

by (Hirano et al., 2000), Webot described in (Woolley,

1993) and Verosim examined by (Jochmann et al.,

2014). The simulation and software framework

used for legged robots are studied in several works

among which we can report (Tikhanoff et al., 2008)

developed for iCub, (Habra et al., 2015) realized for

COMAN, (Ha et al., 2011) developed for DarwinOP,

(Allgeuer et al., 2013) implemented for NimbRo-OP

and (Asfour et al., 2006) realized for ARMAR-III.

Moreover, a simulator of quadruped BIOSBOT is

detailed in (Guan et al., 2004).

This paper presents a simulator framework for an

under-development SEA actuated centaur-like robot

where the ROS middleware software and Gazebo

simulator are exploited. While the passive dynamics

imposed by the inclusion of SEA has signiﬁcant effect

on the system behaviour, it is usually neglected since

the dynamics associated with motors is not embedded

in the Gazebo simulator. In this work, we explore

possible solutions and propose a custom control

plugin consisting of the dynamics brought by the

passive compliance, in addition to a given lower-level

control law. Moreover, the customisation of the

control plugin enables the capability of managing

ROS topics to achieve a computationally efﬁcient

communication. The robot linkage representation is

structured in such a way so that the robot is split into

ﬁve sections, and the system can operate user-deﬁned

section(s) independently.

The rest of the paper is organised as follows:

Section 2 describes the structure of the Centauro

robot, while Section 3 reports on the dynamics and

control of SEA-driven robots. Section 4 delineates

the architecture of the simulator, including the

modular description of the robot linkage structure,

and the proposed compliant dynamics/control

plugin. Section 5 demonstrates the simulation results

validating the accuracy of the approach propounded

in this work, while Section 6 presents the conclusion.

2 ROBOT DESCRIPTION

The robot discussed in this work is a centaur-like

robot composed of a humanoid upper-body mounted

on quadruped lower-body and powered by SEAs to

exploit physical robustness and high ﬁdelity torque

control characteristics. The upper-body comprises

a dual-arm robotic system with seven degrees of

freedom (DOFs) per manipulator relying mostly upon

an anthropomorphic design as follows: the shoulder

complex is constructed on the basis of a 3-DOF

pitch-roll-yaw arrangement, and it is connected to

Figure 1: A snap-shot from the working simulation for the

centaur robot.

the forearm through an elbow joint. The forearm

apparatus is formed upon a 3-DOF yaw-pitch-yaw

conﬁguration replicating the wrist motions. The

length and mass considered for each of the arms

are about 80 cm and 10 Kg. The lower-body

consists of four 3-DOF legs beneﬁting from wheels

at the hip and knee joints. The leg kinematics

arrangement is selected according to the spider-like

conﬁguration (Kashiri et al., 2016) as follows: a

3-DOF yaw-pitch-pitch conﬁguration with a total

length and mass similar to those of the arms. The

pelvis base encompassing the ﬁrst actuator of each

leg is connected to the arms through a 2-DOF torso

composed of a yaw and a pitch joints. Fig. 1 shows

a snap-shot from the simulation environment of the

robot possessing 36 DOFs excluding head and hands.

3 SEA BACKGROUND

For systems powered by SEAs, shown in Fig. 2,

motors do not directly drive the links as the motor

torques are transmitted through compliant elements.

A k−DOF robotic linkage actuated by SEAs therefore

includes 2k DOFs, and the corresponding dynamic

equations are

M(q

q + c

c(q

q) + g

g(q

q) = τ

q, θ

θ,

θ), (1)

θ + D

θ + τ

q, θ

θ,

θ) = τ

, (2)

q, θ

θ,

θ) = K

(θ

θ − q

q) + D

(

θ −

q), (3)

where q

q = [q

, ..., q

]

and θ

θ = [θ

, ..., θ

]

are the

link and motor position vectors, respectively, K

∈

ℜ

k×k

and D

∈ ℜ

k×k

stand for the stiffness and

damping matrices corresponding to passive elements,

∈ ℜ

refers to the vector of transmission torques

applied by the passive elements, whereas τ

∈

ℜ

denotes the motor torque vector, B

∈ ℜ

k×k

symbolises the motor inertia matrix and D

∈

ℜ

k×k

expresses the motor damping matrix. Here,

a collocated-based PD position controller (Tomei,

1991) is used, whose corresponding control law is

described by

controller

= g

g(q

) + K

(θ

− θ

θ) − K

θ, (4)

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

486

Figure 2: Mechanical model of i−th series viscoelastic

actuator (Kashiri et al., 2014).

where K

∈ ℜ

k×k

and K

∈ ℜ

k×k

are the proportional

and derivative gain matrices of the controller,

respectively, and θ

= q

+ K

−1

g(q

) is the desired

motor position vector extracted from the desired link

position vector q

4 SIMULATOR DESIGN

The centaur robot simulation platform exploits the

ROS middleware due to its modularity and the

variety of supported programming languages, while

the simulator is built upon Gazebo software featuring

extensibility through plugins, and choice of the

physics engine; thanks to its open-source architecture.

4.1 Linkage Structure

4.1.1 Robot Linkage Representation

The Uniﬁed Robot Description Format (URDF)

representation of the robot is structured according to

the robot description (presented in Section 2), see

Fig. 3, and the Gazebo simulator associated with the

robot linkages is accordingly generated. The robot

structure is represented by means of a tree topology

with a base link at the pelvis centroid. The tree

is constructed on the basis of ﬁve branches, four of

which are assigned to legs, while the ﬁfth branch

establishes the upper-body by connecting the torso to

three descendant branches associated with the arms

and the robot head.

4.1.2 System Modularity

As the development of control algorithms can be

facilitated by an initial implementation on a section

of the robot, the robot is structured by ﬁve separate

sections: pelvis, torso, arms, legs, wheels; while the

addition of individual wheels to knees and/or hips

can be carried out independently. As a result, apart

from the pelvis as the anchor of the robot structure,

each section can be included or excluded in simulator

and control scheme at will. Nevertheless, when an

ancestor of a section does not spawn, the descendant

branches are disabled automatically. Furthermore,

while the pelvis is connected to a ﬂoating-based

system by default, it turns to a stationary base when a

user grounds the pelvis or disables the legs.

4.2 Control Plugin

4.2.1 Multiple Joints Controller

The ‘ros control’ packages provide the controller

interfaces/managers handling the connection between

the ROS platform and the Gazebo software (or the real

hardware). Given a robot with k DOFs, when one uses

the default ‘ros controllers’ packages, the number

of threads concerning the lower-level controller is

2k as each DOF demands a couple of threads for

sending and receiving data. However, for humanoids,

quadrupeds and centaur-like robots, such an approach

results in many threads that are burdensome for a

system to coordinate; as the large number of threads

aggravates system performance and elevates hardware

requirements. To address this problem, we developed

a control plugin dedicating only two threads to

the lower-level controllers of the robot, while

guaranteeing an independent control of individual

joints, besides ensuring the synchronisation of data

sent/received to/from all DOFs.

The control plugin is structured with two

non-real-time ROS topics: the ‘command’ ROS topic,

and the ‘state’ ROS topic. One thread manages the

data transmitted on the former, that includes three

input variables to be subscribed to the controller

associated with each DOF. The other thread takes

care of the data published to the latter, that comprises

a set of output variables. The input variables

are reference position and velocity values as well

as a centralized torque command, and the output

signals are motor-side position and torque states.

Moreover, the plugin incorporates ﬁve constant gains

Figure 3: URDF ﬁle structure for the centaur robot. – link

centre of mass, – joint frame origin.

A Compliant Actuation Dynamics Gazebo-ROS Plugin for Effective Simulation of Soft Robotics Systems: Application to CENTAURO

Robot

487

Figure 4: rqt graph of simulator depicting system data ﬂow.

for each DOF to be set through the ROS service

and/or through the ROS parameter server during the

controller initialisation

. The data ﬂow in the system

is displayed at Fig. 4 showing rqt graph for the

simulation. It can be seen that the simulator operates

two types of control plugins associated with wheels

and compliant joints, named ‘wheel controller’ and

‘ﬂexiblejoint controller’, respectively.

4.2.2 Series Elastic Actuator Module

SEAs drive the centaur robot links, while the

inclusion of compliance into actuation units has not

been yet taken into account in the Gazebo software.

Possible solutions for this deﬁciency are listed below

1. Addition of an extra DOF per joint replicating

the motor-side dynamics while adding

spring–damper forces to link-side joints;

2. Use of a ‘ros control’ transmission interface;

3. Employment of a Gazebo model plugin;

4. Deﬁnition of an independent ROS node

simulating compliant actuators;

5. Incorporation of compliant system dynamics into

a real-time controller module on the basis of

‘ControllerBase’ plugin.

Solution 1, however, doubles the number of

DOFs that increases the computational burden of the

systems with large number of DOFs. As for solutions

2 and 3, apart from the lack of documentations

elaborating their characteristics, they cannot directly

propagate the motor-side states to the controller

while maintaining the minimal control functionality.

Solution 4 imposes an unknown delay to the system

due to the inclusion of a non-real-time node. It

contravenes the synchronisation of the motor-side

and link-side states, that results in instability of

Although the control law (4) includes only two gains, the

implementation of other schemes such as (Kashiri et al.,

2014) may require a larger number of gains.

the dynamical system. The data ﬂow between the

afore-stated sources needs to be designed in such a

way so that delays in the data ﬂow that can disturb

the synchronisation of the readings are avoided. As

the ‘ros control’ plugin time is coordinated with the

Gazebo time, and it operates in a real-time module,

solution 5 is therefore selected for the implementation

of the SEA dynamics, and the synchronisation of full

state feedbacks is guaranteed.

4.2.3 SEA Module Development

The implementation of the SEA dynamics in the

control plugin requires a digital form of the

corresponding equations. To this end, (2) and (3)

needs to be discretised. Since the afore-said equations

are related to a set of linear time-invariant systems,

they can be expressed by

θ[n] = B

−1

(τ

[n] − D

θ[n] − τ

[n]), (5)

[n] = K

(θ

θ[n] − q

q[n]) +D

(

θ[n] −

q[n]), (6)

when the Euler method is used. Similarly, the

control law, e.g. (4), can also be expressed in a

discrete form from which the motor torque τ

can be

derived. The motor-side angular accelerations

θ can

therefore be computed from (5) with the transmission

torque τ

given by (6). The motor-side positions and

velocities are thus calculated from the integrations of

the acceleration.

Depending on the stiffness of the passive

compliant element, the dynamics of the system

can evolve in different frequencies. Discrete

representation of such a dynamic system may then

cause numerical instability if the sampling frequency

used for the discretisation is too low to include

the major dynamics variations. Since the energy

stored in a discrete system within one sample time

is presumed to be constant, the spring motion can

converge to a stable state provided that the sampling

time is sufﬁciently small to support this assumption.

The simulation of dynamical systems with higher

impedance then requires smaller time steps.

The functionality of the simulator in terms of

stability and accuracy can therefore depend on

the sampling frequency, while it is essential to

set the control loop frequency equal to that of

the real hardware, so that the results extracted

from simulations are comparable with that from

experiments on the robot. On the other hand, the

controller and the actuator dynamics are implemented

at the same thread, and a change in the system

sampling frequency f

affects the controller frequency

, while the later may need to be set lower than the

former. To this end, the control law setting the motor

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

488

Figure 5: Structure of the SEA module and its integration.

torque is revised in a way that the motor torque τ

is updated at a user-deﬁned frequency f

. At any

simulation time t, the motor torque is derived from

[n] =

(

[n − 1] ⇐ t mod(

) > ε

controller

[n] ⇐ t mod(

) < ε

, (7)

where ε is a small constant, and the operator amod(b)

gives the remainder after division of a by b.

Figure 6: On the left – time history of transmission

displacement in step input test: low, medium, and high

stiffness on top, middle, and bottom, respectively. On the

right – results of the time-varying input test: positions on

top, motor torques in the middle, and transmission torques

at the bottom. single line plots below multi line plots show

errors between Matlab and Gazebo-ROS simulation results.

Fig. 5 depicts the structure of the simulator

with the proposed control plugin, in which the

data ﬂow and the role of each part of the

simulation framework are also denoted. The

linkage dynamics (1) is computed by the Gazebo

software, and the real-time ‘gazebo ros control’

bridge sends the link states to the control plugin

and the ‘joint state controller’ from ‘ros controllers’

packages. The ‘joint state controller’ publishes

the data to a non-real-time ROS topic named

‘joint states’ for higher-level control schemes such

as (Ugurlu and Kawamura, 2010). The real-time

‘gazebo ros control’ bridge sends the input torques,

i.e. the transmission torques τ

, to Gazebo from

the ‘ros control’ plugin consisting of motor-side

dynamics (2), transmission unit (3), and the controller

(4). The desired motor positions and the gravity

compensation torques are sent to the control plugin

through the non-real-time ROS topic ‘command’,

while the ROS topic ‘state’ receives the motor states.

5 RESULTS

5.1 Comparison with Matlab

To validate the above implementation, a comparison

between the Gazebo-ROS simulation and a Matlab

simulation is presented

. To this end, simulation of

the last joint-link of the rrbot manipulator, available

in ‘gazebo ros demos’ repository, when powered by

a SEA is carried out. The controller gains are set

to K

= 1000 and K

= 0 with a saturation limit of

max

= 33 N. The motor-side inertia and damping

reﬂected to the link-side through the gearing system

are B

= 0.0742 Kg/m

and D

= 24.768 Nms/rad,

where the motor damping value includes both the

physical damping and the back-EMF effect. The

Matlab simulation was done with a continuous

PD controller when using a ﬁxed-step solver at

1 kHz, and the Gazebo simulation was executed

using the Bullet physics engine with f

= f

1 kHz. The left side of a Fig. 6 illustrates the

evolution of the transmission displacement when

a 1 rad step is sent as the reference trajectory

when the transmission impedance parameters are

set to three impedance sets: K

= 100, 188 and

500 Nm/rad with D

= 0.3, 0.5 and 1.5 Nms/rad,

respectively. The second simulation comparison is

executed when the reference trajectory is composed

of a 0.1 rad/s ramp, a negative step of 1 rad and a

chirp signal described by 0.5 sin(0.02πt + 0.004πt

Simulations in this work are performed using a laptop with

a processor of Intel

Core

i5-5200U 4×2.2 GHz, 8 GB

RAM, and a Graphics card of GeForce 920M.

A Compliant Actuation Dynamics Gazebo-ROS Plugin for Effective Simulation of Soft Robotics Systems: Application to CENTAURO

Robot

489

Figure 7: Evolution of centaur robot posture: Initial

conﬁguration, spider-like posture, and mammal-like pose

on the left, middle and right, respectively.

Figure 8: The whole-body simulation results of shoulder

joint (on the left) and elbow joint (on the right): the

reference and actual link positions, and link velocities

on top; the motor positions/velocities in the middle; the

motor/transmission torques at the bottom.

The right part of a Fig. 6 demonstrates the evolution

of positions and torques over time when using two

simulators with the medium stiffness/damping values.

It shows that the ROS-Gazebo simulator reproduces

the Matlab simulator results with 99.9% matching in

link position data when the corresponding maximum

error and the normalized root mean squared error

(NRMSE) are 1.2e-3 and 4.5e-7 rad, respectively.

The transmission torque and motor torque may

instantaneously show differences up to 0.12 and

2.11 Nm, although the corresponding NRMSE values

of 3.6e-5 and 5.3e-4 Nm expresses that such a high

error occurs only in a few moments.

5.2 Whole-body Simulation

A simulation of the whole robot is presented in this

section, when the robot moves from an initial position

to a spider-like posture providing a larger support

polygon and then a mammal-like pose more suitable

for dynamic locomotion, see Fig. 7. The simulation

was executed at f

= 1 and f

= 2 kHz. Results of the

shoulder pitch and elbow joints of one arm and hip

joints of one leg are illustrated in Fig. 8 and Fig. 9. It

can be seen that joints which are highly loaded by the

gravity exhibit non-negligible steady state position

tracking error resulting from low impedance gains

of the controller. For instance, the hip yaw joint is

not under the gravitational torque, and therefore the

position error can converge to zero, while the pitch

joint presents considerable error.

6 CONCLUSION

This paper presented a simulator for a centaur-like

robot powered by SEAs, utilising a Gazebo-ROS

framework. While the incorporation of passive

elements into the robot actuators using conventional

approaches requires the inclusion of extra DOFs, the

proposed scheme implements the passive dynamics

on the control plugin so that the control scheme can

have access to both motor-side and link-side readings

simultaneously. To this end, the ‘gazebo ros control’

bridge is focused on, and a custom control plugin

is designed in such a way that the dynamics of

motor-side and link-side are synchronised. Moreover,

the proposed approach can be employed to include

the dynamics of variable impedance actuators.

A simulation comparison with Matlab approving

the accuracy of the introduced architecture is

demonstrated. Finally, the proposed control plugin is

exploited in the simulation of the CENTAURO robot.

Figure 9: The whole-body simulation results of hip yaw

joint (on the left) and hip pitch joint (on the right). The

arrangement of variable are similar to that noted in Fig. 8.

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490

ACKNOWLEDGEMENTS

This project has received funding from the European

Unions Horizon 2020 research and innovation

programme under grant agreement No 644839

(CENTAURO).

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