Modeling and Simulation of Humanoid Robot Spine Vertebra

M. Souissi, V. Hugel and P. Blazevic

Université de Versailles Saint Quentin en Yvelines, Versailles, Île-de-France, France

Keywords:

ROMEO Robot, Simulation, Vertebral Column, Mechanical Structure, Kinematics.

Abstract:

In this paper, a parallel mechanism is proposed for the design of humanoid vertebra. This mechanism is

inspired by a ﬂight simulator system, and has been adapted and optimized to enable pitch and roll motion

of a humanoid trunk at reduced energy cost. The system consists of a bottom platform and a top platform

connected by two articulated arms and a vertical central rod. A 3D model of the system has been elaborated

for simulation and design.

1 INTRODUCTION

Robots are expected to live among humans to assist

them in their daily tasks. Current humanoid robots

are not fully suitable for working in our daily environ-

ment. They can do a few limited tasks compared with

what a human can do. Walking humanoids robots

equipped with joints in the trunk are listed in table 1 in

increasing order of spine DOF number starting from

pelvis. All of them feature a yaw joint in the trunk.

The yaw joint is particularly useful for taking larger

strides. It can also be used to compensate for yaw

moment between feet and ground. It allows the robot

to increase the working volume of its upper body for

manipulation. Existing humanoids that have a yaw

joint in the trunk are Asimo presented by (Sakagami

et al, 2002), KHR2, Hubo in (Kim, 2005), Johnnie

analysed by (Lofﬂer et al, 2005), and Lola (Lohmeier

et al, 2006). An additional pitch joint in the trunk

extends the skills of the robot. The pitch joint is help-

ful for the robot to sit down on a chair. Examples of

robots that can sit down are the series of REEM-A/B

presented in (Tellez, 2008). This robot is manufac-

tured by Pal Technology Robotics. Humanoids with

a pitch joint in the trunk can also stand up from lying

position. The HRP2 robot demonstrated its capacity

to lie on the ground and to stand up again using its

pitch joint in the trunk (Kaneko, 2008). Roll joints

can be added to enhance locomotion capacities. That

is the case of the last generation of Wabian robots de-

veloped by Waseda University in Japan (Ogura et al,

2006). Wabian II features two additional roll joints –

one in the middle of the pelvis and the other one at

the end of the trunk kinematic chain – that were in-

troduced to implement new locomotion skills. This

robot is capable of stretching the knee during walk

when the supporting leg comes below the hip. Pitch

and roll joints also increase the working space of the

upper body and they can be used to bend the trunk

forward and /or sideways to grasp something or to re-

sist some perturbation at shoulder level. The DOF in

Table 1: Walking humanoid robots with DOF in the trunk.

DOF type of DOF Prototypes

1 yaw KHR2, Hubo,

Johnnie,

Asimo

2 yaw +pitch HRP-2-3-4,

Reem A/B

4 roll + yaw + pitch + roll Wabian II

the trunk are therefore task-dependent. It is interest-

ing for humanoids to have a vertebral column to deal

with both movement and manipulation skills.

The contribution of this paper consists of adapt-

ing an existing parallel mechanism of ﬂight simulator,

found in thses of (Emilie, 2004), to the design of a

pitch-roll vertebra joint, taking into account the spec-

iﬁcations of forward, backward and left/right side-

ways bending amplitudes given for a humanoid robot.

The objective of the study is to optimize the different

length ratios of the mechanism in order to have a re-

duced torque required for the bending motions.

Section II deals with the description of the paral-

lel mechanism. Section III presents simulation and

results. Section IV is devoted to conclusion and per-

spectives.

415

Souissi M., Hugel V. and Blazevic P..

Modeling and Simulation of Humanoid Robot Spine Vertebra.

DOI: 10.5220/0004013904150418

In Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2012), pages 415-418

ISBN: 978-989-8565-22-8

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

2 DESCRIPTION OF

MECHANISM

This work deals with the adaptation of an existing par-

allel mechanism to a prototype of vertebra that could

be implemented on humanoid robots. The parallel

mechanism consists of 2 platforms – one bottom plat-

form CA

and one top platform OA

, that are

linked by a central vertical rod CO and two arms ar-

ranged at 90[deg] in the initial position (Fig. 1). The

central rod CO is ﬁxed and always remains vertical. It

joins the top platform through a Universal joint whose

drive is responsible for roll and pitch motion of the

top platform. The arm A

is planar and is com-

posed of two segments, two revolute joints at A

and

, and one Universal joint at A

. This is the planar

arm. Figure 2 shows the parallel mechanism.

ℓ

Figure 1: Perspective view of parallel mechanism in initial

position. The central rod is ﬁxed and rigid. It is attached to

the top platform by a Universal joint at O. The mechanism

is actuated by two revolute joints, each of them is located

at the bottom of each arm. The two arms are arranged at

90 [deg]. The arm A

is planar and remains in the (xz)

remains in this plane. It is composed of two revolute joints

and one U-joint. The other arm B

is initially in the

(yz) plane, and does not remain in this plane if the top plat-

form rolls.

Figure 2: Parallel mechanism.

The arm B

also includes two segments, one

revolute joint at B

, one Universal joint at B

and one

ball joint at the attachment locus B

with the top plat-

form. This arm is 3D. The bottom platform is linked

to coordinate frame R

, centered at C with axes i, j

and k.

The top platform rotates about O and is linked to co-

ordinate frame R

, frame centered at O whose axes are

, j

and k

(Fig. 3).

The top platform can be pitched about ﬁxed axis j

by angle θ

, and rolled about axis i

by angle θ

The two active joints are the revolute joints at A

and B

. The associated rotation angles are denoted by

α and β.

Figure 3: Perspective view of parallel mechanism after pitch

and roll rotations.

3 SIMULATION AND RESULTS

3.1 Setup

Two conﬁgurations of mechanism are under study

here. Figure 4 shows both conﬁgurations. The ﬁrst

conﬁguration is rotated 90[deg] and the second one

is rotated 135[deg] with respect to the conﬁguration

of the mechanism depicted on ﬁgure 3. This section

aims to compare both conﬁgurations and shows that

the second one is better than the ﬁrst one in matter of

torque consumption.

In the ﬁrst conﬁguration, the height between the

top platform and the bottom platform in the parallel

mechanism is set to 0.1[m]. The length d

must be

less than half the width of the trunk, which is 0.24[m].

The length `

must be less than half the depth of the

trunk, which is 0.16[m]. These values result from a

space constraint because the vertebrae will be placed

in the lumbar part of the humanoid trunk. A sphere

with a mass M is placed above at the center of the

mechanism to simulate the upper part of a humanoid

robot. The two arms are perpendicular and they do

not have the same dimensions. The mass M is set to

15[kg]. The distance of the sphere center to the top

platform is set to 0.1[m].Table 2 presents the lengths

of the ﬁrst conﬁguration.

In the second conﬁguration d

and l

are the same

as in the ﬁrst conﬁguration. A sphere with a mass M

is placed above the mechanism to simulate the upper

part of a humanoid robot. M is not placed at the center

ICINCO2012-9thInternationalConferenceonInformaticsinControl,AutomationandRobotics

416

Table 2: Parameters of the ﬁrst conﬁguration.

Parameter length [m]

0.07

0.09

0.0316

0.04

0.11

0.09

0.06082

0.05

proto1

MODEL_1

Figure 4: The ﬁrst and second conﬁguration of parallel

mechanism.

of the prototype like in the ﬁrst conﬁguration, but at a

distance of 0.030[m] to the front of the trunk. This en-

ables to put the projection of the center of mass more

inside the center of the support polygon delimited by

the robot’s footprints . Both arms are symmetric and

perpendicular. Table 3 presents the lengths of the sec-

ond conﬁguration.

Table 3: Parameters of the second conﬁguration.

Parameter length [m]

= l

0.17

= l

0.09

= l

0.0443

= l

0.16

Both conﬁgurations are compared in matter of

torque magnitude delivered by the two active joints

for two kinds of motions to be executed by the top

platform.

The ﬁrst motion is obtained by giving the angu-

lar inputs for the pitch/roll joint of the top platform,

namely θ

and θ

. This motion is named pitch in-

clination. The platform is bent 10[deg] forward, then

10[deg] backward. The angles for the joint motors,

namely α and β are calculated thanks to the inverse

geometric model.

In the second motion pitch and roll joint angles

are combined to have a bent circular motion of the

spherical mass. First, the mass is pitched by 10[deg].

Then it executes a complete circular motion about the

vertical. The trajectory for this circular motion uses

spherical notation and precession angles (θ, φ) as in-

puts. These inputs are then converted into θ

and θ

to execute the motion.

Trajectory planning is designed with Matlab-

SIMULINK, which is used to control the ADAMS

model. To control the inclination of the spherical

mass in Adams PID controllers were used for the mo-

tors.

The parameters (d

) of the mechanism

were optimized by testing several conﬁgurations

(Souissi,2012) to check which one was best in matter

of torque magnitude and space occupancy. Each arm

was tested separately by ﬁxing the other one. For the

ﬁrst conﬁguration we concluded that the motor axes

should be located at half-way between the center and

the related external edge of the top platform. For

the second conﬁguration the motor axes should be

located more externally. In addition the upper part of

each arm must be longer than its lower part in both

conﬁgurations. This enables to optimize the lever

arm.

3.2 Torque Comparison between the

First Conﬁguration and Second

Conﬁguration

Figure 5 shows the trajectories of platform pitch and

roll angles θ

and θ

and the related motor angles α

and β in the case of pitch inclination motion. Figure

7 is related to the circular motion. The left-hand part

of each ﬁgure is related to ﬁrst conﬁguration and the

right-hand part to the second conﬁguration.

0 2 4 6 8

-30

-20

-10

Time(s)

Trajectory(deg)

Figure 5: Angle trajectories θ

and θ

of platform and the

related motor angles α and β for the pitch inclination mo-

tion. Left: First conﬁguration. Right: second conﬁguration.

Figure 6 shows the torques of each arm’s motor

joint in both conﬁgurations for the pitch inclination

motion. Figure 8 shows the torques of each arm’s mo-

tor joint in both conﬁgurations for the circular motion.

Regarding pitch motion and circular motion the

second mechanism allows a torque reduction of more

than 50% with respect to the ﬁrst.

ModelingandSimulationofHumanoidRobotSpineVertebra

417

0 2 4 6 8 10 12

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Time(s)

Torque(NM)

first-config

second-config

0 2 4 6 8 10 12

0.2

0.4

0.6

0.8

1.2

1.4

Time(s)

Torque(NM)

first-config

second-config

Figure 6: Active torques in the ﬁrst and second conﬁgura-

tion for the pitch inclination motion. Left: 2D arm. Right:

3D arm.

Figure 7: Angle trajectories θ

and θ

of platform and the

related motor angles α and β for the circular motion. Left:

ﬁrst conﬁguration. Right: second conﬁguration.

0 5 10 15 20 25

0.5

1.5

Time(s)

Trajectory(NM)

first

second

0 5 10 15 20 25

0.2

0.4

0.6

0.8

1.2

1.4

Time(s)

Torque(NM)

first

second

Figure 8: Active torques in the ﬁrst and second conﬁgura-

tions for the circular motion. Left: 2D arm. Right: 3D arm.

3.3 Mechanical Design of the

Mechanism

The second mechanism was simulated with Solid-

works. All joints come from the HPC company. For

both active joints electric motors are used. Torque

versus speed was plotted for both movements of the

top platform. The variation of torque with speed al-

lows to select the motors that best suit our needs.

We use Maxon motors, because these actuators are

lightweight and one of them meets our requirements:

the RE25G. The caracteristics of the motors are given

in table 4.

Table 4: Parameters of the motor.

Characteristic Value

Supply voltage 12V

Rated current 1.2 A

No load speed 202 r / min

Load speed 156 r / min

Rated torque 0.49 Nm

4 CONCLUSIONS AND

PERSPECTIVES

A new vertebra mechanism for a humanoid robot ver-

tebral column has been proposed. It is based on a par-

allel architecture driven by two active arms equipped

with one rotary actuator each. Inverse kinematic

equations have been formulated. A 3D model has

been elaborated with Adams and Solidworks and sim-

ulated for checking the operation feasibility and de-

sign sizes. Simulation results show that the proposed

column system can reproduce some of the human

spine mouvments.

REFERENCES

Emilie (2004) “Analyse d’un mécanisme de simulation de

vol sphérique et son contrôle en temps reel”, Faculté

des sciences et de génie universitaire, Laval, Québec,

2004. In French.

Kaneko et al. (2004). “Humanoid robot HRP-2”, Proceed-

ings of the IEEE International Conference on Rob.

and Aut., 1083–1090, 2004.

Kim et al. (2005). “System Design and Dynamic Walking

of Humanoid Robot KHR-2”, IEEE/RSJ International

Conference on Robotics and Automation, 1431–1436,

2005.

Lofﬂer et al. (2003). “Sensor and Control Design of a Dy-

namically Stable Biped Robot”, Proc. IEEE Int. Con-

ference on Robotics and Automation, 484–490, 2003.

Lohmeier et al. (2006). “Modular joint design for perfor-

mance enhanced humanoid robot lola”, Proceedings

of the IEEE International Conference on Robotics and

Automation, 88–93, 2006.

Ogura et al. (2006). “Development of a New Humanoid

Robot WABIAN-2”, Proceedings of the 2006 IEEE

International Conference on Robotics and Automa-

tion, 76–81, 2006.

Tellez et al. (2008). “Reem-B: an autonomous lightweight

human-size humanoid robot”, 8th IEEE-RAS Interna-

tional Conference on Humanoids. 462–468, 2008.

Sakagami et al. (2002). “The intelligent ASIMO: system

overview and integration”, IEEE/RSJ Int. Conference

on Intelligent Robot and System, vol. 3, 2478–2483,

2002.

Souissi et al. (2012). “Design Optimisation of Parallel Joint

Mechanism for Humanoid Spine” in The 16th IEEE

Mediterranenan Electrotechnical Conference2012

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