HUMANOID

REALISTIC SIMULATOR

The Servomotor Joint Modeling

Jos

e L. Lima

, Jos

e A. Gonc¸alves

, Paulo G. Costa

and A. Paulo Moreira

Polytechnic Institute of Braganc¸a, Braganc¸a, Portugal

Faculty of Engineering of University of Porto, Porto, Portugal

Keywords:

Humanoid, Servomotor, Modeling, Simulation.

Abstract:

This paper presents a humanoid servomotor model that can be used in simulations. Once simulation is a

tool that reduces the software production time, it was developed a realistic simulator that own the humanoid

features. Based on a real platform, the simulator is validated when compared with the reality.

1 INTRODUCTION

Recent research in biped robots has resulted in a vari-

ety of prototypes that resemble their biological coun-

terparts. Legged robots have several advantages, they

can move in rugged terrains, they have the ability

to choose optional landing points, and two legged

robots are more suitable to move in human environ-

ment (Suzuki and Ohnishi, 2006).

The simulator should capture the essential charac-

teristics of the real system. In this paper, the servo-

motor model that powers the real humanoid joints is

addressed. The model of a Dynamixel AX-12 servo-

motor and its characteristics are found by an iterative

method based on a realistic simulator, the SimTwo

(Costa, 2009).

There are several simulators with humanoid simu-

lation capability, like Simspark, Webots, MURoSimF,

Microsoft Robotics Studio, YARP: Yet Another

Robot Platform (Wang et al., 2006) and OpenHRP3

(Ope, 2009), meanwhile, the SimTwo, as a generic

simulator, allows to simulate different types of robots

and allows the access to the low level behaviour, such

as dynamical model, friction model and servomotor

model in a way that can be mapped to the real robot,

with a minimal overhead. This simulator deals with

robot dynamics and how it reacts for several controller

strategies and styles. Using a realistic simulator can

be the key for reducing the development time of robot

control, localization and navigation software. It is not

an easy task to develop such simulator due to the in-

herent complexity of building realistic models for the

robot, its sensors and actuators and their interaction

with the world (Browning and Tryzelaar, 2003).

The purpose of developing such simulator is to

produce a personalized and versatile tool that will

allow the development and validation of the robot’s

software thereby reducing considerably the develop-

ment time.

The paper is organized as follows: Initially, the

real robot (which is the basis of the simulator) and its

main control architecture are presented. Then, sec-

tion 3 presents the developed simulator where the ser-

vomotor model was developed. Further, section 4

presents the validation of the simulator by compar-

ing its results with the real robot. Finally, section 5

rounds up with the conclusions and future work.

2 REAL HUMANOID

There are several humanoid robots kits available. The

commercially available Bioloid robot kit, from Robo-

tis, is the basis of the used humanoid robot and the

overview of the proposed biped robot is shown in Fig-

ure 1.

Figure

1: Real humanoid robot (from Bioloid).

396

Lima J., Gonçalves J., Costa P. and Moreira A. (2009).

HUMANOID REALISTIC SIMULATOR - The Servomotor Joint Modeling.

In Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Robotics and Automation, pages 396-400

DOI: 10.5220/0002183903960400

 SciTePress

The servo motors are connected to the central pro-

cessing unit through a serial 1Mbps network. Next

subsection presents the physical robot in which the

developed humanoid simulator was based.

2.1 Main Architecture

The presented humanoid robot is driven by 19 servo

motors (AX-12): six per leg, three in each arm and

one in the head. Three orthogonal servos set up the

3DOF (degree of freedom) hip joint. Two orthogonal

servos form the 2DOF ankle joint. One servo drives

the head (a vision camera holder). The shoulder is

based on two orthogonal servos allowing a 2DOF

joint and elbow has one servo allowing 1DOF. The to-

tal weight of the robot (without camera and on board

computer) is about 2 kg and its height is 38 cm.

Figure 2: Real humanoid robot control application.

To control the real humanoid robot a high level

application (presented in Figure 2) was developed.

This application is independent from the simulator, al-

though it allows to acquire and share some real robot

data with simulator.

3 SIMULATION MODEL

Designing the robot’s behaviour without real hard-

ware is possible due to a physics-based simulator im-

plementation. The physics engine is the key to make

simulation useful in terms of high performance robot

control (Browning and Tryzelaar, 2003). The dy-

namic behaviour of robot (or multiple robots) is com-

puted by the ODE (Open Dynamics Engine), a free

library for simulating rigid body dynamics.

3.1 Simulator Architecture

The simulator architecture is based on the real hu-

manoid robot. The body masses and dimensions are

used to build a humanoid simulator similar to the real

one. The communication architecture in real robot

brings some limitations to control loop such as lag

time. The developed simulator enhances these prop-

erties. The same architecture levels of the real robot

are implemented in the simulator. At the lowest level,

the servo motor model includes the control loop, just

like the real servomotors. At the highest level, some

predeﬁned joint states are created based on several

methods presented on literature (Kajita et al., 2006)

and (Zhang et al., 2008). At the middle level, an op-

timized trajectory controller that allows to minimize

the energy consumption is introduced as presented in

Figure 3 (Lima et al., 2008b).

Figure 3: Simulator main architecture.

Next subsections describe the servomotor model

that is used in the simulator where the electrical, fric-

tion and controller models are presented.

3.2 DC Motor Model

The servomotor can be modeled by a DC motor

model, presented in Figure 4, where U

is the con-

verter output, R

is the equivalent resistor, L

is the

equivalent inductance and e is the back em f voltage

as expressed by equation 1 (Conceic¸

ao et al., 2006).

Figure 4: DC motor electric model.

= e + R

+ L

∂i

∂t

(1)

The motor can deliver a T

torque and its load

has a J moment of inertia that will be presented by

the physical model ODE. Current i

can be related

with developed torque T

through equation 2 and the

back em f voltage can be related with angular speed

HUMANOID REALISTIC SIMULATOR - The Servomotor Joint Modeling

397

through equation 3, where K

is a motor parameter

that can be found by an experimental setup as pre-

sented in subsection 3.3 (Bishop, 2002).

(t) = K

i(t) (2)

e(t) = K

ω(t) (3)

In fact, the real developed torque (useful) that will

be applied to the load (T

) is the motor torque sub-

tracted by the friction torque (T

) as presented in

equation 4. The friction torque is discussed in sub-

section 3.5.

= T

− T

(4)

3.3 DC Motor Model Measurements

It was used the AX-12 servomotor from Dynamixel as

the base of the humanoid simulator articulations. The

and L

values can be directly measured (R

=8 Ω

and L

= 5 mH). The K

motor parameter can be found

by an indirect estimation. For several angular speeds,

it can be measured the em f voltage while motor is

open circuit.

Figure 5 shows the graphical data of the K

line

and its trend line. The average value of 13 measures

for K

(line slope) is about 0.006810 V.s/rad.

Figure 5: K

value for DC motor model.

3.4 DC Motor Nonlinearities

In a way to better model the real system, where vari-

ables cannot assume all values, there must be some

limits applied to some quantities. The ﬁrst one, is the

voltage applied to the supply terminals U

. This volt-

age is limited by the batteries voltage. Further, current

i is limited by the drive electronics once it is related

to the torque through equation 2 (torque limit is pro-

grammed in the real servomotor). Current gradient is

also implicitly limited by the presence of L

. Figure 6

shows the block diagram computed by the simulator.

There is also a internal gradient limitation to ensure

some numerical stability specially when the integra-

tion step period is signiﬁcantly slower than electric

dynamic.

Figure 6: Servomotor model block diagram computation.

3.5 Friction Model

The friction model has two terms: the static and dy-

namic friction as presented in equation 5.

= F

sign(ω) +B

ω (5)

The ﬁrst one can be modeled as the sign function

(with Fc constant) and the second one can be modeled

as a linear function with slope Bv.

The sum of this two components (T

), the ﬁnal

friction model, is shown in ﬁgure 7.

Figure 7: Servomotor model nonlinearities.

Figure 8 shows the friction model implemented in the

servomotor model.

Figure 8: Servomotor model with friction model.

The F

and B

constants are found using simulator

scanning several possible values minimizing the error

with the real system during an arm fall from 90 to 0

degrees. The error surface function can be minimized.

ICINCO 2009 - 6th International Conference on Informatics in Control, Automation and Robotics

398

As result, Bv=0.01278 N.m.s/rad and

Fc=0.0000171 N.m where found as the best

values. These constants allow the simulator to follow

reality very closely as presented in ﬁgure 9 where

an arm falls from 45, 90 and 135 degrees for both

robots.

Figure 9: Real robot and simulator friction comparison.

3.6 Low-level Controller

The low level controller resembles the closed loop

controller in the real robot implemented by the servo-

motor manufacturer. This controller accepts, from the

higher level, the angle and angular speed references

that deﬁne a trajectory. The controller type present

in the Dynamixel isn’t speciﬁed. However, there are

some possible models for the controller, such as PID

or state feedback. Considering a state feedback con-

troller and assuming K

the position error gain and

the speed error gain for each i joint, the equation

6 deﬁnes the servomotor input (U

) that keeps the de-

sired reference conditions for each i joint. The output

torque is computed by the physic model as presented

in Figure 10.

(t) = K

(θ

re f

(t) − θ

(t)) + K

(ω

re f

(t) − ω

(t))

(6)

Figure 10: Low level controller.

The position error and the speed error gains can be

computed resorting to a least squares approach. Hav-

ing the real robot arm step response (from 0 to 90 de-

grees), it is possible to scan several gains and to de-

termine the quadratic error between the real servo and

the humanoid simulator joint for each solution. The

one that fulﬁll the lowest quadratic error is the chosen

gains to the controller. Figure 11 shows the quadratic

error for the several solutions.

Figure 11: Quadratic error for real and simulator servomo-

tor.

The lowest quadratic error (0.66 degrees

) occurs

for K

equals 30 and for K

equals -1.2. These gains

allow to obtain the step response very close to the real

servo. Figure 12 shows both step responses.

Figure 12: Real and simulator servomotor step response.

3.7 Servomotor Model

With the previous results, it is possible to create the

servomotor model including the DC motor, the fric-

tion and the controller models (with its nonlinearities)

that will represent the real servo motor in the simula-

tor. The ﬁnal model is presented in ﬁgure 13.

Figure 13: Simulator servomotor model.

HUMANOID REALISTIC SIMULATOR - The Servomotor Joint Modeling

399

4 SIMULATOR VALIDATION

To validate the humanoid simulator model it is re-

quired to implement the same control signal to both

robots and to analyze the behaviors. Predeﬁned tra-

jectory states, that allow robot to walk, are based on

the Zero Moment Point (ZMP) method. Figure 14

shows the sequence during walk movements for both

robots (real at left and simulator at right). It is pos-

sible to observe that both robots exhibit very similar

behaviours.

Figure 14: Real and simulator robots walking with the same

predeﬁned gaits.

Figure 15: Real and simulator robots knee angles during a

walk movement.

With this walking movement, it can be acquired

all joint angles for both robots. Figure 15 shows

a knee angle for real and simulated robots, in a

walk movement, that shows simulator behaves as real

robot. Moreover, the power consumption compari-

son between real and simulated robot is presented in

(Lima et al., 2008a).

5 CONCLUSIONS AND FUTURE

WORK

A simulator that allows a humanoid robot simula-

tion capability is addressed and validated. The joints

that emulate the real articulations are based on a re-

alistic servomotor model. The proposed servomotor

model was implemented in the developed simulator,

SimTwo. This simulator is based in a real platform.

The friction model and closed loop controller gains

are found based on the real robot behaviour. It al-

lows to search the optimal values for friction and con-

troller gains based on a heuristic approach. The vali-

dation with the real humanoid robot allows to conﬁrm

the proposed servomotor model. As future work, the

simulator can be useful to ﬁnd several parameters that

optimize a desired condition such as energy consump-

tion in the walk movement and further applied to the

real robot.

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