Hiroshima University
Graduate School of Engineering
Department of System Cybernetics

Study of Dynamic Control for Balanced Walkingof Humanoid Robots
PhD Dissertation

SUNANDAN DUTTA
March 2021

Study of Dynamic Control for Balanced Walkingof Humanoid Robots(ヒューマノイドロボットのバランス歩行のための

動的制御に関する研究)

by
SUNANDAN DUTTA

D174932
A Thesis
Submitted to the Graduate School of Engineering
Hiroshima University
in partial fulfillment of the requirements for the degree ofDoctor of Philosophy(Electrical Engineering)

Hiroshima University, Japan
March 2021

Hiroshima University
Graduate School of Engineering
Kagamiyama, 1-4-1 Higashi-Hiroshima City
Hiroshima, Japan 739-8527
TEL: +81-82-424-7505
FAX: +81-82-422-7039

CERTIFICATE
To whom it may concern
We hereby certify that this is a copy of the original doctoral thesis by
Mr. SUNANDAN DUTTA. This doctoral thesis was successfully
defended and officially accepted in the partial fulfillment of therequirements for the degree of Doctor of Philosophy.
Advisory and Examination Committee:
Prof. Naoto Yorino
Prof. Katsuhiko Takahashi
Prof. Ichiro Nishizaki
Prof. Makoto Tsukai

OFFICIAL SEAL OF
THE GRADUATE SCHOOL________________________
Atsushi Sugeta, Dr.
Dean, Graduate School ofEngineering, Hiroshima
University

Abstract
Humanoid Robots are important targets by roboticists to automate the human-centeredsociety. Therefore humanoid robots are most popular research topics in the field of robotics.
At the same time it is very challenging to implement a humanoid robot in the real world
where the environmental factors like surface profile, rigid obstacles pose serious problems.
Also, the dynamics of humanoid robot is highly nonlinear and difficult to control. Due tothe presence of multiple joints, it is very difficult to implement control system hardware tocontrol all joints at a time. Also the computational complexity for this implementation is
too large to be implemented using open-source hardware platform, making thedevelopment very much restricted to laboratory rooms.
Therefore a lightweight humanoid robot is very much suitable over a heavy humansize robot for analyzing the postural stability of the robot on inclined surface. KONDO
KHR-3HV robot of 1.5 Kg weight and 0.6m height is used for the investigation of the
postural stability on an inclined surface. A force-sensor based position control system is
proposed. The ankle-pitch motor is controlled by force-sensor feedback from the robot foot.
This control system enables the robot to walk on inclined surface up to 8.5 o. Beyond 8.5o,a gyro based control system is designed control the hip motor allowing the robot to stabilize
its posture up to 10o of surface inclination. Theoretically the Inverted Pendulum Model isextended to include the effect of the surface inclination in order to model the stability of
the robot. The model predicts the effect of feedback gain and initial motor-rotation in orderto reduce the maximum overshoot in the transient response of the angular-pitch velocity of
the robot. After implementing static stability control system for the robot on inclined
surface, the dynamic walking of the robot was investigated on the inclined surface. In thatcase a gyro sensor was used to control the ankle-pitch motor up to a surface inclination of
8.88o. The torso-angular velocity is analyzed in both time domain and frequency domain
for studying the vibration in the robot. Vibration in the robot is observed to be an effect due
to the harmonics of the fundamental walking frequency of 1.73 Hz. In addition to theharmonics, the damped natural frequency due to the gyro feedback effects the frequency
response of the robot. This causes increased vibration when the feedback control isintroduced. One way to reduce the vibration is to increase the friction between the robot
feet and surface. Increasing surface friction allows the robot to walk more stably with
reduced vibration.
IAcknowledgement
First I acknowledge my supervisor Prof. Naoto Yorino for giving me this opportunity
to be a part of Electric Power and Energy System Laboratory (EPESL), Graduate Schoolof Engineering, Hiroshima University. I would like to express my gratitude for his
continuous support and guidance during my doctoral work. Also I would like to express
my gratitude to my sub-advisors Prof. Katsuhiko Takahashi, Prof. Ichiro Nishizaki and
Associate Professor Tsukai Makoto.
I would like to pay my sincere regards and gratitude to Prof. Mitiko Miura-Mattauschand Prof. Hans Jürgen Mattausch for their epitomized guidance to carry out the research onlight-weight humanoid robot in HiSIM Research Center, Hiroshima University. Also I
thank Associate Professor Tapas Kumar Maiti of DAIICT, India (former Associate
Professor at Hiroshima University) for guiding me through the basics of robotics andpreparation of experimental setup, in the early years of my doctoral work. I would like tothank my colleagues at HiSIM Research Center for their immense support which helped
me to finish my doctoral thesis.
I would like to thank TAOYAKA Program for their financial support to carry out the
research work for the thesis. Also, it was TAOYAKA program which gave me rareopportunities to develop robots based on the requirements of the society. I am thankful tothem for teaching me the concept of “Reverse Innovation”.
Last but not the least, I would like to express my love and gratitude to my parents,
family members and friends for their constant support though the turbulent days of doctoral
study and research.
SUNANDAN DUTTA
2021

II

Table of Contents
Abstract ......................................................................................................................................I
Acknowledgement .................................................................................................................... II
Table of Contents ....................................................................................................................III
List of Figures........................................................................................................................... V
List of Tables ........................................................................................................................... IX
Abbreviations ........................................................................................................................... X
Chapter 1: Introduction ............................................................................................................ 1
Research Background ........................................................................................................ 1
1.1.1 Why is a humanoid robot chosen? ............................................................................... 1
1.1.2 What field of application? ........................................................................................... 1
1.1.3 What type of humanoid robot is used? ......................................................................... 3
Research Objectives........................................................................................................... 3
1.2.1 Static stability control ................................................................................................. 4
1.2.2 Dynamic stability control ............................................................................................ 5
Thesis Outline ................................................................................................................... 6
Chapter 2: Literature Review ................................................................................................... 8
Background of Static Stability ........................................................................................... 8
Electromechanical Modelling........................................................................................... 10
Push-Force Recovery ....................................................................................................... 11
Walking Dynamics and Gait Analysis .............................................................................. 11
Chapter 3: Force Sensor Based Postural Stability Control ................................................... 14
Introduction ..................................................................................................................... 14
Robot Balancing Experiments .......................................................................................... 15
3.2.1 Experimental setup ................................................................................................... 15
3.2.2 Experimental Results ................................................................................................ 16
Model Development ........................................................................................................ 19
3.3.1 IPM for Robot-Foot-Centric Balancing ..................................................................... 19
3.3.2 Extension of IPM for Inclined Surface ...................................................................... 22
3.3.3 Ankle-Torque Compensation .................................................................................... 24
Analysis of Measured Control Features ............................................................................ 26
Conclusion ...................................................................................................................... 29
Chapter 4: Gyro Sensor Based Postural Stabiity Control ..................................................... 31
Introduction ..................................................................................................................... 31
Electromechanical Modelling........................................................................................... 31
4.2.1 Gyro Sensor .............................................................................................................. 32
4.2.2 Circuits of Gyro Sensor and Modelling ..................................................................... 32III

4.2.3 Simulation Results .................................................................................................... 34
4.2.4 Envelope Detector .................................................................................................... 36
4.2.5 Experimental Verification ......................................................................................... 36
Push-force Disturbance Rejection .................................................................................... 37
4.3.1 Falling Dynamics ...................................................................................................... 37
4.3.2 Control System ......................................................................................................... 39
4.3.3 Experimental Verification ......................................................................................... 41
On-site Implementation ................................................................................................... 42
Conclusion ...................................................................................................................... 44
Chapter 5: Vibration Control in Humanoid Robots .............................................................. 45
Introduction ..................................................................................................................... 45
Robot Walking Experiments ............................................................................................ 48
5.2.1 Motor Control System............................................................................................... 48
5.2.2 Experimental Setup ................................................................................................... 50
5.2.3 Robot-Gait Implementation ....................................................................................... 51
5.2.4 Experimental Results ................................................................................................ 53
Analysis of Experimental Results ..................................................................................... 55
Experiments with Robot-Foot Friction ............................................................................. 58
Model Development for Robot Balancing ........................................................................ 62
5.5.1 Inverted Pendulum Model (IPM) for Robot Walking ................................................. 62
5.5.2 Inverted Pendulum Model for Robot Walking ........................................................... 64
Conclusion ...................................................................................................................... 66
Chapter 6: Conclusions and Future works ............................................................................. 68
Novelty and Conclusions of the Dissertation .................................................................... 68
6.1.1 Static stability of humanoid robot on inclined surface ................................................ 68
6.1.2 Potential application of gyro sensor ........................................................................... 68
6.1.3 Vibration control while walking on an inclined surface ............................................. 68
Future Works ................................................................................................................... 69
References ............................................................................................................................... 70
Development of AIGAMO-I: A Remote Controlled Weeding Robot for
Organic Rice Farming ............................................................................................................. 77
List of Publications .................................................................................................................. 79IVList of Figures
Fig. 1.1. The partially damaged environment inside a Japanese wooden house requires lightweight ‘intelligent’ humanoid robot for risk-free preliminary survey and data acquisition. . 2
Fig. 1.2. Robot standing on an inclined surface faces the ‘static-stability problem’ whichmeans it can continue to stand with the same posture up to a certain surface inclination.
Beyond that surface inclination the robot-posture must be controlled to ensure static stability.
................................................................................................................................................... 4
Fig. 1.3. Robot walking on an inclined surface faces the ‘dynamic-stability problem’ whichmeans additional frequency components are observed in addition to the fundamental walking
frequency. The goal is to reduce the high-frequency contribution making the robot walking
stable. ......................................................................................................................................... 5
Fig. 1.4. A unified picture of the organization of the thesis is given for the readers tounderstand the workflow and major contribution of the thesis............................................... 7
Fig. 3.1. Experimental setup for robot-walking experiments on an inclined surface. ........... 14
Fig. 3.2. Measurement setup (top) for the robot experiments and the stages of robot control
carried out during the experiment (below). ............................................................................ 16
Fig. 3.3. The experiments are carried out for the Single Support Phase (SSP) when the robot
lifts one leg, supporting on the other. ..................................................................................... 17
Fig. 3.4. (a)The heel and toe forces acting on the foot of the robot while the robot is standingon an inclined surface of surface inclination 3.8o. (b) The toe and heel forces measured forvarious surface inclination. ..................................................................................................... 17
Fig. 3.5. The toe and heel forces of the robot for (a) left and (b) right leg measured at the
point indicated with a black arrow in Fig.3.4(a). ................................................................... 18
Fig. 3.6. The difference of the toe and heel forces at the robot-foot, as a function of the surface
inclination. ............................................................................................................................... 19
Fig. 3.7. (a) Inverted pendulum model (IPM) and its simplification considering ankle-pitch
motor control. (b) Free-body diagram of the robot foot. ....................................................... 20
Fig. 3.8. The shift of the oscillation of the motor angle A around A=0 for  > 0. The
asymmetrical nature of the angle is caused by the surface inclination. ................................. 22
Fig. 3.9. Initial ankle-pitch motor angle of the robot determines the static stability margin of
the robot according to the (3.10). ............................................................................................ 24
Fig. 3.10. Comparison of simulated (with low friction) and experimentally measured (withfriction) force differences for both left and right leg of the robot. ......................................... 25
Fig. 3.11. (a) The PID control system implemented in the servomotor controller of the robot.
(b) Measured results of armature voltage Varm as a function of error voltage e for different
reference angles A*. ................................................................................................................ 26
Fig. 3.12. (a) The adjustment of the ankle-pitch-motor angle A according to (3.11), fordifferent surface inclination (b) Simulation result for the torso-angular velocity  of the robot
in comparison to the gyro-sensor measurements. .................................................................. 27
Fig. 3.13. The maximum overshoot of the torso-angular velocity of the robot increases
abruptly beyond surface inclination 7.6o. This indicates the requirement of the hip-pitch
motor-control at higher surface inclination............................................................................ 28

VFig. 3.15. At higher surface inclination, the robot-stability is improved due to feedback motor
control and the adjustment of feedback-control parameters (see (3.13) and (3.14)). ............ 29
Fig. 3.14. The block diagram of the implemented control system for the ankle-pitch-motor
angle A and the hip-pitch-motor angle H. ............................................................................ 29
Fig. 4.1. The vibratory gyro-sensor is based on the Coriolis Effect. ...................................... 32
Fig. 4.2. (a) Driving Circuit of the vibratory MEMS gyro sensor. (b) Sensing circuit of the
gyro sensor............................................................................................................................... 33
Fig. 4.3. The methodology of the electromechanical modeling of the driving and sensing
circuits of the vibratory single axis gyro sensor. .................................................................... 34
Fig. 4.4. The simulation result of the output of the gyro sensor model. The input voltage to thedriving circuit Vin is amplitude modulated by the input angular velocity to give the output
voltage Vout. .............................................................................................................................. 35
Fig. 4.5. A demodulator is designed based on the principle of the envelope detector. The
envelope detector detects the envelope of the sensing circuit output V.................................. 36
Fig. 4.6. Experimental verification of the developed electro-mechanical model of the singleaxis vibratory gyro sensor. ...................................................................................................... 37
Fig. 4.7. An inverted pendulum model is used to model the robot dynamics when it is appliedwith an external push-force. ................................................................................................... 38
Fig. 4.8. Experimental verification of the developed electro-mechanical model of the singleaxis vibratory gyro sensor. ...................................................................................................... 39
Fig. 4.9. Experimental verification of the developed electro-mechanical model of the singleaxis vibratory gyro sensor. ...................................................................................................... 40
Fig. 4.11. The projection of the robot-COM is brought back by the ankle-pitch motor
compensation in order to stabilize the robot posture. ............................................................ 41
Fig. 4.10. The compensation of ankle-pitch motor stabilize the robot posture. The
implemented control system brings the robot within the static stability margin (4.3),
preventing the falling down. ................................................................................................... 41
Fig. 4.12. Push recovery experiments when the robot is undergoing negative pitch motion andpositive pitch motion (b).......................................................................................................... 42
Fig. 4.14. Robot KONDO KHR-3HV with the integrated push-recovery control systemdesigned by HiSIM Research Center, Hiroshima University. The story was covered by
Japanese magazine ROBOCON. (Image Source: ROBOCON Magazine, May Issue, 2019) 43
Fig. 4.13. Battle of light-weight humanoid robot in ROBO-ONE Light Competition. (Image
Source: Biped Robot Association, Japan)............................................................................... 43
Fig. 5.1. KONDO KHR-3HV Humanoid Robot integrated with a gyro sensor for balancing
on an inclined surface with inclination angle . ..................................................................... 45
Fig. 5.2. The gyro-sensor measured angular-pitch velocity of the robot body is used to control
the ankle-pitch motor (MA) above a critical inclination cr0 and is then used additionally tocontrol the hip-pitch motor (MH) above a larger critical inclination cr1, in order to balance
the robot walking. ................................................................................................................... 46
Fig. 5.3. (a) Walking pattern of the robot, illustrating the gait-cycle repetition of the robot,
with one half of a gait cycle at the beginning, then 4 complete gait cycles and finally one halfof a gait cycle at the end. (b) One gait cycle is zoomed to show the gait pattern of the robot
KONDO KHR-3HV. Tgait: period of a gait cycle; Twalk: total time for which the robot has
walked. (c) Photos showing the gait pattern implemented in one gait cycle of the robot withthe zoomed foot-placements patterns at the bottom. .............................................................. 47

VI

Fig. 5.4. (a) Schematic diagram of the control circuit of DC servomotor used in theexperiment. The transfer-function formulation used for modeling the motor-control system
without the gyro-sensor feedback loop. (b) Schematic diagram of the motor-control system,
implemented for adjusting the robot’s ankle-pitch motor on inclined surfaces. ................... 48
Fig. 5.5. (a) Angular-pitch velocity of the robot torso when the robot walks on an uninclined
surface ( = 0o). (b) The angular-pitch velocity of the third gait cycle as detected by the gyro
sensor. The third gait cycle is shown in expanded form, to explain the gait pattern of the robot
on the uninclined surface. ....................................................................................................... 52
Fig. 5.6. Angular velocities of the robot’s pitch motion during a gait cycle, measured for
different surface inclinations. An increase in amplitude and number of oscillations is observed
at higher surface inclinations with feedback control. The results are compared with angularpitch velocities, measured for =0o. ........................................................................................ 53
Fig. 5.7. Angular-pitch velocity for a gait cycle with both ankle-pitch-motor control and hippitch-motor control, measured at different higher surface inclinations. (a) Robot vibrations
increase for KH=14 in the hip-pitch-motor control. (b) KA=12 and KH=13 are an optimized
motor-control setting, allowing stable down-slope walking up to inclinations of =10.2o. .... 55
Fig. 5.8. Fourier analysis of the angular-pitch velocity waveforms measured by the gyro
sensor for the robot-body, when the robot is walking stably on inclined surfaces without ((a),(b-1), (b-2)) and with ((c-1), (c-2), (d)) gyro-sensor feedback. The frequency fA0 = 2.58 Hz (see(c-1) and (c-2)) is induced by the motor feedback with KA=12, which is shifted to fA’0 = 4.74 Hz(see (d)) due to an increased KA............................................................................................... 56
Fig. 5.9. Fourier transformation of the angular-pitch velocity, when both ankle-pitch and hippitch motors are controlled by the gyro sensor. It can be seen that the contribution due to thefundamental walking frequency of 1.73 Hz is no more observable. Instead a peak at higher
frequency is observed. The measured time-domain waveform becomes more oscillatory, as
shown in Fig. 5.7. ..................................................................................................................... 57
Fig. 5.10. Phase plots for the measured pitch velocity in the cases of various surface
inclinations. The contributing frequencies are indicated, confirming the findings from thecorresponding amplitude plots. A tolerance value of 33% of the absolute maximum in theamplitude spectrum is used for the phase-plot calculation. ................................................... 57
Fig. 5.11. Contributing frequencies as extracted from the frequency-response analysis of theangular-pitch velocity as a function of surface inclination .................................................. 58
Fig. 5.12. Fourier analysis of the angular-pitch velocity of the robot walking on an inclined
surface for  = 8.88o with varying KA (18 in (d), 15 in (d-2) and 12 in (d-3)) and for  = 9.7owith varying KH (14 in (a), 13 in (a-2) and 12 in (a-3)) By reducing KA and KH values, the robot
posture becomes unstable due to slipping, as shown in (d-3) and (a-3). ................................ 59
Fig. 5.13. (a) Amplitude plot, which shows the Fourier analysis of the angular-pitch velocity
data when the robot is allowed to walk with higher feet friction and reduced value of KA = 12
on a surface of  = 8.88o inclination. (b) Comparison of amplitude plots, which demonstrates
the shift in the additional frequency due to the feedback control from fA’0=4.74 Hz to fA0=2.58
Hz, when lowering KA from 18 to 12, as becomes possible by the increased feet friction. (c)Phase plot, which confirms the frequency-peak shift to a lower value, due to lowering of the
feedback gain KA at higher surface friction. A tolerance value of 33% of the absolute
maximum in the amplitude spectrum is used for the phase-plot calculation. ....................... 60
Fig. 5.14. (a) shows that robot can walk on a surface of  = 9.7o inclination with KH =12, when
the robot-feet friction is increased. (b) illustrates two important features, which result fromthe increased-friction-enabled KH lowering: First, lowering of the frequency, induced by theadditional hip-pitch motor control, from 8.40 Hz to 7.33 Hz. Second, reappearance of the peakat fundamental walking frequency f0 = 1.73 Hz. (c) Corresponding phase plot, which supportsVIIthe appearance of the peak at f0 and the lowering of KH. A tolerance value of 33% of theabsolute maximum in the amplitude spectrum is used for the phase-plot calculation. ......... 61
Fig. 5.15. IPM to explain the robot walking dynamics. The parameters , m, l and g are angleof robot-torso rotation in the sagittal plane, robot mass, robot-center-of-mass distance fromthe ankle-pitch motor and acceleration due to gravity, respectively. .................................... 62
Fig. A.1. Overview of the TAOYAKA Onsite Team Project………………………………….77
Fig. A.2. Weeding robot AIGAMO-I (right) and the principal physical parameters (left)....78

VIII

List of Tables
Table I. KONDO KHR-3HV Robot Physical Parameters…………………………………….14
Table II. Variables and parameters used in the Inverted Pendulum Model (IPM)…………21
Table III. Gyro Sensor Model Parameters …………………………………………………… 35

IX

Abbreviations‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Abbreviations
IPM

Inverted Pendulum Model

ZMP

Zero Moment Point

MEMS Micro-electromechanical system
SSP

Single Support Phase

DSP

Double Support Phase

COM

Center of Mass

COP

Center of Pressure

PD

Proportional-Derivative

PID

Proportional-Integral-Derivative

XChapter 1: Introduction‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Chapter 1: Introduction
Research Background
Robots are important means to sustain and to develop a comfortable society [1-6] tolive in. The intensive utilization of robot is being realized to reduce the necessity of thehuman efforts in different fields like agricultural [1,2], inspection and maintenance [3,4],or rescue operations [5-7]. The basic philosophy for the research, as followed in this thesis,is ‘Reverse Innovation’ [8] - which allows development of any technology according to theneed of human beings. But at the same time Isaac Asimov’s “Laws of Robotics” [9] arestrictly followed as far as the consequence of the technology is concerned. In this chapter,
three basic questions are answered:
1. Why a humanoid robot is chosen for the research purpose?
2. What field of application inspired this development of the humanoid robot?
3. What type of humanoid robot is chosen or in other words, what is special about thephysical characteristics of the humanoid robot used for the research work?

1.1.1 Why is a humanoid robot chosen?
The working environment around us is built by human beings. The interior of houses
and buildings, the staircase, the lanes between buildings, the walking path beside thedriveways and many more – are specifically designed and planned especially for humandwellers. Then comes the tool used by the human beings. The tools are invented anddesigned so that they can be easily handled and operated by human beings. Shuuji Kajita
has mentioned three important features of the humanoid robots in their book Introduction
to Humanoid Robotics [10]. If those features are carefully followed, then the only robotthat can work in human-based environments as it is and use the tools made for humans, isa humanoid robot having a “human like shape”. So, the best robot to apply in our daily
activities is a humanoid robot.

1.1.2 What field of application?
Humanoid robots are finding various applications in our daily life, but one potential
application is post-disaster survey and rescue [6]. ‘Human-shape’ and human-sized robots
with weight comparable to that of an adult human being are applied to similar situations.
This is observed in both simulation platforms like Choreonoid [11] and real-time testing1

Chapter 1: Introduction‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬like the application of the robot to simulated environments of DARPA Robotics Challenge(DRC) [12].
If those environments are carefully observed, most of the simulation or real-time
experiments are carried out on a concrete surface which is strong enough to bear the robot
load. That is quite usual in case of nuclear power plant or inside a mine. At the same time
it must be kept in mind that the rate of damage to the Japanese household is highest due tovarious natural disaster as compared to the nuclear power plants or other industrial
establishments. For example let’s consider the situation of Japanese wooden houses. Okada
and Takai [13] documented the damage patterns of the wooden houses due to earthquake.
It is observed that significant number of effected houses are partially damaged where thesupporting columns and beams are severely damaged. This reduces the load-bearing
capacity of the supporting-structure.
During the post-disaster surveillance and rescue work it is very dangerous to send
human rescuers to those partially damaged structures because the weight of human rescuers
can cause further damage to the structure. Also it may cause injury even death to therescuers and also to the trapped human life (if any) under the damaged structure. Aftershock
effects may also cause injury to the human rescuers working in the affected environment.
Therefore keeping in the mind the severity of the damaged structure, instead of humanrescuers it is wise to send humanoid robots. Additionally considering the load-bearing
capacity of the partially-damaged structure, the weight of the robot must be low. This
Preliminary survey or dataacquisition in the disastereffected household
We need an “ intelligent
locomotion system” or humanoid
robot with a low payload < 4.5 Kg(Average infant weight)• Danger of aftershock affects• Danger of structure-collapse
due to possible high load
during rescue operations

Optimization problem:
Miniaturization of actuators,
mechanical links, sensors,
control circuits and vision
hardware with the given
constraint• Complete loss of valuable
structure• Injury to Rescuers(Also Death !!!)• Death of trapped human life

Fig. 1.1. The partially damaged environment inside a Japanese wooden house requires
light-weight ‘intelligent’ humanoid robot for risk-free preliminary survey and dataacquisition.

2

Chapter 1: Introduction‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬situation justifies the work carried out with light-weight humanoid robot in this thesis. An
overall picture of the situation discussed above, is shown in Fig.1.1.

1.1.3 What type of humanoid robot is used?
Following the discussion carried out in previous section, the weight of the robot isdetermined to be very lower than the weight of an adult human or conventionally developed
humanoid robots. This is the basic reason behind the working on a light-humanoid robot.
In this thesis a light-weight humanoid robot of 1.5 Kg weight [14] is used.
It is important to revisit the features of the humanoid robots as discussed by Kajita etal. [10]. The third feature says that “humanoid robots have human-like shape”. Sometimes
research works on light-weight humanoid robots or “toy robots” are not considered to be“mainstream robotics-research” by many members of the research community. But basedon the established and accepted features of humanoid robots it can be argued that lightweight toy-sized robots are also humanoid robots even though they are not human-sized.
This is because Kajita et al emphasizes on the ‘shape’ of the robot, rather than ‘size’.

Research Objectives
In the previous section the background of the research is presented and three basic
questions are investigated and answered. The humanoid robots in general, places various
challenges in front of the research community [15]. The dynamics of a humanoid robot ishighly nonlinear leading to unpredictable behavior of the robot. Moreover it is amultivariable system which makes the design of the motor control system highly
complicated to implement. Above all the changing surface profile poses to be a major
problem for a terrain-blind (without vision based feedback) robot.
Also due to the light-weight feature of the robot body, additional problem like vibration
is observed for the robot walking [16]. The primary objective of this thesis is to “stabilize
the light-weight humanoid robot on an inclined surface”.
Question may arise, why is an inclined surface chosen? Three main reasons can begiven as follows:
1. Inclined surface is a very common and structured surface-profile often found in
our surrounding environment.
2. Inclined surface modifies the gravity force on the robot-body allowing to study
the gravity compensation needed to stabilize the robot-posture.
3

Chapter 1: Introduction‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬3. Surface friction due to inclined surface effects the robot-dynamics.
To achieve the objective mentioned above, the investigation presented in the thesis isdivided into two main parts – static stability control and dynamic stability control.

1.2.1 Static stability control
Static stability control discusses the postural stability of the robot when the robot is notwalking. For a robot standing on an inclined surface, there is a threshold surface inclination
beyond which the robot with the reference posture will fall. In static stability control, thecontrol strategies for keeping the robot-posture stable beyond that threshold surface
inclination are discussed.

Static stability problem:

Goal :

Robot becomes unstable for

Method: b  l sin  A,0   sin 

l
cos

A,0



min ( FT  FH )FT  FH  A*   A,0  K A ( FT  FH )

1Position-control based on forcefeedback

H. Hemami et al. 1973


A,0*
A,0

: surface inclination: corrected reference ankle-pitch motor angle: reference ankle-pitch motor angleKA: proportional feedback gain
FT, FH : toe and heel force at the robot foot respectivelyb: length of the robot footl: height of the robot’s center of mass from ankle

Fig. 1.2. Robot standing on an inclined surface faces the ‘static-stability problem’ whichmeans it can continue to stand with the same posture up to a certain surface inclination.
Beyond that surface inclination the robot-posture must be controlled to ensure static
stability.

While investigating the static stability of the robot on inclined surface, it is found that the
gyro-sensor based feedback control is necessary to control the robot posture beyond acertain surface inclination [17]. Therefore the working principle of the vibratory-gyro
sensor is studied and an electromechanical model of the gyro sensor is proposed [18]. This
allows the researcher to incorporate the circuit behavior of the sensor into the dynamics ofthe robot. The gyro-sensor model is used to simulate the robot-dynamics when the robot isapplied with an external push-force [19]. The robot-posture is controlled based on theankle-strategy [20], where the ankle-pitch motor angle is controlled based on the angular

4Chapter 1: Introduction‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Dynamic stability problem:

Goal : min( f1 , f 2 , f 3 , f A0 , f H0 )MA+ MH
Feedback

Method: A*   A,0  K A (ref  meas )

KA=12
KH=13

Position-control based on angularvelocity feedback

MA Feedback
No Feedback

KA=18


A,0*
A,0

: surface inclination: corrected reference ankle-pitch motor angle: reference ankle-pitch motor angleKA: proportional feedback gainfn
: nth harmonic of fundamental walking frequency
fA0, fH0 : damped natural frequency of the control system

KA=12[degree]Fig. 1.3. Robot walking on an inclined surface faces the ‘dynamic-stability problem’ whichmeans additional frequency components are observed in addition to the fundamental
walking frequency. The goal is to reduce the high-frequency contribution making therobot walking stable.

velocity feedback measured by the gyro sensor. This concludes the static stability control
part of the thesis. An overall picture of the static stability control is shown in Fig. 1.2.

1.2.2 Dynamic stability control
In this thesis, dynamic stability explains the stability of the robot when the robot walks
on the inclined surface. When a robot walks, there exists is a gait cycle (and corresponding
fundamental walking frequency f0). The fundamental walking frequency is observed when
the walking pattern of the robot is analyzed in the frequency domain (hereafter f-domain)[16]. Here the walking pattern is characterized by the pitch-angular-velocity of the robot
torso. The angular-pitch velocity is measured by a gyros sensor integrated to the torso of
the robot.
When the robot walks down an inclined surface, it is observed that the robot can walkwith the pre-programmed walking pattern up to a critical surface inclination. Beyond that
surface inclination, the posture of the robot (ankle-pitch motor and hip-pitch motor) is
controlled by the pitch-angular velocity measured by the gyro sensor.
Beyond the critical surface-inclination, vibration is observed in the light-weight
humanoid robot, which changes the walking pattern of the robot. The change in the walking
pattern with increasing the surface inclination, can be explained by analyzing the measured
angular-pitch velocity in the f-domain. Vibration causes instability in the robot-walking.
5

Chapter 1: Introduction‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬The instability can be explained and reduced by identifying the frequency peaks. This is
novel approach where the stability of the robot is analyzed in frequency domain solely
depending on the analysis of one physical quantity: the pitch-angular velocity of the robot.
The position of the contributing frequency-peaks are determined by the surface inclinationand the magnitude of the feedback gain. The origin of the frequency peaks can be explainedby analyzing the response of a second-order velocity-feedback control of a nonlinear
inverted pendulum system. The model gives a method to reduce the high-frequency
contribution reducing the vibration in the robot, making the walking stable. An overall
picture of the dynamic stability control is shown in Fig. 1.3.

Thesis Outline
The thesis consists of six chapters. The research topics discussed in the chapters are
summarized as follows: Chapter 1 discusses the basic objective of the work outlining a brief overview of thedesign and application of the humanoid robot. It discusses the motivation of the workand concluding with the outline of the thesis.
 Chapter 2 discusses the previous work carried out in the field of humanoid walking-stability. Two main aspects of the robot stability are discussed namely, the control
methods for postural stabilization and the vibration control in humanoid robots.
 Chapter 3 presents the investigation of the static stability of the robot. The static
stability of the robot is analyzed on an inclined surface. The proposed positioncontrol system is based on the force-sensor feedback from the robot feet. The robot
can stabilize its posture on inclined surface up to a surface inclination of 8 degrees.
Beyond 8 degrees, a gyro sensor based position control system is used to stabilize
the robot on inclined surface up to a surface inclination of 10.2 degrees.
 Chapter 4 discusses the application of gyro sensor to the humanoid robot. An
electromechanical model of the gyro sensor is experimentally verified from the
dynamic characteristics of analog gyro sensor KRG-4. The gyro sensor model isused to model the push recovery strategy for the robot on a plane surface. The model
was experimentally verified by the push-recovery experiments.

6

Chapter 1: Introduction‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ Chapter 5 discusses the robot walking control based on a novel gyro sensor based
feedback control system. The achievements are divided into two parts. The first part
discusses the walking pattern modelling of the robot and the frequency response of
the robot walking on an uninclined surface. In order to stabilize the robot walking
on an inclined surface, a gyro-sensor based feedback control systems is proposed.
The experimental results shows that as the surface inclination is increased higher
harmonics of the fundamental walking frequency and damped natural frequency ofthe control system effects the robot walking. This increases the vibration in the robot,
thus making the robot walking unstable. So an optimization of the controller gain is
implemented based on the tradeoff between the surface friction and the vibration.
Therefore adjusting the controller gain, the vibration is reduced.
 Chapter 6 provides a conclusion of the thesis, where the contributions of the study are
discussed. In addition, some recommendations for future research are presented.
A unified picture of the organization of the thesis is given below. The author considers it
will be helpful for the readers to understand the workflow and major contribution of thethesis. In the Fig.1.4 the contents of the thesis are divided into three parts, viz.
 Part I. Problem statement, Part II. Static stability control
 Part III. Dynamic stability control
Part I Problem statement•••

Background
Motivation
Literature review

Part II Static stability control
•
•
•
•
•
•

Static stability
Force sensor based control system
Experimental results
Model development
Electromechanical model of gyro sensor
Push-force disturbance rejection

Part III Dynamic stability and vibration
control•••••

Walking pattern modeling
Gyro sensor based control system
Experimental results
Vibration analysis and suppression
Modeling and analysis

Chapter 1

Chapter 2

Introduction

Literature review

Chapter 3

Chapter 4

Force sensor based
postural stability
control

Gyro sensor based
postural stability
control

Chapter 5

Chapter 6

Vibration control inhumanoid robots

Conclusion andfuture research

Fig. 1.4. A unified picture of the organization of the thesis is given for the readers tounderstand the workflow and major contribution of the thesis.

7Chapter 2: Literature Review‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Chapter 2: Literature Review
This chapter discusses the literature review on the stability of humanoid robot. The
organization of the chapter is as given below. In section 2.1 a survey of the control methods
for static stability control of the humanoid robot is given. The survey is followed by theoutcomes and drawbacks of the control methods when their applicability to a lighthumanoid robot is considered. At the end the originalities of this thesis in the field of static
stability of the light-weight humanoid robot is listed. The originalities are discussed indetail in the following chapter 3.
Section 2.2 discusses the theoretical framework and literature over which the proposed
electromechanical model for gyro sensor is developed. The electromechanical model of the
gyro sensor is discussed in chapter 4. As introduced in previous chapter, the model for gyro
sensor is used to analyze the dynamics of the robot when applied with a push-force. Section
2.3 presents the literature survey on the push-force disturbance rejection control. The pushforce dynamics of the robot is discussed in the latter half of chapter 4.
At the end, in section 2.4 the previous works on dynamic stability of humanoid robot is
discussed followed by the brief introduction to the originalities presented by this thesis inchapter 5.

Background of Static Stability
The robotics community have achieved large progress in the in the field of intelligent
humanoid robots for using at various environments under various situations [21-24].
Accurate sensing of the surface-profile information [25-32] is required for controlling thewalking of the robot on a given surface. So far the developments extensively use the terraininformation to stabilize the robot [28-29]. The information from the environment iscollected by vision based sensors [33-34]. So, “blind” humanoid-robot i.e. without any
camera to sense the surrounding, is a worst-case scenario for robot-posture control while
walking [30-32].
So far the publications on the ‘blind’ humanoid robots have focused on the walking
analysis [35-38]. Model based control like Zero Moment Point (ZMP) control was
introduced to analyze the stability of the humanoid robot [10, 39]. This control system wasused in industry-level humanoid robots like HONDA humanoid robot [40] or the HRP
8Chapter 2: Literature Review‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬series of AIST-Japan [41,42]. However, unlike the well-solved control problems as thosefor robot manipulators [43,44], the development of robust control for walking of humanoid
robot has not reached practical implementation till now. Recently, control systems
developed on the principles of Machine Learning (ML) algorithms, such as supervisedlearning algorithms [45-47] and reinforcement-learning algorithms [48,49], are being
applied to biped-stability control [35], [37], [39], [50-52] to achieve better walking stability
and improving the agility of the humanoid robots. To implement such ML-based control
methods in light-weight robots, one faces major problems of increased complexity of
hardware. Unnecessary hardware payload increases the weight on the robot making it lesser
suitable design for potential applications. Therefore, it is difficult to implement such MLbased control methods into a commercial low-cost open-source hardware platform and thenintegrate the platform to the light-weight robot. In summary, the previously proposed
walking-control methods cannot be use to efficiently realize the balancing of the lightweight humanoid robots. Further, the balancing of light-weight robots on an inclined
surface is more difficult as compared to that of a heavy-weight robot [30-32]. This largely
depends on the dimension of the barrier or surface geometry. Considering the scalability
rules [53], very few research works on balancing the light-weight humanoid robots havebeen reported [54-55] so far. Tamura et. al. [54] proposed a method to control the stabilityof light-weight humanoid robots. This avoids the calculation-overhead and also the effectof noise in the measurement of the ZMP. Implementation of the proposed control systemshowed, that the robot can only surpass an object of 0.5 cm height thus avoiding the
obstacle, which is quite inadequate with respect to the more realistic uneven surfaces andobstacles. Moreover, the control scheme of [54] was only limited to surpassing obstacles
and not applied to any kind of inclined surfaces (upslope or downslope). Yi et. al. [55]proposed a ZMP-based on-line-learning system, where the surface inclination is calculated
while walking and the joint angles are adjusted to stabilize the posture robot. They havetested the control system for an uneven surface with 6% finite height change. But in thatcase effects of inclined surface on static stability and walking dynamics of the humanoid
robot are not discussed.
The investigation presented in this thesis focusses on the development of low-cost,robust yet easy-to-control hardware of humanoid-robot-stability control. Considering theabove survey, the novel contributions to this section include:
1. Force-sensor are attached to heel and toe of the robot-feet. The difference
between the toe and heel forces are measured. This difference is measured and9Chapter 2: Literature Review‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬plotted as a function of surface inclination. Based on the trend of the forcedifference, a critical surface inclination is determined. Below the critical surface
inclination, no sensor-based posture control is required.
2. Inverted Pendulum Model (IPM) [56-58] is extended to incorporate theinformation of the surface inclination.
3. Based on this extended IPM, a force sensor based control system is proposed forankle-pitch-motor.
4. Compared to the conventional ZMP control [59], the proposed control systemdoes not require the calculation of ZMP, thus reducing calculation overhead andnoise. It is observed that the ankle-pitch motor plays important role in posture
stabilization [56-57, 60] of humanoid robot, only ankle-pitch-motor is controlled.
This further reduces calculation overhead as compared to the conventional
approach based on inverse kinematics [10].

Electromechanical Modelling
The control systems developed so far incorporates sensors to measure the disturbances
caused by the environment. Therefore the circuit level analysis of these components arevery much necessary prior to the overall analysis of the robot. This robot components likegyro sensors are generally implemented in the robot simulator as a mathematical functions,which do not analyze the circuit-level behavior of the sensor. The performance of the robot
in a macroscopic level is largely guided by the microscopic behavior of the electronic
components. Therefore, analysis of these components are needed for developing a specificrobot system.
Lots of research efforts are given mainly to develop the efficient control algorithms for
robot-system controller [61]. But, the hardware design of the controller and peripherals forthe robust performance of the robot system are analyzed to a much lesser degree [10, 6263]. In this thesis special focus is given on the circuit level analysis of the robot components
and how the circuit level performance effect the overall dynamics of the robot. This is done
to bridge between the electronic behaviors of the robot components to the dynamic behaviorof the multibody systems like humanoid robot. The future purpose of this work is toincorporate the circuit level description into the robot multibody physics simulators.

10Chapter 2: Literature Review‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Push-Force Recovery
Hemami et.al. [57] discussed the static stability of an inverted pendulum in order tomodel robot walking based on the principles of the inverted pendulum. The static stability
margin [57] of a robot is calculated from the potential energy of the footed-inverted
pendulum. The margin is independent of the mass of the robot and depends on the physicalparameters of the robot like height of the center of mass and length of the foot.
Vukobratovic et.al. [59] introduced the ZMP as a criteria to measure the stability-margin
for humanoid robots. The ZMP control is used in order to control the robot-motor angles
based on the feedback of ground reaction force [10]. However, the control strategies varydepending upon the magnitude of the force exerted on the robot body. The most basic
strategy for canceling disturbance due to small-magnitude force, is compensating the torqueat ankle-pitch motor. Hemami et. al. [64] discussed the ankle strategy considering an
inverted pendulum model. The hip strategy i.e. compensating the torque at hip motor was
introduced considering the inverted pendulum model of 2-degrees-of-freedom (DOF).
Hoffmann [65] argued that basic ankle strategy is realized with adjusting the Center ofPressure (COP) or ZMP by changing the tangential ground-reaction force with the ankle
motor. Therefore it is observed that the control strategies indicates towards the utilizationof ZMP approach only. With the hip strategy, larger tangential ground-reaction force isgenerated causing postural stabilization at higher disturbance force. In this thesis as aprimitive step, the ankle strategy is implemented for the light-weight robot based on thepitch-angular velocity of the robot-torso. The use of the gyro sensor instead of force sensor(for calculating the ZMP) reduces the computational complexities as carried out in humanseized robot.

Walking Dynamics and Gait Analysis
The most important feature of an ideal human-walking pattern or “gait pattern” isobserved in its periodicity [67], and this periodic gait-pattern is defined from thephysiological point of view. Various experiments have been carried out by prosthesists, toassess the human gait-pattern [67-77] and include an analysis of basic parameters, likevelocity or number of steps per unit time. [68]. The joint angle of the robot leg and theground-reaction force are most often studied among all the different parameters, tocharacterize the periodicity of the human gait [67-71]. For the characterization purpose, afrequency analysis of these measurable quantities is often carried out using the Fourier
11

Chapter 2: Literature Review‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬series expansion [69-71]. However, such Fourier analysis was in most cases limited to thestudy of human patients, to determine the change in their walking dynamics due to various
physical problems and diseases [74]. With the development of an Inertial Measurement
Unit (IMU), based on a Micro Electro-Mechanical System (MEMS), the studies oforientation and force at each of the joint angles for human beings or humanoid robots havebecome more advanced [76-78].
To analyze the periodicity of any physical signal, frequency-domain analysis isconsidered to be a fundamental approach. In the humanoid-robotics field, the Fourier series
expansion is applied to generate the gait pattern for the robot’s basic walking motion, which
can be modeled as a superposition of sinusoidal joint-angle variations [79,80]. Kajita et al.
[81] used frequency-domain analysis to suppress vertical vibrations in the HRP-4C robot.
In [82], a frequency-domain classification of surfaces, based on the robot vibrations, isreported but not yet applied to the humanoid-robot control. Liu et al. [83] designed avibration-reduction controller for elastic joints, implemented in a humanoid manipulator.
The terminologies of resonant and anti-resonant frequencies with respect to the compliancemodeling in motors were discussed in detail, highlighting the frequency-domain analysisof the vibrations. But the control system was only applied to static manipulators, while thevibration effect on humanoid-robot dynamics was not reported. Very few works on thestability of humanoid robots, which exploit the Fourier analysis of the gait-data, have beenreported. Kim et al. [84] reported vibration responses during leg lifting of a humanoid robot
in the swinging phase, but did not adequately discuss the overall effect on the gait data,e.g., on the COM position or on the angular-pitch velocity components of robot’s COM.
Consequently, the purpose of the dynamic stability control in this thesis is to analyze
the balancing mechanism of a humanoid robot on inclined surfaces, to achieve stable
walking with the help of motor-feedback control and Fourier analysis of the robot’s
angular-pitch velocity, which is measured for one gait-cycle during the experiments. The
angular-pitch velocity of the robot is measured while walking on different surface
inclinations and analyzed in the frequency domain, where the origin of the observed
periodicity disturbances of the robot-gait is investigated. The novel contributions of thispart of the thesis include:Proposal of a gyro-sensor-based feedback-control system to control the ankle-pitch andhip-pitch motors of the robot for stable walking on inclined surfaces. The control
system enables the robot to walk stably on a downslope surface of inclination up to
10.2o. The feedback controller is easy to implement in a commercial, low-cost, mass12

Chapter 2: Literature Review‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬produced and open-source hardware platform that can be integrated easily into a lightweight humanoid robot.


The ankle-pitch and hip-pitch motors play a significant role in posture stabilization[57,10]. Therefore, initially for smaller surface inclinations, the ankle-pitch motor iscontrolled and for larger surface inclinations both ankle-pitch and hip-pitch motors arecontrolled. This reduces the computational complexity compared to the inversekinematics-based approaches in conventional ZMP-based control [10, 85, 86].

The angular-pitch velocity of the robot is considered to be a characteristic of the robotgait, is measured by the gyro sensor for the walking robot and is analyzed in thefrequency domain. A novel usage of the Fourier analysis for the angular-pitch velocity
is proposed to determine the cause of postural instability on inclined surfaces. Also, theeffect of the feedback gain on the robot gait on inclined surfaces is analyzed.

It is experimentally observed that increased friction between robot feet and inclined
surface reduces the robot vibrations at larger surface inclinations. The results of robotwalking experiments with increased friction represents an optimization approach forthe feedback gain to reduce vibrations in the robot at increased surface inclinations.



The IPM, used to model the robot walking, is extended for inclined surfaces. An
additional gyro-sensor-based feedback loop is included in the model to explain the
Fourier response of the angular-pitch velocity. Further, the IPM is extended to include
the nonlinearity, induced by the surface inclination, to explain the harmonics observedin the Fourier Transform of the angular-pitch velocity.

13Chapter 3: Force Sensor Based Postural Stability Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Chapter 3: Force Sensor Based Postural
Stability Control
Introduction
In this chapter the force sensor based static stability control method is discussed. For
analyzing the static stability the light-weight humanoid robot KONDO KHR-3HV [14] isintegrated with force sensors on heel and toes of each foot as shown in a schematic of therobot in Fig. 3.1. This is done to measure the heel and toe forces on each foot. Robotbalancing experiments are carried over to measure the forces on the toe and heel. Based on
the experimentally-measured forces the posture-control system is developed for the robot,
standing on an inclined surface.

Gyro
SensorCOM

M H (Hip)
M K (Knee)Heel

M A (Ankle)

Toe

Toe and Heel
Force Sensors

Fig. 3.1. Experimental setup for robot-walking experiments on an inclined surface.

Table I. KONDO KHR-3HV Robot Physical Parameters
Parameter

Unit

Value

Height of Robot
Height of Robot COM
Length of Robot Foot
Mass+
Degrees of Freedom*

m
m
m
Kg
-

0.4
0.3
0.12
1.5
17

+

The mass of the robot is measured after integrating sensors and the controller in the backpack.
*The degrees of freedom of a robot is equal to the number of motors used in the robot.

14

Chapter 3: Force Sensor Based Postural Stability Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬The chapter is organized as, section 3.2 discusses the experimental setup and the static
experiments carried out with the light-weight humanoid robot on inclined surfaces. Thenthe experimental results are discussed in detail. In section 3.3, the Inverted Pendulum
Model (IPM) is extended to model the robot and to incorporate the surface inclination inorder to explain the experimental results. The hardware of the force sensor based feedback
control system and the necessity of a gyro sensor to stabilize the robot at higher surface
inclination is discussed in section 3.4. Section 3.5 concludes the chapter highlighting theoutcomes of the static stability experiments.

Robot Balancing Experiments
A commercial light-weight humanoid robot KONDO KHR-3HV is used [14] in theexperiment. The investigation for measuring the characteristics for robot stability is carriedout with the robot (see Table I for the physical parameters of the robot). The robot has 17
motors, out of which 3 motors for each leg are used to realize the basic walking of the robot.
A schematic representation of the robot with these 3 motors (MA=Ankle-pitch motor,
MK=Knee Motor and MH=Hip-pitch motor) on each leg are shown in Fig. 3.1.

3.2.1 Experimental setup
Two resistive force sensors (toe and heel) are attached under the bottom of each foot,as shown in Fig. 3.1. In order to analyze the balancing mechanism of the robot, a surface
is inclined by an angle  . The force on each sensor is measured. The surface inclination
is gradually increased from 0o to around 10o. The experimental setup is shown in Fig.3.2
and the experiments are performed in following three stages:
1. The toe and heel forces are measured using the force sensors when the robot is standingon the inclined surface.
2. Due to increasing the surface inclination, the robot becomes unstable at a certain surface
inclination. Beyond that the ankle-pitch motor (MA) is rotated based on the difference
between the toe and heel forces. The ankle rotation makes the robot posture stable.
3. At higher surface inclination of around 8.88o, the robot cannot stand solely based on thecompensating torque at the ankle-pitch motor. So, the hip-pitch motor (MH) is also rotatedaccording to the angular-pitch velocity of the robot-torso measured by the gyro-sensor.
This further allows the robot to stand stably at higher surface inclination around 10o.

15Chapter 3: Force Sensor Based Postural Stability Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Gyro Sensor+
Controller

Hip-pitch
Motor (MH)Ankle-pitch
Motor (MA)Surface
Inclination



 A*

FH

FT

Flat Surface ( = 0o)

FH



FT
Stage-1

FH

 A,0



FT

Stage-2

Fig. 3.2. Measurement setup (top) for the robot experiments and the stages of robot control
carried out during the experiment (below).

3.2.2 Experimental Results
Fig. 3.3 schematically explains the Single Support Phase (SSP) and the Double Support
Phase of the robot walking. The robot is said to be in DSP when the robot is standing on
the inclined surface supporting on both feet and in SSP when the robot stands solely
supporting on one leg while lifting the other. In this investigation, the SSP of the robot is
considered. Fig. 3.4(a) gives toe and heel forces on the left leg as a function of time, when16

Chapter 3: Force Sensor Based Postural Stability Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Balancing

Double Support
Phase (DSP)

Single Support
Phase (SSP)

Fig. 3.3. The experiments are carried out for the Single Support Phase (SSP) when the
robot lifts one leg, supporting on the other.

Heel
Toe

6

7

8

9

10 11 12 13 14

Fig. 3.4. (a)The heel and toe forces acting on the foot of the robot while the robot is standingon an inclined surface of surface inclination 3.8o. (b) The toe and heel forces measured forvarious surface inclination.

the right leg goes through the process of lifting, then being stably lifted and afterwards
touching down again onto the surface of surface inclination of 3.8o. The toe and heel forceson the left foot, are shown in Fig.3.4 (b) for increasing surface inclinations during the SSP,
when the right foot is lifted. The cases of different surface-inclinations, 2.7o, 3.8o and 5.3o
are identified by the different symbols. With increased surface inclination, the difference17Chapter 3: Force Sensor Based Postural Stability Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Fig. 3.5. The toe and heel forces of the robot for (a) left and (b) right leg measured at the
point indicated with a black arrow in Fig.3.4(a).

between the toe and heel forces increases. Fig. 3.5 shows the measured toe- and heel-forces
as a function of surface inclination  (a) for left leg and (b) for right leg. The measurements
are taken the time shown by a black arrow in Fig. 3.4(a). It is observed in Fig. 3.5 that thetoe force increases while the heel force decreases with increasing  when the robot walks
downslope. When the surface inclination reaches to 6.4o, it is observed in the experimentsthat the robot is balanced only on the toe. This is observed in the measurement when theheel force is becoming zero and toe force is approximately equal to the weight of the robot.
It is observed in the experiments, that the robot falls forward when the surface inclinations
is increased beyond  = 6.4o.
Beyond the surface inclination of  = 6.4o, the robot-experiments are performed
following the 2nd stage. The ankle-pitch motor (MA) is adjusted by the difference ()between the toe and heel forces of the supporting leg. This prevents the forward falling of
the robot by assuring that the full contact of the robot foot with the inclined surface. In Fig.
3.6 the measured force difference  is plotted as a function of  for  < 8.5o.
The measurements verify that the robot-posture can be balanced up to a surface of
inclination equal to 7.6o by adjusting only the ankle-pitch motor MA. Beyond that surface
inclination, the robot falls forward again. Therefore, hip-pitch motor MH is additionallycontrolled, corresponding to the 3rd measurement stage. The results of the measured force
differences are shown in Fig. 3.6. The hip-pitch motor is controlled by the pitch-angularvelocity of the robot-torso. With the additional control of the hip-pitch motor the robot cansustain a stable posture up to 9.6o surface inclination.
18

Chapter 3: Force Sensor Based Postural Stability Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Force Sensor
Control max  mg

Force+
Gyro Sensor
Control = 6.4oFig. 3.6. The difference of the toe and heel forces at the robot-foot, as a function of thesurface inclination.

Model Development
The purpose of the modelling is to theoretically explain the measurements obtained
from the experiments. The robot motion on the inclined surface with inclination  ismodeled by extending the Inverted Pendulum Model (IPM) [56-58]. The IPM incorporates
the information of surface inclination and explains the change in the static stability marginof the robot. Based on the IPM, the force sensor based control systems is designed to adjust
the ankle-pitch motor adjustment effective robot balancing.

3.3.1 IPM for Robot-Foot-Centric Balancing
The IPM describes the motion of the robot, where the COM of the robot is connectedby a link to a fulcrum. The model and model parameters are shown in Fig.3.7(a) [56, 58]
and the principal variables and parameters used in the model are listed in Table II. For
simplicity, the entire robot mass m is assumed to be concentrated at the point C of thependulum, which represents the COM of the robot. The connecting links between thefulcrum (point A) and COM of the robot are assumed to be massless. Here a footed IPM isconsidered. The model assumes a massless foot of length 2b, measured from the toe (pointO) as shown in (see Fig. 3.7(b)). The ankle-pitch motor MA is the adjusted first following
the second stage of the experiments. Thus, the two angles H and K are here set to be
19

Chapter 3: Force Sensor Based Postural Stability Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬

(a)

H
Z

C

MH

A

m

m

K

 COM

MK

MA

A

l
MA

O

X

2b

N

(b) Robot Foot

O

A
P d

FH

2b

FT

Fig. 3.7. (a) Inverted pendulum model (IPM) and its simplification considering ankle-pitch
motor control. (b) Free-body diagram of the robot foot.

constants (reference value), so at first, that the robot’s stabilization is studied focusing oncontrolling the ankle-pitch-motor angle A. Therefore, COM is equal to A.
Considering the above assumptions and simplifications, the equation of motion for theIPM can be written as [56]J A A  mgl sin  A  N  (b  d )(3.1)

where JA (= ml2) is the moment of inertia of the pendulum about the point A, and g is
the acceleration due to gravity. The first term on the right-hand side of (3.1) describes therotational torque due to the gravity, and the second term describes the compensating torqueinduced counter the effect of gravity in order to stabilize the robot posture. From (3.1) it
can be seen, that the vertical ground reaction force provides the necessary compensating
20

Chapter 3: Force Sensor Based Postural Stability Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬

Table II. Variables and parameters used in the Inverted Pendulum Model (IPM)
Parameter

SymbolUnit

Robot COM link length
Mass
Earth’s surface acceleration
Ankle-pitch motor
Knee motor
Hip-pitch motor
Ankle-pitch-motor angle
Knee-motor angle
Hip-pitch-motor angle
Center-of-Mass-position angle
Foot length

l
m
g
MA
MK
MH

m
kg
m∙s-2
degreedegreedegreedegree
m

A
K
H
COM
2b

torque for static stability of the robot. The resultant ground reaction force N is acting on the
robot foot at point P, called the Zero Moment Point (ZMP) [58], which is assumed to be ata distance of d from the point O, as shown in Fig. 3.7(b). Here a free-body diagram of therobot foot is considered. The two force sensors, attached to the toe and heel of the robot
foot measures the vertical forces (shown by upward arrow) acting on the robot foot. Thisis shown in Fig. 3.7(b). The forces denoted by FH and FT are respective vertical reaction
forces acting on heel and toe of the robot foot. It is observed in Fig. 3.7(b that the verticalforces N and FH generates moments around the point O. Under equilibrium, the net moment
about the point O should be equal to zero and the torque-balance equation is given by

FH  2b  N  d(3.2)

Therefore, the vertical forces acting on the toe and heel can be expressed in terms of theresultant vertical ground reaction force.

 2b  d 
FT  N  ; 2b 

d 
FH  N   
 2b 

(3.3)

where FT + FH = N. The force-difference  is defined as the difference between toe andheel reaction forces,

bd 
 = FT  FH  N   b 
Now substituting (3.4) into (3.1), the equation of motion can be rewritten as,
21

(3.4)

Chapter 3: Force Sensor Based Postural Stability Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Fig. 3.8. The shift of the oscillation of the motor angle A around A=0 for  > 0. The
asymmetrical nature of the angle is caused by the surface inclination.
..

J A  A  mgl sin  A     b (3.5)

Therefore, the equation of motion is now expressed in terms of the measured sensor
data  = FT-FH. Equation (3.5) confirms, that an increase in the force difference  indicatesthat a higher compensating motor-torque is required to adjust the robot posture.

3.3.2 Extension of IPM for Inclined Surface
Based on the results of the robot-balancing measurements shown in Fig. 3.6, modelingof the inverted pendulum is extended to incorporate the surface inclination . In that casethe equation of motion (3.5) can be written as
J A A  mgl sin( A   )    b(3.6)

where the first term of the right-hand side contains the surface inclination . Fig. 3.8 shows
numerical solution for A of (3.6) for different surface inclinations. As expected the solutionof (3.6) is a sinusoidal waveform which means that the motor angle A oscillates
symmetrically around A=0o for =0o. However, when the surface inclination is increased
the oscillation about the horizontal axis becomes asymmetrical. The target of the control is
to make the waveform symmetrical by adjusting the motor angle.
The robot maintains its equilibrium when the surface inclination is below cr. In thatcaaes it can be assumed that the resultant torque at motor MA is equal to zero. Therefore,
22Chapter 3: Force Sensor Based Postural Stability Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬the force difference  under static stability equilibrium can be derived from (3.6) asmgl sin( A   )
b

(3.7)

(3.7) gives the force difference  as a function of the surface inclination  and the anklepitch motor’s angle A. The maximum theoretical value of  is equal to the weight of therobot (=mg). A0 is the initial value of A which can be calculated from (3.7) by assuming

 = 0o and using the measured value for the force difference  on a flat surface.
The critical inclination cr is measured to be equal to 6.4o. The angle cr can betheoretically calculated by setting  equal to weight of the robot.

max ,theo 

mgl sin( A0  cr,theo )
b

(3.8)

Substituting max,theo = mg and A0 = 0o, it can be seen, that cr,theo is solely determinedby only the robot structure as

b
 

cr,theo  sin 1  
l

(3.9)

Considering the potential energy of the inverted pendulum [57] and minimizing thepotential energy leads to cr,theo= tan-1(b/l), which is reduced to (3.9) in this practical caseof (b/l)<<1. (3.9) is extended to incorporate the initial A0, leading to b  l sin  A0 
 l cos  A0 

cr,theo  sin 1 

(3.10)

Equation (3.10) describes, that the cr,theo is modified by A0, as shown in Fig. 3.9. cr,theocan be calculated with (3.10) for the initial condition A0. In this analysis A0 and cr,theo aredetermined to be equal to 0.05o and 5.7o, respectively. The theoretically calculated forcedifference  calculated form (3.7) are compared with the measured results in Fig. 3.10. It
is observed that measured  is not a linear function of , but has a weak saturating feature.
Also, the measured critical surface inclination cr,exp is equal to 6.4o, while the theoreticalprediction gives cr,theo=5.7o. The reason for this is attributed to the friction effect between
the robot feet and the ground surface. The surface friction can be modelled by the equivalentcircuit method [87-88]. In this presented theoretical investigation, the contribution of the23Chapter 3: Force Sensor Based Postural Stability Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ A0  0o

 A0  0o

 A0  0o
Equation (10)Fig. 3.9. Initial ankle-pitch motor angle of the robot determines the static stability marginof the robot according to the (3.10).

surface friction is neglected for robot balancing on inclined surface, and the measurements
are performed surfaces with less friction.

3.3.3 Ankle-Torque Compensation
The compensating torque of the motor is expressed as a function of the force-difference

 in the equation of motion of the inverted pendulum (see (3.6)).In these experiments, theadjustment of the angle A is started beyond  =cr,exp. The equation of robot motion (3.6)
on an inclined surface is rewritten by expressing the compensating torque as a function thereference angle A* (see also [56])J A A  mgl sin( A   )  K P ( A*   A )  K I  ( A*   A )dt  K Dd( A*   A )dt(3.11)(3.12)

 mgl sin(A   )  u(t )The gains KP, KI and KD in (3.11) are experimentally extracted from the motor-armature
voltage as a function of the difference between feedback-potentiometer voltage (themeasured motor angle A) and reference-voltage value (the reference angle A*). The
difference between the voltages corresponding to A* and A represents an error voltage e.
This error voltage is used to control the armature voltage Varm of the DC motor to generate
the necessary torque. The internal circuitry of the servomotor control system is shown in
Fig.3.11(a). The armature voltage Varm is plotted as a function of the error voltage e for24

Chapter 3: Force Sensor Based Postural Stability Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Equation (7)Measurementmax  mg

cr,theo  5.7o

cr,exp  6.4oFig. 3.10. Comparison of simulated (with low friction) and experimentally measured (withfriction) force differences for both left and right leg of the robot.

three different reference angles A* (namely, -84.3o, 0o and +84.3o). The relation betweene and Varm is used to determine the PID control function u(t) (see (3.12)). Fig. 3.11(b) shows
the procedure to determine the gains KP, KI and KD by fitting the experimental data ofarmature voltage as a function of error voltage. The experimentally determined values of
the gains KP, KI and KD are 69, 40 and 2, respectively, which are also listed in Fig. 3.11(b).
The motor angle A is rotated to A* in to stabilize the robot posture by minimizing the below max. The numerical solutions of (3.11) for different  conditions are shown in Fig.
3.12(a). With increasing , these overshoots of A become larger. This makes the robot
posture increasingly unstable during the motor-adjustment. There is increased oscillation
observed when the adjustment starts. Fig. 3.12(b) shows calculated pitch-angular velocities (=dCOM/dt) of the robot-torso, when the motor adjustment is done. For  = 7.6o only A
is adjusted. But at higher surface inclination, an additional H-rotation is done for  = 9.5o.
It is seen that the extended-IPM can predict the adjustment of the robot-body quite
accurately, especially for the single-motor control for surface inclination  = 7.6o. The
deviation for  = 9.5o is mostly due to the additional H control. The prediction, that a larger induces a larger overshoot in the angular-pitch robot-torso velocity , is confirmed by
the measurements as well.

25

Chapter 3: Force Sensor Based Postural Stability Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬(a)

PID Control

*
A

e(t )

(in Volt)Au (t )  K P e(t )  K I  e(t )dt  K D

de(t )
dt-(in Volt)

Geared DC Motor

Varm MA-

Gear Train(in deg.)

Potentiometer(b) Extracted PID control
parameters :KP = 69;
KI = 40;
KD= 2;

Fig. 3.11. (a) The PID control system implemented in the servomotor controller of therobot. (b) Measured results of armature voltage Varm as a function of error voltage e fordifferent reference angles A*.

The calculated and the measured maximum -overshoot are compared in Fig. 3.13. A
drastic increase of  is observed for  > 7.6o, indicating the requirement of higher torquecompensation at higher surface inclination. The sudden increase in overshoot also implies
that posture control solely based on the force sensors under the robot feet is not sufficient
to make the robot posture stable. This leads to the second stage of the experiments, where
the angular velocity is used to control the robot posture beyond surface inclination of 7.6o.

Analysis of Measured Control Features
In Fig. 3.6, the measured  is plotted as a function of the surface inclination angle .
The robot-posture control is done by implementing feedback control systems based on use
26

Chapter 3: Force Sensor Based Postural Stability Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬

(a)

(b)

Fig. 3.12. (a) The adjustment of the ankle-pitch-motor angle A according to (3.11), fordifferent surface inclination (b) Simulation result for the torso-angular velocity  of therobot in comparison to the gyro-sensor measurements.

measured data for  and  of motion into the robot system, for surface inclinations cr,exp.
The implementation is done as shown in Fig. 3.14. Two online streams of measured data
are fed back independently. In the electrical feedback controlling of the robot, the A* (andalso H*) are controlled by the measured data ( and ) in the form
 A*   A,0  K A (3.13)

 H *   H,0  K H (ref  meas )(3.14)

where meas and ref are measured and reference value of the angular-pitch velocity,respectively. The reference value ref for the angular-pitch velocity is equal to 0 deg/s. KA
27

Chapter 3: Force Sensor Based Postural Stability Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Simulation
Measurement

MA + MH control
MA control

Fig. 3.13. The maximum overshoot of the torso-angular velocity of the robot increases
abruptly beyond surface inclination 7.6o. This indicates the requirement of the hip-pitch
motor-control at higher surface inclination.

and KH are adjustable gain between the motor and its load. For higher compensating torque,needed to stabilize the robot-posture, higher KA and KH values are required.
The KA value is set to 12, so that the most stable condition for  =6.4o are realized.
Based on the A control, the  is reduced allowing the robot to keep a stable posture up to
7.6o surface inclination. According to Fig. 3.9 the A rotation (i.e., the setting of a new A0),
should change the critical surface inclination cr. However, it is found experimentally, thatthe robot falls down at much smaller surface inclinations  than the expected cr,theo. Figure
3.15 adds the extension of the force difference at higher surface inclination when the anklepitch motor is controlled with increased KA. With the increase in the surface inclination, ahigher KA value is required to increase the compensating-torque at the ankle-pitch motorof the robot for postural stabilization. But higher KA causes instabilities due to increased
vibration. Consequently, based on the trade-off between a sufficient torque to control therobot motors and vibration of the robot, KA is optimized and implemented in the control
system. As observed in the experiment, the robot can maintain a stable posture up to surface
inclination of =8.88o, as plotted in Fig. 3.15 for KA=14. Therefore, the control of anklepitch motor according to the  increase is a viable solution to achieve a stable robot posture
up to a certain surface inclination. To further increase the robot stability, the hip-pitch
motor is to be controlled based on the angular-pitch velocity. With this sequential approach
28

Chapter 3: Force Sensor Based Postural Stability Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬PID Control for  A
Hip-Pitch
Servomotor

Ankle-Pitch
Servomotor
PID Control for  H

 A* (in Volt)

KHR-3HV
HumanoidRobot H* (in Volt)
 A,0(in Volt)

+

 H,0

-

KA 

-

(in Volt)

meas

meas

(in deg./s)(in Volt)-

K H (ref  meas )KA  FT  FH

+

KH

-

+

Analog Gyro
Sensor(KRG-4)

ref(in Volt)+

Toe Analog
Force Sensor(FSR 402)

Toe Force
FT (in Volt)

Heel Analog
Force Sensor(FSR 402)

Heel ForceFH (in Volt)

Controller

Toe Force
FT (in N)
Heel ForceFH (in N)

Fig. 3.15. The block diagram of the implemented control system for the ankle-pitch-motor
angle A and the hip-pitch-motor angle H.

Force +
Gyro Sensor
Control

Force Sensor
Control max  mg
KH = 13

KA = 12

KH = 14

KA = 14
New
Measurements

Fig. 3.14. At higher surface inclination, the robot-stability is improved due to feedback motor
control and the adjustment of feedback-control parameters (see (3.13) and (3.14)).

to control, it is found that robot can maintain its stable posture up to 10.2o of surface
inclination.

Conclusion
The focus has been given on the maintenance of static stability of the light-weight
humanoid robot on inclined surfaces. The investigation starts with the experimental
29

Chapter 3: Force Sensor Based Postural Stability Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬observation of the robot posture stability on inclined surface followed by theoreticalinvestigation to explain the experimental measurements. The surface-inclination  is shown
to be determinable from the difference  calculated form the measured toe and heel forcesof each robot foot. The experimental observations and measurements reveal that the robot
requires no feedback control up to a certain critical surface inclination cr. Beyond cr the
robot falls forward on the downslope.
For surface inclinations beyond cr, a force-sensor based feedback control of the anklepitch motor is introduced to sustain the surface connection of the robot feet. This reduces
the force difference  between toe and heel of the robot feet, allowing the robot to keep astable posture. When the surface inclination is increased further, however, the ankle-pitchmotor control alone is no longer sufficient to maintain the stable robot posture. Therefore,a gyro-sensor-based hip-motor adjustment is additionally introduced in order to control therobot posture.
In the theoretical investigation, the Inverted Pendulum Model (IPM) is extended toinclude the surface-inclination in order to explain the static stability margin of the robot
standing on an inclined surface. This extended IPM can also accurately reproduce gyrosensor-measured angular-pitch velocities during feedback control on inclined surfaces..
Generally, the Zero Moment Point (ZMP) is used to characterize robot instabilities on
inclined surfaces. However, the developed method for using the measured force differences between toe and heel forces is an alternative way to measure the robot-instability. The
measurement provides a simpler and yet accurate approach.

30

Chapter 4: Gyro Sensor Based Postural Stabiity Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Chapter 4: Gyro Sensor Based Postural
Stabiity Control
Introduction
The chapter proposes a circuit level implementation of an electro-mechanical model ofa single axis gyro sensor. The electro-mechanical model is developed in order to analyze
the circuit level behavior of the sensor. The purpose of this analysis is to incorporate circuit
behavior of the sensor into the robot-system simulation toolbox. This will enable to analyze
the circuit effect of a particular sensor component on the dynamics of the robot. Generally
speaking, this is an attempt to bridge the dynamic-response of a macroscopic system for agiven microscopic response of a system integrated within it.
In the latter half of this chapter, an attempt is made to incorporate the circuit level modelof the sensor to model a gyro-sensor based feedback control system in order to simulate thedynamic response of the robot to an external disturbance push-force. This work shows how
circuit behavior of the gyro senor is incorporated to simulate the robot dynamics. The
chapter is arranged in the following way.
In Section 4.2, the working principle of a vibratory gyro sensor is discussed followedby the circuit description of the gyro sensors in sections 4.2.2. The simulation results carriedout with a SPICE circuit simulator [87-88] is discussed in section 4.2.3. Section 4.2.4
discusses the design and simulation results of an envelope detector used in the gyro sensor
model. In section 4.2.5 the dynamic characteristics of the developed gyro sensor model areexperimentally verified with the analog gyro sensor KRG-4 [99]. The section 4.3 discusses
dynamics of robot when it is applied with an external push force. A gyro sensor based
feedback control system is proposed in section 4.3.2 to stabilize the robot posture. The
response of the robot dynamics is analyzed incorporating the electromechanical responseof the developed gyro sensor and the control system was experimentally verified in Section
4.3.3. The robot with its push-force disturbance rejection system was exhibited in public
robot competition ROBO-ONE at Kobe, Japan. The outcomes of the competition are briefly
reported in section 4.4. Section 4.5 concludes the chapter.

Electromechanical Modelling
The single-axis vibratory gyro sensor is a micro-electro-mechanical system (MEMS).
The electro-mechanical model is implemented in Verilog-AMS and simulated using an
31

Chapter 4: Gyro Sensor Based Postural Stabiity Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬







Fcor  2m( v   )Fig. 4.1. The vibratory gyro-sensor is based on the Coriolis Effect.

SPICE circuit simulator to analyse the time-domain responses and frequency domaincharacteristics of the sensor circuits.
The vibratory gyro sensor is based on the principle of the Coriolis Effect. According to
the Coriolis Effect, when a linearly moving (with velocity v) mass m is rotated with anangular-pitch velocity , the mass experiences a force proportional to the product of v and, in the direction perpendicular to both v and . The effect is shown in Fig. 4.1.

4.2.1 Gyro Sensor
Based on the principle of Coriolis Effect, the gyro sensor is developed. The vibratory
single-axis gyros sensor has two circuits: driving circuit and sensing circuit [18]. From theprinciple of Coriolis Effect, it is seen that a mechanism is needed to drive the microscopic
mass. For that purpose a driving circuit is used. When the mass detects an external angularvelocity, the mass experiences a Coriolis force. For sensing this Coriolis force the sensing
circuit is used. In the next section, the circuit are discussed in details.

4.2.2 Circuits of Gyro Sensor and Modelling
The driving and the sensing circuits of a single axis vibratory gyro sensor are shown in theFig. 4.2(a) and 4.2(b). The driving circuit moves the central mass to oscillation. This iscalled the driving mode. The movable mass m is subjected to the driving mode by asinusoidal force Fl = F0 cos2ft. In the used gyro-sensor system, the mass is driven by theelectrostatic force inside the combed finger structure, which is induced by the sinusoidal
input voltage Vin of the driving circuit as shown in Fig. 4.2(a). The MEMS push-pull driveris shown to have this comb-like structure in Fig. 4.2(a). The lateral driving induces a linear
velocity v.
32

Chapter 4: Gyro Sensor Based Postural Stabiity Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬+Z-axis(a)+X-axis(b)

Fig. 4.2. (a) Driving Circuit of the vibratory MEMS gyro sensor. (b) Sensing circuit of the
gyro sensor.

The modelling of this driving mechanism can be done by considering a mass suspended
by spring-damper system as shown in electromechanical methodology in Fig. 4.3. The
coordinate system used to represent the dynamics of the central mass is shown in Fig. 4.2.
The mass is driven along X-axis, which is the driving axis. The generated electrostatic force
Fl (see step 1 and 2 of Fig. 4.3) drives the central mass with the driving velocity v. The
second-order differential equation is solved to calculate the driving velocity v, describing
the dynamics of the mass suspended by a spring and a damper (see step 2 of Fig. 4.3).
When the system is rotated around the +Y-axis (normal to the paper plane) with anangular velocity , a force FCor is induced on the moving mass along the +Z axis becauseof the Coriolis Effect. This force causes the central mass to oscillate also along Z-axis,
which initializes the sensing mode of the gyro sensor. In the model, the Coriolis force iscalculated as shown in step 4 of Fig. 4.3. The sensing circuit is used to sense the verticaldisplacement of the central mass due to movement in +Z direction. This is done byproducing an equivalent electric signal which is proportional to the angular velocity applied
to the central mass. The sensing circuit, shown in the Fig. 4.2(b), is based on the differential
capacitive sensing. Initially, when the mass is being driven only along X-axis, the33

Chapter 4: Gyro Sensor Based Postural Stabiity Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Step 5: Solve the sensing
dynamics (z)Step 1: Push-Pull Driving

Fl 

4 N  0W
Vd V0 cos(2 ft )d

Step 2: Solve the driving dynamics

Step 3: Calculate
driving velocity
vxStep 4: Calculate
Coriolis Force

Fcor  2m(v   )xbx  k x
F
x
x l
m
m
m

Applied angularvelocity 



z

F
bz  k zzz  cormmm

Step 6: Calculate output voltage

Vout 

2C0 z
VS
CFB d

Fig. 4.3. The methodology of the electromechanical modeling of the driving and sensing
circuits of the vibratory single axis gyro sensor.

capacitances C1 and C2 are equal. But when the mass oscillates along Z-axis due to the
Coriolis force, C1 and C2 start to differ from each other. The difference between the twocapacitances C1 and C2 is measured by the sensing circuit, which is converted into an
equivalent electric voltage Vout. The difference in the capacitances is a function of thevertical displacement of the central mass. This displacement is calculated by solving thesecond-order differential equation as shown in step 5 of Fig. 4.3. The voltage is proportional
to the vertical displacement (see step 6 of Fig. 4.3) and indirectly proportional to the input
angular velocity  and the Coriolis force FCor. The physical parameters of the gyro sensor
model are given in Table III.

4.2.3 Simulation Results
Simulation results obtained using circuit simulator [87-88] with the developed
equivalent circuit of the gyro sensor are shown in Figs. 4.4. Vin is the input voltage to thedriving circuit (See Fig. 4.2(a)), which drives the central mass of the system. Fig. 4.4 shows
the simulation result, where a sinusoidal angular velocity is considered. It is clearlyobserved that the envelope of Vout contains the information of the applied angular velocity.
The input voltage Vin is amplitude modulated by the input angular velocity to give theoutput voltage Vout.

34

Chapter 4: Gyro Sensor Based Postural Stabiity Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬

Table III. Gyro Sensor Model Parameters
Parameter

Symbol

Unit

Value

Sensor seismic mass
Driving circuit damping coefficientDriving circuit stiffness coefficient
Total number of fingers
Permittivity of space
Width of the comb finger
Finger spacing
Sensing circuit damping coefficient
Sensing circuit stiffness coefficient
Intrinsic capacitance between fingers
Feedback capacitance of sensing circuit

m
bx
kx
N

Kg
Nsm-1Nm-1

1.678×10-11
8.5×10-70.07
1608.854×10-12
40×10-6
3×10-6
0.5×10-7
0.2
3×10-12
4×10-12m-3Kg-1s-4A2mm
Nsm-1
Nm-1
Farad
Farad

0

W
d
bz
kz
C0
CFB

Fig. 4.4. The simulation result of the output of the gyro sensor model. The input voltage tothe driving circuit Vin is amplitude modulated by the input angular velocity to give theoutput voltage Vout.

Therefore sensing circuit gives rise to an amplitude modulated waveform. The
parameters used for the simulations are described in Table III. All the parameters except
damping and stiffness coefficients are fixed initially to predict the dynamic behavior of
gyro sensor. Then the stiffness and damping coefficients are adjusted very precisely todescribe the mechanical model. As the model is based on the underlying physics the minuteadjustments of the model parameters are sufficient to predict the experiment accurately.

35

Chapter 4: Gyro Sensor Based Postural Stabiity Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Vin  Vd  V0 cos(2 ft )Driving Circuit

Fcor
Sensing Circuit

V
Coherent
Multiplier

VMout

RC Low
Pass Filter

Vout ( )

Fig. 4.5. A demodulator is designed based on the principle of the envelope detector. The
envelope detector detects the envelope of the sensing circuit output V.

4.2.4 Envelope Detector
It is discussed in the previous section that the output of the sensing circuit contains theinformation of the angular velocity. For that an envelope detector (demodulator) is designed
and integrated to the gyro sensor model. This is shown schematically in Fig. 4.5. The
detector demodulates the output of the sensing circuit and produces the waveform of theapplied angular velocity, shown also in Fig. 4.5. The RC low pass filter characteristics
determine the accuracy of the output of the detector. The RC filter is designed based on the
Nyquiest frequency of the output of the coherent multiplier.

4.2.5 Experimental Verification
In order to verify the developed electromechanical model, the static characteristics ofthe developed model is verified experimentally with an analog gyro sensor KRG-4 [99].
The results are shown in Fig. 4.6. The model parameters are adjusted so that the model
values fit to the experimental values of output voltage for a given angular velocity applied
to KRG-4. The figure shows that the modeled results predict the measurement nearly
perfectly.
This concludes the development and experimental verification of an electro-mechanicalmodel of a single-axis analog vibratory gyro sensor. Now, this model will integrated to36

Chapter 4: Gyro Sensor Based Postural Stabiity Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Fig. 4.6. Experimental verification of the developed electro-mechanical model of thesingle-axis vibratory gyro sensor.

control system for the robot in order to simulate the dynamics of the robot, when appliedwith an external push force.

Push-force Disturbance Rejection
4.3.1 Falling Dynamics
When an external push force is applied to a robot, the dynamics of the humanoid can bemodelled with a constant-length inverted pendulum as shown in Fig. 4.7(a). Here a simple
inverted pendulum with three degrees of freedom is considered denoted by ankle-pitch
motor MA, knee motor MK and hip-pitch motor MH. The links of motors are assumed to bemassless and the total mass m is considered to be concentrated at center of mass (COM) ofa bob. Initially, the hip, knee and ankle-motor angles are set to zero when the robot isstanding on a flat surface. The distance of the robot COM from point A is equal to l i.e. thesum of the lengths of three links connecting the motors. The pendulum is assumed to havea massless feet of length b. When a constant force F is applied to the robot, the robot bodyrotates around the toe of the feet denoted by point O in Fig. 4.7(b). This is a situation ofunder-actuation [30] for the humanoid robot. Here, when a constant force F is applied to
the robot, the COM of the robot follows a trajectory of an inverted pendulum with constantlength L0. Such a motion of the robot COM can be modelled with an inverted pendulum of
constant length L0, which can be written as

L0  l 2  b2
37

(4.1)

Chapter 4: Gyro Sensor Based Postural Stabiity Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬

(a)

COM

m
MH

MK
MA

(b)
F

F

L0
l

FALLINGFALLING   0AA

A b OB

F

F

O

B

E

A

O

E

A

O

O

Fig. 4.7. An inverted pendulum model is used to model the robot dynamics when it isapplied with an external push-force.

Initially when the robot is not exerted with the push-force, the inverted pendulum is stable
at an angle of  = 0. The initial angle can be geometrically derived from the configurationof the pendulum.

b
 

   0   tan 1  
l

(4.2)

From the potential energy calculation of the pendulum [57] it can be shown that the robot
does not fall forward as long as the angle of the inverted pendulum rotates within the rangeof 0    0(4.3)

It can be seen from (4.2) and (4.3) that this boundary condition for static stability is afunction of robot-height and robot-foot length. This boundary is shown in Fig. 4.7(a) by avertical dotted red line. The equation of motion of the inverted pendulum is given by

mL20

d 2
 mgL0 sin   FL0 cos 
dt 2

(4.4)

where m is the mass of the robot and g is the acceleration due to gravity. The force F isapplied to the robot until it starts to fall down (see Fig. 4.7(b)). The angular velocity of theinverted pendulum undergoing the negative-pitch motion is calculated from the first-orderderivative of the solution to (4.4). The calculation results of the angular velocity as a

38





Chapter 4: Gyro Sensor Based Postural Stabiity Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Fig. 4.8. Experimental verification of the developed electro-mechanical model of thesingle-axis vibratory gyro sensor.

function of time for increasing magnitude of the constant push-force F, are shown in
Fig.4.8.
The transient response of angular velocity as shown in Fig. 4.8 highlights two important
aspects of the control mechanism for stabilizing the robot-posture i.e. to oppose thedisturbance caused by the push-force. First, higher magnitude of applied force requires
higher magnitude of compensating force in order to stabilize the posture of the robot. This
is indicated by the slope of the transient response. Second, the response time plays a crucialrole in case of stabilizing the robot-posture. Higher force requires faster response from therobot to stabilize its posture. The response time of the control system largely depends on
the internal circuit of the feedback control system.

4.3.2 Control System
The implemented control system is shown in Fig. 4.9. In this work, only the ankle-pitch
motor angle is controlled by the pitch-angular velocity measured by the gyro sensor. For
simulating the robot-dynamics based on the (4.4), the electromechanical model of the gyro
sensor is integrated to the conventional control system for geared DC servomotor. Thechange in the angular-pitch velocity of the robot COM is measured by the gyro. The
measured angular-pitch velocity is compared with the reference angular-pitch velocity of
the robot torso. The difference between the reference and measured angular-pitch velocity
is used to control the ankle-pitch motor angle as shown in Fig. 4.9. Now the ankle-pitch
motor rotates changing the motor-angle from reference to a new value. This will change
39

Chapter 4: Gyro Sensor Based Postural Stabiity Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Geared DC Motor
Varm

Ia

1
Ra

+

d

kt

0

n

m

+

l

ml 2 s 2  mgl


1
Jms

m

1 m
s

n

A

1
s

Vb
kb

u (t )  K P e(t )  K I  e(t )dt  K D

de(t )dt

Vin  Vd  V0 cos(2 ft )PID Control

 A*


 A,0

Driving Circuit

Fcor
Sensing Circuit

KA
ref

+

-

meas

Vout
Coherent
Multiplier

SGY

VMout

RC Low
Pass Filter

Feedback Model Gyro Model

VO ( )Fig. 4.9. Experimental verification of the developed electro-mechanical model of thesingle-axis vibratory gyro sensor.

the length of the constant length inverted pendulum form L0 to L and the new length L no
more a constant value but a function of the ankle-pitch motor angle. In order to consider
the change in L, the (4.4) can be re-written as,
ML2

d 2
 MgL sin   FL cos 
dt 2

(4.5)

L20  2bl sin  A

(4.6)

L

The control mechanism of the robot posture by rotating the motor angle A is shown in Fig.
4.10. As the reference ankle-pitch motor angle changes, the motor rotates due to thecompensating torque controlled by the in-built PID controller. The x-axis projection of therobot-COM is considered as a reference point to be controlled by the ankle-torquecompensation. In Fig. 4.11 the transient response of the COM projection is shown. To
ensure the postural stability for this inverted pendulum, the x-axis projection has to follow
the boundary condition (derived from (4.3)) given by40

Chapter 4: Gyro Sensor Based Postural Stabiity Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬qA  A
E



L

MA
A

O
Fig. 4.11. The compensation of ankle-pitch motor stabilize the robot posture. The
implemented control system brings the robot within the static stability margin (4.3),
preventing the falling down.

Fig. 4.10. The projection of the robot-COM is brought back by the ankle-pitch motor
compensation in order to stabilize the robot posture.

b  xCOM  0(4.7)

In Fig. 4.11, it is observed that the gyro sensor based feedback control system brings the xaxis projection of robot-COM within this limit (4.7), thus preventing the robot from fallingdown.

4.3.3 Experimental Verification
The proposed control system is experimentally verified using the humanoid robot
KONDO KHR-3HV. The robot is exerted with a push-force from front and behind to verify
the control system when the robot is undergoing the positive and negative pitch motions
41

Chapter 4: Gyro Sensor Based Postural Stabiity Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬

(a)

(b)

Fig. 4.12. Push recovery experiments when the robot is undergoing negative pitch motion
and positive pitch motion (b).

respectively. The negative and positive pitch-motion control of the are shown in Fig.
4.12(a) and (b) respectively.

On-site Implementation
Recently human-robot interaction (HRI) research has gained momentum specially
focussing on the usefulness of the robots in the real world. The research on the push-force
recovery can be considered to be a very basic part of HRI research. This focusses on thephysical interaction between human and robot. It is true that we say this to be a disturbancefrom the robot-side, but this disturbance is very realistic when we talk from an interaction
point of view.
The disturbance control system proposed in this thesis was tested in a robot-robot
interaction platform. The robot KHR-3HV integrated with the push-force disturbance
control system participated in the 18th ROBO-ONE Light competition and 34th ROBOONE competition held in Kobe, Japan on February 22-23, 2019 (see Fig. 4.13). The
competition staged battle between light-weight robots, where the control strategies ofrobots to encounter external disturbances imparted by opponent robot, is tested. The robot
qualified in the first two rounds and could successfully secure its place up to the semi-final.
42

Chapter 4: Gyro Sensor Based Postural Stabiity Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Fig. 4.14. Battle of light-weight humanoid robot in ROBO-ONE Light Competition.
(Image Source: Biped Robot Association, Japan)

Fig. 4.13. Robot KONDO KHR-3HV with the integrated push-recovery control systemdesigned by HiSIM Research Center, Hiroshima University. The story was covered by
Japanese magazine ROBOCON. (Image Source: ROBOCON Magazine, May Issue, 2019)

The work was covered in the media as well as in the magazine ROBOCON (in Japanese)as shown in Fig. 4.14.

ksjdcnkasd

The observations regarding the performance of the robot during the competition directs theresearcher towards some basic future-work to be carried out for the development of thelight-weight robots. The possible take-over from this work are given as follows:

Development of physics engine based simulation environment for studying therobot-robot interaction.
43

Chapter 4: Gyro Sensor Based Postural Stabiity Control‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬

Implementation of the postural control strategy based on hip-torquecompensation followed by step-over strategy. This strategies are realized inhuman-sized robots, but not yet implemented for light-weight humanoid robot.

Conclusion
This chapter presented an electromechanical model of an analog single-axis vibratory
MEMS gyros sensor. The model is implemented in Verilog-AMS and the circuits are
simulated in a commercial SPICE simulator. The transient characteristics of the gyro sensor
shows the requirement of an envelope detector to detect the applied angular-pitch velocity.
The modulated out of the sensing circuit is fed to the envelope detected comprising of acoherent multiplier and a RC low pass filter. The filter characteristics of the RC low passfilter determines the frequency response of the output of the detector. The static
characteristics of the gyro sensor is experimentally verified with an analog gyro sensor
KRG-4.
Further the gyro sensor model is integrated to a control system for stabilizing the robot
posture when the robot is exerted with an external push force. The dynamics of the robot ismodelled with a constant length inverted pendulum. The pitch-angular velocity of the robot
is measured by the gyro-sensor model to control the ankle-pitch-motor angle. This makes
the robot stable by restricting the COM-projection to be within the static stability marginof the robot. The control system was verified experimentally for the positive and negative
pitch motion of the robot when exerted with a constant force.
This chapter marks the end of the investigation on the static stability of the robot. The
following chapter presents the dynamic control of the robot-walking and discusses thevibration control in light-weight robot.

44

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Chapter 5: Vibration Control in Humanoid
RobotsIntroduction
Light-weight humanoid robots comes with a problem of vibration while walking. Thisvibration is observed when the joint-angle motors are controlled by feedback angularvelocity of the robot. In the previous chapter it is observed that angular velocity of the robot
plays important role in controlling the robot-posture when the robot is subjected to external
disturbance, be it an external push-force or gravity force. For that, an extensive analysis of
the gyro sensor is carried out, as it helps the author to understand the working of the sensor
to measure the angular-pitch velocity of the robot-torso.
In this chapter the measured angular-pitch velocity is used to control the robot posture,when the robot walks on an inclined surface. A gyro-sensor-based feedback-control system
to control the ankle-pitch and hip-pitch motors of the robot for stable walking on inclined
surfaces is proposed. The gyro-sensor is integrated at the backpack of the robot as shownin Fig. 5.1. The ankle-pitch motors and hip-pitch motors are observed to play significant
role in stabilizing the robot posture while walking on an inclined surface. The pitch-motor

Gyro Sensor+
Controller

Hip-pitch
Motor (MH)Ankle-pitch
Motor (MA)Surface
Inclination

Fig. 5.1. KONDO KHR-3HV Humanoid Robot integrated with a gyro sensor for balancing

on an inclined surface with inclination angle .

45

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬angles are controlled in a stepwise manner (see Fig. 5.2) based on the difference between
the measured and reference angular-pitch velocity of the robot. The reference pitch-angularvelocity of robot is modelled using an Inverted Pendulum Model (hereafter IPM). The
walking pattern implemented in the robot is characterized by a gait cycle period of 2.31s
as shown in Fig. 5.3(b). This gait cycle period corresponds to a fundamental walking
frequency f0=1.73 Hz. When the angular-pitch velocity is analyzed in the frequency
domain, the frequency f0 is observed to have a prominent peak.
At higher surface inclination, the ankle-pitch motors and the hip-pitch motors arecontrolled by the measured angular-pitch velocity to stabilize the robot posture. Thisadditional feedback-loop to the motor control systems gives rise to higher frequency-peaks
when the gait pattern (angular-pitch velocity) is analyzed in frequency domain. This is themain reason behind the vibration in the robot.
The structure of this chapter is as follows. Section 5.2 describes the experimental setup
used to carry out the walking experiments with the humanoid robot on an inclined surface
with low surface friction. Then the experimental results are discussed. In section 5.3, thefrequency-domain analysis of the angular-pitch velocity of the humanoid robot, obtained
from the experiments (discussed in section 5.2), are presented. Section 5.4 describes themeasured angular-pitch velocity of the robot walking on an inclined surface with increased

MA control
Gyro
SensorMA and MH
control at thesame timeMHMAcr0    cr1MA

  cr1

Fig. 5.2. The gyro-sensor measured angular-pitch velocity of the robot body is used tocontrol the ankle-pitch motor (MA) above a critical inclination cr0 and is then usedadditionally to control the hip-pitch motor (MH) above a larger critical inclination cr1, inorder to balance the robot walking.

46

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬

(a)

Start

Gait-1Gait-2Gait-3Gait-4

Ends

LL
RL

Position(b)

One Gait Cycle (Tgait = 2.31 s)

RL

LL

RL TakeoffStartsRL TakeoffComplete

RL Fullin
FlightRL
TouchesDown

LL TakeoffStartsRL Full
TouchesDown

LL TakeoffComplete

LL FullIn
Flight

LL
TouchesDown

LL Full
TouchesDown

LL : Left Leg; RL : Right Leg(c)

One Gait Cycle (Tgait = 2.31 s)

RL

t=0s

LL

0.3 s

0.6 s

0.78 s0.9 s1.15 s1.45 s

1.63 s1.75 s2.01 s2.31 sFig. 5.3. (a) Walking pattern of the robot, illustrating the gait-cycle repetition of the robot,
with one half of a gait cycle at the beginning, then 4 complete gait cycles and finally one
half of a gait cycle at the end. (b) One gait cycle is zoomed to show the gait pattern of therobot KONDO KHR-3HV. Tgait: period of a gait cycle; Twalk: total time for which the robot
has walked. (c) Photos showing the gait pattern implemented in one gait cycle of the robot
with the zoomed foot-placements patterns at the bottom.

surface friction. In section 5.5 the IPM is extended to explain the frequency-response of therobot’s gait pattern. A second-order control-system analysis is carried out in order toexplain the response of the implemented motor-control system. To explain the origin of thehigher-order harmonics of f0, a nonlinear IPM is used. The nonlinearity due to the surface
inclination can be explained using the nonlinear IPM. Section 5.6 concludes the paper
highlighting the novel outcomes of the presented work.
47

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Robot Walking Experiments
5.2.1 Motor Control System
The robot is equipped with 17 KONDO KRS-2552RHV DC servomotors [89] forwalking or performing any other work. Among these 17 motors, 4 motors, one ankle-pitch
motor (MA) and one hip-pitch motor (MH) on each leg, are controlled by the feedback(a)

DC Servomotor
12V DC
Motor

Embedded Motor Controller

 ref [V][V]

Integrator
KONDO Robot
Controller (RCB-4)



e(t )

-

Varm (t )  K  e(t )Varm [V]

-

Load

M
Gear

Potentiometer meas [V] meas[degree][degree/s]

 meas[degree]

KONDO Robot Servomotor(KRS-2552RHV ICS)(b)[degree/s]

G(s)

[V]

KONDO Robot
Controller (RCB-4)[V]

Integrator

[V] +

+KA

-

ATMega328P
Controller(External Comparator
Circuit)

KA

=

- KA

[V]

DC Servomotor[degree/s]

KONDO Robot
Servomotor(KRS-2552RHV ICS)

SGY

[V]

AnalogGyro Sensor (KRG-4)[V]

Gf (s)[degree/s]

Fig. 5.4. (a) Schematic diagram of the control circuit of DC servomotor used in theexperiment. The transfer-function formulation used for modeling the motor-control
system without the gyro-sensor feedback loop. (b) Schematic diagram of the motor-control
system, implemented for adjusting the robot’s ankle-pitch motor on inclined surfaces.

48

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬angular-pitch velocity, in order to realize stable walking of the robot on an inclined
surface. The internal control circuit of each DC servomotor is shown in Fig. 5.4(a). The
DC servomotor has a 12V DC geared motor with a potentiometer-based position-feedback
loop. The embedded controller is implemented on a PIC16F690 platform [90]. The
controller controls the DC motor’s armature voltage Varm, based on the difference between
a reference motor angle ref (in [V]) and the motor angle meas (in [V]). The motor anglemeas is measured by the potentiometer. The reference motor angle ref (in [V]) is
programmed in to the robot controller RCB-4 [91] integrating the reference angular–pitch
velocity ref (in [V]). To calculate the output angular-pitch velocity, a transfer-function
formulation is required, as shown in Fig. 5.4(a) [92-98]. The transfer function of the
motor-control system without the external gyro-sensor-feedback loop can be written in
the s-domain (see Fig. 5.4(a)) as

G( s) K
Js 2  Bs  K(5.1)

where J and B are equivalent inertia elements (inertia and viscous friction of the servo
motor) and K is the proportional gain of the controller, embedded inside the KONDO
servomotor KRS-2552RHV.
The discussed motor-control system is integrated with an additional gyro-sensor-based
feedback controller, as shown in Fig. 5.4(b). In the motor-control system with gyro-sensor
feedback, the angular-pitch velocity of the robot is measured by a single-axis analog gyro
sensor KRG-4 [99], which is attached on the robot torso (in the backpack of the robot). The
measured angular-pitch velocity (in [V]) by the gyro sensor is given bymeas [V]  SGY  meas [degree/s](5.2)

where SGY is the sensitivity of this single-axis analog gyro sensor, equal to 0.67mV∙s/degree. The measured angular-pitch velocity meas of the robot (in [V]) is fed back to
an external comparator circuit which is implemented into an ATmega328P controller [100].
The comparator circuit calculates the difference between the measured angular-pitch
velocity meas (in [V]) and a reference angular-pitch velocity ref (in [V]), which is alsopre-programmed into the memory of the external controller. This difference is amplified
with the externally “tunable” feedback gain KA for the ankle-pitch motor (or KH for the hippitch motor). The output of the amplifier is then fed back to the robot-controller RCB-4, to49

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬adjust the reference value of the ankle-pitch-motor angle according the following theequation.

refc  ref  K A  (ref  meas ) [V]  ref  K A   [V](5.3)

where KA is the tunable feedback gain of the amplifier, ref is the reference angle forankle-pitch motor (in [V]) and refc (in [V]) is the adjusted reference angle for motor
rotation. The adjusted reference angle is then used to control the servomotor rotation asshown in Fig. 5.4(b). For other motors, such as the hip-pitch motors MH, the control is
independently done in the same way as for ankle-pitch motor MA.
The feedback gain KA (or KH) increases the sensitivity of the motor-angle control on thecomparator output. Therefore, for a higher effect of the comparator output, a larger KA
value is needed to adjust the motor angle by a larger extent. In the literature of compliancemodelling for actuators [101], gain KA effects the stiffness of a motor-load transmission
system. The frequency-response analysis of such a motor-load-transmission systems
shows, that the proportional feedback-gain largely effects the vibrations in the system.
Therefore, a proportional control is implemented here to analyze the effect of gain KA on
the system performance, before extending it to controllers having multiple tunable gains,e.g., Proportional-Derivative (PD) controllers. This becomes clearer in the following
section, when the effect of the gain KA on the robot’s gait data is discussed in detail.
When the feedback loop with the gyro-sensor control is implemented, it is observedthat the viscous friction coefficient is reduced from B to Bf as

B f  B  K A SGY(5.4)

where SGY is the gyro-sensor sensitivity and KA is the tunable gain in the feedback loop.
Due to the additional gyro-sensor-feedback loop, the modified transfer function Gf of theoverall motor-control system (see Fig. 5.4(b)) isG f ( s) 

(1  sK A SGY ) K
Js 2  B f s  K(5.5)

5.2.2 Experimental Setup
A single-axis analog gyro sensor is attached on the robot torso as indicated in Fig. 5.1.
The locations of ankle-pitch motor (MA) and hip-pitch motor (MH) are also indicated in50

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Fig. 5.1. To analyze the robot walking and the effect of the motor-control scheme for robotposture balancing, a smooth surface is inclined by an angle , as can be seen in Fig. 5.2.
The inclination of the surface is gradually increased from 0o in a stepwise manner, until therobot falls down during walking. The angular-pitch velocity of the robot is measured, when
the robot walks on this surface. This angular-pitch velocity is a characteristic of the robot
gait-pattern. The measurements are performed under following three conditions:
1. The robot is walking on the inclined surfaces without any gyro-sensor-based feedback
control, until it becomes unstable beyond a critical inclination cr0.
2. Beyond the critical inclination cr0, the ankle-pitch motor (MA) is controlled by the
gyro-sensor feedback. This allows the robot to walk up to a higher critical surface
inclination cr1. The robot becomes unstable beyond cr1.
3. Beyond cr1 the hip-pitch motor (MH) is also controlled by the gyro-sensor feedback inaddition to the ankle-pitch motor. This enables the robot to walk stably on inclined
surfaces above the critical surface inclination cr1.
The stepwise adjustments of the motor control, based on the gyro-sensor feedback, isschematically illustrated in Fig. 5.2.

5.2.3 Robot-Gait Implementation
The angular-pitch velocity of the robot is measured, when the robot is walking on an
uninclined surface ( = 0o), as schematically illustrated in Fig. 5.3. The gait-cycle period(Tgait) of the robot is set to 2.31 seconds. In the walking program implemented in the robot
controller RCB-4, there are a start phase (half a gait), four complete gait cycles and an end
phase (half a gait). The measured angular-pitch velocity meas of the robot-torso for  = 0o
is shown in Fig. 5.5(a). It can be observed that the pattern of meas becomes quite identicalafter the second gait cycle. Therefore the meas waveform of the third gait (Gait-3) cycle istaken as a reference pattern for meas for further analysis of the robot’s walking dynamics.
The zoomed waveform of Gait-3 is shown in Fig. 5.5(b), where the schematic robot motionsof this walking cycle are depicted above the graph. The schematic robot motion shows thedominant motor action during the walking. For  = 0o the reference gait cycle ischaracterized by four peaks (1, 2, 3 and 4), as shown in Fig. 5.5(b). Peaks 1 and 2 occur
due to the positive angular-pitch velocity of the robot while swinging the right leg during
first half of the gait cycle.
51

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬(a)Gait- 1Gait- 2 Gait- 3

Gait- 4

Tgait=2.31s

1
2

1
3 4

1 2

2

3 4

3

4

1

2

3

4

Dominant Motor Actions

(b)

MH

MK

MA

MK

Right Leg Swing

1

2

MH
MA
Left Leg Swing

3

4

Fig. 5.5. (a) Angular-pitch velocity of the robot torso when the robot walks on an
uninclined surface ( = 0o). (b) The angular-pitch velocity of the third gait cycle as detectedby the gyro sensor. The third gait cycle is shown in expanded form, to explain the gait
pattern of the robot on the uninclined surface.

Similarly, peaks 3 and 4 occur while swinging the left leg during second half of the gait
cycle. These four peaks characterize a gait cycle in the time-domain. In the following
subsection, it will be discussed how these four peaks are changed due to the effect of surface
inclination and gyro-sensor-based feedback control. This analysis is the core of this chapter.

52

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬(a)  = 0 o

(c-1)

KA=12

(b-1)

(c-2)

KA=12

(b-2)

(d)

KA=18

1

2

3

4

Fig. 5.6. Angular velocities of the robot’s pitch motion during a gait cycle, measured for
different surface inclinations. An increase in amplitude and number of oscillations isobserved at higher surface inclinations with feedback control. The results are compared withangular-pitch velocities, measured for =0o.

The measured gait cycle for  = 0o is considered as the “fingerprint” of the robot walking,which provides the basic gait pattern of the robot.

5.2.4 Experimental Results
The angular-pitch velocities meas of Gait-3 with different increased surface inclinations

 are shown in Fig. 5.6. The robot walking is studied first by increasing  from 0o tocr0=5.55o. In that case the robot’s motor control system is not having the additional
feedback loop of the gyro sensor. It can be seen, that additional oscillatory patterns appear
53

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬in the meas waveforms and these become more obvious as  increases. Due to an amplitude
increase in the additional oscillatory patterns, the designated peaks 1, 2, 3 and 4 become
indistinguishable. As  approaches cr0, the robot becomes more unstable due to the gravity
compensation problem. Beyond the critical surface inclination cr0, the robot falls downwhen it starts to walk. Therefore, the ankle-pitch motor MA is controlled beyond cr0 =5.55o. A proportional control system is implemented into the robot as shown in Fig. 5.4(a).
This proportional control system uses a gain KA to control the ankle-pitch motor angle,
where KA =12 makes the robot walking stable beyond cr0, as shown in Fig. 5.6(c-1). At
lower values of KA, the compensating-torque at the ankle-pitch motor is not sufficient toadjust the gravity effect on the robot. With KA=12 the robot can walk on surfaces withinclinations up to  = 8.88o. Beyond cr0=5.55o it is observed that the oscillatory nature of
the angular-pitch velocity increases largely due to implementation of the gyro-sensor-based
feedback-control system. The characterizing peaks (1, 2, 3 and 4) are no more observed
distinctly and the pattern of the third gait cycle becomes more oscillatory as compared to
the fundamental gait data (Fig. 5.6(a)). At  = 8.88o it is observed, that even though therobot can walk on the downslope, it starts slipping on the surface. If KA is increased further
to 18, the slipping is reduced and the robot can then walk down the slope more safely.
However, the robot body vibrates at much higher frequency when the gain KA is increased
than observed for a surface inclination of  = 5.55o.
At  = 9.7o the robot starts to slip again, even with KA=18. If KA is increased to a value
higher than 18, the vibrations of the robot body dominates the robot motion, which makes
the robot walking very unstable. Therefore, the hip-pitch motor MH is additionallycontrolled beyond  = 9.7o, in the same way as MA. It is important to note here that MA andMH are controlled independently. This MH motor control, while keeping KA = 12 for MAcontrol, reduces the slipping and makes the robot walking stable. But as two motors arecontrolled now, the oscillation increases as compared to the previous case when only anklepitch motor was controlled. The feedback gain KH for the hip-pitch-motor control is varied
from 12 to 14. It is observed, that the vibration increases at the higher value of KH = 14 (seeFig. 5.7(a)), whereas the slipping dominates at lower values such as KH = 12, similar to theresults for the ankle-pitch-motor control with KA. Therefore the KH-value is set to 13, where
both slipping and vibrations are optimized, and the robot can walk down the slope without
falling for a surface inclination up to  =10.2o, as verified in Fig. 5.7(b). For  > 10.2o, therobot walking becomes again unstable, mostly because of an increased slipping.
54

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬

(a)

(b)

KA=12, KH=14

KA=12, KH=13

Fig. 5.7. Angular-pitch velocity for a gait cycle with both ankle-pitch-motor control andhip-pitch-motor control, measured at different higher surface inclinations. (a) Robotvibrations increase for KH=14 in the hip-pitch-motor control. (b) KA=12 and KH=13 are an
optimized motor-control setting, allowing stable down-slope walking up to inclinations of
=10.2o.

Analysis of Experimental Results
The experimental results show that the gyro-sensor based feedback control enables therobot walking on inclined surfaces, but induces vibrations of the robot-body at the sametime. Here, the focus is given to the origin of the vibrations. It can be observed in Fig. 5.6
and Fig. 5.7, that the meas waveform becomes complex and that no clear peaks are visible
at higher surface inclinations. To investigate the origin of the oscillation increase, a Fourier
Transformation is carried out for the time-domain measurements of the angular-pitch
velocity of the robot-torso. Fig. 5.8 and Fig. 5.9 depict the results for measured angularpitch velocity waveforms meas in the frequency domain. Without the MA control for  ≤5.55o, a single dominant peak at f0 =1.73 Hz is observed, which is the fundamental walking
frequency (see Figs. 8(b-1) and 8(b-2)). The same measurements are repeated several times
in order to verify the statistical significance, and are plotted together in the graphs of Fig.
5.8.
For   6.99o, the feedback mechanism is implemented with higher KA values, as shownin Figs. 5.8(c-1), 5.8(c-2) and 5.8(d). It is observed that contributions up to second-orderharmonics (f1 and f2) are significant. These higher frequency oscillations refer to theoscillation increase in the time-domain measurements. For  = 6.99o and 7.68o an additionalfrequency peak fA0 is observed at 2.58 Hz, as shown in Figs. 5.8(c-1) and 5.8(c-2), and thisoriginates from the gyro-sensor-based feedback control of the ankle-pitch motor.
55

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬

(c-1)

(a)
KA=12

f0 =1.73 Hz.

f0

f0 fA0 f1

f2

(c-2)

Spectrum Amplitude

(b-1)

KA=12

f0 =1.73 Hz.
f1 =3.88 Hz.
f2 =5.6 Hz.

f0 f1

f0 fA0 f1

f2

f0 =1.73 Hz
f1 =3.88 Hz
f2 =5.60 Hz
fA0 =2.58 Hz

f2

(d)

(b-2)
KA=18

f0 =1.73 Hz.
f1 =3.88 Hz.
f2 =5.6 Hz.
f0 f1

f0 =1.73 Hz
f1 =3.88 Hz
f2 =5.60 Hz
fA0 =2.58 Hz

f0 =1.73 Hz
f1 =3.88 Hz
f2 =5.60 Hz
fA0 = 4.74 Hzf0 f1 fA0 f2

f2

Fig. 5.8. Fourier analysis of the angular-pitch velocity waveforms measured by the gyro
sensor for the robot-body, when the robot is walking stably on inclined surfaces without ((a),(b-1), (b-2)) and with ((c-1), (c-2), (d)) gyro-sensor feedback. The frequency fA0 = 2.58 Hz (see(c-1) and (c-2)) is induced by the motor feedback with KA=12, which is shifted to fA’0 = 4.74
Hz (see (d)) due to an increased KA.

As the surface inclination increases further to  = 8.88o, oscillation frequencies are
shifted to higher values. This shift to higher frequencies becomes quite drastic whenintroducing the KH control, as can be seen in Fig. 5.9. Under such a condition the robot-gait
pattern is no more detectable in the time-domain measurements. At the surface inclinationof  = 8.88o, an increased feedback gain KA of 18 is required, which however causes larger
oscillatory behavior of the robot, which can be seen in Fig. 5.6(d).

56Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬

(a)

(b)

KA=12, KH=14

KA=12, KH=13
fH0=8.40 Hz

fH0=8.40 Hz

Slipping

fH0

fH0

Fig. 5.9. Fourier transformation of the angular-pitch velocity, when both ankle-pitch andhip-pitch motors are controlled by the gyro sensor. It can be seen that the contribution due
to the fundamental walking frequency of 1.73 Hz is no more observable. Instead a peak athigher frequency is observed. The measured time-domain waveform becomes more
oscillatory, as shown in Fig. 5.7.

f0 fA0 f1 fA’0 f2

fH0

f0 = 1.73 Hz
f1 =3.88 Hz
f2= 5.60 Hz
fA0= 2.58 Hz
fA’0= 4.74 Hz
fH0= 8.40 Hz

Fig. 5.10. Phase plots for the measured pitch velocity in the cases of various surface
inclinations. The contributing frequencies are indicated, confirming the findings from thecorresponding amplitude plots. A tolerance value of 33% of the absolute maximum in theamplitude spectrum is used for the phase-plot calculation.

Frequency responses of the measured angular-pitch velocity at  = 9.7o and  = 10.2oare shown in Fig. 5.9(a) and Fig. 5.9(b), respectively. The frequency peaks are observed at
higher frequencies between 7.5 Hz and 10 Hz for both cases. Corresponding phase plots(spectrum phase vs. frequency) of the angular-pitch velocity are shown in Fig. 5.10. A
relatively high tolerance value of 33% of the maximum absolute value in the amplitude
spectrum is used during the calculation of these phase plots, in order to remove the57

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬MA+ MH
Feedback
KA=12
KH=13

MA Feedback
KA=18

No Feedback

KA=12

Fig. 5.11. Contributing frequencies as extracted from the frequency-response analysis of
the angular-pitch velocity as a function of surface inclination .

unwanted effects of the quite large noise in the measured time-domain data. The phase plotsshow the peaks due to the contributing frequencies, as supported by the amplitude plots forthe angular-pitch velocity. The data suggests, that the linearity of the gait pattern iscompletely lost, as can be observed in particular from the diminished amplitude at f0=1.73
Hz. The dominant frequency peaks as a function of the surface inclination  are summarized
in Fig. 5.11. Initially the regular gait pattern of f0 is observed. By introducing the feedback
control, however, additional control frequencies appear. By increasing the KA value to 18,
the additional frequency due to feedback increases up to fA’0 =4.74 Hz (see Fig. 5.8(d)).
The introduction the KH control causes an additional frequency at fH0 = 8.40 Hz, as shownin Fig. 5.9(a). This relatively high frequency controls the gait pattern of the robot, making
the robot unstable due to increase in vibrations. By increasing the surface inclination up to =10.2o, strong peaks appear also at low frequency (see Fig. 5.9(b)), which are attributed
to the disturbance caused to the walking due to the slipping on the surface.

Experiments with Robot-Foot Friction
It was found that the increase of the feedback gains KA and KH reduces slipping of therobot feet, but at the same time the vibration of the robot-body increases. These robot
vibrations can be attributed to the joint angle control through the gyro sensor feedback.
Figures 5.12(d), 5.12(d-2) and 5.12(d-3) summarize the features of the KA control for  =58

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬

(d)
KA=18

f0 =1.73 Hz
f1 =3.88 Hz
f2 =5.60 Hz
fA0 = 4.74 Hz

(a-2)

(d-2)
KA=15

KA=12, KH=13

f0 =1.73 Hz
f1 =3.88 Hz
f2 =5.60 Hz
fA0 = 4.74 Hz

f1 fA0 f2

fH0=8.40 Hz

fH0

(d-3)
KA=12

f0 f1

fH0=8.40 Hz

fH0

f0 f1 fA0 f2

f0

(a)

KA=12, KH=14(a-3)
KA=12, KH=12

f0 =1.73 Hz.
f1 =3.88 Hz.
f2 =5.6 Hz.

f2

f0 f1

f0 =1.73 Hz.
f1 =3.88 Hz.
f2 =5.6 Hz.

f2

Fig. 5.12. Fourier analysis of the angular-pitch velocity of the robot walking on an inclined
surface for  = 8.88o with varying KA (18 in (d), 15 in (d-2) and 12 in (d-3)) and for  = 9.7owith varying KH (14 in (a), 13 in (a-2) and 12 in (a-3)) By reducing KA and KH values, therobot posture becomes unstable due to slipping, as shown in (d-3) and (a-3).

8.88o. Even though the robot feet become quite slippery, the fundamental walking
frequency f0 is clearly observed for all KA values. With increased KA value, it can be seenthat the nonlinearity of the gait-pattern increases. The nonlinearity continues to increase
with the additional control of KH. This can be seen in Figs. 5.12(a), 5.12(a-2) and 5.12(a3) for  = 9.7o, where the higher frequencies between 7.5 Hz and 10 Hz are due to the
feedback-motor-control system for the hip-pitch motor MH.
Till now the robot walking experiments have been carried out on an inclined surfaces
with low friction, to verify major factors which prevent the robot from stable walking. In
59Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬

(b)

(a)
KA=12 (with high friction)

f0 =1.73 Hz
f1 =3.88 Hz
f2 =5.60 Hz
fA0 =2.58 Hz

f0 =1.73 Hz
fA0 = 2.58 Hz
fA’0 = 4.74 Hz

f0 fA0 fA’0

f0 fA0 f1 f2

(c)

fA0
f1 fA’0 f2

f1 =3.88 Hz
f2= 5.60 Hz
fA0= 2.58 Hz
fA’0= 4.74 Hz

Fig. 5.13. (a) Amplitude plot, which shows the Fourier analysis of the angular-pitch velocity
data when the robot is allowed to walk with higher feet friction and reduced value of KA =12 on a surface of  = 8.88o inclination. (b) Comparison of amplitude plots, which
demonstrates the shift in the additional frequency due to the feedback control fromfA’0=4.74 Hz to fA0=2.58 Hz, when lowering KA from 18 to 12, as becomes possible by theincreased feet friction. (c) Phase plot, which confirms the frequency-peak shift to a lower
value, due to lowering of the feedback gain KA at higher surface friction. A tolerance valueof 33% of the absolute maximum in the amplitude spectrum is used for the phase-plot
calculation.

this section further experiments on an inclined surface with higher surface friction are
described. The robot feet are attached with rubber soles. The experiments are performed at = 8.88o. The results with KA=12 are shown in Fig. 5.13(a). In the case of low surfacefriction (see Fig. 5.12(d)), the frequency fA0=2.58 Hz is not observable, but shifted to
fA’0=4.74 Hz due to the increased value of KA=18 to make the robot-posture stable. Though
the robot was able to walk on the surface stably only with KA=18 for the low friction
surface, the robot can now walk stably with KA=12 in the case of increased friction. In Fig.
5.13(b), the two results for different friction conditions are compared. The frequency f0
becomes dominant and the fA0=2.58Hz reappears for the high friction case. The spectrum60

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬

(a)

(b)

KA=12, KH = 12
(with high friction)

The fundamental, f0 isobserved at lower
feedback when thefriction is increased

f0 =1.73 Hz
fH0 =8.40 Hz

Also the motor vibration
frequency reduces from
8.4 Hz to 7.33 Hz due toreduction of KH.

f0

f0

fH0

(c)

f0

fH’0 fH0

f0 = 1.73 Hz
fH0= 8.40 Hz
fH’0= 7.33 Hz

Fig. 5.14. (a) shows that robot can walk on a surface of  = 9.7o inclination with KH =12,
when the robot-feet friction is increased. (b) illustrates two important features, which
result from the increased-friction-enabled KH lowering: First, lowering of the frequency,
induced by the additional hip-pitch motor control, from 8.40 Hz to 7.33 Hz. Second,
reappearance of the peak at fundamental walking frequency f0 = 1.73 Hz. (c)Corresponding phase plot, which supports the appearance of the peak at f0 and thelowering of KH. A tolerance value of 33% of the absolute maximum in the amplitude
spectrum is used for the phase-plot calculation.

amplitude plot is supported by the corresponding phase plot Fig. 5.13(c), which shows
shifting of the frequency peaks to lower values, due to lowering of the feedback gain KA at
higher surface friction.
Similar measurement results for  = 9.7o, with increased friction, are shown in Fig.
5.14(a). The comparison with the low-friction results, where the robot needed a higher KH
value of 14 for stable walking, is given in Fig. 5.14(b). With increasing the surface friction,
two important improvements are clearly observed in the gait-pattern. First, a stable walking
for the robot was achieved with a lower KH value of 12, having a peak at a lower frequencyof 7.33 Hz (compared to 8.40 Hz at KH = 14 for the lower friction case). Second, the61Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬reappearance of the fundamental walking frequency f0 is confirmed, as highlighted by theencircling in the graph, which is also supported by calculating the phase plot of the angularpitch velocity, as shown in Fig. 5.14(c). This phase plot further verifies, that a frequency
peak appears at f0 in addition to the lowering of the contributing frequency from 8.40 Hz to7.33 Hz, thus supporting the results obtained from the spectrum amplitude plot (see Fig.
5.14(b)). Therefore, the high-frequency vibration, observed around 8.40 Hz, is drasticallyreduced in magnitude and frequency, leading to a more stable gait pattern of the robot.

Model Development for Robot Balancing
5.5.1 Inverted Pendulum Model (IPM) for Robot Walking
For modeling the walking dynamics of the humanoid robot, a basic inverted pendulumin polar coordinates is considered, as shown in Fig. 5.15, which can be written as [57,102]
ml 2

d 2 (t ) mgl sin  (t )  0
dt 2

(5.6)

where , m, l and g are angle of pitch rotation of the robot torso in the sagittal plane, robot
mass, distance of robot’s COM from the ankle-pitch motor and acceleration due to gravity,
respectively, as also indicated in Fig. 5.15. The physical parameters of the robot aredescribed before in Table I. The first derivative of (t) with respect to time is the angularpitch velocity, measured in our experiments (see Fig. 5.6 and Fig. 5.7). Under the condition

mg



l

Fig. 5.15. IPM to explain the robot walking dynamics. The parameters , m, l and g are
angle of robot-torso rotation in the sagittal plane, robot mass, robot-center-of-mass
distance from the ankle-pitch motor and acceleration due to gravity, respectively.

62

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬of small (t), the solution of (5.6) becomes sinusoidal and the angular-pitch velocity can be
written as (t )  a cos 2 f n t(5.7)

Let a and fn be the initial angular-pitch velocity and the natural frequency of the inverted
pendulum, respectively, where fn given by [102]

fn 

1
2

g
 0.9 Hzl

(5.8)

Thus, the ideal walking motion of a humanoid robot can be modeled as the periodic
motion of the inverted pendulum. In that case, one gait cycle can be divided into two halfcycles, where one half cycle is due to the left-leg movement and the other is due to theright-leg movement. Now, in each half cycle there are two motion phases– one Single
Support Phase (SSP) and one Double Support Phase (DSP). The SSP of the left and theright leg can be treated identically. This is quite reasonable, because only frequency f0=1.73
Hz is observed in the gait pattern. During the DSP motion, only the active-leg exchange
happens, and thus the gait pattern is characterized nearly exclusively by SSP in thefrequency-domain analysis. Therefore, based on the experimental observation and theoutlined theoretical justification, we can conclude that the fundamental walking frequency
f0 of the robot’s gait pattern should be twice of the natural frequency fn of the IPM, givenby (5.8). The theoretically calculated f0 of 1.8 Hz is indeed close to the experimentally
extracted value of 1.73 Hz.
Under an ideal walking condition, the reference angular-pitch velocityref is thus given
by a single frequency f0 with amplitude a.

ref (t )  a cos 2 f0t(5.9)

Consequently, only one frequency peak is expected at the f0 =1.73 Hz in the Fouriertransformation of the angular-pitch velocity for =0, i.e., for an uninclined surface. Now,
the output of the modified control system with gyro-sensor feedback (see Fig. 5.4(b)), in
response to a sinusoidal input (5.9) of frequency f0 =1.73 Hz, is then given by0 ( s) (1  sK A SGY ) Ks 22Js  B f s  K s  (2 f 0 )263

(5.10)

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬where the transfer function of the system is given by (5.5). In the time domain, the output
angular-pitch velocity can be obtained by an Inverse-Laplace Transform [92] of (5.10) as

0 (t )  a0 cos(2 f 0t )  b0e



Bf
J

t

cos(2 f A0t )(5.11)

where the frequency fA0 is the damped natural frequency of the motor-control system forthe ankle-pitch motor. The two amplitudes a0, b0 can be written as [102]f A0 

a0 

2K  Bf 
1 

J 
JK 

K  ( B  K A SGY ) 2 
1 

J 
JK


a
( K  J (2 f 0 ) 2 ) 2  (2( B  K A SGY ) f 0 ) 2(5.12)(5.13)

2

b0 

 Bf
1 d0 (t ) 0 (t ) t 0   0 (t ) t 0
2 f 0 dt t 0 
 4 Jf 0(5.14)

Thus, the measured output for the angular-pitch velocity 0(t) is expected to show
fundamental frequency peaks at two frequencies of f0 and fA0 in the corresponding Fouriertransform. From (5.12) it can be seen, that as the feedback gain KA is increased, thefrequency fA0 also increases. This is confirmed by the experimental observations as shownin Figs. 5.8(c-1), 5.8(c-2) and 5.8(d).

5.5.2 Inverted Pendulum Model for Robot Walking
The analysis, carried out in last subsection, assumed the control system to be linear.
This allows the use of transfer-function modeling. The time-domain output (see (5.11)) is
obtained to explain the experimentally-measured results. The model (see (5.11)), discussed
in last subsection, explains the output of a second-order system (see (5.5)) in response to asinusoidal input of frequency 1.73 Hz. The output consists of the input frequency of 1.73
Hz and the damped natural frequency fA0.
Here, the model (see (5.10)) is extended to include the nonlinearity of the robot
dynamics, which is induced in the inverted pendulum by the surface inclination . First theorigin of higher-order harmonics is explained and then the inclusion of the harmonics(nonlinearity) into the model (see (5.11)) is discussed. For understanding the nonlinearity,
time-domain analysis of a nonlinear pendulum is considered. For an inclined surface, (5.6)
changes to [97,102]
64

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ml 2

d 2 (t ) mgl sin( (t )   )  0
dt 2(5.15)

where  is the surface inclination. If we expand the sinusoidal term following the basic
trigonometric identity [104], we get
ml 2

d 2 (t ) mgl  cos  sin  (t )  sin  cos (t )   0
dt 2(5.16)

This result can be rewritten by series expansions of sin (t) and cos(t) into the form
ml 2



  2 (t )  4 (t )d 2 (t ) 3 (t )  5 (t )

mgl
t




mgl

 ...   0
cos


(
)
...
sin



1 
2
6
120
2
24
dt





(5.17)The solution of (5.17) with a sinusoidal input of the fundamental walking frequency f0(see (5.9)) of the robot’s gait pattern is given by [105-113]

meas (t )  A0  a0 cos(2 f0t )  a1 cos(2 f1t )  a2 cos(6 f 2t )(5.18)

where a0 is the amplitude of the fundamental walking-frequency component, given by(5.13). The amplitudes a1 and a2 of the harmonics are functions of the surface inclination

, as shown in (5.19) and (5.20)

a1 

g cos a0
6l

(5.19)a2 

g sin a02l(5.20)

In both time-domain (Fig. 5.6 and Fig. 5.7) and frequency-domain (Fig. 5.8 and Fig. 5.
9), it is experimentally observed that the oscillation amplitudes become larger with anincrease in surface inclination . From above investigation, the theoretical investigation
confirms the experimental findings. The surface inclination  has two main effects on themeasured angular-pitch velocity of the robot. Firstly, there is an increase in nonlinearity,
which causes the appearance of higher-order harmonics. Secondly, the oscillation
amplitudes increase for larger surface inclination. From the results it is confirmed, that theharmonic coefficients a1 and a2 give dominating contributions of the robot motion underhigh  values. Equation (5.18) explains the trend of the measured angular-pitch velocity forsurface inclinations  ≤5.55o (see Fig. 5.8(b-1) and Fig. 5.8(b-2)) and the origin of the65Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬nonlinearity due to the higher-order harmonics of the fundamental frequency of 1.73 Hz. It
is now important to incorporate these higher-order harmonics into the previously discussed
model (see (5.11)).
When the feedback loop of KA is applied for  5.55o, an additional frequency peak isobserved (see Figs. 5.8(c-1), 5.8(c-2) and 5.8(d)). The origin of the peak strength at thisadditional frequency fA0 is explained by (5.11). The theoretical expression for fA0 is givenby (5.12).
The experimentally measured results can be explained by calculating the output of thesecond-order system (see 5.5) in response to an algebraic sum of sinusoids of fundamental
frequency and its higher harmonics.

meas (s) (1  sK A SGY ) K 
s
s
s
 2
 2
 2
2
2
2
2 
Js  B f s  K  s  (2 f 0 ) s  (2 f1 ) s  (2 f 2 ) (5.21)The measured angular-pitch velocity can be analyzed with the following equation, obtainedby inverse-Laplace transform of the (5.21).
2

 meas (t )  A0   an cos 2 f nt  B0  b0e
n 0



Bf
J

t

cos 2 f A0t(5.22)

where meas (t) is the measured angular-pitch velocity when the gyro-sensor feedback isapplied for motor control. As the surface inclination  is increased, the feedback strength
KA has to be also increased to keep the robot posture stable. However, with increasing KA
the vibration of the robot body also increases. The frequency-domain analysis of theangular-pitch velocity is dominated by the KA-induced damped natural frequency fA0, givenin (5.12), and the gravity-induced harmonics of the fundamental walking frequency f0,
given in (5.18). Nevertheless, to keep a sufficiently stable robot walking, the amplitude off0 must dominate over the other frequencies.

Conclusion
In this chapter the origin of the robot-posture instability is investigated, which occurs
during walking on inclined surfaces. It was found, that the higher-order harmonics are
induced by the distorting effects of the gravity force. The contribution of the harmonics
increases when the surface inclination increases, resulting in the robot falling down. Thisis an original way to explain the instability of the robot walking frequency domain. To
66

Chapter 5: Vibration Control in Humanoid Robots‫ـــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬protect the robot from falling down, a gyros sensor based feedback control has been
implemented in the motor-control system of the robot. It is explained in detail that in orderto maintain a stable walking, the fundamental walking frequency must be the only peak in
the frequency domain. The frequency components due to the feedback-control must be kept
lower than the fundamental walking frequency, so that a clear fundamental walking
frequency is still observable. However, it can easily happen, that the necessary feedback
control becomes too large for maintaining the fundamental robot posture on a largely
inclined surface. Thus, strongly enhanced vibration of the robot body is observed, whichcauses instabilities to the robot-walking under large surface inclination becomes. For
solving this stability problem, it was further demonstrated, that a larger friction between
the robot feet and the surface provides an efficient way to improve the robot walking
allowing to reduce the feedback gain. Reducing the feedback gain, causes reduction in theoscillations at higher frequencies. In summary, the frequency-domain analysis of therobot’s periodic gait pattern tool for the understanding the instabilities in the robot-walking
and for deriving suitable methods of gait-pattern stabilization under external disturbances.

67

Chapter 6:Conclusions and Future works‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Chapter 6: Conclusions and Future works
Light-weight humanoid robots have potential application for information acquisition
inside a disaster hit environment where the load-bearing capabilities of the mechanicalstructures are reduced. In that case the walking stability of the robot is of great importancein such environments. The dissertation studies the walking control for lightweight robot on
inclined surface. Three novel contributions of the dissertation are summarized as follows.

Novelty and Conclusions of the Dissertation
The most important new scientific results of the present dissertation can be summarized
as follows:

6.1.1 Static stability of humanoid robot on inclined surface
The static stability of the robot (in a Single Support Phase) is investigated on an inclined
surface, where the inclination is varied from 0 to 10.2 degrees. A force-sensor based
position-control system is proposed and thereafter implemented in the robot hardware. This
allows the robot to stand stably on one foot (Single Support Phase of walking) up to an
inclined surface of 7.68 degrees. Beyond 7.68 degrees, the robot needs higher torque tostabilize its posture. In that case a gyro-sensor based position control for the hip servomotor
is integrated. The position of the hip-motor is controlled by the angular-pitch velocity of
the robot body sensed by the gyro sensor. This allows the robot to stand stable (in Single
Support Phase) up to an inclined surface of 10.2 degrees.

6.1.2 Potential application of gyro sensor
An electromechanical model of the gyro sensor is experimentally verified from the
dynamic characteristics of analog gyro sensor KRG-4. The KRG-4 gyro sensor is used in
the experiments for the stability of the robot. The gyro sensor model is used to model thepush recovery strategy for the robot on a plane surface. The model was experimentally
verified by the push-recovery experiments.

6.1.3 Vibration control while walking on an inclined surface
At the end the the walking stability of the robot is investigated on an inclined surface
and with the proposed gyro sensor based control system the robot can walk upto ana
inclined surface of 10.2 degrees. In order to stabilize the robot walking on an inclined
68Chapter 6:Conclusions and Future works‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬surface, a gyro-sensor based feedback control systems is proposed. The experimental
results shows that as the surface inclination is increased higher harmonics of thefundamental walking frequency and damped natural frequency of the control system effects
the robot walking. This increases the vibration in the robot, thus making the robot walking
unstable. An optimization of the controller gain is implemented based on the tradeoff
between the surface friction and the vibration. Therefore adjusting the controller gain, thevibration is reduced.

Future Works
Humanoid robots are one of the most complex intelligent machine human beings haveever worked upon. There are many open research problems which are yet to be solved. This
thesis gives rise to two interesting research problems in the field of ‘light-weight’ humanoid
robot.
Surface friction is a very important physical phenomena observed in case of robotwalking on an inclined surface. Lower surface friction will most likely limit the criticalsurface inclination cr for a given reference robot-posture. Therefore it is very important toincorporate the effect of surface friction into the IPM to study the dynamics of the robot
theoretically. The problem faced during the surface friction is, it is very difficult to observe
the effect of surface friction on the robot walking during the experiments. So, developmentof experimental setup to measure the effect of surface friction over robot-walking dynamics
can be an envisaged future work.
Another possible future work can be the theoretical analysis of effect of mechanicalstiffness of the robot joints (motor control system) on the vibration of the robot. The
feedback gains of the gyro-sensor based control system effect the equivalent stiffness inthe motor-load transmission system of the ankle-pitch motor and the hip-pitch motor. The
study of vibration in a motor-load transmission system is widely studied. This thesis
suggests that, the study can be taken to one step ahead to the effect of vibration on the robot
walking on a given surface.

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76

Error! Reference source not found.Development of AIGAMO-I: A Remote Controlled W
eeding Robot for Organic Rice Farming‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬Development of AIGAMO-I: A Remote
Controlled Weeding Robot for Organic Rice Farming

iGAM Weeding Robot
Propulsion Technology

Hiroshima Rinku Torai

Hiroshima-ken, Mihara-shi
Daiwa-cho, Kamatika 322

TAOYAKA Onsite
Team-13
Hiroshima University

i-GAM Project(Open Source Design
Project)“AIGAMO-I” robot+
Intelligent Motion Control

Fig. A.1. Overview of the TAOYAKA Onsite Team Project

The TAOYAKA Onsite Team Project is a project carried out under the flagship of
TAOYAKA Program for Leading Graduate Schools. The project title was “Developmentof a Weeding Robot to Support Organic Rice Farmers”. Under the project a remotecontrolled weeding robot, “AIGAMO-I”. First, a prototype was developed and tested forits buoyancy. Then the robot-body is re-designed and 3D-printed. The robot was tested in
the Monozukuri Plaza, Hiroshima University. The project overview is shown in Fig A.1.
The development involved close-cooperation with local community like Hiroshima Rinku
Torai in Mihara, Hiroshima Prefecture of Japan. The community was using a very primitive
design of a robot which they named “i-GAM”. The robot was integrated with two 12V DC
motors running two screw-propellers. The motors were pre-programmed about thedirection of rotation, and based on the direction the robot was changing its direction of
movement in the field. The robot moved randomly in different directions.
The robot had two main problems. First, it was pre-programmed which makes its
movement very much restricted in the field. Second, it was not enabled with any motion
control system. The author of this thesis attempted to solve these two problems. The targetof the project was to develop the motion control technology for the robot and give back to
77

Error! Reference source not found.Development of AIGAMO-I: A Remote Controlled W
eeding Robot for Organic Rice Farming‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬the community. The developed robot was tested in the university workshop, but
unfortunately could not tested in the rice field due to lack of the time. The one-year longproject finished in the month of April, 2019. Though the project finished officially, theresearch group has continued the development of the robot and envisioned to give it backto the community in the near future. The timeline of the project is shown in Fig. A.2 andthe robot is shown in Fig. A.3.

Visit to Shiraichi
November 22,2018

Buoyancy Test-1
March 19, 2019

Prototype Design & Testing• Component purchase• Propeller design (screw)• Integration• Buoyancy Test-1• Disturbance Test-1

WorkshopApril 28, 2019

Body Design• 3D printing• Wing design• Integration• Buoyancy Test-2• Disturbance Test-2

Kyoto Maker Faire
Kyoto, May3-5, 2020

Phase-1 Modelling and Simulation(Sept.12 - Oct.12, 2019)• Propeller modelling• Hydrodynamics modelling
Phase-2 Wireless Control and IMU Experiments(Feb.12 – Mar.29, 2020)• Wireless control of motor-control• Experiments of azimuth-control on water• IMU implementation

Target Event: Kyoto Maker Faire
Prototype

Kyoto, May 3-5, 2020

AIGAMO-I

Fig. A.2. The timeline of the development of the weeding robot AIGAMO-I

Physical parameters
Dimension

30 19 10 cm

Weight

3.5 KgMotor

Brushed DC

Control Board

Arduino Uno

Motor Shield

LM358

IMU

MPU6050 1

RF Transceiver nrF24L01 1
Battery

12 V 2

Fig. A.3. Weeding robot AIGAMO-I (right) and the principal physical parameters (left).

78

List of Publications‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬List of Publications
A. Transactions/ International Journal Papers
A-(1) Sunandan Dutta, Mitiko Miura-Mattausch, Yoshihiro Ochi, Naoto Yorino andHans Jürgen Mattausch, “Gyro-Sensor-Based Vibration Control for Dynamic
Humanoid-Robot Walking on Inclined Surfaces,” Sensors, Vol. 20, 7139, Dec.
2020.
A-(2) Sunandan Dutta, Tapas Kumar Maiti, Mitiko Miura-Mattausch, Yoshihiro
Ochi, Naoto Yorino and Hans Jürgen Mattausch, “Analysis of Sensor-Based
Real-Time Balancing of Humanoid Robots on Inclined Surfaces,” IEEE Access,Vol. 8, pp. 212327-212338, Dec. 2020.
B. International Conference Papers Related to This Thesis
B-(1)

B-(2)

Sunandan Dutta, Tapas Kumar Maiti, Yoshihiro Ochi, Mitiko MiuraMattausch, Sandip Bhattacharya, Naoto Yorino, Hans Jürgen Mattausch,“Stability Analysis of Humanoid Robots with Gyro Sensors Subjected toExternal Push Forces,” Proceedings of the 2nd International Symposium on
Devices, Circuits and Systems (ISDCS 2019), pp.1-4, Mar.4 - 6, 2019,
Hiroshima, Japan.
Sunandan Dutta, Tapas Kumar Maiti, Yoshihiro Ochi, Mitiko MiuraMattausch, Sandip Bhattacharya, Naoto Yorino, Hans Jürgen Mattausch, “Selfcontrolled walking robot with gyro sensor network for stable movement on nonsmooth surfaces,” Proceedings of the IEEE International Conference on
Simulation, Modeling and Programming for Autonomous Robots (SIMPAR
2018), pp.137-143, May.16 - 18, 2018, Brisbane, Australia.
.

Contents of the Thesis and Published Papers Relationship
Chapters
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6

Title of chapters
Introduction
Literature Review
Force Sensor Based Postural Stability Control
Gyro Senor Based Postural Stability Control
Vibration Control in Humanoid Robots
Conclusions and Future works

79

Published papers
A-(1), A-(2), B-(1), B-(2)
A-(1), A-(2), B-(1), B-(2)A-(2)B-(1), B-(2)
A-(1)
A-(1), A-(2), B-(1), B-(2)