Toward a Human-like Locomotion: Modelling Dynamically Stable

Locomotion of an Anthropomorphic Robot in Simulink Environment

Ramil Khusainov, Ilya Shimchik, Ilya Afanasyev and Evgeni Magid

Intelligent Robotic Systems Laboratory (LIRS), Innopolis University

40-42 Profsoyuznay str., Kazan, Republic of Tatarstan, Russian Federation

Keywords:

Anthropomorphic Robot, Biped Robot Locomotion, Dynamic Stability, Modelling, Simulink.

Abstract:

In the near future anthropomorphic robots will turn into an important part of our everyday routine. To suc-

cessfully perform various tasks these robots require stable walking control algorithms, which could guarantee

dynamic balance of the biped robot locomotion. Our research is focused on the development of locomotion

algorithms which could provide effective anthropomorphic walking of a robot. As a target robotic platform

we utilize an experimental model of a human-size robot - a novel Russian robot AR-601M. In this paper we

introduce AR-601M robot and present a model of a biped robot with 11 DoF which simulates a simpliﬁed

AR-601M robot. The simulation model is implemented in Matlab/Simulink environment and uses walking

primitives in order to provide a dynamically stable locomotion.

1 INTRODUCTION

In the last century robotics was mainly the focus of

interest of Ministries of Defense and Space, univer-

sity research laboratories and a few giant corpora-

tions. One of the most critical tasks was to develop

multi-terrain robots in order to operate in danger-

ous environments (e.g., nuclear, chemically or bio-

logically polluted environments) and to perform var-

ious functions in order to support humans in search

and rescue operations, military and space missions.

Today robotic products are rapidly turning into con-

sumer’s goods - yet not affordable and available to

all groups of the population. But that is just a ques-

tion of time, and in the coming decades we will see

the wide-spread of domestic, social and educational

robots. Such robotic systems will replace people in

various operations in unfriendly environments and at

home, and thus require comparable to a human skills

of locomotion inside buildings together with the abil-

ity to operate the devices which were originally cre-

ated for a human. To guarantee the comparable to

a human skills, multi-functionality and ﬂexibility, an

anthropomorphic structure of a robot would be re-

quired. Bipedal locomotion of an anthropomorphic

robot provides mechanisms to step over obstacles,

climb stairs and ladders, and walk on uneven terrain

- the activities which could not be fully performed by

a wheeled or a tracked robot. Anthropomorphic do-

mestic robotic assistants would also facilitate human-

robot interactions and social activities, which often

require the robot to work in a direct physical contact

with a person, to master safe (Amirabdollahian et al.,

2013) and acceptable by a human social behavior, and

to be visually acceptable by a human (Fink, 2012).

Therefore anthropomorphic robotic systems with sta-

ble anthropomorphic movement dynamics and high-

energy efﬁciency become critical. During the decades

of bipedal locomotion research a number of different

approaches targeting for stable locomotion were de-

veloped, and Section 3 presents a brief overview of

the existing approaches. Unfortunately, due to seri-

ous difﬁculties with balance preserving and redundant

degrees of freedom (Wu et al., 2009), walking of hu-

manoid robots is still far from achieving a comparable

to a human level of anthropomorphism and reliabil-

ity (Wright and Jordanov, 2014).

The objectives of our research are to develop solu-

tions of dynamically stable walking for a biped robot

AR-601M. In order to reduce the time of software de-

velopment with the real robot and to provide system

debugging on early stages of algorithm development,

it is essential to create a relevant simulation model

which takes into an account physical properties of the

robot and its interaction with the environment. Dy-

namical mathematical models for legged locomotion

- for animals (Ijspeert, 2008), insects (Holmes et al.,

2006) or humans (Zajac et al., 2003) - help to simu-

141

Khusainov R., Shimchik I., Afanasyev I. and Magid E..

Toward a Human-like Locomotion: Modelling Dynamically Stable Locomotion of an Anthropomorphic Robot in Simulink Environment.

DOI: 10.5220/0005576001410148

In Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2015), pages 141-148

ISBN: 978-989-758-123-6

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

late the balance-based locomotion algorithms behav-

ior prior to experiments with a robot and also may

give clues on ”healthy” or ”pathological” gaits. In

this paper we introduce current stage of our study and

present the simulation model of the biped robot AR-

601M in Matlab/SimMechanics

The rest of this paper is organized as follows. Sec-

tion 2 introduces Russian humanoid robot AR-601M.

Section 3 considers the theoretical background of a

biped robot locomotion methods. Section 4 presents

a designed Simulink model of AR-601M robot. Fi-

nally we conclude and discuss the future steps of our

research in Section 6.

2 SYSTEM SETUP

This section describes the AR-601 robot as the holis-

tic system setup, which is used for dynamically stable

robot locomotion model development.

The anthropomorphic robot AR-601M (ﬁg. 1) is

being developed by Russian company ”Android Tech-

nics”

. It is a full-scale anthropomorphic robot sys-

tem with the height of 144 cm and the weight of 60 kg,

which correspond well with an average human body

parameters

Figure 1: Testing anthropomorphic robot AR-601M, the

shell is removed.

The robot has a lightalloy frame with power elec-

tric motors, two robotic arm-manipulators and two

Multibody Simulation - SimMechanics, http://

www.mathworks.com/products/simmechanics/

Androidnaya Tehnika (Android Technics), AR-601M be-

longs to a generic AR-600 series of robots, http://en.npo-

at.com/products/ar-600/

In human robot interaction in order to maintain a clear

master-slave relationship between the two parties it is impor-

tant that a robot is not emitting any kind of threat to a human

and this requirement is particularly embodied in lower than an

average human height of the robot.

Table 1: Technical characteristics of AR-601 robot.

Parameter Value

Height 1442 mm

Mass 60 kg

Battery life 3 hours

Sensors IR × 16

Camera × 3

Lidar × 2

Accelerometer × 6

Magnetic encoder × 30

Degrees of freedom Total: 69

Active: 45

Type of Motors Electrical

Material of body Plastic

Battery type Li-FePo

Network interfaces Wi-ﬁ, Ethernet

legs, which allows having up to 69 degrees of free-

dom (DoF), of which six DoFs belong to each leg.

To control the robot movement there are 26 large and

12 small electric motors with STM32F103T8U6 con-

trollers and the communication protocol provides data

about all motor states, pressure values in robot’s feet

and on-board gyroscopes. The robot has a built-in

multi-sensor system, speech recognition and synthe-

sis systems. Table 1 presents in details some of the

important parameters of AR-601M which inﬂuenced

our model and algorithms development.

The robot locomotion control is carried out by set-

ting the joint angles for motor’s rotation along with

angular velocities and accelerations. In addition, each

joint could be controlled directly with torque out-

put commands. Therefore, MATLAB Simulink can

be used to reproduce an interface of communications

protocol and simulate on-board robot control system

and input signals to control electric motors. To do this

within the Simulink model, simulated signal packages

are sent to the motors in synchronous mode and the

controllers manage the response packages from sen-

sors. Furthermore, it makes possible to set the coef-

ﬁcients of the PID controller with specially simulated

commands or even to simulate the particular com-

mands like, for example, the brake coupling for ﬁx-

ing the drives position with knee and hip joints lock-

ing. However, in common case, it is sufﬁcient to set

the rotation angles for each joint and ignore particular

mechanisms of motor control.

ICINCO2015-12thInternationalConferenceonInformaticsinControl,AutomationandRobotics

142

3 ON BIPEDAL ROBOT

LOCOMOTION MODELLING

This section familiarizes the reader with popular mod-

els of biped robot locomotion modelling and methods

for robot motion control.

3.1 A Bipedal Robot Model

The widely utilized strategies for simulating a biped

robot are to use a model of inverted pendulum with or

without a spring.

For Inverted pendulum or linear inverted pen-

dulum model a biped robot acts as an inverted pen-

dulum, because the center of mass (CoM) of the robot

is localized in the upper body part. When the biped

robot is doing a step, its swinging leg is similar to an

inverted pendulum whose massless rod connects the

supporting foot to the CoM of the robot (Stephens

and Atkeson, 2009). As an illustration, this ap-

proach had evolved in the following models: virtual

height inverted pendulum model, two masses inverted

pendulum model, multiple masses inverted pendu-

lum model, gravity compensated inverted pendulum

model, etc. (Siciliano and Khatib, 2008)

Spring loaded inverted pendulum model is one

of the best and simplest approximation that describes

the spring-like leg behavior of human and animal

walking or running (Garofalo et al., 2012). Spring

loaded inverted pendulum is represented by a point

mass that is attached to a massless spring with resting

length and leg stiffness.

The important question is what approaches to the

biped robot locomotion control should be applied in

order to supply energy efﬁciency and acceptable loco-

motion speed while maintaining stability of the robot.

Next, we brieﬂy describe a number of methods, which

are broadly applied for biped robot locomotion con-

trol by various research teams. According to (Manch-

ester et al., 2011) all the existing humanoid bipedal

walking robots could be roughly divided into two

groups: ZMP-controlled ones and passive-dynamic

walkers.

3.2 Approaches for Bipedal Robot

Locomotion Control

Zero moment point (ZMP) is a theoretical model of

biped locomotion where ZMP is deﬁned as a point

in which all the forces and moments can be replaced

with a single force and a single moment respec-

tively (Vukobratovic and Borovac, 2004). In other

words this method deﬁnes a special point where the

sum of horizontal inertial and gravitational forces

equals to zero (Erbatur and Kurt, 2006). In order

to maintain biped robot balance its ZMP should lie

within the boundaries of a predeﬁned stability region.

This approach plays a role of a criterion in the stabil-

ity analysis of biped robot locomotion and could be

considered as a dynamic analogue of CoM or center

of gravity (CoG) criterion for static stability analy-

sis (Magid et al., 2011). ZMP approach deﬁnes tra-

jectory of robot bodies without considering the load

of each particular joint which causes poor energy ef-

ﬁciency of the locomotion.

Passive walking method is based on the body’s

momentum. A biped robot which is actuated by this

method usually does not have any motors that pro-

duce forces for leg motion and the robot walks on an

inclined slope without applying any force (McGeer,

1990). It is rather efﬁcient for controlling robot loco-

motion because it creates movements in a similar way

a human does, but due to low stability for external

disturbances, this approach is not broadly used (Iribe

and Osuka, 2006).

Walking primitives is an approach which gener-

ates trajectories for the joints. Usually walking prim-

itives are calculated ofﬂine a-priori and next locomo-

tion planning algorithm generates a sequence of mo-

tions as a combination of these predeﬁned walking

primitives(Denk and Schmidt, 2003) in order to move

from the current posture and location to the goal lo-

cation. The main assumption in this approach is that

before and after applying a walking primitive acceler-

ations and velocities of all joints are equal to zero, and

therefore zero moment point always resides within a

support polygon (Magid et al., 2008). As an example,

a walking primitive can be realized by replacing the

center of pressure from one leg to another. In order

to combine two walking primitives together the initial

state of the second primitive should be the end state

of the previous one. This requirement is referred as a

precondition and a post-condition of a walking prim-

itive. Concatenating together several walking primi-

tives is used to generate locomotion of a biped robot.

This paper applies walking primitivesapproach which

is further described in Section 4.

Artiﬁcial neural networks approach is used to

learn the nonlinear dynamics of biped robot loco-

motion using a neuroadaptive control algorithm and

the robot achieves optimization criterion of dynamic

balance, such as ZMP. Given approach is broadly

used - for example, Boston Dynamics uses this ap-

proach for Atlas robot locomotion algorithms (Atmeh

et al., 2014). Major drawback of neural networks that

makes them less practical for real-time control ap-

plications are the exponential growth of the number

of parameters as a large-scale system becomes more

TowardaHuman-likeLocomotion:ModellingDynamicallyStableLocomotionofanAnthropomorphicRobotinSimulink

Environment

143

complicated.

Full-body posture goal approach to path plan-

ning for humanoid robots computes dynamically-

stable, collision-free trajectories from full-body pos-

ture goals (Kuffner et al., 2001). This method per-

forms a search through conﬁguration space of the

robot in order to ﬁnd a collision-free path to the goal

posture while keeping dynamic balance.

Dimension reduction techniques serve for re-

ducing calculation time: as a robot should make a

decision on a next state within a limited time, a sig-

niﬁcant calculation time may become a reason of an

algorithm’s failure. Thus reducing dimension of lo-

comotion equations directly inﬂuences feasibility of a

locomotion algorithm. Those techniques decrease di-

mension of variables, which are used in the equations

that describe control algorithms of a robot or even

could reduce the number of such equations (Stilman

et al., 2005).

4 MODELLING A STABLE BIPED

ROBOT LOCOMOTION IN

SIMULINK

Simulations became an important tool in robotics re-

search. It helps to create advanced designs, eval-

uate new control algorithms and investigate a wide

range of solutions for complicated problems. Sig-

niﬁcant advantage of such simulations is that there

is no need of constructing or modifying a real robot,

whereas simulated design solutions and experimental

conditionsdepend only on researcher’screativity. Nu-

merous software solutions for modeling multi-body

dynamical systems have been created specially for

robotic simulations, such as Gazebo

, V-Rep

, Mat-

lab/Simulink and others. The later provides efﬁcient

tools for modeling and simulating mechanical sys-

tems (e.g., SimMechanics tool) which save signiﬁcant

time and effort for researchers. SimMechanic uses the

standard Newtonian dynamics differential equations

and simulates 3D translational and rotational motion

by predicting the future state of a system from the

current state. SimMechanics has a great number of

tools to specify geometry, trajectories, mass distribu-

tion, constraints and instruments to initiate and mea-

sure motion, providing quite simple modeling of an

anthropomorphic robot (bodies, joints, and external

forces).

The equations of motion of a multibody system

http://gazebosim.org/

Coppelia Robotics, http://www.coppeliarobotics.com/

can be written in the following descriptor form:

˙q =

Hv (1)

M(q) ˙v = f (t,q,v) +

(q)G

(q,t)λ (2)

g(q,t) = 0 (3)

where t represents time, q is a vector of conﬁguration

variables; H is a kinematic relationship matrix be-

tween the velocity variable v and ˙q so that v = H(q) ˙q

with matrix

H denoting the right inverse of H; M(q)

is a mass matrix; f(t,q,v) represents the contribution

of centrifugal, Coriolis, and external forcing terms;

g(q,t) is a constraint equation and G(q,t) = ∂g/∂q

is a constraint Jacobian; λ represents the vector of

Lagrange multipliers associated with the constraint

forces (Wood and Kennedy, 2003).

In (Velasquez-Lobo et al., 2013) the authors

demonstrate an example of a biped robot model de-

sign and its locomotion veriﬁcation with SimMechan-

ics tool. Their model consists of ﬁve rigid bodies:

a torso (modelled as a parallelepiped) and identical

cylindrical shanks and thighs. These bodies are con-

nected with revolute joints with a single rotational

DoF in each joint and which sum up to 4 DoF in to-

tal. Unfortunately, such model simulates only the bot-

tom part of the robot with its torso moving only in a

sagittal plane relatively to the ﬁxed coordinate system

without rotation (2 DoF); this creates artiﬁcial condi-

tions which prevent the robot from falling down.

In this paper we present a biped robot model

which is free from the above mentioned limitations.

The following simulation steps were performed using

SimMechanics:

• Specify geometry of robot parts and their inertial

properties

• Create links between the robot part - connect the

bodies with rotational joints

• Set up ground reaction forces

• Provide reference signal for positions of each joint

• Start simulation, calling the Simulink solvers

• Visualize the model

Specifying robot geometry begins with deﬁning a

number of links and joints. Our current simpliﬁed

robot model consists of twelve bodies, which are con-

nected with revolute joints for knees, ankles, hips (one

rotational DoF) and ﬁxed (non-rotating) joints for a

neck, elbows and shoulders. The torso and feet have

a shape of a parallelepiped, a head is a sphere, and

all other bodies are cylinders; the body parameters are

described in details in Table 2. With regard to a global

ﬁxed coordinate system the torso has 3 DoF in sagit-

tal plane: a rotation and 2 translations in vertical and

ICINCO2015-12thInternationalConferenceonInformaticsinControl,AutomationandRobotics

144

horizontal directions. Figure 2 shows the model struc-

ture. SimMechanics block diagram of the whole robot

and its leg are shown in Fig. 3 and Fig. 4 respectively.

Figure 2: The robot model in Simulink.

Figure 3: SimMechanics block diagram for the biped robot.

Figure 4: SimMechanics block diagram for the leg.

Deﬁnition of ground contact forces is a very im-

portant issue in biped robot simulation and should

Table 2: Link parameters.

Torso parameters

a, m 0.3

b, m 0.2

c, m 0.5

Mass, kg 30

Shank and Thigh parameters

R, m 0.05

Length, m 0.4

Mass, kg 3.14

Head parameters

Radius, m 0.1

Mass, kg 2.1

Upper and lower arm parameters

R, m 0.01

Length, m 0.3

Mass, kg 0.75

Foot parameters

Width, m 0.1

Length, m 0.3

Height, m 0.05

Mass, kg 1.5

be carefully modeled. When robot’s feet touch the

ground, normal and tangential forces are applied.

There are several different approaches to calculate

these forces. In the current work foot-ground interac-

tion was modeled through a linear system with damp-

ing and stiffness. The following equation represents

normal forces:

= −k

y− b

˙y (4)

where y is the coordinate of the leg tip (y=0 corre-

sponds to ground surface), k

in the elastic constant

and b

is the damping coefﬁcient. Normal force ap-

plied only when y ≤ 0 (i.e. when the leg touches the

ground). In order to avoid leg sticking F

is limited to

positive values only.

The following equation represents tangential

force:

= −b

˙x (5)

where b

is the tangential damping coefﬁcient. Simi-

larly to normal force, tangential force is applied only

when y ≤ 0. The ground coefﬁcients k

should

be large (Table 3) in order to guarantee acceptable

small penetrations of feet below ground level (the re-

sponsible for penetration coefﬁcient is k

) and reason-

ably fast damping of contact velocity (the responsi-

ble for damping coefﬁcients are b

). Equation 5

TowardaHuman-likeLocomotion:ModellingDynamicallyStableLocomotionofanAnthropomorphicRobotinSimulink

Environment

145

Table 3: Ground parameters (coefﬁcients).

Coefﬁcient Label Value / Units

penetration k

1000000 N

normal damping b

10000 (N*s)/m

tangential damping b

1000 (N*s)/m

friction µ 10

works perfect at leg landing, whereas at leg raising a

so-called sticking effect emerges: we cannot provide

strict vertical movement and have a horizontal com-

ponent of velocity, which results in large tangential

force. To avoid this sticking effect, the absolute value

of tangential force should be limited to µF

, where µ

is a friction coefﬁcient. At leg landing normal force

value is large, so the tangential force will be large

enough to prevent the robot from sliding. At leg rais-

ing normal force F

is small enough to avoid sticking.

As far as the robot moves only in sagittal plane, there

are no contact forces in

Z direction.

There are several ways in SimMechanics to ac-

tivate robot locomotion. The simplest one is to set

positions of revolute joints. SimMechanics module

calculates necessary torques to achieve desired angles

in joints at each time step. These nominal trajectories

can be set up a-priori, e.g., by utilizing motion capture

system. In our work we realized dynamically stable

robot motion using the method of walking primitives

described in Section 3.2. It means that robot move-

ment is divided into identical periods with walking

primitives, at the beginning and at the end of which

the robot returns to the same position. The leg move-

ment pattern is the same in each primitive and can be

divided into four phases (assuming generically that

the step primitive starts from the left foot): (1) lift

the left foot by specifying desired angles for hip and

knee joints; (2) perform the inverted pendulum mo-

tion until the left foot touches the ground; (3) move

the right foot forward by specifying the joint angles

which make the knee and the hip joint angles equal to

zero; (4) damp forward motion by applying torque in

the ankles. Next, the same phases are repeated start-

ing the step from the right leg. The input signals for

the knee and thigh joint positions of the robot’s legs

are shown in Fig. 5– 8.

In the last walking phase the robot’s forward mo-

tion is damped by applying torque in ankles when

hip and knee joint angles become zero. The value of

torque is calculated according to the following equa-

tion:

T = −cφ − d

φ (6)

where φ is the ankle joint angle, c=10 is stiffness, d=4

is the damping coefﬁcient. Equation 6 is a standard

Figure 5: The input angle for the right knee.

Figure 6: The input angle for the left knee.

Figure 7: The input angle for the right hip.

Figure 8: The input angle for the left hip.

representation of damping oscillations. As far as os-

cillations cannot be damped simultaneously, a pause

△t is required before starting new movement with an-

other leg.

5 SIMULATION RESULTS

To solve differential equations described above, the

Simulink solver method ”ODE 23t” was used. Fig. 9

shows a sequence of the biped robot frames at differ-

ent time while performing a single step. The smooth

character of simulated robot walking illustrates rea-

sonable settings for the angle positions of the joints

and contact forces within the model. The horizontal

locomotionof the torso center with the mean robot ve-

locity of 0.3-0.4 m/s is shown in Fig. 10, demonstrat-

ing the periodical body movement during two second

time period. At the beginning of each motion period

the body velocity is zero. Torque values in the hip

and the knee joints obtained from the simulation are

shown in Fig. 11-14, which help to estimate motor

characteristics.

The simulation shows that maximum torque is ap-

proximately 500 N*m in the thigh joint and 300 N*m

ICINCO2015-12thInternationalConferenceonInformaticsinControl,AutomationandRobotics

146

Figure 9: A single step of the biped robot. The robot moves

from right to left as the time passes.

Figure 10: Horizontal velocity of torso.

Figure 11: Torque in the left knee.

Figure 12: Torque in the right knee.

Figure 13: Torque in the left hip.

Figure 14: Torque in the right hip.

in the knee joint. At the same time we see discon-

tinuous jumps in calculated torque values, which are

caused by discontinuities in ground reaction forces.

Torque values in ankles are shown in Fig. 15 and

Fig. 16. As it was expected, torque is applied only

in the last phase of robot’s motion in order to damp

robot’s movement. In our work the duration of one

Figure 15: Torque in the left ankle.

Figure 16: Torque in the right ankle.

walking primitive is 2 seconds with a pause of

△t = 0.5 seconds between the primitives.

6 CONCLUSIONS AND FUTURE

WORK

Our research is focused on creating effective hu-

man like locomotion for the novel anthropomorphic

human-size Russian robot AR-601M. In this paper

we introduced AR-601M biped robot, and presented

its simpliﬁed model with 11 DoFs. The simulation

model has been implemented in Matlab/Simulink us-

ing SimMechanics tool. This model uses walking

primitives in order to provide a dynamically stable lo-

comotion and serves as a starting point for the stable

bipedal locomotion algorithms development for the

AR-601M robot. The smooth character of simulated

robot walking with the mean velocity of 0.3-0.4 m/s,

reasonable settings for the angles of joints and contact

forces illustrates the suitability of the proposed robot

model.

Next we are going to extend this simpliﬁed model

by increasing the number of DoFs (i.e. the num-

ber of robot joints) in order to match the simulation

robot model to the exact kinematic structure of AR-

601M. To achieve AR-601M anthropomorphic walk-

ing, the human walking data will be acquired and

analyzed by Motion Capture (MoCap) system with

the key features detection for a human gait. They

will be initially mapped to the AR-601M locomotion

within Matlab/Simulink simulation and then into the

real robot gait together with the adaptive gait genera-

tion algorithm with the ZMP control. To apply these

algorithms with a real robot it is also required to de-

velop algorithms for sensory data collection and pro-

cessing; in turn, these modules will provide input for

decision-making and control actions computation al-

gorithms.

TowardaHuman-likeLocomotion:ModellingDynamicallyStableLocomotionofanAnthropomorphicRobotinSimulink

Environment

147

ACKNOWLEDGEMENTS

This research has been supported by Russian Min-

istry of Education and Science as a part of Sci-

entiﬁc and Technological Research and Develop-

ment Program of Russian Federation for 2014-2020

years (agreement 14.609.21.0004, research grant

ID RFMEFI60914X0004) and by Android Technics

company, the industrial partner of the research.

REFERENCES

Amirabdollahian, F., Dautenhahn, K., Dixon, C., Eder, K.,

Fisher, M., Koay, K., Magid, E., Pipe, T., Salem, M.,

Saunders, J., and Webster, M. (2013). Can you trust

your robotic assistant? In 5th International Confer-

ence in Social Robotics. Springer.

Atmeh, G., Ranatunga, I., Popa, D., Subbarao, K., Lewis,

F., and Rowe, P. (2014). Implementation of an adap-

tive, model free, learning controller on the atlas robot.

In IEEE American Control Conference.

Denk, J. and Schmidt, G. (2003). Synthesis of walk-

ing primitive databases for biped robots in 3d-

environments. In IEEE International Conference on

Robotics and Automation.

Erbatur, K. and Kurt, O. (2006). Humanoid walking robot

control with natural zmp references. In IEEE Annual

Conference on Industrial Electronics.

Fink, J. (2012). Anthropomorphism and human likeness in

the design of robots and human-robot interaction. In

Social Robotics. Springer.

Garofalo, G., Ott, C., and Albu-Schaffer, A. (2012). Walk-

ing control of fully actuated robots based on the

bipedal slip model. In IEEE International Conference

on Robotics and Automation.

Holmes, P., Full, R., Koditschek, D., and Guckenheimer, J.

(2006). The dynamics of legged locomotion: Models,

analyses, and challenges. Siam Review, vol. 48(2).

Ijspeert, A. J. (2008). Central pattern generators for loco-

motion control in animals and robots: a review. In

Neural Networks.

Iribe, M. and Osuka, K. (2006). A designing method of

the passive dynamic walking robot via analogy with

the phase locked loop circuits. In IEEE International

Conference on Robotics and Biomimetics.

Kuffner, J., Nishiwaki, K., Kagami, S., Inaba, M., and In-

oue, H. (2001). Motion planning for humanoid robots

under obstacle and dynamic balance constraints. In

IEEE International Conference on Robotics and Au-

tomation.

Magid, E., Ozawa, K., Tsubouchi, T., Koyanagi, E.,

and Yoshida, T. (2008). Rescue robot navigation:

static stability estimation in random step environment.

In Simulation, Modeling, and Programming for Au-

tonomous Robots. Springer Berlin Heidelberg.

Magid, E., Tsubouchi, T., Koyanagi, E., and Yoshida, T.

(2011). Building a search tree for a pilot system of a

rescue search robot in a discretized random step envi-

ronment. In Journal of Robotics and Mechatronics.

Manchester, I., Mettin, U., Iida, F., and Tedrake, R. (2011).

Stable dynamic walking over uneven terrain. In

The International Journal of Robotics Research. Sage

Publications.

McGeer, T. (1990). Passive dynamic walking. In The Inter-

national Journal of Robotics Research, vol.9(2).

Siciliano, B. and Khatib, O. (2008). Biped robots in the zmp

scheme. In Springer Handbook of Robotics. Springer.

Stephens, B. and Atkeson, C. (2009). Modeling and control

of periodic humanoid balance using the linear biped

model. In IEEE-RAS International Conference on Hu-

manoid Robots.

Stilman, M., Atkeson, C., Kuffner, J., and Zeglin, G.

(2005). Dynamic programming in reduced dimen-

sional spaces: Dynamic planning for robust biped lo-

comotion. In Robotics Institute, vol.73.

Velasquez-Lobo, M., Ramirez-Cortes, J., Rangel-

Magdaleno, J., and Vazquez-Gonzalez, J. (2013).

Modeling a biped robot on matlab/simmechanics.

In IEEE International Conference on Electronics,

Communications and Computing.

Vukobratovic, M. and Borovac, B. (2004). Zero-moment

point - thirty ﬁve years of its life. In International

Journal of Humanoid Robotics, vol.1(1).

Wood, G. D. and Kennedy, D. C. (2003). Simulating

mechanical systems in simulink with simmechanics.

Tech. Rep., The MathWorks.

Wright, J. and Jordanov, I. (2014). Intelligent approaches

in locomotion - a review. Journal of Intelligent and

Robotic Systems.

Wu, Q., Liu, C., Zhang, J., and Q.Chen (2009). Survey of

locomotion control of legged robots inspired by bio-

logical concept. Science in China Series F: Informa-

tion Sciences, vol.52(10).

Zajac, F. E., Neptune, R. R., and Kautz, S. A. (2003).

Biomechanics and muscle coordination of human

walking: part ii: lessons from dynamical simulations

and clinical implications. Gait and posture, vol.17(1).

ICINCO2015-12thInternationalConferenceonInformaticsinControl,AutomationandRobotics

148