VARIABLE GEOMETRY TRACKED UNMANNED GROUNDED

VEHICLE

Model, Stability and Experiments

Jean-Luc Paillat, Phillipe Lucidarme and Laurent Hardouin

Laboratoire d’Ing

enierie des Syst

emes Automatis

es (LISA), 62 Avenue Notre Dame du Lac, Angers, France

Keywords:

UGV (Unmanned ground vehicle), Variable Geometry Single Tracked Vehicle (VGSTV), Obstacle clearing

capabilities, Teleoperation, Stability, Geometric model, Dynamic model.

Abstract:

This paper introduces an originally designed tracked robot. This robot belongs to the VGSTV (Variable

Geometry Single Tracked Vehicle) category. It is equipped with two tracks mounted on an actuated chassis.

The ﬁrst joint is used to articulate the chassis and the second one to keep the tracks tightened. By controlling

the chassis joint it becomes possible to adapt the shape of the tracks to the ground and even to release the

tracks in order to pass through speciﬁc obstacles. A prototype has been build ; technical speciﬁcations and

dynamic model are presented in this paper. Tele-operated experiments have been conducted and have shown

that the stability of the robot have to be addressed. We experimented and compared two classical criterions

based on the center of mass and on the zero moment point technique. Experimental results are discussed in

the case of a staircase clearing.

1 INTRODUCTION

UNMANNED GROUNDED VEHICLE (UGV) is a

topically research ﬁeld applied to a wide range of ap-

plications like for example exploration or missions

in hostile environments. Research laboratories and

robotics companies are currently working on the de-

sign of tele-operated and autonomous robots. Accord-

ing to (Casper and Murphy, 2003) and (Carlson and

Murphy, 2005) UGVs can be classiﬁed into three cat-

egories :

• Man-packable delineates the robots that can be

carried by one man in backpacks.

• Man-portable delineates the robots that are too

heavy to be easily carried by men, but small

enough to be transported in a car or a HUMMV.

• Not man-portable delineates the robots that must

be carried by a truck, a trailer or a crane.

The robots presented in this paper are classiﬁed

in the man-packable and man-portable categories. In

this class of robots, designers have to face the follow-

ing dilemma: on one hand, build a small robot that

can be easily carried and move into narrow environ-

ments. Unfortunately, it will generally result in poor

obstacle clearing capability. On the other hand, build

a bigger robot will increase its ability to surmount ob-

stacles but will not enable the robot to go through nar-

row openings. The challenge is then to build a robot

as small as possible with the higher obstacle clear-

ing capability. Based on this observation the ﬁrst part

of this paper introduces the existing experimental and

commercial robots and discusses about their clearing

capabilities. The following of the paper describes

an originally designed UGV (Fig. 2b). This robot

can be classiﬁed into the Variable Geometry Single

Tracked Vehicle (VGSTV) category, i.e. it has the

mechanical ability to modify its own shape according

to the ground conﬁguration. The design of our proto-

type is described in the third part with a short discus-

sion about the technical choices (information can be

found on the project website: http://www.istia.univ-

angers.fr/LISA/B2P2/b2p2.html). The next section

introduces the dynamic model of the robot. The ﬁrst

tele-operated experiments have shown that the mass

distribution is crucial to pass through large obstacles.

This is why the last section discusses about the sta-

bility of the robot. The presented survey has been

conducted for three reasons. First of all, the informa-

tion computed about the stability of the robot may be

useful to the operator during tricky operations. Sec-

ondly, this information may also be used to automati-

cally disable clumsy commands and prevent the robot

Paillat J., Lucidarme P. and Hardouin L. (2009).

VARIABLE GEOMETRY TRACKED UNMANNED GROUNDED VEHICLE - Model, Stability and Experiments.

In Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Robotics and Automation, pages 21-28

DOI: 10.5220/0002182000210028

 SciTePress

from toppling over. And ﬁnally, the stability cannot

be ignored during autonomous motion which is our

long term goal. The survey has been conducted on

two criterions : static (the center of mass) and dy-

namic (based on the well known zero moment point

technique). Experimental results are compared and

discussed in the case of a staircase clearing. A gen-

eral conclusion ends the paper.

2 EXISTING UGVs

2.1 Wheeled and Tracked Vehicles with

Fixed Shape

This category gathers non variable geometry robots.

Theoretically, this kind of vehicles are able to climb a

maximum step twice less high than their wheel diam-

eter. Therefore their dimensions are quite important

to ensure a large clearing capability. This concep-

tion probably presents a high reliability (Carlson and

Murphy, 2003) but those robots cannot be easily used

in unstructured environments like after an earthquake

(Casper and Murphy, 2003).

Figure 1: a) Talon-Hazmat robot (Manufacturer: Foster-

Miller) b)ATRV-Jr robot. Photo Courtesy of AASS,

Orebro

University.

2.2 Variable Geometry Vehicle

A solution to ensure a large clearing capability and to

reduce the dimensions consists in developing tracked

vehicles which are able to modify their geometry in

order to move their center of mass and climb higher

obstacles than their wheel’s diameters.

Figure 2: a)Packbot (manufacturer: IRobot), b)RobuROC

6(Manufacturer: Robosoft) c)Helios VII.

The Packbot robot (Fig. 2a) is probably one of the

most famous commercial VGTV (Variable Geometry

Tracked Vehicle). This robot is equipped with tracks

and two actuated tracked ﬂippers (372 mm long). The

ﬂippers are used to step over the obstacles. The obsta-

cle clearing capability of this kind of VGTV depends

on the size of the ﬂippers. For more information and a

detailed survey on clearance capability of the Packbot

the reader can consult (Frost et al., 2002).

The robuROC6 (Fig. 2b) is equipped with 46.8

cm diameters wheels and can clear steps until 25cm

(more than half the diameter of the wheels). Joints

between the axles make this performance possible.

An other original system called Helios VII (Fig 2c)

(Guarnieri et al., 2004) is equipped with an arm ended

by a passive wheel which is able to elevate the chassis

along a curb.

2.3 Variable Geometry Single Tracked

Robots

Actually, there is a subgroup in VGTV called Variable

Geometry Single-Tracked Vehicles (VGSTV) (Kyun

et al., 2005). It gathers robots equiped with as tracks

as propulsion motors. In most cases those robots are

equipped with one or two tracks (one for each side).

It can be divided into two groups :

• robots with deformable tracks,

• robots with non deformable tracks.

2.3.1 Non-deformable Tracks VGSTV

Figure 3: a) Micro VGTV (manufacturer: Inuktun Ltd)

b)B2P2 prototype c)VGSTV mechanism.

The most famous example is the Micro VGTV. Il-

lustrations of a prototypes manufactured by the com-

pany Inuktun are presented on Fig. 3a. This robot

is based on an actuated chassis used to modify the

shape of the robot. The right picture of Fig. 3a shows

the superimposing conﬁgurations. The tracks are kept

tightened by a passive mechanism. The robot is thus

equipped with three motors: two for the propulsion

and one for the chassis joint.

Non commercial vehicles exists in the literature

as the VGSTV mechanism (Fig. 3c) which is ded-

icated to staircase clearing. It is composed of two

tracks and two articulations which allow it to have

many symmetrical conﬁgurations such as a rectangle,

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

trapezoids, inverse trapezoids etc.

Many other VGTV architecture exist, for further

information reader can consult (Vincent and Tren-

tini, 2007), (Misawa, 1997), (Clement and Villedieu,

1987), (Guarnieri et al., 2004) and (Kyun et al., 2005).

2.3.2 Deformable Tracks VGSTV

Some single tracked robots have the ability to modify

the ﬂexing of their tracks. Two examples presented

on Fig. 4, are able to adapt their shape to obstacles

(Kinugasa et al., 2008). However, even if the control

of the robot seems easier with a ﬂexible track than

with a non ﬂexible one, the mechanical conception

could be more complicated.

Figure 4: a) Viper robot (Manufacturer: Galileo) b)Rescue

mobile track WORMY.

According to the presented state of the art, for gen-

eral purpose missions we beleive that the best com-

promise between design complexity, reliability, cost

and clearing capabilities is the Variable geometry sin-

gle tracked robots category. The next section will in-

troduce and describe our prototype of VGSTV.

3 PROTOTYPE DESCRIPTION

The main interest of VGSTV (equipped with de-

formable tracks or not) is that it is practicable to

overcome unexpected obstacles (Kyun et al., 2005).

Indeed, thanks to the elastic property of the tracks

the clearance of a rock in rough terrain will be more

smoothly with a VGSTV (e. g. Fig 3 and 4) than with

a VGTV (Fig. 2). On the Micro VGTV presented

on Fig. 3, the tension of the tracks is mechanically

linked with the chassis joint so it is constant during

the movement. Nevertheless, in some cases, less

tense tracks could increase the clearance capability

by increasing the adherence. An interesting study

about this point was developed by (Iwamoto and

Yamamoto, 1983) giving a VGSTV able to climb

staircases where the tension of the tracks was me-

chanically managed as on the MicroVGTV (Fig. 3a).

However, this system was equipped with a spring to

allow the tracks to adapt their shape to the ground

(depending on the strength of the spring).

Figure 5: B2P2: clearing of a curb.

The conception of our prototype is based on this

previous work, but we decided to actuate the tension

of the tracks. Indeed, by using two motors instead

of one (Fig. 6) it is possible to increase the tracks

adaptation to the ground developed by (Iwamoto and

Yamamoto, 1983) and reach new conﬁgurations for

the robot. As example, the solution proposed in this

paper allows our robot to adopt classical postures of

VGSTV (Fig. 5(a), 5(b) and 5(c) ), but also other in-

teresting positions. On Fig. 5 B2P2 is clearing a curb

of 30 cm height with tense tracks. The position of the

robot on Fig 5(c) can also be obtained with the Mi-

cro VGTV, but it is a non-safety position and B2P2 is

close to topple over. On Fig. 5(d) the tracks have just

been released. They take the shape of the curb and it

can be cleared safely. This last conﬁguration outlines

the interest of using an active system instead of a pas-

sive one. Consequently, although our prototype (Fig.

3b) belong to the VGSTV category and have not de-

formable tracks, it has the ability to adapt them to the

ground (as deformable ones).

Besides, even if there is a risk of the tracks coming

off, loosening the tracks may be an efﬁcient mean of

increase the surface in contact with the ﬂoor in rough

terrain and then to improve the clearing capability of

the structure. By the way, the risk could decreased

by using sensor based systems to control the tension

of the tracks or by modifying the mechanical struc-

ture of the robot (adding some kind of cramps on the

tracks or using a guide to get back the tracks before it

comes off).

3.1 Mechanical Description

This UGV is equipped with four motors. Fig. 6

presents the integration of the motors in the robot.

Motors 1 and 2 are dedicated to the propulsion

(tracks).

The actuated front part is composed of motors 3

and 4 :

• Motor 3 actuates the rotational joint, it allows the

rotation of the front part around the second axle.

• Motor 4 actuates a driving screw, it controls the

VARIABLE GEOMETRY TRACKED UNMANNED GROUNDED VEHICLE - Model, Stability and Experiments

distance between the second axle and the third

one.

Figure 6: Overview of the mechanical structure, side and

top view of the real robot.

To keep the tension of the tracks the trajectory of

the third axle is given by an ellipse deﬁned by two

seats located on the ﬁrst and the second axle.

L + (L

+ L

) = K (1)

where the lengths L, L

and L

are referenced on

Fig. 6. K is a constant parameter depending on the

length of the tracks, L

evolves in order to achieve

equality (1) and is linked to the angle θ in the follow-

ing manner:

− K

2(L

cos(π− | θ |) − K)

− L

(2)

3.2 Sensors and Command Systems

The robot is equipped with multiple sensors, on-

board/command systems and wireless communica-

tion systems.

• Onboard command systems :

– PC104 equipped with a Linux OS compiled

speciﬁcally for the robot needs based on a LFS

(Home made light linux distribution).

– An home-made I2C/PC104 interface.

– Four integrated motor command systems run-

ning with RS232 serial ports.

– Four polymer batteries which allow more than

one hour of autonomy.

• Sensors :

– An analog camera for tele-operation.

– A GPS to locate the robot in outdoor environ-

ments.

– A compass to know the orientation of the robot.

– A two axis inclination sensor (roll and pitch).

• Wireless communication systems :

– A 2.4 GHz analog video transmitter.

– A bidirectional 152 MHz data transmitter.

4 DYNAMIC MODEL

Z4, X 5, Z1

Z5, X 6

O4, O5, O6

Y 0

+ L

Figure 7: B2P2’s geometric model. Joints 1,2 and 3 rep-

resents the robot position. Joints 4, 5 and 6 symbolize re-

spectively the yaw, roll and pitch, 7 and 8 are the actuated

joints.

This section deals with the dynamic model of the

robot which is based on the geometric model (Fig. 7)

detailed on (Paillat et al., 2008). According to this

model, the robot motion in a 3D frame (R

) is de-

scribed by the vector q of the 8 joints variables :

q = [q

]

The dynamic model of a mechanical system es-

tablishes a relation between the effort applied on the

system and its coordinates, generalized speeds and ac-

celerations ((Craig, 1989) and (Khalil and Dombre,

2004)). In this section, the following notations are

used:

• j describes the joints from 1 to 8,

• i describes the segments from 1 to 3 (referenced

on Fig 6),

• n and m describes indexes from 1 to 8.

4.1 The Dynamic Equations

The general dynamic equations of a mechanical sys-

tem is:

∂ L

∂ ˙q

−

∂ L

∂ q

= Q

+ T

(3)

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

• L is the Lagrangien of the system. It is composed

of rigid segments, so there is no potential energy.

Although the Lagrangien corresponds to the ki-

netic energy.

• q

is the j

joint variable of the system.

• Q

is the gravity’s torque applied to the j

joint

of the system.

• T

is the external force’s torque applied to the j

joint of the system.

The kinetic energy is given by:

K =

∑

i=1

. (4)

• m

is the mass of the i

element of the model,

• v

is the linear speed of the i

element’s center of

gravity,

• w

is the angular speed of the i

element’s center

of gravity,

• I

is the matrix of inertia of the i

element of the

system.

In order to have homogeneous equations, w

is de-

ﬁned in the same frame as I

; it allows to formulate v

and w

according to q :

= J

(q) ˙q (5)

= R

0 j

(q) ˙q (6)

where J

and J

are two matrices and R

0 j

is the

transport matrix between the frame R

and the frame

j linked to the segment i.

The kinetic energy formula is:

K =

˙q

∑

(q)

(q) + J

(q)R

0 j

(q)] ˙q

(7)

which can be rewritten as :

K =

˙q

D(q) ˙q (8)

by developing the previous formula, we obtain :

K =

∑

m,n

(q) ˙q

˙q

(9)

where d

m,n

(q) is the m, n

element of the matrix D(q).

The gravity’s torque is given by:

∑

∂ G

∂ q

. (10)

• G

is the z coordinate of the CoG of the i

seg-

ment’s computed in the base frame (R

• g is the gravity acceleration.

Vector T (deﬁned in (3)) is composed of the

external forces’ torque. For the robot presented here,

there is no consideration of external forces, so the T

vector only describes the motorized torques. Joints

1, 4, 7 and 8 are motorized, so the vector T is given

by those four parameters. T

and T

are computed

from the torques of motors 1 and 2 while T

and T

are deduced from motors 3 and 4.

The Euler-Lagrange equations can be written as:

∑

(q) ¨q

∑

n,m

nm j

(q) ˙q

˙q

= Q

+ T

(11)

nm j

[

∂ d

∂ q

∂ d

∂ q

−

∂ d

∂ q

] (12)

which is classically written as:

D(q) ¨q +C(q, ˙q) ˙q = Q + T (13)

where D(q) represents the matrix of inertia and

C(q, ˙q) the centrifuge-coriolis matrix where X

, the

element of this matrix, is deﬁned as :

∑

nm j

˙q

Finally, the J

and J

matrix considered in (5)

and (6) have to be computed.

4.2 J

and J

Matrix Formulation

The matrix which links articular speed and general

speed of a segment is computed from the linear and

angular speeds formulas. The goal is to ﬁnd a matrix

for each segment. They are composed of 8 vectors

(one for each joint of the model).

The computation consists in formulating in the

base frame, the speed (V

( j − 1, j)

) of a point P

given by a motion of the joint q

attached to the frame

j according to the frame j − 1. Those parameters

can be deduced from the law of composition speeds

and the Denavitt Hartenberg (DH) formalism used for

the geometric model (Paillat et al., 2008). Indeed,

the general formulation is simpliﬁed by the geometric

model. Only one degree of freedom (DoF) links two

frames using the DH model and this DoF is a revolute

or a prismatic joint. Moreover, the Z axis is always the

rotation or translation axis, so the angular and linear

speeds are given by four cases:

• The angular speed of a point for a revolute joint:

VARIABLE GEOMETRY TRACKED UNMANNED GROUNDED VEHICLE - Model, Stability and Experiments

( j − 1, j)

= R

0, j









˙q

. (14)

• The linear speed of a point for a revolute joint:

( j − 1, j)

= V

j−1

+ w

∧ O

= ˙q

0, j









∧ R

0, j

(15)

• The angular speed of a point for a prismatic joint:

( j − 1, j) =









. (16)

• The linear speed of a point for a prismatic joint:

( j − 1, j)

= R

0, j









˙q

(17)

where P

is the P point’s coordinates in R

Thus, the matrix of a segment i is formulated by com-

puting speeds for each joints as :





= J(q) ˙q = [J

1,i

(q),J

2,i

(q),...J

8,i

(q)] ˙q (18)

where J

j,i

(q) is a vector which links the speed of

the i

segment according to the j

joint. The ﬁrst

segment is not affected by the motion of joints 7 and

8 while the second is not affected by joint 8, therefore

7,1

(q), J

8,1

(q) and J

8,2

(q) are represented by a null

vector.

5 BALANCE CRITERION

The balance criterion used here are the ZMP (Zero

Moment Point), widely used for the stability of hu-

manoid robots and the Center of Gravity (CoG). Pre-

vious theoretical works and experiments have proved

the ZMP efﬁciency (Vukobratovic and Borovac,

2004). It consists in keeping the point on the ground

at which the moment generated by the reaction forces

has no component around x and y axis ((Kim et al.,

2002) and (Kajita et al., 2003)) in the support poly-

gon of the robot. When the ZMP is at the border of

the support polygon the robot is teetering. Unlike the

ground projection of the center of gravity, it takes into

account the robot’s inertia.

The purpose of the following is to deﬁned the co-

ordinates of this point in any frame of the model ac-

cording to the conﬁguration of the robot. The deﬁni-

tion can be implemented into the Newton equations

to obtain those coordinates. In any point of the model

: M

= M

+ OZ ∧ R (M

and M

deﬁne respectively

the moment generated by the reaction force R at the

points 0 and z).

According to the previous deﬁnition, there is no

moment generated by reaction forces at the Zero Mo-

ment Point. Consequently, if Z deﬁnes the ZMP co-

ordinates M

= OZ ∧ R. This formulation can be im-

plemented into the Newton equations as:

= M

OG ∧

P +

OG ∧

(19)

where P is the gravity force, G is the robot’s center

of gravity and F

is the inertial force (the ﬁrst New-

ton’s law gives F

= −m

G). According to the ZMP

deﬁnition, the equation (19) can be formulated as :

OZ ∧

R +

OG ∧

P +

OG ∧

(20)



= Z

+ G

− G

= −Z

+ G

− G

(21)







−G

−δ

−G

(22)

Also, it is possible to compute the position of the

ZMP as a function of q (δ

depends on the matrix

D(q)).

Assuming the ground knowledge, the ZMP com-

putation gives a criterion to determinate the stability

of the platform.

6 RESULTS

This section presents the numerical computation of

the criterion in the case of the clearance of a stair-

case (staircase set of 15 cm risers and 28 cm runs)

with an average speed of 0.13 m.s

−1

(Fig. 9). The

robot is equipped with a 2-axis inclination sensor that

provides rolling and pitching. Vector q entries are

measured using encoders on each actuated axis of the

robot. Data have been stored during the experiments

and the models (CoG and ZMP) have been computed

off-line. This computation does not take into account

the tracks’ weight which is negligible in regard to the

robot’s weight. Fig. 8 presents the evolution of the

ZMP (left) and the difference between those two cri-

terion (right) during all the clearance. P

and P

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

Figure 8: Experiment’s results. The left chart represents the evolution of the ZMP and the right one, the difference between

CoG and ZMP.

represents the z-coordinates in the frame R

(Fig. 7)

of three points of the robot which localization are no-

ticed on Fig. 6.

The following section ﬁnely details the results of

the experiment and the correlation with the sensors

data is described. This analyze is divided into three

parts: the approach of the ﬁrst step, the clearance of

the middle steps and the clearance of the ﬁnal step.

6.1 The Clearance of the First Step

Figure 9: Clearance of a staircase.

First of all, the robot is approaching while moving

up the front part (Fig. 9(a)) in order to go onto the ﬁrst

step. Then, it has to move forward and move down

the elevation articulation in order to keep the stability

(Fig. 9(b)). Once the robot is step onto the ﬁrst stair,

the operator have to switch in the next conﬁguration.

The area noted A1 on Fig. 8 shows the evolution of the

ZMP projection during the clearance of the ﬁrst step.

Note that the tracks are tense because when the front

part is rising up, there is a large difference between P

and P

6.2 The Clearance of the Middle Steps

This stage starts in the position noticed on Fig. 9(c).

By moving forward, the robot naturally climbs the

stairs. At each step, the robot is gently swaying when

the ZMP is passing over the step. This phenomenon

is illustrated by the oscillation of the ZMP which are

visible on the area noted A2 on Fig. 8. Note that, this

oscillation is dependent on the ratio between the size

of the robot and the size of the steps (”size-step” ra-

tio). It fully disappears when the length of the robot

is superior to the size of three steps. On the other

hand, oscillations may be more important until reach-

ing a ”size-step” ratio where the robot cannot climb

the step.

6.3 The Clearance of the Final Step

The robot is moving forward while moving down its

front part (Fig. 9(d)). This operation brings the ZMP

closer to the limits of the support polygon, i.e. the

corner of the last step. This operation allows a smooth

swing of the ZMP. Area A3 on Fig. 8 shows the evo-

lution of the ZMP during the clearing of the last step.

Note that the tracks releasing was not used dur-

ing this experiment because it was not necessary to

overcome this staircase. It could become essential for

bigger obstacles.

This experiment allows us to validate the pre-

sented model and conﬁrms the computation of the

ZMP criterion. However, as it is shown on Fig. 8, the

average difference between the ZMP and the COG is

insigniﬁcant (about 0.21%). Moreover, the two peaks

(A and B) on the Fig. 8 are not due to the dynamics of

the system but to measurement errors. As the accel-

eration is measured with the encoders (linked to the

motor shaft), when the tracks slip, the measurement

is erroneous. The ZMP is computationally more ex-

pensive, needs more sensor measurements and the dif-

ference with the CoG is negligible. For these reasons,

we conclude that the CoG seems well suited for this

kind of experiments. Anyway, in the case where fast

obstacle clearance may be necessary, the CoG may

not longer be considered and the ZMP must be used

instead.

VARIABLE GEOMETRY TRACKED UNMANNED GROUNDED VEHICLE - Model, Stability and Experiments

7 CONCLUSIONS

In this paper, an original prototype of VGSTV has

been presented. The dynamic model have been intro-

duced. From this model, a stability criterion based on

the ZMP technique has been computed. This model

have been validated on the real robot in the context of

a staircase clearance.

Future works will focus on the autonomy of the

robot. In a short term work, a real time stability as-

sistance will be provided to the operator based on the

model (CoG or ZMP) presented in this paper. The

presented results are also a preliminary survey for

a long term work that will be oriented on the au-

tonomous obstacle clearance. Actual work (based on

the model and results presented here) is focused on

the automatic control of the robot.

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