ROBUST SENSOR BASED NAVIGATION FOR AUTONOMOUS

MOBILE ROBOT

Immanuel Ashokaraj, Antonios Tsourdos, Peter Silson and Brian White

DAPS Department, RMCS, Cranﬁeld University,

Shrivenham, Swindon, UK - SN6 8LA

Keywords:

Interval analysis, Robotics, Navigation.

Abstract:

This paper describes a new approach for mobile robot navigation using an interval analysis based adaptive

mechanism for an Unscented Kalman ﬁlter. The robot is equipped with inertial sensors, encoders and ultra-

sonic sensors. The map used for this study is two-dimensional and it is assumed to be known a-priori. Multiple

sensor fusion for robot localisation and navigation has attracted a lot of interest in recent years. An Unscented

Kalman Filter (UKF) is used here to estimate the robots position using the inertial sensors and encoders. Since

the UKF estimates are affected by bias, drift etc, we propose an adaptive mechanism using interval analysis

with ultrasonic sensors to correct these defects in estimates. Interval analysis has been already successfully

used in the past for robot localisation using time of ﬂight sensors. But this IA algorithm has been extended to

incorporate the sensor range limitation as in many real world sensors such as ultrasonic sensors. One of the

problems of the use of interval analysis sensor based navigation and localisation is that it can be applicable

only in the presence of land marks. This problem is overcome here using additional sensors such as encoders

and inertial sensors, which gives an estimate of the robot position using an Unscented Kalman ﬁlter in the

absence of land marks. In the presence of land marks the complementary robot position information from the

Interval analysis algorithm using ultrasonic sensors is used to estimate and bound the errors in the UKF robot

position estimate.

1 INTRODUCTION

Robot navigation is primarily about guiding a mobile

robot to a desired destination or along a pre-speciﬁed

path in which the robots environment consists of land-

marks and obstacles. In order to achieve this objective

the robot needs to be equipped with sensors suitable

to localize the robot throughout the path it has to fol-

low. Most of these sensors may give overlapping or

complementary information and sometimes be redun-

dant as well. There are many different architectures to

fuse these information. Mobile robots generally carry

dead reckoning sensors such as wheel encoders and

inertial sensors, such as accelerometers, gyroscopes,

to measure acceleration, angle rate and obstacle de-

tecting and map making sensors such as time of ﬂight

ultrasonic sensors. All these sensor measurements

can be fused to estimate the robots position by us-

ing a sensor fusion algorithm. Sensor fusion in this

case is the method of integrating data from distinctly

different sensors to estimate the robots position.

Classical data fusion algorithms use stochastic ﬁl-

ters such as Kalman ﬁlters for robot position estima-

tion (Jetto et al., 1999). But one of the main disad-

vantages of using Kalman ﬁlters with ultrasonic sen-

sors for robot localisation problems is that the data

association step in Kalman ﬁlters is complex and also

the fact that they are often affected by bias and drift.

Moreover an accurate model of the robot system and

accurate statistics of the sensor noises are needed,

which is not available accurately in many cases.

The paper is organised as follows. This introduc-

tory section continues by presenting a background for

the problem of autonomous robot localisation in sec-

tion 1.1, followed by a summary of previous work

in robot localisation using IA and standard stochas-

tic ﬁlters in section 1.2. The novelty of the proposed

approach is presented in section 1.3. Section 2 ex-

plains the implementation of the UKF with inertial

sensors and encoders for this problem. Section 3 gives

a brief explanation of the interval analysis algorithm

for robot localisation and also describes how the sen-

sor range limitation is corporated and when multiple

sets of ultrasonic sensor measurements are taken. In

section 4 the implementation of the adaptive mech-

anism for the UKF robot position estimation using

Ashokaraj I., Tsourdos A., Silson P. and White B. (2004).

ROBUST SENSOR BASED NAVIGATION FOR AUTONOMOUS MOBILE ROBOT.

In Proceedings of the First International Conference on Informatics in Control, Automation and Robotics, pages 64-70

DOI: 10.5220/0001140500640070

 SciTePress

Interval Analysis with ultrasonic sensors is described

and the results are shown and ﬁnally in section 5 the

conclusions are given.

1.1 Background

The problem considered here is that of robot navi-

gation and localisation using multiple low cost sen-

sors such as inertial sensors, encoders and ultra-

sonic sensors. Conventionally stochastic ﬁlters such

as Extended Kalman ﬁlter or Unscented Kalman ﬁl-

ters (UKF) are used for robot localisation (Clark

et al., 2001). One of the main prerequisites for using

Kalman ﬁlter is to have an accurate model of the robot

and also accurate sensor noise statistics (i.e) bias, drift

etc. But in practice it is difﬁcult to have these parame-

ters accurately, especially drift in accelerometers and

gyroscopes, which affects the outcome of the UKF,

there by contributing to errors in the estimated posi-

tion of the robot over a period of time.

Moreover time of ﬂight sensors such as ultrasonic

sensors are used to measure the distance of land marks

from the robot and to recognize the presence of any

obstacles in the robots path. When the 2-D map of

the environment in which the robot travels is known a

priori, the distance measurements from the ultrasonic

sensors can be used independently to estimate the po-

sition of the robot in the map. EKF or UKF can be

used for this purpose as well (Castellanos and Tardos,

1999). But one of the main limitations encountered

when using this approach is the problem of data as-

sociation, as the data association problem in EKF or

UKF is extremely complex and is of the third order

. There are ways in which this problem can be

simpliﬁed to O

, but the solution may be suboptimal.

In order to get the best estimate of the robots po-

sition, we can use different types of sensors with dif-

ferent algorithms which have different sources of er-

ror. In this case we use an Unscented Kalman ﬁl-

ter for fusing the data from the accelerometers, gy-

roscopes and encoders and use an Interval Analysis

(IA) algorithm for estimating the robots position us-

ing ultrasonic sensors. IA algorithm is used instead

of EKF or UKF for the ultrasonic sensors because

the IA algorithm can overcome the problems of not

having an accurate model and accurate sensor noise

statistics in the Kalman Filters, as the IA gives a guar-

anteed estimate of the robot position. It should also

be noted that the IA algorithm for ultrasonic sensors

bypasses the complex data association step and han-

dles the problem in a nonlinear way even while been

robust to outliners. Thus we have two independent

sets of the measurements for the robot position. The

estimated robot position using UKF from inertial sen-

sors, which might be affected by bias and drift, are

then fused with the estimated interval robot position

using IA from ultrasonic sensors. The fused robot po-

sition estimate is much better than either one them

alone since the errors in UKF estimated position are

identiﬁed and corrected using the IA algorithm.

1.2 Prior work: Robot localisation

with IA using range

measurements

Interval analysis is basically about guaranteed numer-

ical methods for approximating sets. Guaranteed in

this context means that outer (and sometimes inner)

approximations of the sets of interest are obtained,

which can (at least in principle), be made as precise as

desired. Thus interval computation is a special case of

computation on sets, and set theory provides the foun-

dations for interval analysis.

The localisation of an autonomous robot while nav-

igating in a known or partially known environment is

an important problem in mobile robotics. In this sec-

tion an approach for the localisation of the robot us-

ing interval analysis (Kieffer et al., 2000) with sensor

readings from ultrasonic sensors is described brieﬂy.

The main advantage of this method is that it bypasses

the data-association step, which is very complex in

other methods such as Extended Kalman Filters, and

it handles the problem in a nonlinear way without any

linearisation and it is very much robust to outliners.

The robot model described above moves in a

known 2D environment and its motion is planned with

respect to a set of obstacles and landmarks. These

obstacles and landmarks deﬁne the world reference

frame W and a robot frame R which is with respect

to the body of the robot.

The robots position is described by the parameters

, y

and θ,which form the conﬁguration vector p =

, y

, θ)

So the task now is to estimate the value of the con-

ﬁguration vector p, from a map representing the envi-

ronment of the robot and from distance measurements

provided by a belt of n

time of ﬂight sensors with un-

limited range present in the mobile robot. Moreover

since it is assumed that the bounds on the measure-

ment error is known, the resulting distance measure-

ment is in terms of intervals which is stored in an in-

terval vector

[d] = ([d

], ...., [d

]) (1)

If a model is available to model the ultrasonic sen-

sor interval distance measurements represented by the

interval vector d

(p), when the robot conﬁguration

is p, the robot localization problem now becomes a

bounded error parameter estimation problem, namely

that of characterizing the set

P = {p ∈ [p

] | d

(p) ∈ [d]} (2)

ROBUST SENSOR BASED NAVIGATION FOR AUTONOMOUS MOBILE ROBOT

where [p

] is an initial search box, assumed to be large

enough to contain all the possible robot conﬁgura-

tions. P then contains all the conﬁgurations vectors

that are consistent with the given map and measure-

ments.

But the task is to ﬁnd the conﬁguration vector p and

so the equation given above can be rearranged as

= [p

] ∩ (d

)

−1

([d]) (3)

(i.e.) for a given conﬁguration vector p the robot eval-

uates the measurements that its sensors would return

and compares then with the actual measurements to

check whether they are consistent.

The problem described by the above mentioned

equation 3 could then be solved using any of the two

approaches namely SIVIA (Set Inversion Via Interval

Analysis) (Jaulin and Walter, 1993) and ImageSP (Ki-

effer et al., 1998). Both the above approaches have

been described in detail in the book by Jaulin et al

(Jaulin et al., 2001) and a brief introduction to both

SIVIA and IMAGESP is given in Sections 3.1, 3.2.

1.3 Novelty

This paper differs for the work in section 1.2 in three

main aspects. Firstly, the above algorithm has been

modiﬁed to incorporate sensor range limitation as in

many real world applications. Secondly instead of

using interval values in the kinematic model while

tracking the robot, we use the physical constraints of

the robot model to predict the robot position. Finally

inorder to overcome the scenario when there are no

land marks in the vicinity of the robot, in which case

there will be no measurements from the TOF sensors,

it is proposed to use inertial sensors (INS). Thus in the

presence of land marks, the fusion of the robot posi-

tion from the the INS and TOF sensors is proposed.

2 ROBOT LOCALISATION USING

UKF WITH INERTIAL

SENSORS AND ENCODERS

By fusing the measurement data from the sensors -

wheel encoders, gyroscopes and accelerometers - in

the mobile robot, a reliable estimation of the posi-

tion and heading of the robot can be obtained. There

are basically two well established approaches avail-

able in literature: one is the Kalman ﬁlter and the

other is the extended Kalman ﬁlter (EKF) (Alessandri

et al., 1997). The Kalman ﬁlters are well known meth-

ods used in the theory of stochastic dynamic systems,

which can be used to improve the quality of estimates

of unknown quantities. The difference between the

two methods is that for the ﬁrst one a linear kinematic

model is used, while for the second one, the EKF a

nonlinear dynamic model is used. We know that, if

we use the nonlinear model, it is much more difﬁcult

to tune the performances of the ﬁlter. From the the-

oretical point of view there are no theoretical results

about the convergence properties as well. But in order

to use all the available information, a nonlinear model

is preferred. Most often in real world engineering ap-

plications, the most widespread and reliable state es-

timator for nonlinear systems is the extended Kalman

ﬁlter (Sorenson, 1990).

The EKF is the Kalman ﬁlter of an approximate

model of the nonlinear system, which is linearised to

the ﬁrst order around the most recent estimate. As-

suming all the stochastic processes are Gaussian, the

ﬁrst order linearisation must be carried out at every

iteration before applying the KF algorithms.

For the extended Kalman ﬁlter, the robot model

equations can be rewritten as the state equation of the

form shown below,

k+1

= f (x

, u

, w

) (4)

which, when linearized will be of the form

k+1

≈ ˜x

k+1

+ A(x

− ˆx

) + Bu

+ W w

k−1

, (5)

where, A and B are the jacobian matrix of partial

derivatives.

This ﬁrst order linearisation using the Taylor series

expansion may introduce errors in the estimated pa-

rameters which may lead to suboptimal performance

and sometimes divergence of the ﬁlter.

The above described problem can be overcome to

a certain extent by using a method ﬁrst described by

Julier and Uhlman as the unscented transform in the

Kalman ﬁlter for the linearisation process (Julier and

Uhlmann, 1997). This formulation of the Kalman ﬁl-

ter is called the Unscented Kalman Filter. The un-

scented transform is basically a deterministic sam-

pling approach, where the state distribution is approx-

imated by a gaussian random variable, but is now de-

scribed using a minimal set of carefully chosen sam-

ple points. These sample points are chosen using the

unscented transform method which completely de-

scribes the true mean and covariance of the gaussian

random variable. When these chosen points are prop-

agated through the true non-linear system, it can cap-

ture the posterior mean and covariance accurately up

to the 3rd order for Taylor series expansion, where as

in a EKF we can achieve only up to ﬁrst-order accu-

racy. It should also be noted that the computational

complexity of the UKF is the same order as that of

EKF. The basic equations for the UKF has been given

in detail in the book (Wan and der Merwe, 2001)

All the process noises are assumed to be zero mean,

uncorrelated white random noises only.

In the measurement model for this robot there are

four sources of observations that are considered:

ICINCO 2004 - ROBOTICS AND AUTOMATION

1. velocity measurements from the wheel encoders,

2. acceleration from the accelerometers, which when

integrated gives the velocity of the robot,

3. robot heading angle measurement from the en-

coders and

4. the angular velocity measurements from the rate

gyroscope which when integrated once gives the

heading angle of the robot.

Thus, for both the velocity and heading angle of the

robot there are two sets of measurements from two in-

dependent sensors. These two sets of measurements

are then given as input to the Kalman ﬁlter which esti-

mates the robots speed and heading angle, from which

the robots position can then be calculated.

3 ROBOT LOCALISATION WITH

INTERVAL ANALYSIS USING

RANGE MEASUREMENTS

In this section the robot localisation using IA as ﬁrst

described brieﬂy in section 3 is further improved us-

ing multiple measurements from the ultrasonic sensor

measurements.

A brief overview of the algorithm for a single mea-

surement has been given in the Figures 3, 4 and 5 .

The main improvement in this version of the algo-

rithm in the descriptions in the tables is that the range

of the ultrasonic sensor has been limited to 3 meters,

where as in (Kieffer et al., 2000) the range was unlim-

ited. This is implemented by identifying the sensors

that only give readings less than 3 meters (which

is done by setting all the interval ranges greater than

3 meters to inﬁnity in Figure 5) and substituting them

for instead of n

(where the inclusion function was

calculated for all the n

number of sensors) in the

Figure 4. Also it is assumed that the land marks are

spaced sparsely (i.e) there is a distance of at least 3

meters between the landmarks. This is because when

the land marks are close some of the land marks may

not be visible to the robot sensor model in the IA algo-

rithm. Additionally the land marks which are visible

to the robot in the 3 meter radius are only given to the

inclusion function in Figure 4 instead of all the n

segments, there by saving computational time.

This problem as given in equation 3 is then solved

using any of the two approaches namely SIVIA (Set

Inversion Via Interval Analysis) (Jaulin and Walter,

1993) and ImageSP. A brief introduction to both

SIVIA and IMAGESP is given in the next two sub-

sections.

Figure 1: Robot and Sensor model

SIVIA AlgorithmImageSp Algorithm

Figure 2: A schematic representation of ImageSp and

SIVIA algorithm

3.1 Set Inversion Via Interval

Analysis (SIVIA)

Set inversion is the computation of the reciprocal im-

age

X = {x ∈ R

| f (x) ∈ Y } = f

−1

(Y ) (6)

of a regular subpaving Y of R

by a possibly nonlin-

ear function f : R

→ R

and SIVIA is a method to

compute two subpavings X

and X of R

such that

X ⊂ X ⊂ X (7)

A subpaving is a ﬁnite set of non-overlapping boxes

that are all included in the same root box. It is called

regular if each of the boxes can be obtained by a ﬁnite

succession of bisections and selections (Jaulin et al.,

2001).

In this problem for robot localisation, P = {p ∈

] | t(p) = 1}, SIVIA can be applied (Kieffer

et al., 2000). Therefore in this case, if t

[]

([p

]) = 1,

is in the solution set P and is stored in

P . If

[]

([p

]) = 0 then [p

] has an empty intersection

with P and is dropped from further consideration. If

[]

([p

]) = [0, 1] and if the width of [p

] is larger

than the pre-speciﬁed precision parameter ² , then p

is bisected, leading to two child sub boxes L(p) and

ROBUST SENSOR BASED NAVIGATION FOR AUTONOMOUS MOBILE ROBOT

Algorithm d

(in: p; out: d

)

1 for i := 1 to n

2 s

cos θ − sin θ

sin θ cos θ

−→

cos(θ +

− γ)

sin(θ +

− γ)

;

−→

cos(θ +

+ γ)

sin(θ +

+ γ)

;

4 (d

)

(p) := +∞;

5 for j := 1 to n

)

(p) :=

min

)

(p) , r

−→

, a

, b

¢¢

Figure 3: Model for calculating the distance expected from

ultrasonic sensor when the conﬁguration is p

R(p), and the test t

[]

(.) is recursively applied to both

of them. Any box with width smaller than ² is con-

sidered to be small enough and it is added to

P . A

diagram explaining SIVIA is given in Figure 2.

3.2 IMAGE SubPaving (IMAGESP)

When f is not invertible, a speciﬁc and computation-

ally more demanding procedure is used. The basic

idea of IMAGESP algorithm is to describe the ini-

tial search box p

using a subpaving consisting of p

boxes whose width are less than ². Then IMAGESP

evaluates the image of each of these p boxes using an

inclusion function f

[]

of f and stores them on a list.

Therefore we will be getting p image boxes, each of

which contains the true image set of the associated

initial box. At last, IMAGESP merges all these im-

age boxes into a subpaving to allow further processing

(Kieffer et al., 1999). A diagrammatic representation

of IMAGESP is given in Figure 2.

Thus the actual position of the robot represented

here by the conﬁguration vector p at any given instant

of time can be found using SIVIA or IMAGESP algo-

rithms.

The Figure 1 gives a brief description of a map that

represents the surroundings in which the robot travels

(which is assumed to be known in order to calculate

(p)) and also the measurement process.

A detailed description of the above inclusion func-

tions has been provided by (Kieffer et al., 2000).

Also a better version of the above algorithm in terms

of computational time, incorporating the interval ele-

mentary tests to eliminate some of the infeasible con-

ﬁgurations in the conﬁguration vector has been de-

scribed in (Kieffer et al., 2000), in which the problem

is reformulated as P = {p ∈ [p

] | t(p) holdstrue}

(i.e.) P = {p ∈ [p

] | t(p) = 1} , where t(p) is

a global test. The global test t(p) consists of vari-

ous elementary tests (three tests (Kieffer et al., 2000))

and they are robust to outliners as well. Also the

Algorithm [d

] (in: [p;] out: [d

])

1 for i := 1 to n

2 [s

] :=

cos[θ] − sin[θ]

sin[θ] cos[θ]

−−→

] :=

cos([θ] +

− γ)

sin([θ] +

− γ)

;

−−→

] :=

cos([θ] +

+ γ)

sin([θ] +

+ γ)

;

4 [d

]

([p]) := +∞;

5 for j := 1 to n

]

([p]) :=

min

]

([p]) , [r]

] ,

−−→

], a

, b

´´

Figure 4: Inclusion function for the measurement model

Algorithm [r] (in : [s], [

−→

], [

−→

], a, b; out : [r]);

1. [t

] :=

det

−→

ab,

−→

≥ 0

if [t

] = 0 then [r] := +∞; return;

2. [t

] :=

³D

−→

ab,

−−→

a [s]

≥ 0

∧

³D

−→

ba,

−→

b[s]

≥ 0

∧

³D

−→

ab,

−−→

]

≤ 0

∧

³D

−→

ab,

−−→

]

≥ 0

;

3. [r

] := [χ] ([t

] , [l] ([s] , (a, b)) , +∞) ;

4. [t

] :=

det

−−→

[s] a

≥ 0

∧

det

−−→

[s] a

≤ 0

;

5. [r

] := [χ]

] ,

−−→

[s] a

, +∞

;

6. [t

] :=

det

−−→

[s] b

≥ 0

∧

det

−−→

[s] b

≤ 0

;

7. [r

] := [χ]

] ,

−−→

[s] b

, +∞

;

8. for i := 1 to 2

det

−−→

[s] a,

−→

]

≥ 0

∧

det

−−→

[s] b,

−→

]

≤ 0

;

10.

:= [χ]

−−→

]

([s] , (a, b)) , +∞

;

11. [r] := min

] , [r

] ,

¤¢

;

12. [r] := [χ] ([t

] , [r] , +∞) .

Figure 5: Inclusion function for the remoteness of the cone

from a segment

purpose of the ﬁrst two tests is to eliminate some in-

feasible conﬁgurations there by saving computational

time. But if all the three tests are used when the range

of the sensor is limited, it leads to scenarios in which

some feasible conﬁgurations are ignored prematurely.

Therefore only two tests were used (inroom test and

the data test in (Kieffer et al., 2000)). The main con-

sequence of not using the leg-in test when the sensor

range is limited is that it may increase the computa-

tion time.

In the case when the robot is moving the robots po-

sition needs to be tracked, in which case the robots

position needs to predicted at the next instant to esti-

mate the robots position at that instant. This is done

by using the physical limitations of the robot based

on the maximum speed and heading angle rate of the

robot, instead of using a kinematic model of the robot.

Thus we obtain an independent position of the robot

from the ultrasonic sensors.

ICINCO 2004 - ROBOTICS AND AUTOMATION

forInterval Analysis algorithm

robot position estimation

coordinates

Interval X and Interval Y

robot coordinates which forms

a box or a plane

Inertial Sensors

Ultrasonic

sensors

Map of robot

environment

Sensor fusion block diagram

Encoders

robot speed and orientation

Robot

X and Y coordinate

UKF Sensor fusion for estimating

UKF estimated X and Y robot

Check whether the UKF robot position is inside the interval robot position box.

If so the robot position is the UKF estimated X and Y coordinates.

If not the robot position is the point which is closest to the UKF estimate in the interval box.

Figure 6: Block diagram of IA based adaptive mechanism

for UKF

−10 −5 0 5 10

−10

−5

UKF only estimated robot position

X coordinate (m)

Y coordinate (m)

Land Marks

Actual robot

position

UKF estimated

robot position

Figure 7: UKF only estimated robot position

4 INTERVAL ANALYSIS BASED

ADAPTIVE MECHANISM FOR

UKF

Sensor fusion is a very important and keenly re-

searched topic in the domain of mobile robotics. This

is due to the fact that, instead of using bespoke expen-

sive sensors for estimating the robots position, mul-

tiple low cost sensors can be used, there by reducing

the cost of developing the robot. Moreover these same

sensors can be used to do other tasks other than esti-

mating the robots position such as building the map of

the robots environment using ultrasonic sensors etc.

Also the source of errors in one sensor may be differ-

ent from another one and this fact can be exploited to

eliminate the errors in the measurements.

For the problem of sensor fusion stochastic ﬁlters,

such as Kalman ﬁlters, are commonly used. But they

suffer from the same disadvantages described before

−10 −5 0 5 10

−10

−5

X coordinate (m)

Y coordinate (m)

UKF estimated robot position with IA based adaptive mechanism using SIVIA algorithm

Land Marks

Actual robot

position

Interval robot

position

IA based adaptive

UKF robot

postion estimate

Figure 8: Fused robot position using SIVIA algorithm as

adaptive mechanism in UKF

(i.e.) an accurate model of the system and statics are

needed. In order to overcome these difﬁculties while

using the UKF, a new approach has been introduced in

this paper. As described above the robots position are

estimated using two independent sources namely, the

robot position from inertial sensors and the interval

robot position from ultrasonic sensors.

The position obtained using interval analysis is up-

dated only once every second, where as the position

from inertial sensors and encoders are updated 100

times per second as it has a sampling time of 0.01

seconds. Moreover we know that the robots interval

position to be guaranteed (even though in a few cases

it may not be due to the way the boxes are subdivided

but still they are very close to the actual position). The

interval position thus obtained will therefore be like a

plane or rectangle. Then the estimated position using

the inertial sensors is checked whether they are inside

this rectangle. In case they are present inside the rect-

angle then they are trusted to be accurate and used.

Alternatively if they are not then both the measure-

ments are fused by selecting the point on the rectangle

(box) (i.e.) the interval robot position, which is geo-

metrically closest to the robot position estimated us-

ing UKF with inertial sensors, thereby bounding the

error in the UKF estimates. A block diagram of the

sensor fusion method is given in Figure 6.

But since the UKF estimates of inertial sensors is

not accurate as they may be affected by bias, drift etc

and also as the robot is slow moving, instead of using

a dynamic interval model of the robot to predict the

next step as in (Jaulin et al., 2001) we use the physical

limitations of the robot to predict the next step in the

Interval Analysis algorithm.

The above described algorithm was successfully

implemented and tested in simulation using MAT-

LAB and C++ software. The Figure 8 shows the robot

position after using the adaptive UKF robot position

ROBUST SENSOR BASED NAVIGATION FOR AUTONOMOUS MOBILE ROBOT

−10 −5 0 5 10

−10

−5

UKF estimated robot position with IA based adaptive mechanism using IMAGESP

X coordinate (m)

Y coordinate (m)

Obstacles or

Land Marks

Actual robot

position

Interval robot

position

IA based adaptive

UKF robot position

estimate

Figure 9: Fused robot position using IMAGESP algorithm

as adaptive mechanism in UKF

estimate using the SIVIA interval robot position esti-

mate for adaptation. It can be seen that the interval po-

sition estimate is very conservative when there are no

land marks in one coordinate, for example at the be-

ginning of the robot path in Figure 8. Moreover it can

be observed that the UKF estimate with the interval

analysis based adaptive mechanism has signiﬁcantly

improved the UKF robot position estimate when com-

pared with the UKF position estimate without the IA

adaptive mechanism shown in Figure 7. Similarly the

Figure 9 shows the UKF robot position estimation us-

ing the IMAGESP algorithm for the adaptive mecha-

nism. It should be noted that the SIVIA interval posi-

tion uncertainty is more when compared with the IM-

AGESP algorithm, but the computational complexity

for the IMAGESP algorithm is more when compared

with the SIVIA algorithm.

5 CONCLUSION

An Unscented Kalman ﬁlter (UKF) using an Inter-

val Analysis based adaptive mechanism has been de-

scribed. The UKF uses accelerometers, gyroscopes

and encoders to measure the robots speed and head-

ing angle, so that the robots position can be estimated.

But the UKF robot position estimate is affected by er-

rors in robot model, sensor bias, drift etc. The Interval

Analysis (IA) is a deterministic approach to estimat-

ing the robots position without using a model of the

robot system, thereby minimizing errors due to robot

model. The interval analysis algorithm with ultra-

sonic sensor measurement to estimate robot position

has been described. Additionally previous work on

robot localisation and navigation using interval anal-

ysis has been extended so to incorporate sensor range

limitation. Moreover instead of using dynamic inter-

val model of the robot to predict the next step of the

interval robot position while tracking the robot posi-

tion, the physical limitations of the robot are used to

predict the next step in the interval analysis algorithm.

The IA robot position estimate is then used for an

adaptive mechanism to correct the errors in the UKF

robot position estimate. Then the newly implemented

approach to fuse both these robot position estimation

has been described and it can be observed that the

UKF with the IA based adaptive mechanism gives a

much accurate estimate when compared to estimates

with UKF without the adaptive mechanism.

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