Improving Decision-Making-Process for Robot Navigation

Under Uncertainty

Mohamed Ibn Khedher

, Mallek Sallami Mziou

and Makhlouf Hadji

IRT - SystemX, 8 Avenue de la Vauve, 91120 Palaiseau, France

CEA, The French Alternative Energies and Atomic Energy Commission, France

Keywords:

Uncertainty in AI, Neural Network Robustness, Data Augmentation, Abstract Interpretation, Pareto Front.

Abstract:

Designing an autonomous system is a challenging task nowadays, and this is mainly due to two challenges such

as conceiving a reliable system in terms of decisions accuracy (performance) and guaranteeing the robustness

of the system to noisy inputs. A system is called efﬁcient, if it is simultaneously reliable and robust. In

this paper, we consider robot navigation under uncertain environments in which robot sensors may generate

disturbed measures affecting the robot decisions. We aim to propose an efﬁcient decision-making model,

based on Deep Neural Network (DNN), for robot navigation. Hence, we propose an adversarial training step

based on data augmentation to improve robot decisions under uncertain environment. Our contribution is

based on investigating data augmentation which is based on uncertainty noise to improve the robustness and

performance of the decision model. We also focus on two metrics, Efﬁciency and Pareto Front, combining

robustness and performance to select the best data augmentation rate. In the experiment stage, our approach is

validated on a public robotic data-set.

1 INTRODUCTION

The autonomy of a system is its ability to analyze the

environment, make decisions and perform actions in

order to achieve goals assigned beforehand.

Decision-Making Process (DMP) is, then, one of

the key elements in the conception of autonomous

systems in order to have successful behavior. It re-

quires an accurate and adequate representation of the

environment to choose the optimal decision. Often,

the environment is uncertain due to external factors

that highly impact the system. Generally, these difﬁ-

culties are related essentially to the fact that: i) per-

ception environment is absent or partially observable

and ii) sensors values are false or disturbed due to a

software or hardware anomalies.

In this context, it is important to study the behav-

ior of the DMP in uncertain environment, i.e given

noisy inputs. In fact, nowadays, the difﬁculty is not

only to construct a reliable decision-making model in

terms of decision accuracy (Performance), but also

the challenge is to construct a robust decision-making

model in terms of stability to noisy inputs (Robust-

ness). For a clearer deﬁnition of the robustness, it

consists in checking the capacity of the neural net-

work to take the same label for all similar inputs even

if they are noisy.

In this paper, we focus on the impact of data

augmentation on the decision model behavior against

noisy inputs. Our intuition leads us to study the capac-

ity of data augmentation to improve the performance

and/or the robustness of decision model. Hence, given

a decision model based on Deep Neural Networks

(DNN), several data augmentation rates are applied.

For each rate, the model performance and robustness

are evaluated. To measure the robustness, we pro-

pose to use the Abstract Interpretation that aims to

check systems for resistance to unsatisﬁed speciﬁca-

tions (Cousot, 2008). Its principle consists in check-

ing that DNN still output the same label even if inputs

are noisy.

To the best of our knowledge, this is the ﬁrst paper

dealing with the fusion of Performance and Robust-

ness to select the best decision model. We propose to

investigate two metrics: Efﬁciency based on F-score

measure (Chinchor, 1992) and Pareto front (Ehrgott,

2005) metric.

Pareto front metric is often used for preferences’

comparison when each preference is represented by

vectors containing at least two scores. It is based on a

set of decision points that are not dominated by other

points. Further mathematical details and formulations

Khedher, M., Mziou, M. and Hadji, M.

Improving Decision-Making-Process for Robot Navigation Under Uncertainty.

DOI: 10.5220/0010323311051113

In Proceedings of the 13th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2021) - Volume 2, pages 1105-1113

ISBN: 978-989-758-484-8

1105

on Pareto front points and the notion of Dominance

will be provided in next sections. In our case, Pareto

front solution will be used to select solutions that meet

the multiple objectives or criteria such as robustness

and performance trade-offs.

The rest of the paper is organized as follows. In

section 2, a state of the art is presented. The structure

of our approach is described in section 3. Sections 4

and 5 detail respectively the decision-making model

construction and decision-making model evaluation.

Section 6 includes the experimental results and sec-

tion 7 concludes the paper.

2 STATE OF THE ART

In this section, the state of the art is split into two ma-

jor topics: i) the ﬁrst is about the solutions proposed

to construct a DMP model for autonomous systems

and ii) the second concerns approaches to verify the

robustness of a constructed DMP model based on neu-

ral networks.

2.1 Decision-making Approaches

Decision-making approaches can be roughly classi-

ﬁed into two major approach categories: i) Learning-

free approaches and ii) Learning-based approaches.

Regarding Learning-free approaches, system de-

cisions are taken without any prior trained model

(Khedher et al., 2012; Khedher and El Yacoubi,

2015). Mostly, it is based on the use of rules, cost

functions and graphs. First, Finite State Machines

(FSM) and Rule Based manual programming ap-

proaches are the simplest. Physically, states corre-

spond to system behaviors and transitions are the rules

(or constraints) to transit from one state to another.

Second, decision-making can be performed by deﬁn-

ing a cost function. It consists in evaluating each ac-

tion or sequence of actions using optimization algo-

rithms in order to ﬁnd the one with the lowest cost. Fi-

nally, decision-making can be modeled using graphs.

Mostly, a tree-like graph is created to model different

decisions and their consequences in order to select the

optimal action.

In (Kammel et al., 2009; Aleluya et al., 2018),

a FSM-based approaches are proposed. The team

AnnieWay, authors of (Kammel et al., 2009), uses

FSM for autonomous driving decisions where states

included driving behavior and transitions are deﬁned

according to a manually written conditions. The au-

thors of (Aleluya et al., 2018) use FSM to control a

robot in soccer-playing context. It models the process

of selecting the optimal robot-action according to its

environment.

In (Vitus and Tomlin, 2013), the authors proposed

a Chance Controlled Optimization approach to solve

lane change overtaking in urban areas. The objective

function minimizes, in the one hand, the traditional

objectives such as minimization of fuel, and in the

other hand, the nominal planned trajectory prediction

against potential crashes.

Regarding Learning-based approaches, a prior

decision-making model is trained (Jmila et al., 2017).

Among these models, we quote Support Vector Re-

gression (Zhang et al., 2017), Deep Learning (Shabbir

and Anwer, 2018) and reinforcement learning (Hoel

et al., 2018).

In (Zhang et al., 2017), a Support Vector Regres-

sion is proposed to model the driving decisions. It

takes as input the environment parameters (e.g. vehi-

cle states, road conditions, etc.) and retrieves the driv-

ing decision (e.g. steering angle, speed, etc.). Using

the same technique, authors of (Abdessemed, 2012)

propose the use of Support Vector Machine (Vapnik,

1995) to achieve the tracking trajectory task of a robot

manipulator.

In the other hand, Deep Learning (DL) approaches

have been gaining popularity in recent years across a

variety of applications (Khedher et al., 2018; Jmila

et al., 2019) such as decision-making. In (Shab-

bir and Anwer, 2018), a survey of Deep Learning

techniques for mobile robot applications including

decision-making is proposed. In (Gallardo et al.,

2017), authors use Deep Learning techniques to help

the navigation of a driverless car through an urban en-

vironment.

Besides, the authors of (Hoel et al., 2018) for-

mulate the decision-making task as a reinforcement

learning problem. The goal is to learn a policy

that aims to automatically generate a decision-making

function to handle speed and lane change decisions.

2.2 Neural Networks Veriﬁcation

Approaches

The Neural Network Veriﬁcation (NNV) is the task

studying the evolution of its outputs in uncertain envi-

ronment. Otherwise, it consists of checking the neural

network capacity to take the same output for all sim-

ilar inputs even if they are noisy. The principle of a

NNV system consists in: i) ﬁrst calculating, from the

input data, all possible inputs that can be obtained by

adding noises and ii) second, checking that the prop-

erties of the input data is kept for noisy data. The

properties are ﬁxed beforehand and, for example, they

can be deﬁned as range of values, as an object class,

ICAART 2021 - 13th International Conference on Agents and Artiﬁcial Intelligence

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etc.

To verify a Neural Network (NN), several ap-

proaches have been proposed, mainly: i) satisﬁability

approaches and ii) reachability approaches.

Regarding satisﬁability approaches, it consists

in transforming the NN into a feasibility problem

to prove the existence of a counter-example. If a

counter-example has been found, the NN is not se-

cure, else if no counter-example has been found, the

NN is secure.

In (Katz et al., 2017), the authors propose an ex-

tension of the simplex algorithm, a standard algorithm

for solving linear programming (LP) instances, to

support non-linear ReLU activation function (ReLU

for " Rectiﬁed Linear Unit"). The algorithm is called

Reluplex, i.e. ReLU with the simplex method. Relu-

plex uses the simplex algorithm to search a feasible

activation pattern that leads to an in-feasible output.

The authors of (Ehlers, 2017) propose PLANET (for

"a Piece-wise LineAr feed-forward NEural network

veriﬁcation Tool"). It consists ﬁrst on replacing the

non-linear functions of the NN by a set of linear equa-

tions. Then, it tries to ﬁnd a solution for the resulting

system of equations.

Regarding the reachability approaches, it consists

in calculating the reachable set (outputs) of all inputs

and checking if it is included in the desired set. Given

a neural network N and an input set

X, the reach-

ability set

Y is deﬁned as all the possible outputs:

Y = {~y,~y = N(~x),∀~x ∈

X}. If the reachable set is in-

cluded in the desired set, the NN is declared secure,

else if the reachable set is not included, totally or par-

tially, in the desired set, the NN is not secure.

The calculation of the reachable set can be exact

(Xiang et al., 2017b) or approximate (Xiang et al.,

2017a; Gehr et al., 2018).

In (Xiang et al., 2017b), authors compute the ex-

act reachable set for a neural network includes only

ReLU activation. In fact, they assume that if the input

is a union of polytopes, then the output reachable set

is also a union of polytopes. In their paper, the entries

of the NN are represented by the union of polyhedra

(a polyhedron is an example of the more general poly-

tope in any number of dimensions). Moreover, any

over-approximation is applied. Hence, the number of

polytopes grows exponentially with each layer.

In (Gehr et al., 2018), authors propose AI2 (for

"Abstract Interpretation for Artiﬁcial Intelligence")

that approximates the reachable set. The main idea

is to over-approximate inputs by a set of zonohedron

(a special case of the polyhedron geometric form).

Then, a set of abstract operators are deﬁned to follow

the evolution of the zonohedron through the layers of

the network.

The satisﬁability approaches does not adopt any as-

sumptions, however their execution time grows expo-

nentially with the augmentation of NN hidden layers

(depth). In the other hand, reachability approaches are

based on over-approximation but are more scalable

to a large NN. Since the importance of the execution

time in our study, our approach lies to the reachability

approaches.

3 OUR APPROACH

Figure 1 shows the ﬂowchart of our approach. The

input is a dataset composed of ultrasound sensor mea-

surements collected from a mobile robot during its

movement inside a room. The output is an efﬁcient

decision model under uncertainly sensor measures.

Our approach considers three stages described as fol-

lows:

• Data-set augmentation

• Decision model construction

• Decision model evaluation

We start by a data augmentation algorithm which is

applied to increase the variety of the training dataset.

The original dataset is composed of i) ultrasound sen-

sor measurements and ii) the corresponding robot de-

cision (label). The data augmentation algorithm con-

sists in injecting a Gaussian noise to generate noisy

inputs. In this work, several data augmentation rates

are used.

Next, a decision model is trained on the aug-

mented training dataset, based on Deep Neural net-

works. The trained model learns the robot decision

depending on sensor measurements.

Hence, for each data augmentation rate, the de-

cision model robustness is evaluated by adapting the

Abstract Interpretation algorithm to heterogeneous in-

puts.

Finally, two metrics are proposed to evaluate the

decision model taking into account its performance

and robustness. The metric is used to select the best

model in terms of performance and robustness trade-

offs.

4 DECISION-MAKING MODEL

CONSTRUCTION

Our decision model is based on a Deep Neural Net-

work. In this section, DNN principle and its applica-

tion in robot decision-making are presented.

Improving Decision-Making-Process for Robot Navigation Under Uncertainty

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Figure 1: Proposed approach.

4.1 Deep Neural Network Principles

A Deep Neural Network is a extension of neural net-

work with several hidden layers. It consists of three

typical types of layers: i) an input layer, ii) hidden

layers of neuron computations and iii) an output layer.

Each neuron is a simple processing element that re-

sponds to the weighted inputs it received from other

neurons.

The action of a neuron depends on its activation

function, which is described by:

= f

∑

j=1

i j

× x

+ θ

(1)

where x

is the j

input of the i

neuron, w

i j

is the

weight from the j

input to the i

neuron, θ

is the

bias of the i

neuron, y

is the output of the i

neu-

ron and f (.) is the activation function. The activation

function is, mostly, a nonlinear function describing

the reaction of i

neuron according to inputs.

4.2 Model Construction

Our DNN architecture consists of N fully-connected

layers, each of them are followed by an activation

function and a dropout layer, and a ﬁnal softmax layer

indicating robot decision. As activation function, we

used the non-linear function "Rectiﬁed Linear Units

(ReLU)" deﬁned by:

R(x) = max(0,x) (2)

The dropout layer is used to prevent over-ﬁtting

(Krizhevsky et al., 2012). Figure 2 shows the detailed

architecture of our DNN. It takes, as input, vectors of

dimension 24 components and outputs a probability

distribution vector of 4 components (the number of

decisions in the dataset).

4.3 Data Augmentation

Data augmentation is the process of modifying the

available data in a realistic and randomized method.

This is used to increase the dataset variety. In this pa-

per, we propose to enhance the training dataset by in-

jecting a Gaussian noise. Our intuition that injecting

noise during training phase makes the decision model

more efﬁcient. This intuition should be conﬁrmed ex-

perimentally.

In this paper, we propose to inject a Gaussian

noise based on the sensor uncertainty. It consists in

adding noisy samples x

noise

to the training set with

the following manner: for an input sample x

init

, we

generate: x

noise

= x

init

± ε, where ε follows a Gaus-

sian distribution centred on [-∆X,∆X]. ∆X is the sen-

sor uncertainty computed as following: For N multi-

ple sensor measures x

with average x, ∆X is given by

Eq.3.

∆X =

N − 1

∑

i=1

− x)

(3)

In our work, the robot is equipped with 24 ultrasound

sensors. Hence, the dimension of x

init

is 24 where

each component is associated with a sensor measure.

Moreover, each sensor i has its own (∆X)

. To form

noise

, each component is disrupted independently of

the others by adding the term ε

∈ [−(∆X)

,(∆X)

ICAART 2021 - 13th International Conference on Agents and Artiﬁcial Intelligence

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Figure 2: Our DNN architecture.

To prevent overﬁtting, only a randomly R% of the

training dataset is noisy and injected in the training

process. R is a hyper-parameter of our data augmen-

tation algorithm.

5 DECISION MODEL

EVALUATION BASED ON

ABSTRACT INTERPRETATION

The evaluation of the decision model is based on the

abstract interpretation. In this section, abstract inter-

pretation principles and its application in the context

of robot navigation are presented.

5.1 Principles of Abstract

Interpretation

The abstract interpretation is a technique used for ana-

lyzing speciﬁcations and checking programs for resis-

tance to speciﬁcation unsatisfaction (Cousot, 2008).

In (Gehr et al., 2018; Singh et al., 2018), authors have

reused the abstract interpretation for verifying the ro-

bustness of neural networks. This approach lies in the

reachability approaches.

The formulation of verifying the robustness of a

neural network is detailed as following. Given x

sample input and x

generated from x

by applying a

perturbation A, verifying the robustness R

,A)

con-

sists of checking the robustness condition over the

whole possible x

resulting from x

. The robustness

condition is deﬁned as: «the neural network outputs

the same label for x

and x

i.e. x

and x

belongs the

same class ».

The condition R

,A)

is checked and two cases are

possible:

• if all possible x

veriﬁed R

,A)

, the neural net-

work is called robust to the perturbation A given

the input x

• if at least one x

not veriﬁed R

,A)

, the neural

network is called not robust to the perturbation A

given the input x

5.2 Robustness Evaluation based on the

Abstract Interpretation

To measure the robustness of the decision model, the

abstract interpretation is applied to each sample from

the test dataset (Only samples correctly classiﬁed by

the decision model are used). Hence, each sample is

represented by a polyhedra. Later should includes all

possible samples resulting by adding perturbation re-

lated to sensor uncertainty. In other words, the shape

should include all possible sample ∈ [low, upper]

(where low = sample − ∆X, upper = sample + ∆X,

∆X is the sensor uncertainty deﬁned in section 4.3).

We recall that (∆X)

associated with the i

sensor is

different from one sensor to another.

Then, the shape is propagated through the abstract

transformer of each layer, obtaining a new shape. Fi-

nally, the ﬁnal shape should be checked if they kept

the the same label as the original sample.

Mathematically, the robustness is formulated as

follows. Given M the number of correctly classiﬁed

samples, the robustness is provided by:

Robust =

∑

i=1

veriﬁed(Net, s

) (4)

where:

• veriﬁed(Net, s

) = 1, if the neural network Net re-

turns the same label for all points of the shape gen-

erated from s

• Otherwise, veriﬁed(Net, s

) = 0.

5.3 Evaluation Metrics

Our goal in this phase is to select the best model in

terms of performance (Per f ) and robustness (Robust).

• Per f : is deﬁned as the rate of correct decisions

predicted by the neural network.

• Robust: is deﬁned as the rate of samples keeping

their original labels after perturbation (Eq.4).

The proposed metrics are used to combine the two

characteristics of the model (performance and robust-

ness) in order to select the best one. The proposed

metrics are: the model efﬁciency and Pareto front.

Improving Decision-Making-Process for Robot Navigation Under Uncertainty

1109

(a) Performance and robustness (b) Pareto Front

Figure 3: Decision-making model evaluation.

5.3.1 Efﬁciency Metric

The efﬁciency metric is based on the F

score (Chin-

chor, 1992) that is the harmonic mean of the perfor-

mance and robustness.

Mathematically, the harmonic mean is one of sev-

eral types of average, and in particular, one of the

Pythagorean means. The harmonic mean H of given

positive real numbers x

,. .. ,x

is deﬁned by:

H =

+···+

∑

i=1





∑

i=1

−1





−1

In this work, the efﬁciency metric E f f iciency corre-

sponds to the harmonic average of the performance

and robustness (Eq.5).

E f f iciency = 2 ∗

Per f ∗ Robust

Per f + Robust

(5)

The highest possible value of E f f iciency is 1, indi-

cating perfect performance and robustness, and the

lowest possible value is 0, if either the performance

or the robustness is close to zero.

5.3.2 Pareto Front Metric

Pareto ranking is often used for vectors or tensors

comparison with multiple criteria. This metric can be

embedded and used easily for evaluation process of a

given algorithm.

We ﬁrst deﬁne the concept of dominance that is

important to assess the quality of the solutions and to

make sure that the best solutions are selected.

Deﬁnition 1 (Dominance). For a given problem iden-

tiﬁed by a vector

f = ( f

,. .. , f

) under a set of de-

ﬁned constraints. Then, vector ~u dominates vector ~v

if and only if

∀i ∈ {1,. .. ,n}, u

≤ v

∧ ∃ j( j 6= i)u

< v

This is denoted by ~u ~v.

The above deﬁnition reports that a vector is dom-

inated if and only if another vector exists which is

better in at least one objective, and at least as good

in the remaining objectives. In our work, these objec-

tives are represented by robustness and performance

scores. A set of dominant points are representing the

Pareto front set.

Pareto front method is based on the dominance

strategy considering the bi-dimensional vector of

points. This approach is agnostic to the generation

of the considered points and will not change for new

generated datasets.

6 EXPERIMENTAL RESULTS

6.1 Dataset and Evaluation Protocol

To validate our approach, we use the experimental

sensor dataset proposed in (Freire et al., 2009) for

wall-following robot navigation. The dataset is a

collection of sensor readings obtained by the mobile

robot «SCITOS G5» during its navigation inside a

room. To navigate, 24 ultrasound (US) sensors were

used, and arranged circularly around its waist with an

arc distance of 15 degrees. The dataset ﬁle contains

5456 rows. Each raw values corresponds to the mea-

surements of all 24 US and the corresponding deci-

sion label (i.e. direction where the robot should nav-

igate next). All the 24 US readings are synchronized

(i.e collected at the same time step). The possible de-

cisions of the robot are: 1) Move-Forward, 2) Slight-

Right-Turn, 3) Slight-Left-Turn and 4) Sharp-Right-

Turn.

For the evaluation, 70% of the available data is

used for training and the resting 30% for evaluation.

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6.2 Results

To assess our decision model, several data augmenta-

tion rates R are evaluated as described in section 4.3.

In our study, R varies from 0% to 1000% by step of

5%. For each rate, performance and robustness are

computed to measure the two proposed metrics.

The behavior of our decision model according to

the two metrics is presented in Fig.3. Figure 3a shows

the evaluation in terms of three indicators: model per-

formance, model robustness and the efﬁciency metric

(Eq.5). Figure 3b shows the evaluation of our model

according to the Pareto front metric. It shows the cou-

ples (Per f ormance,Robustness) as well as the pareto

front.

Table 1 shows the evolution of model perfor-

mance, robustness and efﬁciency according to the

data augmentation rate.

6.3 Discussion

The standard experience, where no data augmentation

is applied, achieves a performance of 85.03%. More-

over, an improvement of 8% is obtained by augment-

ing the training dataset by 50%. This improvement is

signiﬁcant given the large size of the test dataset (8%

is equivalent to 131 robot decisions) and proves the

importance to augment the training dataset by inject-

ing noisy inputs. Afterwards, the decision model per-

formance decreases with the augmentation of training

dataset (R > 50%). This is explained by the fact that

when the reference dataset is signiﬁcantly augmented,

it becomes slightly different from the test dataset.

Table 1 shows that augmenting the training dataset

by 10% led to a stable robustness. Then, by augment-

ing more the training dataset (R > 10%), the robust-

ness is decreasing. From a data augmentation of 90%

(R >= 90%), the robustness attains its initial value

(before data augmentation). These results lead us to

two remarks: 1) the dataset augmentation is very im-

portant to improve the performance of the neural net-

work face to sensor uncertainty perturbation however

2) the data augmentation rate should be controlled to

keep a acceptable robustness level.

In the following, we discuss and show the conﬂict-

ing behavior of robustness and performance accord-

ing to the data augmentation rate. Taking the experi-

ence of a data augmentation of 30%, the performance

is improved by 7.08% however, the robustness is de-

creased by 1.85%. Table 1 illustrates results accord-

ing to the efﬁciency metric that combines robustness

and performance. Experimentally, data augmentation

has a slight impact on the efﬁciency metric. Table 1

shows that augmenting training dataset by 50% leads

to the best model in terms of efﬁciency. In fact, aug-

menting the training dataset by 50%, the efﬁciency is

improved by 3.08%.

Figure 3b depicts the results of the Pareto front

metric. This metric allowed us to select rapidly few

Pareto efﬁcient points (on the Pareto front) dominat-

ing the reminder points.

In this Pareto front, the lowest value for the ro-

bustness is close to 94.2% while the performance is

close to 93%. A major set of points indicated by F-

Score metric are dominated by the Pareto Front set.

We can conclude that for the considered data set, the

Pareto Front set allows to easily eliminating domi-

nated points while considering performance and ro-

bustness trade-offs.

7 CONCLUSION AND

PERSPECTIVES

In this paper, we examined the efﬁciency of a robot

system navigation against sensors uncertainty. We

are interested in the case where the robot decision is

based on deep neural network. Our challenge was the

impact of noisy inputs on robot decision. To cope

with this issue, we proposed to enhance the training

dataset by injecting noisy inputs. From one side, An

adversarial training based on data augmentation has

improved the decision model efﬁciency by 3.17%,

and from the other side the efﬁciency metric is in-

sufﬁcient to conclude on the best data augmentation

rate. The Pareto Front allows us to select a wider

value range of data augmentation rates. It allowed us

to consider only non dominated points combining the

robustness and performance scores at the same time.

In the future work, we plan to study the correlation

between sensor measurements. The goal is to select

sensors disturbing more the decision-making process.

This selection will help experts to replace faulty sen-

sors. Moreover, we plan to validate our proposed ap-

proach on several datasets in different contexts.

ACKNOWLEDGMENT

This research work has been carried out in the frame-

work of IRT SystemX, Paris-Saclay, France, and

therefore granted with public funds within the scope

of the French Program Investissements d’Avenir. This

work is a part of the project EPI project (EPI for "AI-

based Decision Making Systems’ Performance Eval-

uation").

Improving Decision-Making-Process for Robot Navigation Under Uncertainty

1111

Table 1: Decision-making model evaluation.

Data augmentation rate (R%) Performance (%) Robustness (%) Efﬁciency (%)

No augmentation 85.03 96.47 90.39

10 90.59 96.49 93.45

20 92.11 95.55 93.80

30 92.11 94.62 93.35

40 91.63 95.40 93.47

50 93.03 94.09 93.56

60 92.36 94.70 93.52

70 91.32 93.97 92.63

80 91.87 94.94 93.38

90 90.89 96.43 93.58

100 91.50 96.06 93.72

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