Teaching Fundamentals ofRobotics to Computer ScientistsNOURDINE ALIANE

Universidad Europea de Madrid, Villaviciosa de Odon, s/n (28670) Madrid, Spain

Received 11 October 2008; accepted 2 February 2009

ABSTRACT: This article presents a methodology to reinforce the teaching of fundamentals of robotics to

computer scientists. The pedagogical basis is focused on engaging students in an in-depth study of the subject

using computing in a substantive way. The approach consists in complementing the lectures by programming

assignments focused on giving students a deeper understanding of how robotic systems work from the inside. This

article presents the author’s experience in the use of this approach, as well as a set of proposed assignment

projects. � 2009 Wiley Periodicals, Inc. Comput Appl Eng Educ 19: 615�620, 2011; View this article online at

wileyonlinelibrary.com/journal/cae; DOI 10.1002/cae.20342

Keywords: fundamentals of robotics; teaching/learning through programming; Matlab

INTRODUCTION

As a multidisciplinary subject, robotics encompasses a diversity

of topics ranging from mathematics and physics, to mechanics,

automatic control, electronics, and computer sciences. An ad-

equate profile of a robotics course depends on the curricula to

which it belongs [1], the most frequent being mechanical engine-

ering, electrical engineering, and computer engineering, among

others. Robotics is also recognized as an excellent vehicle for

involving students in science and engineering, and is used in a

variety of ways and for a multitude of purposes. Within the wide

scope and use of robotics in education, the present article deals

with the teaching of fundamentals of robotics to computer

scientists.

The traditional method for teaching fundamentals of

robotics courses includes lectures and problem-solving sessions,

where the theoretical framework is complemented by the use of

some simulators such as the Robotics Toolbox for Matlab [2,3], or

hands-on laboratory robotic systems [4,5].

The syllabus outline for introducing fundamentals of

robotics is well presented through existing textbooks, such as

the texts written by Craig [6], Spong et al. [7], or Sciavicco and

Siciliano [8], to cite a few. These texts have been written from a

mechanical and electrical engineering perspective. Computer

scientists interested in learning fundamentals of robotics are

faced with the problem that existing bibliography contain a lot of

mathematics, and provide little intuition. Textbook [6], however,

is somewhat different, since it emphasizes many computational

aspects, and its third edition includes exercises and programming

assignments oriented towards the use of the Robotics Matlab

Toolbox [2,3], which makes it an appropriate reference for

computer scientists.

It is easy to realize, while glancing at any book on

fundamentals of robotics, that many of the basic concepts, such

as spatial localization, kinematics, dynamics, or trajectories

planning, are formulated as mathematical problems. In fact,

several topics require a mathematical background beyond the

undergraduate level and various central concepts, such as

homogenous transforms or cubic-spline interpolation, to cite

only two examples, are presented to students for the first time in

the robotics course. Many students are then surprised to discover

that robotics involves so much mathematical machinery. The

preponderating amount of mathematics in robotics is neither well

received, nor perceived as important by the students. Many

robotics topics should not be presented to computer scientists in

the same way they are presented to mechanical or electrical

engineering groups. The main challenge then, for the robotics

instructor, is teaching the material and making sure that the

lectures do not become pure mathematical dissertations. Funda-

mentals of robotics can be confusing due to the mathematical

machinery involved, rather than the complexity of the material.

From a computer science perspective, robotics is an

authentic context for computing. Thus, to give computer science

students the opportunity to acquire the knowledge embodied in

the course, the pedagogical basis is focused on engaging them in

an in-depth study of the subject, using computing in a substantive

way. The approach consists in complementing the traditional

lectures by programming assignments focused on giving students

a deeper understanding of how robotic systems work from the

inside. The programming assignments, undertaken as small

software projects, are exploited to alleviate the mathematical

core and promote interest in robotics among students.

The remainder of the article is organized as follows. The

second section describes the motivation of the approach and gives

key considerations in the pedagogy. The third section presentsCorrespondence to N. Aliane (nourdine.aliane@uem.es).

� 2009 Wiley Periodicals Inc.

615

some of the proposed homework assignments. The fourth section

discusses pedagogical issues offering some thoughts on the

approach, as well as presenting the students’ feedback. Finally,

conclusions are reported in the last section.

KEY CONSIDERATIONS IN PEDAGOGY

Robotics is a prolific field for interactions between mathematics

and computer science, and such interactions should be discovered

in a natural way. To do so, key considerations in pedagogy

consists in focusing classroom activities on programming

assignments, and exploiting computer science students’ skills

and abilities as programmers. On the other hand, to stimulate the

students and make them more involved in their own learning

process, the assignment projects are focused on designing small

robotics applications with some sort of visualization and

animated graphs. Obviously, the projects require an under-

standing of the mathematical representations behind the topics

being studied, and this practice would enhance and consolidate

the students’ theoretical knowledge gained from the lectures.

Advantages of Programming Activities

In general, students make connections between the material they

are learning and their prior knowledge, and taking advantage of

their skills would be beneficial to the learning/teaching process.

In this aspect, we expect computer science students to be good at

programming techniques. Thus, the learning of fundamentals of

robotics concepts can be undertaken from an algorithmic and

programming point of view by exploring the algorithms and

designing programs that real robotic systems execute.

Programming is an effective activity in the learning process.

Students act as software developers and systems designers.

Programming represents an analysis and design activity at the

same time. The task of formulating an algorithm as a correct

executable program involves many steps: understanding the

problem, coming up with a solution, designing the algorithm and

implementing it, debugging the program and testing the solution.

All these steps together constitute an excellent exercise for the

students to construct their own knowledge and learn about the

concepts involved in the problem. In this sense, programming

facilitates rigorous thinking and helps students understand many

abstract concepts. According to Marvin Minsky [9], ‘‘Program-

ming is a good medium for expressing poorly understood and

sloppily formulated ideas. In expressing many poorly understood

concepts in a computer program, we come to understand them

better.’’ Programming was also considered fundamental in an

early article [10], where authors claimed that ‘‘Programming

provides a set of experiences for discussing mathematical

concepts and problems. Programs are more discussable than

mathematics activities: students can talk about their structures

and developments, and ultimately discuss the original problem.’’

Thus, suitable programming activities can contribute to a better

learning of fundamentals of robotics, and students can acquire

more insight from the designing, testing, and debugging

processes, than from traditional lectures.

Visualization and Animation

Visualization and graphics animation are widely used to illustrate

abstract concepts in many areas of engineering education [11].

Visualization is a natural way to convey knowledge. In robotics,

indeed, many of the basic ideas can be explained better using

some sort of visualization. For example, animated graphs would

be advantageous for explaining spatial localization, kinematics,

and many others concepts, compared to the use of static figures.

In Ref. [12], the author suggests that students should build their

own visualizations. Such constructions enable them to gain

insight into what is important about the problem under study, and

programming visual applications constitutes a great stimulus for

developing the students’ intuition.

Thus, our approach is that the proposed assignments consist

in designing robotics simulations with some sort of visualization

and animated graphs. Pedagogically, visualization and animated

graphs are used as a means, not only for enhancing the

conceptualization of mathematics concepts, but also to stir up

students’ curiosity for learning.

Matlab Environment

Although the programming language is not the main focus, it still

plays an important role in the development of the projects. What

is suitable programming software for developing the assign-

ments? Firstly, we should be concerned about how clearly the

theoretical topics will be handled, as well as how easy it is to

program and visualize these topics. Secondly, the programming

tool should not add a cognitive load on the students.

Considering this perspective, Matlab was chosen as the

platform for developing the assignments, since it meets the

conditions mentioned above. Indeed, Matlab is a high perform-

ance language for technical computing, which integrates

computation, visualization and programming in an easy-to-use

environment. Furthermore, it is the ‘‘lingua franca’’ of engineer-

ing programming and is by far more productive than many other

high level programming languages. Therefore, using the fast

development capabilities of Matlab coupled with students’

imagination, constitutes the basis for providing the desired

pedagogical outcomes.

Methodology

Each assignment is set up through a comprehensive tutorial,

which provides a brief theoretical background and some

resources, such as Matlab code (m-files), illustrative graphics,

and some hints for developing the project. The assignments are

given to students in advance and they start working on their

project at the same time as they attend lectures. The time allotted

for each project is about 3 weeks.

Engineers and scientists usually work in groups. Thus,

courses such as robotics should serve to improve the students’

teamwork skills for their future professions. We therefore suggest

that students work in groups of two’s or three’s. In order to

facilitate working in teams, they are allowed to organize the

groups on their own.

Each group should submit a final report and give an oral

presentation. The reports focus on the technical aspects of the

projects, and include some scripts as ready-made demonstrations

to show their achievements. The oral presentations have some-

what of a free format. A single group would take about 5�10 min

for the presentation, and another 5�10 min for discussion. The

presentations are aimed at sharing the students’ accomplishments

and experiences.

616 ALIANE

The assignments were graded on a competitive basis, with

only one project judged as the best, receiving 100% of the

possible grade. This lead to each group keeping their project

development and design a secret in the hopes that they would

receive the highest grade.

THE ASSIGNMENT PROJECTS

The following are four proposed assignments. The first assign-

ment is aimed at the use of homogenous transformation matrices

for rendering solid objects. The second one deals with the use of

Deneavit�Hartenberg convention for simulating a simple

manipulator. The third deals with path control, placing emphasis

on the simulation of a 2-dof planar robot following a straight-line

using linear and cubic-spline interpolation techniques and so

forth. Finally, the fourth assignment deals with the joint control

and digital implementation of PID controllers. Some of the m-

files of these projects can be downloaded from the Web [13], and

readers can run the accompanying scripts.

Spatial Localization and Homogeneous Transforms

The aim of this project is to explore the use of homogeneous

transformations, and simulate spatial moves of simple geo-

metrical objects. The models used are elementary forms

represented by facets such as cube, prism, pyramid, etc.

In this assignment, students are asked to build their own

rendering engine. The project includes the development of

various functions, such as handling 3D objects, handling the

rotation about a given vector that passes through a given point by

an angle, or the translation about a given vector, etc. Many other

functions concerning rendering graphical objects with respect to a

fixed or local frame are also necessary to perform simple

animations. Students are free to build their own compounding

rotations and translations to define sophisticated moves, such as

screw and spiral movement. Figure 1 shows the screenshot of a

simulation performing spatial moves of a cube, and Table 1 shows

a model of scripts that students have to write to perform their tests

and demonstrations.

With this assignment, the students are more concerned with

the mathematical aspect of spatial localization, and they easily

grasp the meaning of homogenous transformations and their use

in robotics.

Simulation of an SCARA Manipulator

The aim of this project is to study motion robot simulation, and

design an animation of manipulators in a realistic fashion. This

project covers issues such as forward and inverse kinematics,

workspace calculation, etc. An SCARA manipulator is chosen as

an example. It is complex enough to demonstrate nearly all the

principle used in a general manipulator simulation. The graphical

representation of the arm is done by means of rectangular shapes.

The students are asked to write functions that perform tasks

such as loading data of the links of the SCARA to Matlab

workspace, calculating the direct and inverse kinematics,

displaying the graphical representation of the SCARA skeleton,

returning Cartesian and joint positions, checking if a specified

Cartesian (or joint) position lie within the workspace, etc. Many

other functions related to rendering the SCARA skeleton are also

needed. Figure 2 shows the screenshot of a simulation of the

SCARA skeleton after the execution of the script given in Table 2.

In this project, concepts such as forward and inverse

kinematics, multiple solutions, workspace calculation, etc, are

discovered by the students in a natural way.

Trajectory Generation

The goal of this assignment is to study trajectory generation in

its different aspects, and the project is composed of two parts.

The first part deals with the velocity control algorithms, such as

parabolic, trapezoidal and sinusoidal profiling. In the second part,

Figure 1 Simulation of a cube performing spatial moves.

Table 1 Script Controlling the Simulation Given in Figure 1

% Rotation of a cube about a vector v% that passes through the point p% by an angle a followed by a

translationinit;objeto(‘cubo’); % Loading a cube

objectv¼[0 0 1];p¼[1.5 1.5 0];a¼pi;% Rotationrotar_x (v, p, a);% translationv¼[�3 0 0];trans_x(v);

Figure 2 Simulation of an SCARA manipulator.

ROBOTICS TO COMPUTER SCIENTISTS 617

algorithms for generating trajectories using linear and cubic-

spline interpolation techniques are addressed. A 2-dof planar

manipulator is used as a model to test all these strategies

simulating individual axis moves, point-to-point motion, and

straight-line motion. The graphical representation of the manip-

ulator is done by means of rectangular shapes.

In this assignment, students re-use parts of the first and

second projects. However, many other algorithms are addressed,

such as following a straight line with a predefined accuracy using

Taylor’s algorithm, or applying parabolic or trapezoidal profiling

in Cartesian space.

Figure 3 shows the screenshot of a simulation of a 2-dof

planar manipulator performing three straight-line moves gen-

erated through cubic-spline interpolation: the first move uses two

intermediate points, the second uses four points, and the third

uses six intermediate points, generated by the script given in

Table 3.

At the beginning, students believe that generating a straight-

line trajectory is a simple task. However, with the help of this

assignment, they realize that this is not the case.

Dynamics and Control

In this project, the joint control of one degree of freedom (1-dof)

robot manipulator is addressed. The control is focused on the

single-loop control using a PID controller. The tutorial of this

assignment provides the students with some Matlab/Simulink

resources containing a dynamic simulation and a graphical

animation of the 1-dof arm manipulator. It also includes a

Simulink model of a single joint manipulator masked in a unique

sub-system, which can be used as a block in a closed loop control,

as depicted in Figure 4. As it can be seen in this diagram, the

controller is a simple Matlab function, rather than the typical

continuous or discrete block function. This block is used to tackle

the digital implementation and programming aspect of the PID

controller.

In the tutorial, students are also provided with the technique

of transforming continuous transfer functions to discrete ones by

using one of the many approximation methods that maps the

s-domain into z-domain, such as Euler’s or Tustin’s methods. The

implementation of the PID controller (as a Matlab function) using

Euler’s approximation is given in Table 4. This function uses the

constants and variables defined in the secondary script.

Finally, a graphical animation of the arm (provided by

Simulink demo package) is added to the simulation (Fig. 5).

Table 2 Script Controlling the Simulation Given in Figure 2

% Simple moves of SCARA skeletoninitscara; % loading SCARAinit_s; % Initial position% Cartesian movex¼[1 0 0 pi];move_x(x);% Joint moveq1¼[pi/2 0 0.5 0];move_q(q1);% Cartesian movex¼[0 1 0.2 pi];move_x(x);% interpolating movess1¼[�1 0 0.2 0];s2¼[�1 0 0.5 0];ss¼[s1; s2];move_s(ss);

Figure 3 Simulation of a 2-dof planar manipulator performing straight-

line moves.

Table 3 Script for Performing the Simulation Given in Figure 3

% Cartesian moves using cubic-splineinittitle (‘Click on 4 points’);[X, Y]¼ginput(4);T¼3; % Time of each move% Move with one (1) intermediate pointN¼1;PosInicial¼[X(1) Y(1)];P¼[X(2) Y(2)];moves(P, N, T);% Move with 2 intermediate pointsN¼2;PosInicial¼P;P¼[X(3) Y(3)];moves(P, N, T);% Move with 4 intermediate pointsN¼4;PosInicial¼P;P¼[X(4) Y(4)];moves(P, N, T);

Figure 4 Simulink diagram for simulating control of 1-dof arm

manipulator.

618 ALIANE

Results of the simulation can then be viewed in different ways:

through the animation of the arm itself and through time-series

plots.

In this assignment, students are asked to perform several

simulations to explore the effect of tuning parameters. At a first

stage, students should get a feel for the qualitative aspects of

control, exploring what happens if a given tuning parameter is

increased or decreased. The quantitative aspects do not matter

as much. This routine enables students to quickly perceive the

significance of a closed loop and understand the meaning of the

controller’s tuning parameters better. In a second part, they are

also asked to perform a simulation of a two-link planar arm with

two revolute rigid links and perform joint control using a discrete

decentralized PID. The digital implementation is now drawn from

Tustin’s approximation.

DISCUSSION

This approach was implemented in a robotics course offered to

students in their final year of computer engineering, for five

consecutive years from 2000 to 2005 at Universidad Europea de

Madrid. The class consists of 4 h weekly: 2 h of lecture and 2 h of

laboratory work dedicated to working on the assigned projects.

By the end of the course, the laboratory sessions are dedicated to

programming industrial robots. The robotics class had an average

of 15 students over the last 5 years.

Students responded well to the method, and in general they

did not have problems understanding and tackling the assign-

ments’ challenges from a programming point of view. The first

project, which deals with homogenous transforms, is clearly the

most important, and several m-files developed in this assignment

have been re-used in the succeeding assignments. The fourth one

is the least demanding, since students have no background in

dynamics and control.

From a pedagogical point of view, programming activities

fall under a student-centered education methodology. When

students undertake these types of activities, they are immersed in

a self-learning dynamic, and therefore take an active role in their

learning process. Students continually analyze their programs and

the effectiveness of their ideas, which ultimately enables them to

construct their knowledge, rather than memorize abstract

formulae.

Concerning the use of Matlab, although almost 30% of the

students had not used the software before and there was very little

formal instruction given in class on Matlab, they were

enthusiastic about the language because it is easy to learn, and

allows for coding relatively complex programs quickly compared

to traditional languages, such as C/Cþþ. However, some students

suggested the use of alternative software, such as Python or the

Java 3D package.

The students’ opinions are also important for the teacher. To

this end, a focus group interview [14] and the traditional course

survey are used to find out the students’ perceptions of the

methodology and how effectively the programming activities

helped them understand the material. The interview consists in

debating a set of questions. A numerical rate is also attributed to

the topics being discussed. The questionnaires from two

consecutive academic years, from 2003 to 2004 and 2004 to

2005, are summarized in Table 5.

Basically, students uniformly agreed that the methodology

is effective in supplementing the course material, and they believe

that the programming approach helped them gain more insight

and understanding of the material than a purely mathematical

approach would have. Most of them also agreed that the

incorporation of visual elements and animated graphs in the

assignments made them more active and involved in their own

learning process.

They were also grateful for the flexibility of working at their

convenience, and many of them suggested decreasing the lecture

part and extending the homework assignments. In this aspect,

many students advocated to shift to the project-based learning

methodology.

Basically, the interview findings and survey results were

consistent with the teacher’s observations.

Table 4 Matlab Function of a PID Controller

% Digital PID controller% Kp, Ki, Kd: PID gains, T, sample period% A¼KpþKi*TþKd/T;% B¼�Kp �2*Kd/T;% C¼Kd/T;function [u]¼pid(e)global A B Cglobal u_1 e_1 e_2% Control signalu¼u_1þA*eþB*e_1þC*e_2;% Variables actualizatione_2¼e_1;e_1¼e;u_1¼u;

Figure 5 Graphical animation of a 1-dof arm manipulator.

Table 5 Student Questionnaire: A Total of 28 Students Took Part in

the Interview and Survey

No. Questionnaire Score

1 The programming approach is helpful in understanding

the material

4.2

2 The tutorials are useful for developing the projects 3.8

3 The time allocated for the project is sufficient 3.3

4 The Matlab is adequate for developing the projects 4.5

5 The robotics course is motivating 4.1

The mean scores express the level of convenience from 1 to 5.

ROBOTICS TO COMPUTER SCIENTISTS 619

CONCLUSION

In this article, a methodology for teaching fundamentals of

robotics to computer scientists has been addressed. The

instruction of the subject is focused on the computational issues

that govern robotic systems. The approach is based on taking

advantage of students’ abilities as computer practitioners and

complementing lectures with programming assignments. The

programming activities are used as instruments to help students

grasp robotics concepts without being weighed down by the

complexity of mathematical machinery. Some assignment

projects are also included. This approach is appropriate for

computer science students, and seems to be effective, since

software activities stimulate and capture their interest, and make

the robotics course more enjoyable.

REFERENCES

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learning technologies in robotics, Proc of the IEEE Inter. Conf. on

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BIOGRAPHY

Nourdine Aliane obtained the electrical

engineering degree in 1990 from the Ecole

Nationale Polytechnique d’Alger, and the PhD

in physics in 1995 from the Universidad

Complutense de Madrid. He is currently a

professor of control engineering and robotics

at the Universidad Europea de Madrid, Spain.

His interests include control systems, robotics,

and education.

620 ALIANE