Subject

Mathematical Methods in Robotics

Course Title

Mathematical Methods in Robotics
Mathematical Methods in Robotics

Code

m23_s_006

Study Programme

—

Organizer of the study programme (unit, institute, department or division)

Faculty of Computer Science and Engineering

Degree level (first, second, third cycle)

Second cycle

Academic year / semester

10 / Summer

Number of ECTS credits

Teacher

Vesna Dimitrievska Ristovska

Prerequisites for enrolling in the course

—

10.

Objectives of the course programme (competences)

The course will cover techniques for modeling 3D objects. The course covers a spectrum of different methods for representing the geometry of real objects, depending on their functionality and application. The goal is for the student to become familiar with the basic theoretical concepts and fundamental principles of constructing various types of models. Emphasis will be placed on modeling robot motion.

11.

Course content

Point, line, and segment; relative positions; polylines. Polynomial interpolation and approximation, Convex and concave polygon; polyhedron; convex hull. Different types of geometric models. Models for representing boundaries. Operations for representing boundaries. Introduction to GSG; interval arithmetic. GSG pruning tree; blends; integral properties. Introduction to splines; Bézier curves. Spline drawing; degree evaluation. Sculpted surfaces: applications. Construction of splines from Bézier curves. B-splines; interpolating splines. Voronoi diagram; Delaunay triangulation. Largest empty circle, optimization, computational geometry, differential geometry.

12.

Learning methods

Lectures, exercises, projects, seminar papers, independent problem solving

13.

Total available time

6 ECTS x 30 hours = 180 hours

14.

Distribution of available time

65 + 0 + 45 + 45 + 30 = 180 hours

15.

Forms of teaching activities

15.1.	Lectures - theoretical instruction	65 hours
15.2.	Exercises (laboratory, auditory), seminars, teamwork	0 hours

16.

Other forms of activities

16.1.	Project assignments	45 hours
16.2.	Independent assignments	45 hours
16.3.	Home study	30 hours

17.

Assessment method

17.1.	Tests	0 points
17.2.	Seminar paper / project (presentation: written and oral)	45 points
17.3.	Activities and learning	10 points
17.4.	Final exam	30 points

18.

Grading criteria (points / grade)

up to 50 points	5 (five) (F)
from 51 to 60 points	6 (six) (E)
from 61 to 70 points	7 (seven) (D)
from 71 to 80 points	8 (eight) (C)
from 81 to 90 points	9 (nine) (B)
from 91 to 100 points	10 (ten) (A)

19.

Requirement for obtaining a signature and taking the final exam

Completed activities 15, 16

20.

Language of instruction

Macedonian or English

21.

Method for monitoring the quality of teaching

internal evaluation and surveys

22.

Literature

22.1.	Required literature 1. J. M. Selig \| Geometric Fundamentals of Robotics (Monograph) \| Springer \| 2010 2. J. David Logan \| Applied Mathematics \| John Wiley & Sons \| 2006 3. Mark de Berg, Otfried Cheong, Marc van Kreveld, Mark Overmars \| Computational Geometry: Algorithms and Applications \| Springer \| 2008
22.2.	Additional literature No. Author Title Publisher Year