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Kyiv – 2025 Description of the discipline Modern methods of optimization of robotic systems (title) Studying the course Modern Methods of Optimization in Robotic Systems is crucial for developing advanced, efficient, and intelligent robotic applications. Optimization lies at the heart of robotics, enabling tasks such as motion planning, control, sensor fusion, and machine learning integration. This course equips students with the tools to model and solve complex problems using techniques like convex optimization, evolutionary algorithms, and real-time decision-making strategies. As robotic systems become more autonomous and adaptive, mastering these modern optimization methods ensures better performance, resource efficiency, and safety. Furthermore, this knowledge is key to innovation in fields like autonomous vehicles, industrial automation, and medical robotics, where optimal solutions are essential for reliability and competitiveness in rapidly evolving technological environments. Area of knowledge, specialty, academic programme, academic degreeAcademic degree MasterSpecialty G11 «Mechanical Engineering (by specializations)»Academic programmeRobotic systems and complexes of agricultural productionCharacteristics of the disciplineTypeMandatoryGeneral volume of hours120Number of credits ECTS 4Number of modules3Course project-Control formExamIndicators of the discipline for full-time forms of university studyYear of study1Term2Lectures45 h.Practical classes and seminars-Laboratory classes30 h.Self-study45 h.Number of hours per week for full-time students5 h. 1. Aim, competences and expected learning outcomes of the discipline The aim of the discipline is to acquaint students with modern optimization methods and their application in various areas of mechanical engineering, in particular for robotic systems. The training course is aimed at forming in students a deep understanding of the theoretical aspects of optimization, as well as practical skills for their implementation. Tasks of the discipline: review of modern optimization methods (genetic algorithms, simulation modeling, direct search methods, gradient-oriented methods, etc.), determination of the main advantages and disadvantages of each method; optimization application models for solving optimization problems of industrial mechanical engineering (synthesis of optimal laws of movement of forklifts and robotic systems, automatic control systems, training of artificial neural networks, etc.). Competences acquired: integral competence: the ability to solve complex tasks and problems of industrial mechanical engineering, which involve research and/or innovation and are characterized by uncertainty of conditions and requirements. general competences (GC): GC2. Ability to learn and master modern knowledge. GC 4. Ability to be critical and self-critical. GC 6. Ability to generate new ideas (creativity). special (professional) competencies (SC): SC3. Ability to create new equipment and technologies in the field of mechanical engineering. SC4. Awareness of the promising tasks of modern production aimed at meeting the needs of consumers, mastery of trends in innovative development of technologies in the industry. SC7. Ability to use intelligent technologies to ensure the sustainable development of robotic systems of agricultural production. Expecting learning outcomes (ELO): ELO2. Knowledge and understanding of mechanics and mechanical engineering and the prospects for their development. ELO4. Perform engineering calculations to solve complex tasks and practical problems in the field of mechanical engineering. ELO6. Find the necessary scientific and technical information in available sources, in particular, in a foreign language, analyze and evaluate it. ELO8. Knowledge of the production advantages and features of the use of robotic systems and complexes in the agricultural sector. Programme and structure of the discipline Modules and topicsNumber of hoursfull-timetotalincludinglplabinds.stweeks12345678Module 1. General characteristics of optimization robotics problems and approaches to their solutionTopic 1. Formulation of the optimization problem126---61-2Topic 2. Peculiarities of objective functions and problems with constraints206-4-102-3Total for module 13212-4-16-Module 2. Methods of solving optimization robotics problemsTopic 3. General characteristics of optimization methods. Features of optimization methods for robotics62-4--4-5Topic 4. PSO optimization method and review of its application in robotics optimization185-8-55-7Topic 5. DE optimization method and review of its application in robotics optimization134-4-58-9Topic 6. GWO optimization method and review of its application in robotics optimization124-4-410-11Topic 7. HS optimization method and review of its application in robotics optimization44----12Total for module 25319-20-14-Module 3. Problems of optimization of robotic systemsTopic 8. Synthesis of optimal robot motion control systems156-4-512-13Topic 9. Synthesis of optimal robot movement trajectories114-2-513-14Topic 10. Optimal setting of frequency-controlled drives of robotic systems94---515Total for module 33514-6-15-Total hours12045-30-45- 3. Topics of lectures !TopicHours1Formulation of the optimization problem62Peculiarities of objective functions and problems with constraints63General characteristics of optimization methods. Features of optimization methods for robotics24PSO optimization method and review of its application in robotics optimization55DE optimization method and review of its application in robotics optimization46GWO optimization method and review of its application in robotics optimization47HS optimization method and review of its application in robotics optimization48Synthesis of optimal robot motion control systems69Synthesis of optimal robot movement trajectories410Optimal setting of frequency-controlled drives of robotic systems4 4. Topic of laboratory (practical, seminars) classes !TopicHours1Study of topological characteristics of objective functions of optimization robotics problem42Study of the influence of parameters of swarm dimension and the number of iterations on the efficiency of the PSO algorithm43Study of the operation of modifications of the PSO method with local connections between particles44Investigation of search properties of the DE differential evolution method and its modifications45A study of the search properties of the GWO gray wolf method46Comparative study of search properties of optimization algorithms of optimization robotics problem47Optimum setting of the PI controller of the motion of the robot link48Planning the optimal movement trajectory of the gripping body of the robot manipulation system2 Topics of self-study !TopicHours1Formulation of the optimization problem for dynamic systems62Summary of optimization problems using penalty functions. Types of penalty functions53Non-differentiability of objective functions and approaches to optimization of non-differentiable objective functions54Modifications of the PSO method55Modifications of the DE method56Modifications of the GWO method47Types of restrictions and criteria for optimal control of robot movement58Approaches to solving the problem of synthesis of optimal robot movement trajectories59Mathematical models of frequency-controlled drives and optional settings of frequency converters5 6. Methods of assessing expected learning outcomes: When teaching this discipline, the following diagnostic tools are used: oral interview; exam; module tests; defense of laboratory work. 7. Teaching methods: When teaching this discipline, the following methods are used: problem-based learning method; practice-oriented learning method; research-based learning method; educational discussions and debates method; teamwork and brainstorming method. Results assessment The knowledge of a higher education applicant is assessed on a 100-point scale, which is translated into a national assessment in accordance with the current "Regulations on Examinations and Tests at the ÌÇÐÄVlog of Ukraine." Distribution of points by types of educational activities Type of training activitiesResults teachingEvaluationModule 1. General characteristics of optimization robotics problems and approaches to their solutionSelf-study work 1ELO2, ELO4, ELO8. To know main topological features of objective functions. To be able to separate objective functions by their features20Self-study work 230Lab 120Module 1 test-30Overall on 1st module-100Module 2. Methods of solving optimization robotics problemsLab 2ELO2, ELO6, ELO8. To know the main ideas of metaheuristics. To be able to apply them to find minimum or maximum of an objective function, to be able to set proper setting of optimization algorithms.Lab 310Self-study work 310Lab 410Self-study work 410Lab 510Self-study work 510Lab 610Module 2 test-30Overall on 2nd module-100Module 3. Problems of optimization of robotic systemsLab 7ELO4, ELO6, ELO8. To know how to reduce a robotic problem to the problem of optimization. To be able to select proper algorithm to solve it. 15Self-study work 615Lab 815Self-study work 715Self-study work 810Module 3 test-30Overall on 3rd module-100Class work-(1+2+3)/3*0,7 d"70Exam-30Overall-(Class work+Exam)d"100 8.2 Scale for assessing student s knowledge Student s rating, pointsNational grading (exam/credits)90-100excellent74-89good60-73satisfactory0-59unsatisfactory 8.3 Assessment policy Deadlines and exam retaking rules works that are submitted late without valid reasons will be assessed with a lower grade. Module tests may be retaken with the permission of the lecturer if there are valid reasons (e.g. a sick leave). Academic integrity rulescheating during tests and exams is prohibited (including using mobile devices). Term papers and essays must have correct references to the literature usedAttendance rulesattendance is compulsory. For good reasons (e.g. illness, international internship), training can take place individually (online by the faculty dean’s consent) Teaching and learning aids Course on E-learn: https://elearn.nubip.edu.ua/course/view.php?id=5499 lecture notes and their presentations (in electronic form); methodological materials for studying the academic discipline for higher education students. 10. Recommended sources of information . . 04VT20. 5B>48 >?B8HC:C >?B8<0;L=8E @VH5=L. 02G0;L=89 ?>AV1=8:. V<. 3>@O !V:>@AL:>3>. 2023. - 73 A. ... C7=TF>2, .. @840;L=89 "5>@VO B5E=VG=8E A8AB5< 2 0A?5:B0E 4>A;V465=L B0 B5E=VG=>W B2>@G>ABV. 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„°„˜þÆ°^„°`„˜þ‡hˆH.€ „€„˜þÆ€^„€`„˜þ‡hˆH.‚ „P„LÿÆP^„P`„Lÿ‡hˆH.h „Ð„˜þ^„Ð`„˜þ6‡hˆH.h „ „˜þ^„ `„˜þ‡hˆH.’h „p„Lÿ^„p`„Lÿ‡hˆH.h „@„˜þ^„@`„˜þ‡hˆH.h „„˜þ^„`„˜þ‡hˆH.’h „à„Lÿ^„à`„Lÿ‡hˆH.h „°„˜þ^„°`„˜þ‡hˆH.h „€„˜þ^„€`„˜þ‡hˆH.’h „P„Lÿ^„P`„Lÿ‡hˆH.h„Ð„˜þÆÐ^„Ð`„˜þ5o(‡hˆH.€ „ „˜þÆ ^„ `„˜þ‡hˆH.‚ „p„LÿÆp^„p`„Lÿ‡hˆH.€ „@„˜þÆ@^„@`„˜þ‡hˆH.€ „„˜þÆ^„`„˜þ‡hˆH.‚ „à„LÿÆà^„à`„Lÿ‡hˆH.€ „°„˜þÆ°^„°`„˜þ‡hˆH.€ „€„˜þÆ€^„€`„˜þ‡hˆH.‚ „P„LÿÆP^„P`„Lÿ‡hˆH.„8„˜þ^„8`„˜þo(.€ „„˜þ^„`„˜þ‡hˆH.‚ „Ø „Lÿ^„Ø `„Lÿ‡hˆH.€ „¨„˜þ^„¨`„˜þ‡hˆH.€ „x„˜þ^„x`„˜þ‡hˆH.‚ „H„Lÿ^„H`„Lÿ‡hˆH.€ „„˜þ^„`„˜þ‡hˆH.€ „è„˜þ^„è`„˜þ‡hˆH.‚ „¸„Lÿ^„¸`„Lÿ‡hˆH.@»OJQJ^Jo(.„Ð„˜þÆÐ^„Ð`„˜þo(.„ „˜þÆ ^„ `„˜þ.‚„p„LÿÆp^„p`„Lÿ.€„@„˜þÆ@^„@`„˜þ.€„„˜þÆ^„`„˜þ.‚„à„LÿÆà^„à`„Lÿ.€„°„˜þÆ°^„°`„˜þ.€„€„˜þÆ€^„€`„˜þ.‚„P„LÿÆP^„P`„Lÿ.„Ð„˜þÆÐ^„Ð`„˜þ.€„ „˜þÆ ^„ `„˜þ.€„p„˜þÆp^„p`„˜þ.€„@„˜þÆ@^„@`„˜þ.€„„˜þÆ^„`„˜þ.€„à„˜þÆà^„à`„˜þ.€„°„˜þÆ°^„°`„˜þ.€„€„˜þÆ€^„€`„˜þ.€„P„˜þÆP^„P`„˜þ.h „8„˜þ^„8`„˜þ6‡hˆH.h „„˜þ^„`„˜þ‡hˆH.’h „Ø „Lÿ^„Ø `„Lÿ‡hˆH.h „¨„˜þ^„¨`„˜þ‡hˆH.h „x„˜þ^„x`„˜þ‡hˆH.’h „H„Lÿ^„H`„Lÿ‡hˆH.h „„˜þ^„`„˜þ‡hˆH.h „è„˜þ^„è`„˜þ‡hˆH.’h „¸„Lÿ^„¸`„Lÿ‡hˆH.h „„˜þ^„`„˜þ‡hˆH.h „×„˜þ^„×`„˜þ‡hˆH.’h „§ „Lÿ^„§ `„Lÿ‡hˆH.h „w „˜þ^„w `„˜þ‡hˆH.h „G„˜þ^„G`„˜þ‡hˆH.’h „„Lÿ^„`„Lÿ‡hˆH.h „ç„˜þ^„ç`„˜þ‡hˆH.h „·„˜þ^„·`„˜þ‡hˆH.’h „‡„Lÿ^„‡`„Lÿ‡hˆH.„Ð„˜þÆÐ^„Ð`„˜þ.€„ „˜þÆ ^„ `„˜þ.€„p„˜þÆp^„p`„˜þ.€„@„˜þÆ@^„@`„˜þ.€„„˜þÆ^„`„˜þ.€„à„˜þÆà^„à`„˜þ.€„°„˜þÆ°^„°`„˜þ.€„€„˜þÆ€^„€`„˜þ.€„P„˜þÆP^„P`„˜þ.„G„˜þ^„G`„˜þo(.€ „ „˜þ^„ `„˜þ‡hˆH.‚ „ç„Lÿ^„ç`„Lÿ‡hˆH.€ „·„˜þ^„·`„˜þ‡hˆH.€ „‡„˜þ^„‡`„˜þ‡hˆH.‚ „W„Lÿ^„W`„Lÿ‡hˆH.€ „'„˜þ^„'`„˜þ‡hˆH.€ „÷„˜þ^„÷`„˜þ‡hˆH.‚ „Ç„Lÿ^„Ç`„Lÿ‡hˆH.Ð„8„˜þ^„8`„˜þo(.€ „„˜þ^„`„˜þ‡hˆH.‚ „Ø „Lÿ^„Ø `„Lÿ‡hˆH.€ „¨„˜þ^„¨`„˜þ‡hˆH.€ „x„˜þ^„x`„˜þ‡hˆH.‚ „H„Lÿ^„H`„Lÿ‡hˆH.€ „„˜þ^„`„˜þ‡hˆH.€ „è„˜þ^„è`„˜þ‡hˆH.‚ „¸„Lÿ^„¸`„Lÿ‡hˆH. „ß„‰þ^„ß`„‰þo(.€ „ „˜þ^„ `„˜þ‡hˆH.‚ „p„Lÿ^„p`„Lÿ‡hˆH.€ „@„˜þ^„@`„˜þ‡hˆH.€ „„˜þ^„`„˜þ‡hˆH.‚ „à„Lÿ^„à`„Lÿ‡hˆH.€ „°„˜þ^„°`„˜þ‡hˆH.€ „€„˜þ^„€`„˜þ‡hˆH.‚ „P„Lÿ^„P`„Lÿ‡hˆH.„Ð„˜þ^„Ð`„˜þOJPJQJ^Jo(-€„ „˜þ^„ 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