A geometric approach for generating feasible configurations of robotic manipulators

doctoral thesis

• Title (croatian): Geometrijski pristup generiranju ostvarivih konfiguracija robotskih manipulatora
• Author: Filip Marić; MBZ: -391147
• Mentor: Ivan Petrović (mentor)
• Mentor: Jonathan Kelly https://orcid.org/0000-0002-5528-6136 (komentor)
• Committee member: Ivan Petrović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; (Department of Control and Computer Engineering); Zagreb
• Granter: Canada: University of Toronto; Toronto
• Defense date and country: 2023, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Electrical Engineering; Automation and Robotics
• Universal decimal classification (UDC): 621.3 - Electrical engineering

Abstract

Most robotic manipulators, and especially those designed with autonomous operation in mind, consist of a series of joints that rotate about a single axis, also known as revolute joints. These mechanisms give robotic manipulators the degrees of freedom and versatility similar to that of the human arm, which they are designed to outperform. However, this results in a geometry of motion or kinematics that makes all aspects of robotic manipulation challenging from a computational perspective. A major part of this challenge lies in the fact that computing joint configurations adhering to a specific set of constraints (i.e., gripper pose) is a non-trivial problem. The procedure of finding feasible joint configurations and the mathematical problem associated with it are known as inverse kinematics - a core part of motion planning, trajectory optimization, calibration and other important challenges in successfully performing robotic manipulation. In recent years, the overall decrease of computation time required to perceive and process environmental and proprioceptive information has helped realize the potential of robotic manipulation in dynamic environments. Concurrently, a new standard in manipulator design has emerged, where additional degrees of freedom are added in order to increase their overall dexterity and capacity for motion. These two developments have vastly increased the requirements for inverse kinematics algorithms, which are now expected to deal with infinite solution spaces and difficult, nonlinear constraints. On the other hand, the addition of degrees of freedom in recent robot designs has enabled algorithms to search for locally optimal configurations with respect to some performance criteria in an infinitely large solution space. This property has motivated approaches that leverage non-Euclidean geometries to replace conventional constraints and optimization criteria, thereby overcoming computational bottlenecks and common failure modes. The contributions presented in this thesis propose three such approaches, that aim to develop new ways of looking at the problems associated with inverse kinematics through the use of geometric representations that are not widely utilized in robotic manipulation.

Abstract (croatian)

Većina robotskih manipulatora, posebno onih dizajniranih za autonomno obavljanje zadataka, sastoji se od niza zglobova koji se okreću oko jedne osi rotacije. Ovi mehanizmi omogućuju robotskim manipulatorima stupnjeve slobode slične onima ljudske ruke, što je ujedno i cilj pri njihovom projektiranju. Međutim, ovi mehanizmi rezultiraju geometrijom gibanja ili kinematikom, koja čini sve aspekte robotske manipulacije izazovnima iz računske perspektive. Glavni dio ovog izazova leži u činjenici da je izračun konfiguracija zglobova koje se pridržavaju određenog skupa ograničenja (npr. položaja izvršnog člana) netrivijalan problem. Postupak pronalaska izvedivih konfiguracija zglobova i matematički problem asociran s tim postupkom poznati su kao inverzna kinematika, te čine ključni dio planiranja kretanja, optimizacije putanje, kalibracije i drugih važnih izazova pri uspješnom izvođenju robotske manipulacije. Nedavno smanjenje vremena izračuna potrebnog za opažanje i obradu okolišnih i proprioceptivnih informacija pomoglo je ostvarenju potencijala robotske manipulacije u dinamičnim okruženjima. Istodobno se postavlja novi standard u dizajnu manipulatora koji uključuje dodavanje redundantnih stupnjeva slobode sa ciljem povećanja sposobnosti kretanja. Ova su dva čimbenika uvelike povećala zahtjeve za algoritme inverzne kinematike, od kojih se sada očekuje operacija pri beskonačnim prostorima rješenja i teškim, nelinearnim ograničenjima. S druge strane, redundantni stupnjevi slobode omogućuju algoritmima potragu za lokalno optimalnim konfiguracijama s obzirom na specifične kriterije izvedbe u beskonačno velikom prostoru rješenja. Ovo svojstvo je motiviralo pristupe koji koriste neeuklidsku geometriju za svladavanje konvencionalnih ograničenja i kriterija optimizacije, čime se prevladavaju računska uska grla i razni uobičajeni problemi pri optimizaciji. Doprinosi obrazloženi u ovoj disertaciji predlažu tri takva geometrijska pristupa. Njihov je cilj razvoj novih načina gledanja na probleme povezane s inverznom kinematikom korištenjem geometrijskih prikaza koji još nemaju široku upotrebu u robotskoj manipulaciji.

• Keywords: robotic manipulators; robot kinematics; non-Euclidean geometry; geometry-aware singularity avoidance; distance-geometric inverse kinematics
• Keywords (croatian): robotski manipulatori; kinematika robota; neeuklidska geometrija; izbjegavanje singularnosti svjesno geometrije; inverzna kinematika udaljenosti i geometrije
• Language: english
• URN:NBN: urn:nbn:hr:168:530971
• Promotion: 2023
• Study programme: Title: Doctoral study programme "Electrical Engineering and Computing"; Study programme type: university; Study level: postgraduate; Academic / professional title: doktor/doktorica znanosti, po-dručje tehničkih znanosti (doktor/doktorica znanosti, po-dručje tehničkih znanosti)
• Type of resource: Text
• Extent: ix, 96 str. : graf. prikazi ; 31 cm
• File origin: Born digital
• Access conditions: Open access
• Created on: 2023-04-11 08:36:51