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Orbital stabilization of a pre-planned periodic motion to swing up the Furuta pendulum: theory and experiments
Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics.
Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics.
Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics.
Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics.
2009 (English)In: ICRA: 2009 IEEE International conference in robotics an automation, 7 vol., 2009, 3562-3567 p.Conference paper (Refereed)
Abstract [en]

The problem of swinging up inverted pendulums has often been solved by stabilization of a particular class of homoclinic structures present in the dynamics of the standard pendulum. In this article new arguments are suggested to show how different homoclinic curves can be preplanned for dynamics of the passive-link of the robot. This is done by reparameterizing the motion according to geometrical relations among the generalized coordinates. It is also shown that under certain conditions there exist periodic solutions surrounding such homoclinic orbits. These trajectories admit designing feedback controllers to ensure exponential orbital stabilization. The method is illustrated by simulations and supported by experimental studies.

Place, publisher, year, edition, pages
2009. 3562-3567 p.
Keyword [en]
Furuta pendulum, virtual holonomic constraints, motion planning, orbital stabilization of periodic trajectories, implementation
URN: urn:nbn:se:umu:diva-37685OAI: diva2:369757
IEEE International Conference on Robotics and Automation, Kobe, JAPAN, MAY 12-17, 2009
Available from: 2010-11-11 Created: 2010-11-11 Last updated: 2011-02-08Bibliographically approved
In thesis
1. Underactuated mechanical systems: Contributions to trajectory planning, analysis, and control
Open this publication in new window or tab >>Underactuated mechanical systems: Contributions to trajectory planning, analysis, and control
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Nature and its variety of motion forms have inspired new robot designs with inherentunderactuated dynamics. The fundamental characteristic of these controlled mechanicalsystems, called underactuated, is to have the number of actuators less than the number ofdegrees of freedom. The absence of full actuation brings challenges to planning feasibletrajectories and designing controllers. This is in contrast to classical fully-actuated robots.A particular problem that arises upon study of such systems is that of generating periodicmotions, which can be seen in various natural actions such as walking, running,hopping, dribbling a ball, etc. It is assumed that dynamics can be modeled by a classicalset of second-order nonlinear differential equations with impulse effects describing possibleinstantaneous impacts, such as the collision of the foot with the ground at heel strikein a walking gait. Hence, we arrive at creating periodic solutions in underactuated Euler-Lagrange systems with or without impulse effects. However, in the qualitative theory ofnonlinear dynamical systems, the problem of verifying existence of periodic trajectoriesis a rather nontrivial subject.The aim of this work is to propose systematic procedures to plan such motions and ananalytical technique to design orbitally stabilizing feedback controllers. We analyze andexemplify both cases, when the robotmodel is described just by continuous dynamics, andwhen continuous dynamics is interrupted from time to time by state-dependent updates.For trajectory planning, systems with one or two passive links are considered, forwhich conditions are derived to achieve periodicmotions by encoding synchronizedmovementsof all the degrees of freedom. For controller design we use an explicit form tolinearize dynamics transverse to the motion. This computation is valid for an arbitrarydegree of under-actuation. The linear system obtained, called transverse linearization, isused to analyze local properties in a vicinity of the motion, and also to design feedbackcontrollers. The theoretical background of these methods is presented, and developedin detail for some particular examples. They include the generation of oscillations forinverted pendulums, the analysis of human movements by captured motion data, and asystematic gait synthesis approach for a three-link biped walker with one actuator.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, Institutionen för tillämpad fysik och elektronik, 2011. 64 p.
Robotics and control lab, ISSN 1654-5419 ; 5
Underactuated mechanical systems, mechanical systems with impacts, trajectory planning, periodic trajectories, orbital stabilization, walking robots, virtual holonomic constraints, transverse linearization
National Category
Control Engineering
Research subject
Automatic Control
urn:nbn:se:umu:diva-39719 (URN)978-91-7459-149-1 (ISBN)
Public defence
2011-03-01, KBC-huset , KB3A9, Umeå Universitet, Umeå, 09:00 (English)
Available from: 2011-02-08 Created: 2011-02-04 Last updated: 2011-03-01Bibliographically approved

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La Hera, Pedro M.Shiriaev, Anton S.Freidovich, Leonid B.Mettin, Uwe
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