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Underactuated mechanical systems : Contributions to trajectory planning, analysis, and control
2011 (English)Doktorsavhandling, sammanläggning (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, pages
Umeå: Umeå universitet, Institutionen för tillämpad fysik och elektronik, 2011. 64 p.
Series
Robotics and control lab, ISSN 1654-5419 ; 5
Keyword [en]
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
Identifiers
urn:nbn:se:umu:diva-39719 (URN)978-91-7459-149-1 (ISBN)oai:DiVA.org:umu-39719 (OAI)
Public defence
2011-03-01, KBC-huset , KB3A9, Umeå Universitet, Umeå, 09:00 (English)
Opponent
Supervisors
Available from2011-02-08 Created:2011-02-04 Last updated:2011-03-01Bibliographically approved
List of papers
1. Orbital stabilization of a pre-planned periodic motion to swing up the Furuta pendulum
Open this publication in new window or tab >>Orbital stabilization of a pre-planned periodic motion to swing up the Furuta pendulum : theory and experiments
2009 (English)In: ICRA: 2009 IEEE International conference in robotics an automation, 7 vol., 2009, 3562-3567Konferensbidrag (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.

Keyword
Furuta pendulum, virtual holonomic constraints, motion planning, orbital stabilization of periodic trajectories, implementation
Identifiers
urn:nbn:se:umu:diva-37685 (URN)
Conference
IEEE International Conference on Robotics and Automation, Kobe, JAPAN, MAY 12-17, 2009
Available from2010-11-11 Created:2010-11-11 Last updated:2011-02-08Bibliographically approved
2. New approach for swinging up the Furuta pendulum
Open this publication in new window or tab >>New approach for swinging up the Furuta pendulum : theory and experiments
2009 (English)In: Mechatronics (Oxford), ISSN 0957-4158, Vol. 19, no 8, 1240-1250Artikel i tidskrift (Refereed) Published
Abstract [en]

The problem of swinging up inverted pendulums has often been solved by stabilizing a particular class of homoclinic structures present in the dynamics of a physical pendulum. Here, new arguments are suggested to show how other homoclinic curves can be preplanned for dynamics of the passive-link of the robot. This is done by reparameterizing the motions according to geometrical relations among the generalized coordinates, which are known as virtual holonomic constraints. After that, conditions that guarantee the existence of periodic solutions surrounding the planned homoclinic orbits are derived. The corresponding trajectories, in contrast to homoclinic curves, admit efficient design of feedback control laws ensuring exponential orbital stabilization. The method is illustrated by simulations and supported by experimental studies on the Furuta pendulum. The implementation issues are discussed in detail.

National Category
Physical Sciences Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:umu:diva-30767 (URN)10.1016/j.mechatronics.2009.07.005 (DOI)
Available from2010-01-15 Created:2010-01-15 Last updated:2012-08-07Bibliographically approved
3. Shaping stable periodic motions of inertia wheel pendulum
Open this publication in new window or tab >>Shaping stable periodic motions of inertia wheel pendulum : theory and experiment
Show others...
2009 (English)In: Asian journal of control, ISSN 1561-8625, Vol. 11, no 5, 549-556Artikel i tidskrift (Refereed) Published
Abstract [en]

We consider an underactuated two-link robot called the inertia wheel pendulum. The system consists of a free planar rotational pendulum and a symmetric disk attached to its end, which is directly controlled by a DC-motor. The goal is to create stable oscillations of the pendulum, which is not directly actuated. We exploit a recently proposed feedback-control design strategy based on motion planning via virtual holonomic constraints. This strategy is shown to be useful for design of regulators for achieving orbitally exponentially stable oscillatory motions. The main contribution is a step-by-step procedure on how to achieve oscillations with pre-specified amplitude from a given range and an arbitrary independently chosen period. The theoretical results are verified via experiments with a real hardware setup.

Keyword
Orbital stabilization, periodic motions, nonlinear feedback control, inertia wheel pendulum, underactuated systems
National Category
Electrical Engineering, Electronic Engineering, Information Engineering Physical Sciences
Identifiers
urn:nbn:se:umu:diva-26263 (URN)10.1002/asjc.135 (DOI)
Available from2009-10-01 Created:2009-10-01 Last updated:2012-08-07Bibliographically approved
4. Generating human-like motions for an underactuated three-link robot based on the virtual constraints approach
Open this publication in new window or tab >>Generating human-like motions for an underactuated three-link robot based on the virtual constraints approach
2007 (English)In: Proceedings of the 46th IEEE conference on decision and control, 2007, 5138-5143Konferensbidrag (Refereed)
Abstract [en]

In the field of robotics there is a great interest in developing strategies and algorithms to reproduce human-like behavior. In this paper, we consider motion planning and generation for humanoid robots based on the concept of virtual holonomic constraints. For this purpose, recorded kinematic data from a particular human motion are analyzed in order to extract geometric relations among various joint angles defining the instantaneous postures. The analysis of a simplified human body representation leads to dynamics of a corresponding underactuated mechanical system with parameters based on anthropometric data of an average person. The motion planning is realized by considering solutions of reduced system dynamics assuming the virtual holonomic constraints are kept invariant The relevance of such a mathematical model in accordance to the real human motion under study is shown. An appropriate controller design procedure is presented together with simulation results of a feedback-controlled robot.

Series
Proceedings / IEEE Conference on Decision and Control ; IEEE Control Systems Society, ISSN 0743-1546, 0191-2216 (ISDS)
Keyword
motion planning, underactuated mechanical systems, humanoid robots, virtual holonomic constraints
Identifiers
urn:nbn:se:umu:diva-37701 (URN)10.1109/CDC.2007.4434799 (DOI)978-1-4244-1497-0 (ISBN)
Conference
46th IEEE Conference on Decision and Control, New Orleans, LA, DEC 12-14, 2007
Available from2010-11-11 Created:2010-11-11 Last updated:2011-02-08Bibliographically approved
5. Motion planning for humanoid robots based on virtual constraints extracted from recorded human movements
Open this publication in new window or tab >>Motion planning for humanoid robots based on virtual constraints extracted from recorded human movements
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2008 (English)In: Intelligent Service Robotics, ISSN 1861-2776, Vol. 1, no 4, 289-301Artikel i tidskrift (Refereed) Published
Abstract [en]

In the field of robotics there is a great interest in developing strategies and algorithms to reproduce human-like behavior. In this paper, we consider motion planning for humanoid robots based on the concept of virtual holonomic constraints. At first, recorded kinematic data of particular human motions are analyzed in order to extract consistent geometric relations among various joint angles defining the instantaneous postures. Second, a simplified human body representation leads to dynamics of an underactuated mechanical system with parameters based on anthropometric data. Motion planning for humanoid robots of similar structure can be carried out by considering solutions of reduced dynamics obtained by imposing the virtual holonomic constraints that are found in human movements. The relevance of such a reduced mathematical model in accordance with the real human motions under study is shown. Since the virtual constraints must be imposed on the robot dynamics by feedback control, the design procedure for a suitable controller is briefly discussed.

Springer-Verlag, 2008
Keyword
Motion planning, Humanoid robots, Virtual holonomic constraints, Underactuated mechanical systems
Identifiers
urn:nbn:se:umu:diva-26261 (URN)10.1007/s11370-008-0027-2 (DOI)
Available from2009-10-01 Created:2009-10-01 Last updated:2011-02-08Bibliographically approved
6. Stable walking gaits for a three-link planar biped robot with one actuator
Open this publication in new window or tab >>Stable walking gaits for a three-link planar biped robot with one actuator
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2013 (English)In: IEEE Transactions on robotics, ISSN 1552-3098, IEEE transactions on robotics, Vol. 29, no 3, 589-601Artikel i tidskrift (Refereed) Published
Abstract [en]

We consider a benchmark example of a three-link planar biped walker with torso, which is actuated in between the legs. The torso is thought to be kept upright by two identical torsional springs. The mathematical model reflects a three-degree-of-freedom mechanical system with impulse effects, which describe the impacts of the swing leg with the ground, and the aim is to induce stable limit-cycle walking on level ground. The main contribution is a novel systematic trajectory planning procedure for solving the problem of gait synthesis. The key idea is to find a system of ordinary differential equations for the functions describing a synchronization pattern for the time evolution of the generalized coordinates along a periodic motion. These functions, which are known as virtual holonomic constraints, are also used to compute an impulsive linear system that approximates the time evolution of the subset of coordinates that are transverse to the orbit of the continuous part of the periodic solution. This auxiliary system, which is known as transverse linearization, is used to design a nonlinear exponentially orbitally stabilizing feedback controller. The performance of the closed-loop system and its robustness with respect to various perturbations and uncertainties are illustrated via numerical simulations.

Keyword
Biped robots, holonomic servoconstraints, limit-cycle walking, orbital stabilization, trajectory planning with dynamic constraints, transverse linearization, underactuated mechanical systems, virtual holonomic constraints
National Category
Robotics Veterinary Science
Identifiers
urn:nbn:se:umu:diva-39717 (URN)10.1109/TRO.2013.2239551 (DOI)000320137200001 (ISI)
Funder
Swedish Research Council
Note
<p>Funding Agency, Grant Number:</p><p>Russian Federal Agency for Science and Innovation, 02.740.11.505</p><p>Russian Federal Target Program "Research &amp; Development in Priority Areas", 11.519.11.4007</p><p>Norwegian Research Council under KMB grant Next Generation Robotics for Norwegian Industry</p><p>Norwegian Research Council under FRIPRO Grant, 214525/F20</p><p>Russian Foundation for Basic Research, 12-01-00808</p><p></p>Available from2011-02-04 Created:2011-02-04 Last updated:2013-07-29Bibliographically approved
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8. Traversing from Point-to-Point along a straight line with a ballbot
Open this publication in new window or tab >>Traversing from Point-to-Point along a straight line with a ballbot
2010 (English)In: 8th IFAC Symposium on Nonlinear Control Systems, 2010Konferensbidrag (Refereed)
Identifiers
urn:nbn:se:umu:diva-39715 (URN)
Available from2011-02-04 Created:2011-02-04 Last updated:2011-02-08Bibliographically approved

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