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Principles for planning and analyzing motions of underactuated mechanical systems and redundant manipulators
Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics. (Robotics and Control Lab)
2009 (English)Doctoral thesis, comprehensive summary (Other academic)Alternative title
Metoder för rörelseplanering och analys av underaktuerade mekaniska system och redundanta manipulatorer (Swedish)
Abstract [en]

Motion planning and control synthesis are challenging problems for underactuated mechanical systems due to the presence of passive (non-actuated) degrees of freedom. For those systems that are additionally not feedback linearizable and with unstable internal dynamics there are no generic methods for planning trajectories and their feedback stabilization. For fully actuated mechanical systems, on the other hand, there are standard tools that provide a tractable solution. Still, the problem of generating efficient and optimal trajectories is nontrivial due to actuator limitations and motion-dependent velocity and acceleration constraints that are typically present. It is especially challenging for manipulators with kinematic redundancy.

A generic approach for solving the above-mentioned problems is described in this work. We explicitly use the geometry of the state space of the mechanical system so that a synchronization of the generalized coordinates can be found in terms of geometric relations along the target motion with respect to a path coordinate. Hence, the time evolution of the state variables that corresponds to the target motion is determined by the system dynamics constrained to these geometrical relations, known as virtual holonomic constraints. Following such a reduction for underactuated mechanical systems, we arrive at integrable second-order dynamics associated with the passive degrees of freedom. Solutions of this reduced dynamics, together with the geometric relations, can be interpreted as a motion generator for the full system. For fully actuated mechanical systems the virtually constrained dynamics provides a tractable way of shaping admissible trajectories.

Once a feasible target motion is found and the corresponding virtual holonomic constraints are known, we can describe dynamics transversal to the orbit in the state space and analytically compute a transverse linearization. This results in a linear time-varying control system that allows us to use linear control theory for achieving orbital stabilization of the nonlinear mechanical system as well as to conduct system analysis in the vicinity of the motion. The approach is applicable to continuous-time and impulsive mechanical systems irrespective of the degree of underactuation. The main contributions of this thesis are analysis of human movement regarding a nominal behavior for repetitive tasks, gait synthesis and stabilization for dynamic walking robots, and description of a numerical procedure for generating and stabilizing efficient trajectories for kinematically redundant manipulators.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, Institutionen för tillämpad fysik och elektronik , 2009. , 88 + 8 papers p.
Series
Robotics and control lab, ISSN 1654-5419 ; 4
Keyword [en]
Motion Planning, Underactuated Mechanical Systems, Redundant Manipulators, Virtual Holonomic Constraints, Orbital Stabilization, Human Movement, Walking Robots, Hydraulic Manipulators
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Automatic Control
Identifiers
URN: urn:nbn:se:umu:diva-30024ISBN: 978-91-7264-914-9 (print)OAI: oai:DiVA.org:umu-30024DiVA: diva2:280586
Public defence
2010-02-05, Naturvetarhuset, N200, Umeå universitet, Umeå, 09:00 (English)
Opponent
Supervisors
Available from: 2009-12-15 Created: 2009-11-30 Last updated: 2011-02-09Bibliographically approved
List of papers
1. 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, 289-301 p.Article in journal (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.

Place, publisher, year, edition, pages
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 from: 2009-10-01 Created: 2009-10-01 Last updated: 2011-02-08Bibliographically approved
2. Stable dynamic walking over rough terrain: Theory and experiment
Open this publication in new window or tab >>Stable dynamic walking over rough terrain: Theory and experiment
2009 (English)In: 14th International Symposium on Robotics Research: Lucerne, Switzerland, Springer-Verlag , 2009, 1-16 p.Conference paper, Published paper (Refereed)
Abstract [en]

We propose a constructive control design for stabilization of non-periodic trajectories of underactuated mechanical systems. An important example of such a system is an underactuated ``dynamic walking'' biped robot walking over rough terrain. The proposed technique is to compute a transverse linearization about the desired motion: a linear impulsive system which locally represents dynamics about a target trajectory. This system is then exponentially stabilized using a modified receding-horizon control design. The proposed method is experimentally verified using a compass-gait walker: a two-degree-of-freedom biped with hip actuation but pointed stilt-like feet. The technique is, however, very general and can be applied to higher degree-of-freedom robots over arbitrary terrain and other impulsive mechanical systems.

Place, publisher, year, edition, pages
Springer-Verlag, 2009
Keyword
Dynamic Walking, Underactuated Mechanical Systems, Predictive Control, Virtual Holonomic Constraints
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Automatic Control
Identifiers
urn:nbn:se:umu:diva-30193 (URN)
Conference
ISRR 2009
Available from: 2009-12-10 Created: 2009-12-10 Last updated: 2009-12-14
3. A passive 2-DOF walker: hunting for gaits using virtual holonomic constraints
Open this publication in new window or tab >>A passive 2-DOF walker: hunting for gaits using virtual holonomic constraints
2009 (English)In: IEEE Transactions on Robotics, ISSN 1552-3098, Vol. 25, no 5, 1202-1208 p.Article in journal (Refereed) Published
Abstract [en]

A planar compass-like biped on a shallow slope is one of the simplest models of a passive walker. It is a 2-degree-of-freedom (DOF) impulsive mechanical system that is known to possess periodic solutions reminiscent of human walking. Finding such solutions is a challenging computational task that has attracted many researchers who are motivated by various aspects of passive and active dynamic walking. We propose a new approach to find stable as well as unstable hybrid limit cycles without integrating the full set of differential equations and, at the same time, without approximating the dynamics. The procedure exploits a time-independent representation of a possible periodic solution via a virtual holonomic constraint. The description of the limit cycle obtained in this way is useful for the analysis and characterization of passive gaits as well as for design of regulators to achieve gaits with the smallest required control efforts. Some insights into the notion of hybrid zero dynamics, which are related to such a description, are presented as well.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers, 2009
Keyword
Limit cycles, underactuated mechanical systems, virtual holonomic constraints, walking robots.
Identifiers
urn:nbn:se:umu:diva-26281 (URN)10.1109/TRO.2009.2028757 (DOI)
Available from: 2009-10-02 Created: 2009-10-02 Last updated: 2011-01-29Bibliographically approved
4. Parallel elastic actuators as a control tool for preplanned trajectories of underactuated mechanical systems
Open this publication in new window or tab >>Parallel elastic actuators as a control tool for preplanned trajectories of underactuated mechanical systems
2009 (English)In: The international journal of robotics research, ISSN 0278-3649, E-ISSN 1741-3176, Vol. 29, no 9, 1186-1198 p.Article in journal (Refereed) Published
Abstract [en]

A lack of sufficient actuation power as well as the presence of passive degrees of freedom are often serious constraints for feasible motions of a robot. Installing passive elastic mechanisms in parallel with the original actuators is one of a few alternatives that allows for large modifications of the range of external forces or torques that can be applied to the mechanical system. If some motions are planned that require a nominal control input above the actuator limitations, then we can search for auxiliary spring-like mechanisms complementing the control scheme in order to overcome the constraints. The intuitive idea of parallel elastic actuation is that spring-like elements generate most of the nominal torque required along a desired trajectory, so the control efforts of the original actuators can be mainly spent in stabilizing the motion. Such attractive arguments are, however, challenging for robots with non-feedback linearizable non-minimum phase dynamics that have one or several passive degrees of freedom. We suggest an approach to resolve the apparent difficulties and illustrate the method with an example of an underactuated planar double pendulum. The results are tested both in simulations and through experimental studies.

Place, publisher, year, edition, pages
Sage journals online, 2009
Keyword
compliant actuators, underactuated mechanical systems, motion planning, walking robots, virtual holonomic constraints
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Automatic Control
Identifiers
urn:nbn:se:umu:diva-30194 (URN)10.1177/0278364909344002 (DOI)
Available from: 2009-12-10 Created: 2009-12-10 Last updated: 2010-08-26Bibliographically approved
5. Optimal ball pitching with an underactuated model of a human arm
Open this publication in new window or tab >>Optimal ball pitching with an underactuated model of a human arm
2010 (English)Conference paper, Published paper (Refereed)
Abstract [en]

A new approach for solving an optimal motion planning problem for a simplified 2-degrees-of-freedom model of a human arm is proposed. The motion of interest resembles ball pitching. The model of a planar two-link robot is used with actuation only at the shoulder joint and a passive spring at the elbow joint representing the stiffness of the arm. The goal is formulated as finding a trajectory and the associated torque of the active joint that maximizes the velocity of the end effector in horizontal direction at the moment of crossing a vertical ball-release line. The basic idea is to search for an optimal motion parametrized by the horizontal displacement of the end-effector from the start point to the release point. The suggested procedure leads to analytical expressions for the coefficients of a nonlinear differential equation that governs the geometric relation between the links along an optimal motion. The motion planning task is reformulated to a finite-dimensional search for the corresponding initial conditions.

Place, publisher, year, edition, pages
New York: IEEE, 2010
Series
Proceedings / IEEE international conference on robotics and automation, ISSN 1050-4729
Keyword
Underactuated Mechanical Systems, Optimal Control, Motion Planning
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Automatic Control
Identifiers
urn:nbn:se:umu:diva-30251 (URN)10.1109/ROBOT.2010.5509879 (DOI)000284150004153 ()978-1-4244-5038-1 (ISBN)
Conference
ICRA 2010, Anchorage, USA, May 2010
Available from: 2009-12-14 Created: 2009-12-14 Last updated: 2011-02-07Bibliographically approved
6. Ball dribbling with an underactuated continuous-time control phase
Open this publication in new window or tab >>Ball dribbling with an underactuated continuous-time control phase
2010 (English)In: 2010 IEEE International Conference on Robotics and Automation (ICRA), 2010, 4669-4674 p.Conference paper, Published paper (Refereed)
Abstract [en]

Ball dribbling is a central element of basketball. One main challenge for realizing basketball robots is to stabilize periodic motions of the ball. This task is nontrivial due to the hybrid (discrete-continuous) nature of the corresponding dynamics. The ball can be only controlled during ball-manipulator contact and moves freely otherwise. We propose a manipulator equipped with a spring that gets compressed when the ball bounces against it. Hence, we can have continuous-time control over this underactuated Ball-Spring-Manipulator system until the spring releases its accumulated energy back to the ball. This paper illustrates the motion-planning procedure for a ball-dribbling cycle with such an underactutated continuous-time control phase. An orbital stabilizing controller is designed based on a transverse linearization along a desired periodic motion. Numerical simulations show the performance of the control system in preparation to experimental studies.

Keyword
Underactuated Mechanical Systems, Motion Planning, Orbital Stabilization, Virtual Holonomic Constraints
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Automatic Control
Identifiers
urn:nbn:se:umu:diva-30250 (URN)10.1109/ROBOT.2010.5509901 (DOI)000284150005021 ()
Conference
IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, MAY 03-08, 2010
Note

The paper is submitted.

Available from: 2009-12-14 Created: 2009-12-14 Last updated: 2015-10-12Bibliographically approved
7. Analysis of human-operated motions and trajectory replanning for kinematically redundant manipulators
Open this publication in new window or tab >>Analysis of human-operated motions and trajectory replanning for kinematically redundant manipulators
2009 (English)In: 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems: St.Louis, USA, 2009, 795-800 p.Conference paper, Published paper (Refereed)
Abstract [en]

We consider trajectory planning for kinematically redundant manipulators used on forestry machines. The analysis of recorded data from human operation reveals that the driver does not use the full potential of the machine due to the complexity of the manipulation task. We suggest an optimization procedure that takes advantage of the kinematic redundancy so that time-efficient joint and velocity profiles along the path can be obtained. Differential constraints imposed by the manipulator dynamics are accounted for by employing a phase-plane technique for admissible path timings. Velocity constraints of the individual joints are particularly restrictive in hydraulic manipulators. Our study aims for semi-autonomous schemes that can provide assistance to the operator for executing global motions.

Keyword
Motion Planning, Kinematically Redundant Manipulators, Robotics in Agriculture and Forestry
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Automatic Control
Identifiers
urn:nbn:se:umu:diva-30078 (URN)
Conference
IROS 2009
Available from: 2009-12-03 Created: 2009-12-03 Last updated: 2014-05-20Bibliographically approved
8. Trajectory planning and time-independent motion control for a kinematically redundant hydraulic manipulator
Open this publication in new window or tab >>Trajectory planning and time-independent motion control for a kinematically redundant hydraulic manipulator
Show others...
2009 (English)In: Advanced Robotics, 2009. ICAR 2009. International Conference on, IEEE conference proceedings, 2009, 1-6 p.Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we consider the problem of motion planning and control of a kinematically redundant manipulator, which is used on forestry machines for logging. Once a desired path is specified in the 3D world frame, a trajectory can be planned and executed such that all joints are synchronized and constrained to the Cartesian path. We introduce an optimization procedure that takes advantage of the kinematic redundancy so that time-efficient joint and velocity profiles along the path can be obtained. Differential constraints imposed by the manipulator dynamics are accounted for by employing a phase-plane technique for admissible path timings. In hydraulic manipulators, such as considered here, the velocity constraints of the individual joints are particularly restrictive. We suggest a time-independent control scheme for the planned trajectory which is built upon the standard reference tracking controllers. Experimental tests underline the benefits and efficiency of the model-based trajectory planning and show success of the proposed control strategy.

Place, publisher, year, edition, pages
IEEE conference proceedings, 2009
Keyword
Trajectory Planning, Motion Control, Robotics in Agriculture and Forestry, Kinematically Redundant Manipulator
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Automatic Control
Identifiers
urn:nbn:se:umu:diva-30079 (URN)978-1-4244-4855-5 (ISBN)978-3-8396-0035-1 (ISBN)
Conference
14th International Conference on Advanced Robotics (ICAR 2009), 22-26 June 2009, Munich
Available from: 2009-12-03 Created: 2009-12-03 Last updated: 2014-04-09Bibliographically approved

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