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Ball dribbling with an underactuated continuous-time control phase
Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics. (Robotics and Control Lab)
Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics. (Robotics and Control Lab)
Institute of Automatic Control Engineering, Technical University of Munich.
Institute of Automatic Control Engineering, Technical University of Munich.
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.

Place, publisher, year, edition, pages
2010. 4669-4674 p.
Keyword [en]
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: urn:nbn:se:umu:diva-30250DOI: 10.1109/ROBOT.2010.5509901ISI: 000284150005021OAI: oai:DiVA.org:umu-30250DiVA: diva2:281186
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
In thesis
1. Principles for planning and analyzing motions of underactuated mechanical systems and redundant manipulators
Open this publication in new window or tab >>Principles for planning and analyzing motions of underactuated mechanical systems and redundant manipulators
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Metoder för rörelseplanering och analys av underaktuerade mekaniska system och redundanta manipulatorer
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
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:nbn:se:umu:diva-30024 (URN)978-91-7264-914-9 (ISBN)
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

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Mettin, UweShiriaev, Anton

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