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Optimal ball pitching with an underactuated model of a human arm
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)
Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics.
Tokyo Institute of Technology, Department of Mechanical and Control Engineering.
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. 5009-5014 p.
Series
Proceedings / IEEE international conference on robotics and automation, ISSN 1050-4729
Keyword [en]
Underactuated Mechanical Systems, Optimal Control, Motion Planning
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Automatic Control
Identifiers
URN: urn:nbn:se:umu:diva-30251DOI: 10.1109/ROBOT.2010.5509879ISI: 000284150004153ISBN: 978-1-4244-5038-1 (print)OAI: oai:DiVA.org:umu-30251DiVA: diva2:281187
Conference
ICRA 2010, Anchorage, USA, May 2010
Available from: 2009-12-14 Created: 2009-12-14 Last updated: 2011-02-07Bibliographically 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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Citation style
  • apa
  • ieee
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  • Other style
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