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  1. Mathematics of Control, Signals, and Systems
  2. Mathematics of Control, Signals, and Systems : Volume 20
  3. Mathematics of Control, Signals, and Systems : Volume 20, Issue 4, December 2008
  4. Planning rigid body motions using elastic curves
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Mathematics of Control, Signals, and Systems : Volume 29
Mathematics of Control, Signals, and Systems : Volume 28
Mathematics of Control, Signals, and Systems : Volume 27
Mathematics of Control, Signals, and Systems : Volume 26
Mathematics of Control, Signals, and Systems : Volume 25
Mathematics of Control, Signals, and Systems : Volume 24
Mathematics of Control, Signals, and Systems : Volume 23
Mathematics of Control, Signals, and Systems : Volume 22
Mathematics of Control, Signals, and Systems : Volume 21
Mathematics of Control, Signals, and Systems : Volume 20
Mathematics of Control, Signals, and Systems : Volume 20, Issue 4, December 2008
A generalisation of Jury’s conjecture to arbitrary dimensions and its proof
Weakly coprime factorization and state-feedback stabilization of discrete-time systems
Planning rigid body motions using elastic curves
Mathematics of Control, Signals, and Systems : Volume 20, Issue 3, August 2008
Mathematics of Control, Signals, and Systems : Volume 20, Issue 2, June 2008
Mathematics of Control, Signals, and Systems : Volume 20, Issue 1, March 2008
Mathematics of Control, Signals, and Systems : Volume 19
Mathematics of Control, Signals, and Systems : Volume 18
Mathematics of Control, Signals, and Systems : Volume 17
Mathematics of Control, Signals, and Systems : Volume 16
Mathematics of Control, Signals, and Systems : Volume 15
Mathematics of Control, Signals, and Systems : Volume 14
Mathematics of Control, Signals, and Systems : Volume 13
Mathematics of Control, Signals, and Systems : Volume 12
Mathematics of Control, Signals, and Systems : Volume 11
Mathematics of Control, Signals, and Systems : Volume 10

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Planning rigid body motions using elastic curves

Content Provider SpringerLink
Author Biggs, James Holderbaum, William
Copyright Year 2008
Abstract This paper tackles the problem of computing smooth, optimal trajectories on the Euclidean group of motions SE(3). The problem is formulated as an optimal control problem where the cost function to be minimized is equal to the integral of the classical curvature squared. This problem is analogous to the elastic problem from differential geometry and thus the resulting rigid body motions will trace elastic curves. An application of the Maximum Principle to this optimal control problem shifts the emphasis to the language of symplectic geometry and to the associated Hamiltonian formalism. This results in a system of first order differential equations that yield coordinate free necessary conditions for optimality for these curves. From these necessary conditions we identify an integrable case and these particular set of curves are solved analytically. These analytic solutions provide interpolating curves between an initial given position and orientation and a desired position and orientation that would be useful in motion planning for systems such as robotic manipulators and autonomous-oriented vehicles.
Starting Page 351
Ending Page 367
Page Count 17
File Format PDF
ISSN 09324194
Journal Mathematics of Control, Signals, and Systems
Volume Number 20
Issue Number 4
e-ISSN 1435568X
Language English
Publisher Springer-Verlag
Publisher Date 2008-10-11
Publisher Place London
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Rigid body motion Optimal control Elastic curves Helical motions Systems Theory, Control Communications Engineering, Networks Control Engineering
Content Type Text
Resource Type Article
Subject Control and Optimization Applied Mathematics Signal Processing Control and Systems Engineering
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