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Planning rigid body motions using elastic curves

Biggs, James and Holderbaum, William (2008) Planning rigid body motions using elastic curves. Mathematics of Control, Signals, and Systems, 20 (4). pp. 351-367. ISSN 0932-4194

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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.

Item type: Article
ID code: 7309
Keywords: rigid body motion, optimal control, elastic curves, helical motions, control systems, Mechanical engineering and machinery, Motor vehicles. Aeronautics. Astronautics, Aerospace Engineering, Control and Systems Engineering
Subjects: Technology > Mechanical engineering and machinery
Technology > Motor vehicles. Aeronautics. Astronautics
Department: Faculty of Engineering > Mechanical and Aerospace Engineering
Depositing user: Strathprints Administrator
Date Deposited: 27 Nov 2008 12:11
Last modified: 18 Jun 2015 10:04
URI: http://strathprints.strath.ac.uk/id/eprint/7309

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