Controllability and motion algorithms for underactuated Lagrangian systems on Lie groups
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Authors
Bullo, Francesco
Leonard, Naomi E.
Lewis, Andrew D.
Date
2000
Type
preprint
Language
en
Keyword
Alternative Title
Abstract
In this paper, we provide controllability tests and motion control algorithms for underactuated mechanical control systems on Lie groups with Lagrangian equal to kinetic energy. Examples include satellite and underwater vehicle control systems with the number of control inputs less than the dimension of the configuration space. Local controllability properties of these systems are characterised, and two algebraic tests are derived in terms of the symmetric product and the Lie bracket of the input vector fields. Perturbation theory is applied to compute approximate solutions for the system under small-amplitude forcing; in-phase signals play a crucial role in achieving motion along symmetric product directions. Motion control algorithms are then designed to solve problems of point-to-point reconfiguration, static interpolation and exponential stabilisation. We illustrate the theoretical results and the algorithms with applications to models of planar rigid bodies, satellites and underwater vehicles.
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Citation
IEEE Transactions on Automatic Control 45(8), pages 1437-1454, 2000
Publisher
IEEE