Abstract
In this paper we construct motion primitives as algorithm building blocks for stabilization and control of a class of underactuated systems that includes spacecraft, submersibles and planar vehicles. The underactuated systems are modelled as Lagrangian systems on Lie groups; thus, they are systems with drift and with accessibility distributions described by the operation of Lie bracket and symmetric product. Directions of motion that are not directly actuated are identified with symmetric products of the input vector fields, and in-phase sinusoidal forcing is used in the primitives to generate motion in these directions. These primitives can then be used for a variety of low velocity maneuvers. For example, we demonstrate their use for exponential point stabilization and for static interpolation. We evaluate our algorithms and investigate the advantage of planning motions along relative equilibria.
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