Optimal control of underactuated nonholonomic mechanical systems

@article{Hussein2006OptimalCO,
  title={Optimal control of underactuated nonholonomic mechanical systems},
  author={Islam I. Hussein and Anthony M. Bloch},
  journal={2006 American Control Conference},
  year={2006},
  pages={6 pp.-}
}
In this paper we use a nonholonomic affine connection formulation to study an optimal control problem for a class of nonholonomic, under-actuated mechanical systems. The class of nonholonomic systems we study in this paper includes, in particular, wheeled-type vehicles, which are important for many robotic locomotion systems. We illustrate our ideas by considering a simple example on a three-dimensional manifold 
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