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Creators/Authors contains: "Zhu, Zhifei"

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  1. ; (, International Journal of Control)
    We propose a method to analyze the three-dimensional nonholonomic system known as the Brockett integrator and to derive the (energy) optimal trajectories between two given points. For systems with nonholonomic constraint, it is well-known that the energy optimal trajectories corresponds to sub-Riemannian geodesics under a proper sub-Riemannian metric. Our method uses symmetry reduction and an analysis of the quotient space associated with the action of a (symmetry) group on R^3. By lifting the Riemannian geodesics with respect to an appropriate metric from the quotient space back to the original space R^3, we derive the optimal trajectories of the original problem. 
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  2. ; ; (, Journal of Mathematical Physics)