Trey Smith's Publications

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Trajectory Optimization On Manifolds with Applications to $SO(3)$ and $\bboldR^3 \times S^2$.

Michael Watterson, Sikang Liu, Ke Sun, Trey Smith, and Vijay Kumar. In Proc. Rob. Sci. Systems, 2018.

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Abstract

Manifolds are used in almost all robotics applications even if they are not explicitly modeled. We propose a differential geometric approach for optimizing trajectories on a Riemannian manifold with obstacles. The optimization problem depends on a metric and collision function specific to a manifold. We then propose our Safe Corridor on Manifolds (SCM) method of computationally optimizing trajectories for robotics applications via a constrained optimization problem. Our method does not need equality constraints, which eliminates the need to project back to a feasible manifold during optimization. We then demonstrate how this algorithm works on an example problem on SO(3) and a perception-aware planning example for visual- inertially guided robots navigating in 3 dimensions. Formulating field of view constraints naturally results in modeling with the manifold R3 × S2 which cannot be modeled as a Lie group.

BibTeX Entry

@InProceedings{watterson18:trajectory_manifolds,
  author =       {Michael Watterson and Sikang Liu and Ke Sun and Trey Smith and Vijay Kumar},
  title =        {Trajectory Optimization On Manifolds with Applications to $SO(3)$ and $\bbold{R}^3 \times S^2$},
  booktitle = {Proc. Rob. Sci. Systems},
  year =      2018,
}

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