Robotics: Science and Systems XIV

Trajectory Optimization On Manifolds with Applications to SO(3) and R3XS2

Michael Watterson, Sikang Liu, Ke Sun, Trey Smith, Vijay Kumar

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 R3XS2 which cannot be modeled as a Lie group.

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Bibtex:

  
@INPROCEEDINGS{Watterson-RSS-18, 
    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 R3XS2}, 
    BOOKTITLE = {Proceedings of Robotics: Science and Systems}, 
    YEAR      = {2018}, 
    ADDRESS   = {Pittsburgh, Pennsylvania}, 
    MONTH     = {June}, 
    DOI       = {10.15607/RSS.2018.XIV.023} 
}