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


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.



    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}