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 KumarAbstract:
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.
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} }