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Michael Watterson, Trey Smith, and Vijay Kumar. In Proc. IEEE Int. Conf. Rob. Sys. (IROS), 2016.
We propose a new optimal trajectory generation technique on SE(3) which avoids known obstacles. We harness differential geometry and Lie algebraic techniques to formulate a cost functional which considers the geometric structure of this space and makes physical sense. We propose an approximation technique to generate trajectories on the subgroup SO(3) and use Positive Semidefinite Programming (PSD) to approximate an NP-Hard problem with one which is tractable to compute. From this trajectory on the subgroup, the trajectory generation on the other dimensions of the group becomes a Quadratic Program (QP). For obstacle avoidance, we use a computational geometric technique to decompose the environment into convex regions to confine the trajectory. We generalize a method from cubes to polyhedrons to expand these regions to better condition the QP. We leverage control techniques on SE(3) and dexterous grasping literature to control our unique platform and compare our method to similar methods for calculate optimal trajectories on SO(3) and SE(3), in the absence of obstacles. In addition, we show generated simulated SE(3) trajectories avoiding obstacles within a non-convex environment.
@InProceedings{watterson16:smooth_trajectory_se3,
author = {Michael Watterson and Trey Smith and Vijay Kumar},
title = {Smooth Trajectory Generation on {SE}(3) for a Free Flying Space Robot},
booktitle = {Proc. IEEE Int. Conf. Rob. Sys. (IROS)},
year = 2016,
}
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