  Computing optimal, collision-free trajectories for high-dimensional systems
is a challenging problem. Sampling-based planners struggle with the
dimensionality, whereas trajectory optimizers may get stuck in local minima due
to inherent nonconvexities in the optimization landscape. The use of
mixed-integer programming to encapsulate these nonconvexities and find globally
optimal trajectories has recently shown great promise, thanks in part to tight
convex relaxations and efficient approximation strategies that greatly reduce
runtimes. These approaches were previously limited to Euclidean configuration
spaces, precluding their use with mobile bases or continuous revolute joints.
In this paper, we handle such scenarios by modeling configuration spaces as
Riemannian manifolds, and we describe a reduction procedure for the
zero-curvature case to a mixed-integer convex optimization problem. We
demonstrate our results on various robot platforms, including producing
efficient collision-free trajectories for a PR2 bimanual mobile manipulator.
