  We present CCO-VOXEL: the very first chance-constrained optimization (CCO)
algorithm that can compute trajectory plans with probabilistic safety
guarantees in real-time directly on the voxel-grid representation of the world.
CCO-VOXEL maps the distribution over the distance to the closest obstacle to a
distribution over collision-constraint violation and computes an optimal
trajectory that minimizes the violation probability. Importantly, unlike
existing works, we never assume the nature of the sensor uncertainty or the
probability distribution of the resulting collision-constraint violations. We
leverage the notion of Hilbert Space embedding of distributions and Maximum
Mean Discrepancy (MMD) to compute a tractable surrogate for the original
chance-constrained optimization problem and employ a combination of A* based
graph-search and Cross-Entropy Method for obtaining its minimum. We show
tangible performance gain in terms of collision avoidance and trajectory
smoothness as a consequence of our probabilistic formulation vis a vis
state-of-the-art planning methods that do not account for such nonparametric
noise. Finally, we also show how a combination of low-dimensional feature
embedding and pre-caching of Kernel Matrices of MMD allows us to achieve
real-time performance in simulations as well as in implementations on on-board
commodity hardware that controls the quadrotor flight
