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We present CCO-VOXEL: the very first chance-constrained optimization (CCO)algorithm that can compute trajectory plans with probabilistic safetyguarantees 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 adistribution over collision-constraint violation and computes an optimaltrajectory that minimizes the violation probability. Importantly, unlikeexisting works, we never assume the nature of the sensor uncertainty or theprobability distribution of the resulting collision-constraint violations. Weleverage the notion of Hilbert Space embedding of distributions and MaximumMean Discrepancy (MMD) to compute a tractable surrogate for the originalchance-constrained optimization problem and employ a combination of A* basedgraph-search and Cross-Entropy Method for obtaining its minimum. We showtangible performance gain in terms of collision avoidance and trajectorysmoothness as a consequence of our probabilistic formulation vis a visstate-of-the-art planning methods that do not account for such nonparametricnoise. Finally, we also show how a combination of low-dimensional featureembedding and pre-caching of Kernel Matrices of MMD allows us to achievereal-time performance in simulations as well as in implementations on on-boardcommodity hardware that controls the quadrotor flight

CCO-VOXEL: Chance Constrained Optimization over Uncertain Voxel-Grid Representation for Safe Trajectory Planning