  Safe autonomous driving critically depends on how well the ego-vehicle can
predict the trajectories of neighboring vehicles. To this end, several
trajectory prediction algorithms have been presented in the existing
literature. Many of these approaches output a multi-modal distribution of
obstacle trajectories instead of a single deterministic prediction to account
for the underlying uncertainty. However, existing planners cannot handle the
multi-modality based on just sample-level information of the predictions. With
this motivation, this paper proposes a trajectory optimizer that can leverage
the distributional aspects of the prediction in a computationally tractable and
sample-efficient manner. Our optimizer can work with arbitrarily complex
distributions and thus can be used with output distribution represented as a
deep neural network. The core of our approach is built on embedding
distribution in Reproducing Kernel Hilbert Space (RKHS), which we leverage in
two ways. First, we propose an RKHS embedding approach to select probable
samples from the obstacle trajectory distribution. Second, we rephrase
chance-constrained optimization as distribution matching in RKHS and propose a
novel sampling-based optimizer for its solution. We validate our approach with
hand-crafted and neural network-based predictors trained on real-world datasets
and show improvement over the existing stochastic optimization approaches in
safety metrics.

Robotics