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Safe autonomous driving critically depends on how well the ego-vehicle canpredict the trajectories of neighboring vehicles. To this end, severaltrajectory prediction algorithms have been presented in the existingliterature. Many of these approaches output a multi-modal distribution ofobstacle trajectories instead of a single deterministic prediction to accountfor the underlying uncertainty. However, existing planners cannot handle themulti-modality based on just sample-level information of the predictions. Withthis motivation, this paper proposes a trajectory optimizer that can leveragethe distributional aspects of the prediction in a computationally tractable andsample-efficient manner. Our optimizer can work with arbitrarily complexdistributions and thus can be used with output distribution represented as adeep neural network. The core of our approach is built on embeddingdistribution in Reproducing Kernel Hilbert Space (RKHS), which we leverage intwo ways. First, we propose an RKHS embedding approach to select probablesamples from the obstacle trajectory distribution. Second, we rephrasechance-constrained optimization as distribution matching in RKHS and propose anovel sampling-based optimizer for its solution. We validate our approach withhand-crafted and neural network-based predictors trained on real-world datasetsand show improvement over the existing stochastic optimization approaches insafety metrics.

Hilbert Space Embedding-based Trajectory Optimization for Multi-Modal Uncertain Obstacle Trajectory Prediction