Chance-Constrained Trajectory Planning With Multimodal Environmental Uncertainty

We tackle safe trajectory planning under Gaussian mixture model (GMM) uncertainty. Specifically, we use a GMM to model the multimodal behaviors of obstacles' uncertain states. Then, we develop a mixed-integer conic approximation to the chance-constrained trajectory planning problem with deterministic linear systems and polyhedral obstacles. When the GMM moments are estimated via finite samples, we develop a tight concentration bound to ensure the chance constraint with a desired confidence. Moreover, to limit the amount of constraint violation, we develop a Conditional Value-at-Risk (CVaR) approach corresponding to the chance constraints and derive a tractable approximation for known and estimated GMM moments. We verify our methods with state-of-the-art trajectory prediction algorithms and autonomous driving datasets.

Automated summary

In this paper, we address the problem of safe trajectory planning under Gaussian mixture model (GMM) uncertainty. We propose a mixed-integer conic approximation approach to solve the chance-constrained trajectory planning problem with deterministic linear systems and polyhedral obstacles. We also develop a Conditional Value-at-Risk (CVaR) method for tackling constraint violation. The proposed methods are validated using state-of-the-art trajectory prediction algorithms and autonomous driving datasets.