Non-Gaussian Chance-Constrained Trajectory Planning for Autonomous Vehicles in the Presence of Uncertain Agents

Agent behavior is arguably the greatest source of uncertainty in trajectory planning for autonomous vehicles.This problem has motivated significant amounts of work in the behavior prediction community on learning rich distributions of the future states and actions of agents. However, most current work on trajectory planning in the presence of uncertain agents or obstacles is limited to the case of Gaussian uncertainty with linear constraints, which is a limited representation, or requires sampling, which can be computationally intractable to encode in an optimization problem. In this paper, wepresent a general method for enforcing chance-constraints on the probability of collision with other agents in trajectory planning problems for autonomous driving that can be used with non-Gaussian mixture models of agent positions. Our method involves using statistical moments of the non-Gaussian distributions in concentration inequalities to upper bound the probability of polynomial constraint violation. In experiments,we show that the resulting optimization problem can be solved with state-of-the-art nonlinear program (NLP) solvers to plan trajectories with 5 second horizons with low latency.