Reliable automated driving technology is challenged by various sources of uncertainties, in particular, behavioral uncertainties of traffic agents. It is common for traffic agents to have intentions that are unknown to others, leaving an automated driving car to reason over multiple possible behaviors. This paper formalizes a behavior planning scheme in the presence of multiple possible futures with corresponding probabilities. We present a maximum entropy formulation and show how, under certain assumptions, this allows delayed decision-making to improve safety. The general formulation is then turned into a model predictive control formulation, which is solved as a quadratic program or a set of quadratic programs. We discuss implementation details for improving computation and verify operation in simulation and on a mobile robot.
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