We propose an integrated prediction and planning system for autonomous driving which uses rational inverse planning to recognise the goals of other vehicles. Goal recognition informs a Monte Carlo Tree Search (MCTS) algorithm to plan optimal manoeuvres for the ego vehicle. Inverse planning and MCTS utilise a shared set of defined manoeuvres and macro actions to construct plans which are explainable by means of rationality principles. Evaluation in simulations of urban driving scenarios demonstrate the system’s ability to robustly recognise the goals of other vehicles, enabling our vehicle to exploit non-trivial opportunities to significantly reduce driving times. In each scenario, we extract intuitive explanations for the predictions which justify the system’s decisions.

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