Route planning is essential to mobile robot navigation problems. In recent years, deep reinforcement learning (DRL) has been applied to learning optimal planning policies in stochastic environments without prior knowledge. However, existing works focus on learning policies that maximize the expected return, the performance of which can vary greatly when the level of stochasticity in the environment is high. In this work, we propose a distributional reinforcement learning based framework that learns return distributions which explicitly reflect environmental stochasticity. Policies based on the second-order stochastic dominance (SSD) relation can be used to make adjustable route decisions according to user preference on performance robustness. Our proposed method is evaluated in a simulated road network environment, and experimental results show that our method is able to plan the shortest routes that minimize stochasticity in travel time when robustness is preferred, while other state-of-the-art DRL methods are agnostic to environmental stochasticity.
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