Autonomous electric vehicles (AEVs) will become an inevitable trend in the future transportation network and have an important impact on the power grid. It is difficult to find the optimal distributed charging solution for AEVs to minimize the system cost with some uncertainties. In this paper, we investigate an AEVs charging and discharging problem with vehicle-to-grid (V2G) services. We aim to minimize the total electricity cost and battery degradation cost of AEVs and charging station batteries with V2G services, which takes the random arrival and departure of AEVs into account. We first propose a distributed charging framework of AEVs and charging stations by clustering method with the constraint of limited AEVs for each charging station in a region and formulate a distributed offline optimization problem. Then we formulate a distributed online charging optimization problem and propose a distributed online AEV charging scheduling (DOAS) algorithm to get an optimal charging solution. To study a more practical case, we reformulate the distributed online optimization problem with the uncertainties from base loads, renewable energy and charging demands. Furthermore, to improve the time efficiency of DOAS algorithm, we reduce the dimension of the distributed problem and design a dimension-reduction DOAS (DDOAS) algorithm. To seek a robust solution with some uncertainties, we propose a DDOAS algorithm with DRO based on Wasserstein distance (DDODW). Simulation results show that DOAS and DDOAS algorithms can have a close-to-optimal charging cost and a significantly less battery degradation cost of charging stations, compared with centralized online charging scheduling algorithm and DDOAS algorithm is more time-efficient than DOAS algorithm. The proposed DDODW algorithm can provide a robust solution for the energy schedule