This paper presents an optimization model for Home Energy Management Systems from an aggregator's standpoint. The aggregator manages a set of resources such as PV, electrochemical batteries and thermal energy storage by means of electric water heaters. Resources are managed in order to participate in the day-ahead energy and local flexibility markets, also considering grid constraint support at the Point of Common Coupling. The resulting model is a Mixed-Integer Linear Programming problem in which the objective is to minimize day-ahead operation costs for the aggregator while complying with energy commitments in the day-ahead market and local flexibility requests. Three sources of uncertainty are considered: energy prices, PV production and load. Adjustable Robust Optimization is used to find a robust counterpart of the problem for including uncertainty. The results obtained show that using robust optimization allows strategic bidding to capture uncertainties while complying with obligations in the wholesale and local market. Data from a real-life energy community with 25 households is used to validate the proposed robust bidding methodology.