the network lifetime based on a new Energy-Aware Objective Function used to design a Routing Protocol for Low-Power and Lossy Networks. The proposed Objective Function uses the Expected Transmission Count Metric and the Remaining Energy on each sensor node to compute the best paths to route data packets across the network.So EAOF prolongs the network lifetime and reduces the need for human intervention on battery changing, thereby enhancing the system wearability and reducing operational costs.