Energy is a very scarce resource in Wireless Sensor Networks. While most of the current proposals focus on minimizing the global energy consumption, we aim here at designing an energy-balancing routing protocol that maximizes the lifetime of the most constraint nodes. To improve the network lifetime, each node should consume the same (minimal) quantity of energy. We propose the Expected Lifetime metric, denoting the residual time of a node (time until the node will run out of energy). We design mechanisms to detect energy-bottleneck nodes and to spread the traffic load uniformly among them. Moreover, we apply this metric to RPL, the de facto routing standard in low-power and lossy networks. In order to avoid instabilities in the network and problems of convergence, we propose here a multipath approach. We exploit the Directed Acyclic Graph (DAG) structure of the routing topology to probabilistically forward the traffic to several parents. Simulations highlight that we improve both the...