Abstract—To satisfy the quality of service requirements for some applications in the Internet of Things (IoT) network with mobile nodes, routing protocols must be adaptable to make better routing decisions. Routing Protocol for Lowpower and Lossy Networks (RPL) is one of the routing protocols that support metrics and constraints while building a Destination Oriented Directed Acyclic Graphs (DODAG) using a specific Objective Function (OF). However, RPL metrics that use standard OFs do not guarantee the performance criteria for a specific mobile IoT in terms of received and lost packets, overhead, throughput and power consumption. In this paper, we propose a new version of mrhof based on a combination of metrics such as total energy, the number of neighbors, and expected transmission count (ETX) to evaluate RPL performances in a mobile context. Then, we compare the assessment of this function to existing OFs based on various mobility models (Random Waypoint (RWP), Reference Point Group Mobility (RPGM), Nomadic) and node densities. The results show that this new function is more efficient than the standards OF in terms of packets received and packets lost with Random Way Point and RPGM models. Regardless of the number of nodes, it also reduces ETX and traffic overhead for all mobility models, as well as convergence time in the Random Waypoint environment. Furthermore, this new function contributes to the improvement of Rtmetric, the enhancement of throughput at low density only in favor of RWP and RPGM models, and an effective power consumption reduction through all densities and mobility models.