Smart healthcare has been one of the major use cases of the Internet of Things (IoT) and Wireless sensor network (WSN) applications. WSN as a technique for sensing and acquiring data in IoT applications must work upon providing an efficient routing for proper data transfer. One of the fundamental concerns of the routing in WSNs is the energy consumption and the lifetime of sensors, since most of them rely on a battery and neither cable-powered nor frequent battery replacement or recharging are appealing options. The required routing technique must balance the goals: selecting the most reliable minimum energy path when all nodes have high energy and avoiding the low residual energy nodes while supporting mobility. This paper introduces a theoretical framework for RPL (Routing Protocol for Low power and Lossy Networks) based routing protocols whose aim is to provide energy efficiency while taking into account the mobility of sensor nodes in WSNs consisted of both static and mobile nodes. The simulation results indicate that the proposed routing model's Objective Function (OF) gives better performance in comparison to the default OFs in terms of duty cycle, energy consumption and total control overhead, while having a small degradation in the packet delivery ratio