Many devices on an Internet of Things (IoT) network have severe constraints on computing resources in terms of memory, processing, and power, which make these networks generally known as Low power and Lossy Networks (LLNs). Device mobility in these scenarios has several negative impacts on the network, particularly in terms of connectivity, as node movement affects the routes established by the routing protocol. The network performance is highly related to the adjacent routing protocol. The protocol considered as standard for IoT networks was designed for static networks, and it has a low reactivity in mobility scenarios, besides other limitations. Lightweight On-demand Ad hoc Distance-vector Routing-Next Generation (LOADng) is currently the primary reactive protocol for LLNs. Considering that mobility is a crucial feature for the future of IoT, this article proposes Extended Kalman Filter (EKF)-LOADng, a solution built from LOADng for LLNs in the mobility context. The solution aims to make the mobile nodes aware of its location, as well as to predict the nonlinear trajectory of these nodes through the EKF. The location obtained is used to improve the connectivity of the mobile nodes and to shorten paths while messages are exchanged on the network. EKF-LOADng was compared with the standard version and an enhanced version of the LOADng protocol in two different scenarios in the Contiki OS. Simulation results show the proposed solution is capable of locating mobile nodes with an average error of 1.46 m while maintaining connectivity to other nodes, as well as outperforms the compared proposals in some network metrics in terms of packet delivery ratio, latency, power consumption, and control bit overhead.