## 1 Introduction  
RPL is a routing protocol devised for low power and lossy networks (LLN) that consist of resource-limited devices. As a routing protocol that operates among IoT (Internet of Things) devices, RPL was designed to be suitable for wireless sensor network environments, and it supports various routing metrics to accommodate the requirements of various applications [1]. The RPL forms a wireless sensor network using a directed acyclic graph (DAG) topology so that the cost of every node reaching the LLN border router is minimized. Moreover, a trickle algorithm is used to maintain consistency among the nodes that comprise the network [1, 2]. While such a design is optimized for IoT services where the network topology does not vary, it is difficult to maintain the routing paths in a stable manner in an IoT service environment where the devices move frequently [3, 4]. Therefore, considering that mobility is an important property of mobile devices in an IoT environment, there is a need for a mechanism that is energy efficient and that provides for stable and reliable data transmission.  
Mobility support is a fundamental issue in RPL. Previous works on mobility support in RPL mostly aimed to achieve rapid detection of the movement of mobile nodes and the provision of better links through an efficient selection of parent nodes. In other words, mobility support in RPL is directly related to a fast search for appropriate nodes to become the parent node when a mobile node makes a movement. Moreover, previous works on mobility support in RPL focused on improving the trickle algorithm used in RPL [5, 6, 7, 8, 9, 10, 11]. From a methodological perspective, previous works mostly used algorithms that increase or decrease the time interval for the selection of parent nodes by multiplying or dividing a predefined interval by a certain integer value. This was based on the respective methods proposed in each work in order to support the mobility of the nodes. However, mobile nodes are objects that move in a random manner in a network. Therefore, the methods proposed by previous works can lead to losses in the intervals during which the mobile nodes select the parent node in an RPL network. This loss may cause the increase of the packet loss rate and energy consumption while the information is delivered. Hence, considering these characteristics of mobile nodes, the interval during that a mobile node selects a parent node must be allocated dynamically based on the speed and direction of the movement of the node.  
This paper proposes an algorithm for the timely transmission of solicitation messages for node mobility support in IoT environments that require the movement of the nodes or things. The proposed algorithm provides mobility support by dynamically adjusting the transmission period of the messages for selecting the parent node. This is based on the speed and direction of the movement of a mobile node.  
The rest of this paper is organized as follows. Section 2 explains the basic concepts of RPL and the trickle algorithm related to our study and brings the problems occurred when nodes have mobility in RPL. To solve these problems, Section 3 proposes an algorithm that supports mobility considering the velocity and direction of the node in RPL. Section 4 presents the simulation environment. Section 5 compares the proposed algorithm with the existing algorithms based on the simulation results, and the performance is evaluated. Finally, this paper is concluded with future research directions in Section 6.