## 1 Introduction  
The Internet of things (IoT) provides a big picture and foundation for a new era. Diverse types of \"things\", ranging from tiny chip-embedded physical objects to powerful computers, are allowed to connect and communicate with each other through the IoT [1]. The IoT has attracted plenty of application implementations and protocol designs from industry and academia [2]. Applications can run on the IoT, along with a set of supporting technologies, such as designated modifications of IPv6, network stacks with light-weight requirements for hardware, etc. Currently, there are still open issues in several areas, such as interoperation with different networks, heterogeneity adaption resolutions, efficient routing with hardware constraints, transmission security, and so on [3, 4]. There are plenty of categories of IoT networks, among which the low-power and lossy network (LLN) was considered as a key target network scenario by the Routing over Low Power and Lossy Network Working Group (ROLL WG) of the Internet Engineering Task Force (IETF) ([[https://datatracker.ietf.org/wg/roll/about/](https://datatracker.ietf.org/wg/roll/about/)]([https://datatracker.ietf.org/wg/roll/about/](https://datatracker.ietf.org/wg/roll/about/)) (accessed on 5 February 2023)), which is an essential building block in the IoT-based infrastructure [5]. LLN works with unstable connections and resource-constrained devices. The unstable connections cannot sustain reliable long-range communications, while the resource-constrained devices bring strong limitations in data computing and storage capabilities. In the designs of the routing protocol for LLN, all the above features play important roles, which makes conditions more limited than that in traditional host networks [6]. In order to meet these challenges, the IPv6 routing protocol for low-power and lossy networks(RPL) [7; 8] is proposed and adopted as a routing solution to the scenarios defined in IEEE 802.15.4e [9]. In around 2009, RPL was discussed to perform as a routing protocol to meet the particular requirements of wireless sensor networks, through a gradient routing strategy [10]. Specifically, IETF ROLL WG worked to implement it and proposed the early foundational works [11; 12]. With continuous improvements, RPL was recognized as a standard for LLN in RFC 6550 [13] in 2012. RPL adopts an ad hoc logical routing topology, which is based on, but different from, a physical device layer topology. The basic unit of RPL is an instance. One instance consists of one or more destination-oriented directed acyclic graphs (DODAGs) [14; 15]. Each instance has different environment parameter settings, and a DODAG can be upgraded by issuing a new version number. Briefly, a DODAG is a directed acyclic graph anchored on a single root that is also called a LLN border router (LBR) [16; 17]. LBR governs the internal RPL network, and also acts as a bridge to interoperate between the internal RPL network and the external IPv6 networks. Figure 1 illustrates this high-level structure. In the RFC 6550 [13], RPL is designed with three in-built categories of communications: (1) point-to-point (P2P); (2) point-to-multipoint (P2 MP); and (3) multipoint-to-point (MP2P) communications. Specifically, P2P refers to the data traffic from any node to any node, P2 MP means the data traffic from root to multiple nodes, and MP2P indicates the data traffic from multiple nodes to root. Two distinct routing schemes, upward routing and downward routing, are proposed to support these communication patterns. Upward routing refers to the data flow from leaf node, through routers, to the root. On the contrary, the data flow from root to leaf nodes is defined as downward routing. MP2P is implemented by upward routing, P2 MP utilizes downward routing. Finally, P2P adopts a combination of upward routing and downward routing. However, that three types of communications are supported differently according to RFC 6550.