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Low Power and Lossy Networks (LLNs) are inherently dynamic-nodes move or experience link perturbations. Routing packets in LLNs is generally performed by the IETF IPv6 Routing Protocol for Low-Power and Lossy Networks (RPL). To face the dynamics of LLN, RPL is helped by external mechanisms such as Neighbor Unreachability Detection (NUD) or Bidirectional Forwarding Detection (BFD). In this article, we focus our analysis on mobility support. We first show that NUD and BFD fail to mitigate node disconnection. We therefore propose a new cross-layer protocol operating between the MAC and routing layers known as Mobility-Triggered RPL (MT-RPL). MT-RPL has been implemented in Contiki OS and is evaluated together with NUD and BFD through an extensive experimentation campaign. Results show that our solution significantly reduces the disconnection time, which increases the packet delivery ratio from the mobile node to the root and reduces control traffic in the network.