In recent years, there have been significant efforts to standardize a routing protocol for Low-power and Lossy Networks (LLNs). This effort has culminated in standard IPv6 routing protocol for LLNs (RPL). The main interest of RPL is to improve routing in a LLN minimizing the usage of network resources. For this, RPL build acyclic graphs and applies an Objective Function (OF) which is responsible of choosing the preferred parent and the best links during the construction of the Destination Oriented Directed Acyclic Graph (DODAG). This paper introduces a new OF, based on a Non-Linear Length (NL-OF) which takes into account any number of metrics and constraints for QoS routing. NL-OF ensures that each path in the DODGA respects the input constraints. The NL-OF can be used to meet the requirements of sensible applications, such as real-time applications. A significant part of this work aims at studying the theoretical of the NL-OF. Finally, using Cooja simulator, we evaluate the performance of NL-OF. We show that our new Objective Function gives a good result and outperforms the three existing OFs when considering three QoS parameters which are End-to-End Delay, Packet Loss and Jitter.