Federated Machine Learning (Fed ML) is a new distributed machine learning technique applied to collaboratively train a global model using clients' local data without transmitting it. Nodes only send parameter updates (e.g., weight updates in the case of neural networks), which are fused together by the server to build the global model. By not divulging node data, Fed ML guarantees its confidentiality, a crucial aspect of network security, which enables it to be used in the context of data-sensitive Internet of Things (IoT) and mobile applications, such as smart geo-location and the smart grid. However, most IoT devices are particularly energy constrained, which raises the need to optimize the Fed ML process for efficient training tasks and optimized power consumption. In this paper, we conduct, to the best of our knowledge, the first Systematic Mapping Study (SMS) on FedML optimization techniques for energy-constrained IoT devices. From a total of more than 800 papers, we select 67 that satisfy our criteria and give a structured overview of the field using a set of carefully chosen research questions. Finally, we attempt to provide an analysis of the energy-constrained Fed ML state of the art and try to outline some potential recommendations for the research community.