Controlling an assistive robotic manipulator can play a crucial role in improving lives of individuals with motor impairments. Here, we propose the use of state-of-the-art machine learning techniques for dimensionality reduction—non-linear autoencoder (AE) networks—within a Body-Machine Interface (BoMI) framework for controlling a 4D virtual manipulator. Compared to their linear counterparts, non-linear AEs allow retaining more of the original variance and spreading it more uniformly along the latent dimensions. This advantage has the potential to facilitate an effective control of devices with multiple degrees of freedom (DoFs). We tested the approach on a cohort of unimpaired participants practicing a reaching task in 3D space. As a result, all participants were able to reach a high level of control skills after training with the interface. Such findings highlight the potential of BoMIs based on non-linear AEs as a control platform for assistive manipulators.