We present an auto-encoder version of gated networks for learning visuomotor transformations for reaching targets andrepresentating the location of the robot arm. Gated networks use multiplicative neurons to bind correlated images fromeach others and to learn their relative changes. Using the encoder network, motor neurons categorize the induced visualdisplacements of the robot arm when applying their corresponding motor commands.Using the decoder network, it ispossible to infer back the visual motion and location of the robot arm from the activity of the motor units, aka bodyimage.Using both networks at the same time, near targets can simulate a fictious visual displacement of the robot armand induce the activation of the most probable motor command for tracking it. Results show the effectiveness of ourapproach for 2 degree of freedom and 3 degree of freedom robot arms. We discuss then about the network and its use forreaching task and body representation, future works and its relevance for modeling the so-called gain-field neurons in theparieto-motor cortices for learning visuomotor transformation.