Alternative ways of communication such as brain-computer interfaces (BCI) can establish new ways of interaction with the surrounding environment which are especially useful in assisting people with motor disabilities. The challenge of BCI systems for robotic control is to rapidly and accurately produce reliable control commands. The aim of the present paper is to develop a BCI system that is able to control a robot by means of ocular movements (blinks and winks). In this work, the goal is to develop lightweight algorithms that can accurately discriminate four eye movement classes (voluntary and involuntary blink, right and left winks), associate every class to a command for the robot, and be able to work in real time. To this end, electroencephalographic (EEG) signals were collected during the execution of eye movements and used to construct a dataset. The proposed system is composed of an event detection algorithm which detects spikes possibly related to blinking or winking and a subsequent custom 1D convolutional neural network (CNN) to carry out the classification. Our system allows for a three DoF control of the robot movement (move forward, right, left) achieving an average classification accuracy of 99.3%.