An apparatus and methods for training and/or operating a robotic device to follow a trajectory. A robotic vehicle may utilize a camera and stores the sequence of images of a visual scene seen when following a trajectory during training in an ordered buffer. Motor commands associated with a given image may be stored. During autonomous operation, an acquired image may be compared with one or more images from the training buffer in order to determine the most likely match. An evaluation may be performed in order to determine if the image may correspond to a shifted (e.g., left/right) version of a stored image as previously observed. If the new image is shifted left, right turn command may be issued. If the new image is shifted right then left turn command may be issued.