Developing an artificial biomimetic model of tactile perception is a key goal for both practical applications in dexterous robotics and in our understanding of human touch. Here, we present a novel, embodied model of tactile perception that mimics physical and computational features of the peripheral and central nervous systems. We deploy the model on a grating discrimination task, showing how integrating sensory evidence over time improves perceptual accuracy. We also provide a method for learning evidence thresholds which optimise the speed accuracy trade-off. Our model therefore provides a novel implementation of robotic tactile perception and sheds light on the computational features of this process in humans.