Our sense of touch can pick up thousands of nuances because we have soft flesh. Try to touch an object with your nails and you'll miss a lot of the sensations that your fingertips can provide.
Robots are facing a similar problem. Having a rigid surface they have a limited touch sensitivity. However, with the recent progress in 3D printing of soft materials it has become possible to create soft skin for robotic "hands" and to fill it with sensors able to pick up a broader set of sensations.
This is what has been done at Cornell University where a team of researchers have created a robotic hand optoelectronically innervated that is able to sense object with a resolution similar to the one of a human hand.
In a demonstration, watch the clip, they have shown that the robot is able to identify the ripest tomato among a set of three by touching it, just like we do at the supermarket, judging the ripeness by touching the softness and texture of the tomato. Clearly, this capability can improve the range of application of a robot making it more aware of its environment.
However, the long term goal is to create a prosthetic hand for amputees that can pick up touch sensation and relate them to the brain by connecting with the nerves in the arm.