Praise be to Allaah.
Making a robot comes under the ruling on image-making. To sum up, if the machine is made in the shape of a man or an animate being, that is forbidden, and comes under the stern warning that is issued to those who make images and try to imitate the creation of Allaah. It will be said to them on the Day of Resurrection: “Give life to that which you have created.” It also comes under the words of the Prophet (peace and blessings of Allaah be upon him): “Those who will be most severely punished on the Day of Resurrection will be the image-makers.” (Narrated by al-Bukhaari, no. 5606; Muslim, 2109.
But if the machine is not in the form of an animate being or is incomplete and would not be taken as a human being or animate creature, there is nothing wrong with that.
It should be noted that no matter how far man advances in the field of technology, he will never be able to make anything that is anywhere near the creation of Allaah. Allaah says (interpretation of the meaning):
“So Blessed is Allaah, the Best of creators”