With the rapid development of artificial intelligence (AI) technology, the application of robots is widening and deepening. Due to the fact that robots are capable of machine learning and deep learning, we establish a theoretical model of the production process by considering the difference in learning ability between robots and labor forces, namely the difference in "learning by doing" ability. Based on this, the influence of robots on long-term economic growth is investigated. Our analytical results show that when the learning ability of robots is stronger than human capital, there will be no balanced growth path for the economy, and the economy will eventually show a sustained growth pattern, and the growth rate of capital per capita, output per capita and robot per capita will keep growing. However, more robots are not always better. There is an optimal robot investment ratio to maximize the long-term growth rate of output per capita. Managers should not only increase investments in robots. How to improve the learning ability of robots is also of great importance.