The rising number of the elderly incurs growing concern about healthcare, and in particular rehabilitation healthcare. Assistive technology and and assistive robotics in particular may help to improve this process. We develop a robot coach capable of demonstrating rehabilitation exercises to patients, watch a patient carry out the exercises and give him feedback so as to improve his performance and encourage him. We propose a general software architecture for our robot coach, which is based on imitation learning techniques using Gaussian Mixture Models. Our system is thus easily programmable by medical experts without specific robotics knowledge, as well as capable of personalised audio feedback to patients indicating useful information to improve on their physical rehabilitation exercise.