This paper presents a proof-of-concept of a robot that is adapting its behaviour on-line, during interactions with a human according to detected play styles. The study is part of the AuRoRa project which investigates how robots may be used to help children with autism to overcome some of their impairments in social interactions. The paper motivates why adaptation is a very desirable feature of autonomous robots in human-robot interaction scenarios in general, and in autism therapy in particular. Two different play styles namely `strong' and `gentle' are investigated experimentally. The model relies on Self-Organizing Maps and on Fast Fourier Transform to preprocess the sensor data. First experiments were carried out which discuss the performance of the model. Related work on adaptation in socially assistive and therapeutic work are surveyed. In future work, with typically developing and autistic children, the concrete choice of the robot's behaviours will be tailored to...