In the past few decades, the research of assistant mobile rollators for the elderly has attracted more and more investigation attention. In order to satisfy the needs of older people or disabled patients, this paper develops a neural approximation based predictive tracking control scheme to improve and support the handicapped through the novel four-wheeled rollator. Firstly, considering the industrial product theory, a novel Kano-TRIZ-QFD engineering design approach is presented to optimize the mechanical structure combined with humanistic care. At the same time, in order to achieve a stable trajectory tracking control for the assistant rollator system, a neural approximation enhanced predictive tracking control is discussed. Finally, autonomous tracking mobility of the presented control scheme has received sufficient advantage performance in position and heading angle variations under the external uncertainties. As the market for the medical device of the elderly rollators continues to progress, the method discussed in this article will attract more investigation and industry concerns.