  Home-based physical therapies are effective if the prescribed exercises are
correctly executed and patients adhere to these routines. This is specially
important for older adults who can easily forget the guidelines from
therapists. Inertial Measurement Units (IMUs) are commonly used for tracking
exercise execution giving information of patients' motion data. In this work,
we propose the use of Machine Learning techniques to recognize which exercise
is being carried out and to assess if the recognized exercise is properly
executed by using data from four IMUs placed on the person limbs. To the best
of our knowledge, both tasks have never been addressed together as a unique
complex task before. However, their combination is needed for the complete
characterization of the performance of physical therapies. We evaluate the
performance of six machine learning classifiers in three contexts: recognition
and evaluation in a single classifier, recognition of correct exercises,
excluding the wrongly performed exercises, and a two-stage approach that first
recognizes the exercise and then evaluates it. We apply our proposal to a set
of 8 exercises of the upper-and lower-limbs designed for maintaining elderly
people health status. To do so, the motion of volunteers were monitored with 4
IMUs. We obtain accuracies of 88.4 \% and the 91.4 \% in the two initial
scenarios. In the third one, the recognition provides an accuracy of 96.2 \%,
whereas the exercise evaluation varies between 93.6 \% and 100.0 \%. This work
proves the feasibility of IMUs for a complete monitoring of physical therapies
in which we can get information of which exercise is being performed and its
quality, as a basis for designing virtual coaches.
