A Progression and Retrogression Mathematical Model for the Motor Learning Process

Ko Watanabe, Hiroshi Tanaka, Yosuke Kurihara, Kajiro Watanabe

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We present a novel mathematical model based on the concepts of progression and retrogression. The goal of the model is to provide a more general description of the motor learning process. The model structure is given as a set of two autonomous linear differential equations with two coefficients that characterize the learning process. The coefficients are estimated using data obtained from the learning process. This paper examines how well the data complied with the model and whether the model reflects the human learning process with three biofeedback learning methods. To evaluate them, trainees used our prepared motor learning program for the motion of 'walking without vertical acceleration of the head.' 82.2% of the learning process data complied with the assumptions of the P-R model. To evaluate the impact of feedback, trainees used three motor learning programs. Audio feedback was perceived as 'clearer,' the somatosensory feedback as 'clear,' and the visual feedback as 'fuzzy,' for learning the motion, and the results were evaluated based on the progression speed normalized by retrogression speed calculated by the model, which was 0.25 for the visual feedback learning program, 0.28 for the somatosensory feedback, and 0.69 for the audio feedback. These values had statistically significant differences. Thus, the descriptive model can express successive repeated learning processes under progression and retrogression components.

Original languageEnglish
Article number7234898
Pages (from-to)159-164
Number of pages6
JournalIEEE Transactions on Human-Machine Systems
Issue number1
Publication statusPublished - 2016 Feb


  • Biofeedback
  • evaluation of learning process
  • mathematical model
  • motor learning

ASJC Scopus subject areas

  • Human Factors and Ergonomics
  • Control and Systems Engineering
  • Signal Processing
  • Human-Computer Interaction
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence


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