Design and Validation of a Virtual Player for Studying Interpersonal Coordination in the Mirror Game

Chao Zhai, Francesco Alderisio, Piotr Slowinski, Krasimira Tsaneva-Atanasova, Mario di Bernardo

Research output: Contribution to journalArticle (Academic Journal)peer-review

7 Citations (Scopus)
370 Downloads (Pure)


The mirror game has been recently proposed as a simple, yet powerful paradigm for studying interpersonal interactions. It has been suggested that a virtual partner able to play the game with human subjects can be an effective tool to affect the underlying neural processes needed to establish the necessary connections between the players, and also to provide new clinical interventions for rehabilitation of patients suffering from social disorders. Inspired by the motor processes of the central nervous system (CNS) and the musculoskeletal system in the human body, in this paper we develop a novel interactive cognitive architecture based on nonlinear control theory to drive a virtual player (VP) to play the mirror game with a human player (HP) in different configurations. Specifically, we consider two cases: 1) the VP acts as leader and 2) the VP acts as follower. The crucial problem is to design a feedback control architecture capable of imitating and following or leading an HP in a joint action task. The movement of the end-effector of the VP is modeled by means of a feedback controlled Haken-Kelso-Bunz (HKB) oscillator, which is coupled with the observed motion of the HP measured in real time. To this aim, two types of control algorithms (adaptive control and optimal control) are used and implemented on the HKB model so that the VP can generate a human-like motion while satisfying certain kinematic constraints. A proof of convergence of the control algorithms is presented together with an extensive numerical and experimental validation of their effectiveness. A comparison with other existing designs is also discussed, showing the flexibility and the advantages of our control-based approach.

Original languageEnglish
Pages (from-to)1018-1029
Number of pages12
JournalIEEE Transactions on Cybernetics
Issue number3
Early online date7 Mar 2017
Publication statusPublished - Mar 2018


  • Virtual player
  • Joint action
  • Mirror game
  • Motor coordination
  • Nonlinear control

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