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.

中文翻译：

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镜像游戏中人际协作学习虚拟玩家的设计与验证

镜像游戏最近被提出为研究人际互动的一种简单而强大的范例。已经提出，能够与人类受试者一起玩游戏的虚拟伙伴可以是一种有效的工具，可以影响在玩家之间建立必要联系所需的潜在神经过程，并且还可以为患有以下疾病的患者的康复提供新的临床干预措施社会障碍。受到人体中枢神经系统（CNS）和肌肉骨骼系统的运动过程的启发，本文基于非线性控制理论开发了一种新颖的交互式认知架构，以驱动虚拟玩家（VP）进行镜像游戏与人类玩家（HP）在不同的配置中。具体来说，我们考虑两种情况：1）副总裁担任领导者，2）副总裁担任跟随者。关键问题是设计一种反馈控制体系结构，该体系结构能够模仿和跟踪或领导HP开展联合行动任务。VP末端执行器的运动是通过反馈控制的Haken–Kelso–Bunz（HKB）振荡器建模的，该振荡器与实时观察到的HP运动相关。为此，在HKB模型上使用并实现了两种控制算法（自适应控制和最佳控制），以便VP可以在满足某些运动学约束的同时生成类人的运动。提出了控制算法收敛性的证明，并对其有效性进行了广泛的数值和实验验证。还讨论了与其他现有设计的比较，