The sense of agency – the subjective feeling of being in control of our own actions – is one central aspect of the phenomenology of action. Computational models provided important contributions toward unveiling the mechanisms underlying the sense of agency in individual action. In particular, the sense of agency is believed to be related to the match between the actual and predicted consequences of our own actions (comparator model). In the study of joint action, models are even more necessary to understand the mechanisms underlying the development of coordination strategies and how the subjective experiences of control emerge during the interaction. In a joint action, we not only need to predict the consequences of our own actions; we also need to predict the actions and intentions of our partner, and to integrate these predictions to infer their joint consequences. Understanding our partner and developing mutually satisfactory coordination strategies are key components of joint action and in the development of the sense of joint agency. Here we discuss a computational architecture which addresses the sense of agency during intentional, real-time joint action. We first reformulate previous accounts of the sense of agency in probabilistic terms, as the combination of prior beliefs about the action goals and constraints, and the likelihood of the predicted movement outcomes. To look at the sense of joint agency, we extend classical computational motor control concepts - optimal estimation and optimal control. Regarding estimation, we argue that in joint action the players not only need to predict the consequences of their own actions, but also need to predict partner’s actions and intentions (a ‘partner model’) and to integrate these predictions to infer their joint consequences. As regards action selection, we use differential game theory – in which actions develop in continuous space and time - to formulate the problem of establishing a stable form of coordination and as a natural extension of optimal control to joint action. The resulting model posits two concurrent observer-controller loops, accounting for ‘joint’ and ‘self’ action control. The two observers quantify the likelihoods of being in control alone or jointly. Combined with prior beliefs, they provide weighing signals which are used to modulate the ‘joint’ and ‘self’ motor commands. We argue that these signals can be interpreted as the subjective sense of joint and self agency. We demonstrate the model predictions by simulating a sensorimotor interactive task where two players are mechanically coupled and are instructed to perform planar movements to reach a shared final target by crossing two differently located intermediate targets. In particular, we explore the relation between self and joint agency and the information available to each player about their partner. The proposed model provides a coherent picture of the inter-relation of prediction, control, and the sense of agency in a broader range of joint actions.
In the last years, artificial partners have been proposed as tools to study joint action, as they would allow to address joint behaviors in more controlled experimental conditions. Here we present an artificial partner architecture which is capable of integrating all the available information about its human counterpart and to develop efficient and natural forms of coordination. The model uses an extended state observer which combines prior information, motor commands and sensory observations to infer the partner's ongoing actions (partner model). Over trials, these estimates are gradually incorporated into action selection. Using a joint planar task in which the partners are required to perform reaching movements while mechanically coupled, we demonstrate that the artificial partner develops an internal representation of its human counterpart, whose accuracy depends on the degree of mechanical coupling and on the reliability of the sensory information. We also show that human-artificial dyads develop coordination strategies which closely resemble those observed in human-human dyads and can be interpreted as Nash equilibria. The proposed approach may provide insights for the understanding of the mechanisms underlying human-human interaction. Further, it may inform the development of novel neuro-rehabilitative solutions and more efficient human-machine interfaces.
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