Extending Feynman's Formalisms for Modeling Human Joint Action Coordination

Abstract

The recently developed Life-Space-Foam approach to goal-directed human action deals with individual actor dynamics. This paper applies the model to characterize the dynamics of co-action by two or more actors. This dynamics is modelled by: (i) a two-term joint action (including cognitive/motivatonal potential and kinetic energy), and (ii) its associated adaptive path integral, representing an infinitedimensional neural network. Its feedback adaptation loop has been derived from Bernstein's concepts of sensory corrections loop in human motor control and Brooks' subsumption architectures in robotics. Potential applications of the proposed model in human-robot interaction research are discussed.Recently [1] we have suggested a generalized motivational/cognitive action, generating Lewinian force-fields [2, 3] on smooth manifolds. On the other hand, cognitive neuroscience investigations, including fMRI studies of human co-action, suggest that cognitive and neural processes supporting co-action include joint attention, action observation, task sharing, and action coordination [4,5,6,7]. For example, when two actors are given a joint control task (e.g., tracking a moving target on screen) and potentially conflicting controls (e.g., one person in charge of acceleration, the other -deceleration), their joint performance depends on how well they can anticipate each other's actions. In particular, better coordination is achieved when individuals receive real-time feedback about the timing of each other's actions [7].

Entropic Geometry of Crowd Dynamics

“…where we expect the inter-phase chaotic behavior (see [53]). To show that this chaotic interphase is caused by the change in Riemannian geometry of the crowd 3n-manifold M, we will first simplify the CD action functional (22) as…”

“…Note that the cognitive intentions of any two agents generally occur at different times t i and t j unless t i = t j , when cognitive synchronization occurs. This term effectively represents the crowd cognitive controller (see [53]). …”

“…In our path-integral language this means that suitable topology changes of equipotential submanifolds of the CD-manifold M can entail thermodynamic-like phase transitions [25; 26; 27], according to the general formula: (53) where the last term is written using the so-called co-area formula [18], and v labels the equipotential hypersurfaces M v of the CD manifold M, 13 3 13 ={( , , ) | ( , , )= }. (53) shows that the relevant statistical information is contained in the canonical configurational partition function defined on the {M v } v∈R .…”

Crowd behavior dynamics: entropic path-integral model

“…Note that the cognitive intentions of any two agents generally occur at different times t i and t j unless t i = t j , when cognitive synchronization occurs. This term effectively represents the crowd cognitive controller (see [45]). The second term in (18) represents kinetic energy of the physical interaction of agents.…”

“…Recall that CD transition map ( 5) is defined by the chaotic crowd phase-transition amplitude where we expect the inter-phase chaotic behavior (see [45]). To show that this chaotic inter-phase is caused by the change in Riemannian geometry of the crowd 3n−manifold M , we will first simplify the CD action functional (18) as…”