Game Theory for Eye Robot Movement: Approach and Hardware Implementation

Abstract

Robotic eyes imitate human eye appearance, but, they lack human-like movements. Also, there are no criteria to select one eye as the leader in eyes simultaneous movement. To solve these challenges, this paper proposes two algorithms to coordinate the movement of two separately controlled eyes, and, to select the leader eye in their synchronous movement. In the first algorithm-called Gazist-eyes apply the concept of bi-matrix games in noncooperative game theory to decide between their vertical and horizontal options. In the second algorithm-called Leaf-we consider game trees for sequential eye movements. Nash equilibrium for each game tree (found by backward induction) is our proposed criteria to choose the leader eye. Our algorithms are validated through experiments on a 3D printed eye robot that tracks the face for a person walking before it. To the best of our knowledge, Gazist algorithm constitutes one of the first examples of coordinated movement for robotic eyes by game theory. Also, Leaf algorithm proposes the first criteria for choosing the leader in eyes synchronous movement.