Oscillations in two-person avoidance control

Abstract

Social interaction dynamics are a special type of group interactions that play a large part in our everyday lives. They dictate how and with whom a certain individual will interact. One of such interactions can be termed "avoidance control". This everyday situation occurs when two fast-walking persons suddenly realize that they are on a frontal collision course and begin maneuvering to avoid collision. If the two walkers' initial maneuverings are in the same direction that can lead to oscillations that lengthen time required to reach a stable avoidance trajectory. We introduce a dynamical model with a feedback loop to understand the origin and properties of this oscillation. For the emergence of the oscillatory behavior, two conditions must be satisfied: i) the persons must initiate the avoidance maneuver in the same direction; ii) the time delays in the feedback loop must reverse the phase of the players' positions at the oscillation frequency. The oscillation can be terminated at any time if one of the walkers decides to stop and/or to communicate. By taking over the control of the situation the walker cuts the feedback loop. Similar oscillatory situations may potentially cause major collisions between autonomous vehicles and airplanes with airborne communications, but in autopilot mode.