Who is the leader in a multiperson ensemble? - Multiperson human-robot ensemble model with leaderness

This paper presents a state space model for a multiperson ensemble and an estimation method of the onset timings, tempos, and leaders. In a multiperson ensemble, determining one explicit leader is difficult because (1) participants' rhythms are mutually influenced and (2) they compete with each other. Most ensemble studies however assumed that one leader exists at a time and the others just follow the leader. To deal with the multiple and time-varying leaders, we define leaderness indicating the power to influence the others as the product of the tempo stability and the distance from the ensemble tempo. This definition means that a leader should have a strong desire to change the current tempo. Using the leaderness, we present a state space model of a multiperson ensemble and an unscented Kalman filter based estimation method. The model consists of the leaderness update, the ensemble tempo update, the individual tempo update, and the onset timing adaptation, each of which has a relationship to psychological results of an ensemble. We evaluate our method using simulation and human behavior. The simulation results show that our model is stable for various initial tempos and the number of participants. For the human behavior, pairs and triads of participants are asked to tap keys in synchronization with the others. The results show that the leaderness successfully indicate the dynamics of the leaders, and the onset errors are 181msec and 241msec for pairs and triads on average, respectively, which are comparable to those of humans (153msec and 227msec for pairs and triads, respectively.)