Proportional Likelihood Estimation for Integrating Vibrotactile and Force Cues in 3D User Interaction

A model of integration for vibrotactile and force cues is important for facilitating human users' task performance in human-machine systems. One of such human-machine systems is an interactive three-dimensional (3D) virtual environment (VE). In this paper, we proposed proportional likelihood estimation (PLE) as a model of integration for vibrotactile and force cues. Assuming human responses to cues as Gaussian distributions, PLE integrates these cues proportionally according to certain weighted contributions. We conducted an experiment to verify the suitability of PLE. For the experiment, we created a VE in which a human user executed interactively an identification task. The task required the user to identify visually indiscernible defects on a transmission line with a flying drone. The defects were indicated to the user through vibrotactile and/or force cues. These cues were in a co-located or dis-located setting, respectively, on the user's right hand and/or forearm. The PLE predictions of integrating the vibrotactile and force cues were able to match the empirical observation of these combined cues. PLE also elucidated this cue integration successfully when applying to an existing dataset acquired under a different experimental condition. Further analyses revealed that the cue integration may not be entirely additive. Hence, PLE could shed a light on the cue integration for facilitating user interaction in human-machine systems, like VEs.