  Using a dual-task paradigm, we explore how robot actions, performance, and
the introduction of a secondary task influence human trust and engagement. In
our study, a human supervisor simultaneously engages in a target-tracking task
while supervising a mobile manipulator performing an object collection task.
The robot can either autonomously collect the object or ask for human
assistance. The human supervisor also has the choice to rely upon or interrupt
the robot. Using data from initial experiments, we model the dynamics of human
trust and engagement using a linear dynamical system (LDS). Furthermore, we
develop a human action model to define the probability of human reliance on the
robot. Our model suggests that participants are more likely to interrupt the
robot when their trust and engagement are low during high-complexity collection
tasks. Using Model Predictive Control (MPC), we design an optimal
assistance-seeking policy. Evaluation experiments demonstrate the superior
performance of the MPC policy over the baseline policy for most participants.
