Evaluating critical points in trajectories

People form beliefs about intentions and preferences of robots as they observe robot movement. However, robots rarely optimize their movement to allow people to easily determine state preferences. In this work, we define critical points along robot trajectories that convey information about state preferences: inflection points are changes in direction and compromise points are the relative proportion of preferred states to non-preferred ones. We contribute an approach for automatically generating trajectory demonstrations with specified critical points, and test observers' abilities to understand and generalize our robot's preferences based on our generated demonstrations. Our results show that inflection points helped participants understand state preference ordering and allowed them to more accurately predict paths through new environments, while compromise points hindered understanding. We conclude that robots should evaluate their trajectories for critical points to increase human observer understanding.