  In situations where humans and robots are moving in the same space whilst
performing their own tasks, predictable paths taken by mobile robots can not
only make the environment feel safer, but humans can also help with the
navigation in the space by avoiding path conflicts or not blocking the way. So
predictable paths become vital. The cognitive effort for the human to predict
the robot's path becomes untenable as the number of robots increases. As the
number of humans increase, it also makes it harder for the robots to move while
considering the motion of multiple humans. Additionally, if new people are
entering the space -- like in restaurants, banks, and hospitals -- they would
have less familiarity with the trajectories typically taken by the robots; this
further increases the needs for predictable robot motion along paths.
  With this in mind, we propose to minimize the navigation-graph of the robot
for position-based predictability, which is predictability from just the
current position of the robot. This is important since the human cannot be
expected to keep track of the goals and prior actions of the robot in addition
to doing their own tasks. In this paper, we define measures for position-based
predictability, then present and evaluate a hill-climbing algorithm to minimize
the navigation-graph (directed graph) of robot motion. This is followed by the
results of our human-subject experiments which support our proposed
methodology.
