  This paper presents a solution for the problem of optimal planning for a
robot in a collaborative human-robot team, where the human supervisor is
intermittently available to assist the robot in completing tasks more quickly.
Specifically, we address the challenge of computing the fastest path between
two configurations in an environment with time constraints on how long the
robot can wait for assistance. To solve this problem, we propose a novel
approach that utilizes the concepts of budget and critical departure times,
which enables us to obtain optimal solutions while scaling to larger problem
instances than existing methods. We demonstrate the effectiveness of our
approach by comparing it with several baseline algorithms on a city road
network and analyzing the quality of the solutions obtained. Our work
contributes to the field of robot planning by addressing the critical issue of
incorporating human assistance and environmental restrictions, which has
significant implications for real-world applications.
