### Path-planning with uncertainty: a simple model

There are already plenty of work on planning under uncertainty. Here we consider a simple model, where the uncertainty can be removed at a later time \( T\) with different variations:

- A fixed deterministic \(T\)
- A random \(T\) with a discrete distribution
- A random \(T\) with a discrete, stage-different distribution
- A random \(T\) with an exponential distribution

The stage-differently distributed \(T\) can be illustrated by the following motion picture.
Assuming there are 4 possible target locations but only one of them is the true one.
Starting from the source, we send out 3 drones to check each location while move to a better waypoint in the meantime.

See paper for more details. Joint work with Adam Dhillon and Alexander Vladimirsky.