Robotic path planning problems

We are interested in problems related to the following questions:

1) How to optimize the visibility of an observer in an environment that has complicated obstruction of line-of-sights?

2) How to move a robot to efficiently learn an unknown piece of domain?

Simple greedy approach:

Step 1: At an observing location, sample the nearby environment.

Step 2: Analyze all the perviously obtained data, and determine the next observation location.

Repeat Steps 1 and 2 until no further gain in information is possible.

Gallery: Proof of concept of a full 3D autonomous algorithm that learns a complex structure by adaptively adding a sequence of observing locations (shown as the vertices of the polygonal path).