This paper investigates the problem of finding
shortest paths through 3-dimensional cluttered environments.
In particular, an algorithm is presented that determines the
shortest path between two points in an environment with
obstacles which can be implemented on robots with capabilities
of detecting obstacles in the environment. As knowledge of the
environment is increasing while the vehicle moves around, the
algorithm provides not only the global minimizer – or shortest
path – with increasing probability as time goes by, but also
provides a series of local minimizers. The feasibility of the
algorithm is demonstrated on a quadrotor robot flying in an
environment with obstacles.