The Piano Mover's Problem of moving a robot through an environment with obstacles can be defined mathematically and solved with algorithms with known asymptotic complexity.
It is amazing that such algorithms exist; however, it is also unfortunate that they are both extremely challenging to implement and not efficient enough for most applications.
While every new thesis on robot motion planning has to mention Canny's Roadmap Algorithm, it is doubtful if it has ever been implemented:
no general implementation of Canny's algorithm appears to exist at present.
