SURVEY ON ADVANCES IN THE THEORY OF COMPUTATIONAL ROBOTICS.
This paper describes work on the computational complexity of various movement planning problems relevant to robotics. This paper is intended only as a survey of previous and current work in this area. The generalized mover's problem is to plan a sequence of movements of linked polyhedra through 3-dimensional Euclidean space, avoiding contact with a fixed set of polyhedra obstacles. We discuss our and other researchers' work showing generalized mover's problems are polynomial space hard. These results provide strong evidence that robot movement planning is computationally intractable, i. e. , any algorithm requires time growing exponentially with the number of degrees of freedom. We also briefly discuss the computational complexity of four other quite different types of movement problems (1) movement planning in the presence of friction, (2) minimal movement planning, (3) dynamic movement planning with moving obstacles and (4) adaptive movement planning problems.
