Exact combinatorial solutions to the motion planning problem in robotics, which use precise computational geometry techniques, especially for systems with few degrees of freedom, tend to be more robust than heuristic or approximating solutions; they can achieve performance that is theoretically faster than that of naive solutions by an order of magnitude or more, and it is therefore desirable to test their pragmatic feasibility in real systems context, both to complete the somewhat abstract algorithm variants typical of theoretical developments in computational geometry, and to show that they indeed perform well in practice. This project undertakes the development of an `industrial-strength' motion planning system for bodies translating in 3-dimensional polyhedral environments. This system utilizes efficient and precise geometric algorithms obtained through ongoing theoretical work, whose worst-case complexity attains the best theoretical bounds known for the problem, and also turn out to be very efficient in practice.
