The primary research objective is to develop a framework based on the recently discovered differential equation approach for solving motion related problems that arise in manufacturing automation. It is of particular interest to produce an advance in the theory of swept volumes, which will lead to improved means of representing and analyzing sweeps and swept volumes that occur in numerically controlled (NC) machining, robot manipulation, etc. Also of interest is to investigate the full potential of the differential equation approach as a tool for characterizing intersections of swept volumes, which leads to solutions for collision detection and other motion planning problems. The method will be applied to program verification and motion planning problems in NC machining and robotics. The tasks include identification of classes of sweeps, characterization of singularities in swept volumes and detection of collision with obstacles (both static and dynamic). The project will include work on implementing the results for practical applications.
