An exact and practical method for translational motion planning with many degrees of freedom is derived. It is shown that certain $D-$dimensional arrangements of hyperplanes can be searched in the following way: only a single connected component is traversed during the search, and the arrangement is searched as an arrangement of surface patches rather than full hyperplanes. This reduction in search effort allows for polynomial time bounds in appropriate cases. Heuristic and randomized planners cannot return an information about infeasibility of planning problems. Experiments with an implementation of the new methods suggest that translational infeasibility can be detected in practical cases.     «

An exact and practical method for translational motion planning with many degrees of freedom is derived. It is shown that certain $D-$dimensional arrangements of hyperplanes can be searched in the following way: only a single connected component is traversed during the search, and the arrangement is searched as an arrangement of surface patches rather than full hyperplanes. This reduction in search effort allows for polynomial time bounds in appropriate cases. Heuristic and randomized planners c...     »