Motion Planning with Six Degrees of Freedom. Revision
MASSACHUSETTS INST OF TECH CAMBRIDGE ARTIFICIAL INTELLIGENCE LAB
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The motion planning problem is of central importance to the fields of robotics, spatial planning, and automated design. An implemented algorithm is presented for the classical formulation of the three-dimensional Movers problem Given an arbitrary rigid polyhedral moving object p with three translational and three rotational degrees of freedom, find a continuous, collision free path taking p from some initial configuration to a desired goal configuration. This thesis describes the first known implementation of a complete algorithm at a given resolution for the full six degree of freedom Movers problem. The algorithm transforms the six degree of freedom planning problem into a point navigation problem in a six-dimensional configuration space called C-Space. The C-Space obstacles, which characterize the physically unachievable configurations, are directly represented by six-dimensional manifolds whose boundaries are five dimensional C-surfaces. By characterizing these surfaces and their intersection collision-free paths may be found by the closure of three operators which i slide along 5-dimensional level C-surfaces parallel to C-Space obstacles ii slide along 1- to 4-dimensional intersections of level C-surfaces and iii jump between 6-dimensional obstacles.