Motion Planning with Six Degrees of Freedom

The motion planning problem is of central importance to the fields of robotics, spatial planning, and automated design. In robotics we are interested in the automatic synthesis of robot motions, given high-level specifications of tasks and geometric models of the robot and obstacles. The Mover's problem is to find a continuous, collision-free path for a moving object through an environment containing obstacles. We present an implemented algorithm for the classical formulation of the three-dimensional Mover's 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 intersections, collision-free paths may be found by the closure of three operators which (i) slide along 5-dimensional intersections of level C-Space obstacles; (ii) slide along 1- to 4-dimensional intersections of level C-surfaces; and (iii) jump between 6 dimensional obstacles. Implementing the point navigation operators requires solving fundamental representational and algorithmic questions: we will derive new structural properties of the C-Space constraints and shoe how to construct and represent C-Surfaces and their intersection manifolds. A definition and new theoretical results are presented for a six-dimensional C-Space extension of the generalized Voronoi diagram, called the C-Voronoi diagram, whose structure we relate to the C-surface intersection manifolds. The representations and algorithms we develop impact many geometric planning problems, and extend to Cartesian manipulators with six degrees of freedom.

Ameliorating the Overhead of Dynamic Optimization

Dynamic optimization has several key advantages. This includes the ability to work on binary code in the absence of sources and to perform optimization across module boundaries. However, it has a significant disadvantage viz-a-viz traditional static optimization: it has a significant runtime overhead. There can be performance gain only if the overhead can be amortized. In this paper, we will quantitatively analyze the runtime overhead introduced by a dynamic optimizer, DynamoRIO. We found that the major overhead does not come from the optimizer's operation. Instead, it comes from the extra code in the code cache added by DynamoRIO. After a detailed analysis, we will propose a method of trace construction that ameliorate the overhead introduced by the dynamic optimizer, thereby reducing the runtime overhead of DynamoRIO. We believe that the result of the study as well as the proposed solution is applicable to other scenarios such as dynamic code translation and managed execution that utilizes a framework similar to that of dynamic optimization.