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#### Publication Date

2008-12-19

#### Availability

UM campus only

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy (PHD)

#### Department

Computer Science (Arts and Sciences)

#### Date of Defense

2008-11-21

#### First Committee Member

Victor Milenkovic - Committee Chair

#### Second Committee Member

Hongtan Liu - Committee Member

#### Third Committee Member

Brian Coomes - Committee Member

#### Fourth Committee Member

Elisha Sacks - Committee Member

#### Fifth Committee Member

Geoff Sutcliffe - Committee Member

#### Abstract

We present robust explicit construction of 3D configuration spaces using controlled linear perturbation. The input is two planar parts: a fixed set and a moving set, where each set is bounded by circle segments. The configuration space is the three-dimensional space of Euclidean transformation (translations plus rotations) of the moving set relative to the fixed set. The goal of constructing the 3D configuration space is to determine the boundary representation of the free space where the intersection of the moving set and fixed set is empty. To construct the configuration space, we use the controlled linear perturbation algorithm. The controlled linear perturbation algorithm assigns function signs that are correct for a nearly minimal input perturbation. The output of the algorithm is a consistent set of function signs. This approach is algorithm-independent, and the overhead over traditional floating point methods is reasonable. If the fixed and moving sets are computer representations of physical objects, then computing the configuration space greatly aids in many computational geometry problems. The main focus of computing the configuration space is for the path planning problem. We must find if a path exists from the start to the goal, where the fixed set is the obstacle, and the moving set is the object trying to reach the goal.

#### Keywords

SEE; Path Plotting; Events; Exact Methods; Algorithms; LAPACK; Primitives; Path Plan; SVE; Perturbation; Arrangements; Resolution Complete; Inconsistency Sensitive; Criticality; Probabilistic Complete; Free Space; 3D Manifold; Sampling; Safety Margin; LP; CPLEX; Linear Programming; Ray Tracing

#### Recommended Citation

Trac, Steven Cy, "Robust Explicit Construction of 3D Configuration Spaces Using Controlled Linear Perturbation" (2008). *Open Access Dissertations*. 189.

http://scholarlyrepository.miami.edu/oa_dissertations/189