Report for 991 - 058 , Sep . 1 st

Chapter 1 and 2 of [Lat91]: Chapter 1 is an overview of motion planning and some overview of planning algorithms, such as Roadmap, Cell Decomposition and Potential field. Chapter 2 gives mathematical description about configuration space and obstacles, especially about the manifold structure of configuration space (embedding, parameterization, chart, atlas, connectedness, path, metric definition, and some set properties (or assumptions) of space and obstacle, e.g. compactness, regularity). First 3 lecture notes of [sta07] give an more intuitive description about above contents. And chapter 3.4, 3.5, 3.6 of [CLH∗05] introduce manifold properties in a simpler way. It also includes a more in-depth discussion about body-frame transformation and world-frame transformation. Chapter 2 of [Him08] gives a more complete review about planning algorithms, including Probabilistic Roadmap Planner (PRM), Rapidly-Exploring Random Tree (RRT), Iterative Path Planner (IPP), Manhattanlike RRT, both their basic ideas and some comparisons. Chapter 3.1, 3.2 and 3.3 of [Him08] introduce the technology about how to compute wrapped volume (or swept volume) for polygon soup.