Spatial Reasoning and Planning

From the reviews: "This book especially deals with the problems of spatial reasoning and planning which are especially important for design stages of mechanical systems where system parameters have not yet been specified ... . The presentation of the material is very interesting and will be an excellent example for further work at similar problems. ... This book can be used for graduate students in several areas, but also ... for the continuous education of people that are already working in a given field." (Christian Posthoff, Zentralblatt MATH, Vol. 1054, 2005)

• 1 Introduction.- 1.1 Motivation.- 1.2 Issues.- 1.3 Scope of the Book.- 1.4 Organization of the Book.- 2 Overview of Spatial Reasoning and Planning Techniques.- 2.1 Computer-Aided Kinematic Design of Mechanisms.- 2.2 Geometric Path Planning.- 2.2.1 Path Search in Configuration Space.- 2.3 Qualitative Reasoning.- 3 Interesting Problems in Spatial Reasoning and Planning.- 3.1 Terminology and Notation.- 3.2 The Problems.- 3.3 Assumptions.- 4 How to Represent Qualitative Spatial Relationships.- 4.1 Qualitative Distance.- 4.2 Qualitative Angle.- 4.3 Notes on Label-Based Distance and Angle Descriptions.- 4.4 Completeness.- 4.5 Minimum-Spanning Edge (m-Edge) between Two Polygons.- 4.6 Qualitative Location in a Convex Polygonal Environment.- 4.7 Graphic Representation of the m-Edge Partitioned Free-Space.- 4.8 Notes on Qualitative Location.- 5 Methodology of Spatial Reasoning and Planning.- 5.1 Spatial Inferencing.- 5.2 Envisionments.- 5.3 Spatial Planning in Q-Space.- 5.4 Quantitative Configuration Generation with Simulated Annealing.- 6 How to Reason about Mechanism Configurations.- 6.1 An Overview of the Method.- 6.2 Qualitative Configuration Analysis.- 6.3 Quantitative Configuration Generation.- 6.4 Discussions.- 6.6 Summary.- 7 How to Reason about Velocity Relationships.- 7.1 Instantaneous Rotation Center.- 7.2 Velocity Relationship Analysis.- 7.3 Examples.- 7.4 Notes on the Application of Velocity Analysis.- 7.5 Relative Motion Method of Analyzing Velocities.- 7.5.2 Kinematic Modeling.- 7.6 Qualitative Analysis of Relative Velocities.- 7.7 An Example.- 7.8 Summary.- 8 How to Plan Robot Motions.- 8.1 An Overview of the Method.- 8.2 Qualitative Route Planning in the m-Edge Partitioned Euclidean Free-Space.- 8.3 Constructing Exact Paths from Qualitative Routes.- 8.4 GraphicalSimulations.- 9 How to Make Spatial Measurements and Maps.- 9.1 Mapping.- 9.2 m-Uncertainty and FS Theory.- 9.3 Incorporating m-Uncertainty.- 9.4 Collective Spatial Map Construction.- 9.5 Self-Organization of a Potential Map.- 9.6 Experiments.- 9.7 Summary.- 10 Concluding Remarks.- 10.1 Key Concepts Revisited.- 10.2 Practical Application.- 10.3 Limitations.- 10.4 Future Challenges.- Appendices.- B The Boltzmann Distribution in Simulated Annealing.- C Qualitative Route Search Based on A. Algorithm.- References.