| The mapping from workspace to configuration space (C-space) plays a major role in the field of kinematics, with applications including robotics path planning, packing and nesting, automated assembly, and mechanism analysis. Over the past 20 years, research into the problem has resulted in many techniques that can be combined to suit a specific application. This survey aims to provide the developer of a C-space-based system with an overview of those techniques that map the global C-space of a single robot in a static environment. We discuss issues concerning how the robot and its environment are modeled (including how approximations can be used to make C-space mapping easier) and describe a range of schemes used to represent a C-space map. We then discuss the key techniques used to generate a C-space map for mobile robots and manipulators. The survey of literature is summarized by tables that list some 50 individual mapmaking papers, classifying each according to criteria identified in earlier sections. Finally, we draw conclusions from the findings of the survey. Note that, although reference is made throughout to robots, the controlled objects may equivalently be components or assemblies. In particular, results for mobile robots are fundamental to all C-space mapmaking problems.