The usual framework to study the trajectory planning problem among static or dynamic obstacles is the configuration space (C-space). The main idea of the C-space is to represent the robot as a point, called a configuration.
A robot configuration is a vector of parameters specifying position, orientation and all the characteristics of the robot in the environment. The C-space is the set of all possible configurations. Its dimension is the number of parameters that defines a configuration. C-free is the set of configurations that are free of obstacles. Obstacles in the workspace become C-obstacles in the C-space.
Usually a simple rigid body transformation (Latombe, 1991) is used to map the real environment into the C-space. We focus on 2D and 3D C-spaces in this chapter, nonetheless this framework holds for C-spaces of any dimensions.
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