I-space interpretation

In terms of an I-space over the set of environments, the GNT considers large sets of environments to be equivalent. This means that an I-map was constructed on which the derived I-space is the set of possible GNTs. Under this I-map, many environments correspond to the same GNT. Due to this, the robot can accomplish interesting tasks without requesting further information. For example, if two environments differ only by rotation or scale, the GNT representations are identical. Surprisingly, the robot does not even need to be concerned about whether the environment boundary is polygonal or curved. The only important concern is how the gaps events occur. For example, the environments in Figure 12.37 all produce the same GNTs and are therefore indistinguishable to the robot. In the same way that the maze exploring algorithm of Section 12.3.1 did not need a complete map to locate an object, the GNT does not need one to perform optimal navigation.

Steven M LaValle 2012-04-20