7.3 Mixing Discrete and Continuous Spaces

Many important applications involve a mixture of discrete and
continuous variables. This results in a state space that is a
Cartesian product of the C-space and a finite set called the *mode
space*. The resulting space can be visualized as having layers of
C-spaces that are indexed by the modes, as depicted in Figure
7.11. The main application given in this section is
manipulation planning; many others exist, especially when other
complications such as dynamics and uncertainties are added to the
problem. The framework of this section is inspired mainly from *hybrid systems* in the control theory community
[409], which usually model mode-dependent
dynamics. The main concern in this section is that the allowable
robot configurations and/or the obstacles depend on the mode.

Steven M LaValle 2012-04-20